diff --git a/obj/src/internal/version.h b/obj/src/internal/version.h new file mode 100644 index 0000000..6eb98ed --- /dev/null +++ b/obj/src/internal/version.h @@ -0,0 +1 @@ +#define VERSION "" diff --git a/src/math/__cos.c b/src/math/__cos.c deleted file mode 100644 index 46cefb3..0000000 --- a/src/math/__cos.c +++ /dev/null @@ -1,71 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/k_cos.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* - * __cos( x, y ) - * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 - * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. - * - * Algorithm - * 1. Since cos(-x) = cos(x), we need only to consider positive x. - * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. - * 3. cos(x) is approximated by a polynomial of degree 14 on - * [0,pi/4] - * 4 14 - * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x - * where the remez error is - * - * | 2 4 6 8 10 12 14 | -58 - * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 - * | | - * - * 4 6 8 10 12 14 - * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then - * cos(x) ~ 1 - x*x/2 + r - * since cos(x+y) ~ cos(x) - sin(x)*y - * ~ cos(x) - x*y, - * a correction term is necessary in cos(x) and hence - * cos(x+y) = 1 - (x*x/2 - (r - x*y)) - * For better accuracy, rearrange to - * cos(x+y) ~ w + (tmp + (r-x*y)) - * where w = 1 - x*x/2 and tmp is a tiny correction term - * (1 - x*x/2 == w + tmp exactly in infinite precision). - * The exactness of w + tmp in infinite precision depends on w - * and tmp having the same precision as x. If they have extra - * precision due to compiler bugs, then the extra precision is - * only good provided it is retained in all terms of the final - * expression for cos(). Retention happens in all cases tested - * under FreeBSD, so don't pessimize things by forcibly clipping - * any extra precision in w. - */ - -#include "libm.h" - -static const double -C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ -C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ -C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ -C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ -C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ -C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ - -double __cos(double x, double y) -{ - double_t hz,z,r,w; - - z = x*x; - w = z*z; - r = z*(C1+z*(C2+z*C3)) + w*w*(C4+z*(C5+z*C6)); - hz = 0.5*z; - w = 1.0-hz; - return w + (((1.0-w)-hz) + (z*r-x*y)); -} diff --git a/src/math/__cosdf.c b/src/math/__cosdf.c deleted file mode 100644 index 2124989..0000000 --- a/src/math/__cosdf.c +++ /dev/null @@ -1,35 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/k_cosf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - * Debugged and optimized by Bruce D. Evans. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -/* |cos(x) - c(x)| < 2**-34.1 (~[-5.37e-11, 5.295e-11]). */ -static const double -C0 = -0x1ffffffd0c5e81.0p-54, /* -0.499999997251031003120 */ -C1 = 0x155553e1053a42.0p-57, /* 0.0416666233237390631894 */ -C2 = -0x16c087e80f1e27.0p-62, /* -0.00138867637746099294692 */ -C3 = 0x199342e0ee5069.0p-68; /* 0.0000243904487962774090654 */ - -float __cosdf(double x) -{ - double_t r, w, z; - - /* Try to optimize for parallel evaluation as in __tandf.c. */ - z = x*x; - w = z*z; - r = C2+z*C3; - return ((1.0+z*C0) + w*C1) + (w*z)*r; -} diff --git a/src/math/__cosl.c b/src/math/__cosl.c deleted file mode 100644 index fa522dd..0000000 --- a/src/math/__cosl.c +++ /dev/null @@ -1,96 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/ld80/k_cosl.c */ -/* origin: FreeBSD /usr/src/lib/msun/ld128/k_cosl.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - - -#include "libm.h" - -#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -#if LDBL_MANT_DIG == 64 -/* - * ld80 version of __cos.c. See __cos.c for most comments. - */ -/* - * Domain [-0.7854, 0.7854], range ~[-2.43e-23, 2.425e-23]: - * |cos(x) - c(x)| < 2**-75.1 - * - * The coefficients of c(x) were generated by a pari-gp script using - * a Remez algorithm that searches for the best higher coefficients - * after rounding leading coefficients to a specified precision. - * - * Simpler methods like Chebyshev or basic Remez barely suffice for - * cos() in 64-bit precision, because we want the coefficient of x^2 - * to be precisely -0.5 so that multiplying by it is exact, and plain - * rounding of the coefficients of a good polynomial approximation only - * gives this up to about 64-bit precision. Plain rounding also gives - * a mediocre approximation for the coefficient of x^4, but a rounding - * error of 0.5 ulps for this coefficient would only contribute ~0.01 - * ulps to the final error, so this is unimportant. Rounding errors in - * higher coefficients are even less important. - * - * In fact, coefficients above the x^4 one only need to have 53-bit - * precision, and this is more efficient. We get this optimization - * almost for free from the complications needed to search for the best - * higher coefficients. - */ -static const long double -C1 = 0.0416666666666666666136L; /* 0xaaaaaaaaaaaaaa9b.0p-68 */ -static const double -C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */ -C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */ -C4 = -0.00000027557319215507120, /* -0x127e4fb7602f22.0p-74 */ -C5 = 0.0000000020876754400407278, /* 0x11eed8caaeccf1.0p-81 */ -C6 = -1.1470297442401303e-11, /* -0x19393412bd1529.0p-89 */ -C7 = 4.7383039476436467e-14; /* 0x1aac9d9af5c43e.0p-97 */ -#define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*C7))))))) -#elif LDBL_MANT_DIG == 113 -/* - * ld128 version of __cos.c. See __cos.c for most comments. - */ -/* - * Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]: - * |cos(x) - c(x))| < 2**-122.0 - * - * 113-bit precision requires more care than 64-bit precision, since - * simple methods give a minimax polynomial with coefficient for x^2 - * that is 1 ulp below 0.5, but we want it to be precisely 0.5. See - * above for more details. - */ -static const long double -C1 = 0.04166666666666666666666666666666658424671L, -C2 = -0.001388888888888888888888888888863490893732L, -C3 = 0.00002480158730158730158730158600795304914210L, -C4 = -0.2755731922398589065255474947078934284324e-6L, -C5 = 0.2087675698786809897659225313136400793948e-8L, -C6 = -0.1147074559772972315817149986812031204775e-10L, -C7 = 0.4779477332386808976875457937252120293400e-13L; -static const double -C8 = -0.1561920696721507929516718307820958119868e-15, -C9 = 0.4110317413744594971475941557607804508039e-18, -C10 = -0.8896592467191938803288521958313920156409e-21, -C11 = 0.1601061435794535138244346256065192782581e-23; -#define POLY(z) (z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+ \ - z*(C8+z*(C9+z*(C10+z*C11))))))))))) -#endif - -long double __cosl(long double x, long double y) -{ - long double hz,z,r,w; - - z = x*x; - r = POLY(z); - hz = 0.5*z; - w = 1.0-hz; - return w + (((1.0-w)-hz) + (z*r-x*y)); -} -#endif diff --git a/src/math/__expo2.c b/src/math/__expo2.c deleted file mode 100644 index 248f052..0000000 --- a/src/math/__expo2.c +++ /dev/null @@ -1,17 +0,0 @@ -#include "libm.h" - -/* k is such that k*ln2 has minimal relative error and x - kln2 > log(DBL_MIN) */ -static const int k = 2043; -static const double kln2 = 0x1.62066151add8bp+10; - -/* exp(x)/2 for x >= log(DBL_MAX), slightly better than 0.5*exp(x/2)*exp(x/2) */ -double __expo2(double x, double sign) -{ - double scale; - - /* note that k is odd and scale*scale overflows */ - INSERT_WORDS(scale, (uint32_t)(0x3ff + k/2) << 20, 0); - /* exp(x - k ln2) * 2**(k-1) */ - /* in directed rounding correct sign before rounding or overflow is important */ - return exp(x - kln2) * (sign * scale) * scale; -} diff --git a/src/math/__expo2f.c b/src/math/__expo2f.c deleted file mode 100644 index 538eb09..0000000 --- a/src/math/__expo2f.c +++ /dev/null @@ -1,17 +0,0 @@ -#include "libm.h" - -/* k is such that k*ln2 has minimal relative error and x - kln2 > log(FLT_MIN) */ -static const int k = 235; -static const float kln2 = 0x1.45c778p+7f; - -/* expf(x)/2 for x >= log(FLT_MAX), slightly better than 0.5f*expf(x/2)*expf(x/2) */ -float __expo2f(float x, float sign) -{ - float scale; - - /* note that k is odd and scale*scale overflows */ - SET_FLOAT_WORD(scale, (uint32_t)(0x7f + k/2) << 23); - /* exp(x - k ln2) * 2**(k-1) */ - /* in directed rounding correct sign before rounding or overflow is important */ - return expf(x - kln2) * (sign * scale) * scale; -} diff --git a/src/math/__fpclassify.c b/src/math/__fpclassify.c deleted file mode 100644 index f7c0e2d..0000000 --- a/src/math/__fpclassify.c +++ /dev/null @@ -1,11 +0,0 @@ -#include -#include - -int __fpclassify(double x) -{ - union {double f; uint64_t i;} u = {x}; - int e = u.i>>52 & 0x7ff; - if (!e) return u.i<<1 ? FP_SUBNORMAL : FP_ZERO; - if (e==0x7ff) return u.i<<12 ? FP_NAN : FP_INFINITE; - return FP_NORMAL; -} diff --git a/src/math/__fpclassifyf.c b/src/math/__fpclassifyf.c deleted file mode 100644 index fd00eb1..0000000 --- a/src/math/__fpclassifyf.c +++ /dev/null @@ -1,11 +0,0 @@ -#include -#include - -int __fpclassifyf(float x) -{ - union {float f; uint32_t i;} u = {x}; - int e = u.i>>23 & 0xff; - if (!e) return u.i<<1 ? FP_SUBNORMAL : FP_ZERO; - if (e==0xff) return u.i<<9 ? FP_NAN : FP_INFINITE; - return FP_NORMAL; -} diff --git a/src/math/__fpclassifyl.c b/src/math/__fpclassifyl.c deleted file mode 100644 index e41781b..0000000 --- a/src/math/__fpclassifyl.c +++ /dev/null @@ -1,42 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -int __fpclassifyl(long double x) -{ - return __fpclassify(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -int __fpclassifyl(long double x) -{ - union ldshape u = {x}; - int e = u.i.se & 0x7fff; - int msb = u.i.m>>63; - if (!e && !msb) - return u.i.m ? FP_SUBNORMAL : FP_ZERO; - if (e == 0x7fff) { - /* The x86 variant of 80-bit extended precision only admits - * one representation of each infinity, with the mantissa msb - * necessarily set. The version with it clear is invalid/nan. - * The m68k variant, however, allows either, and tooling uses - * the version with it clear. */ - if (__BYTE_ORDER == __LITTLE_ENDIAN && !msb) - return FP_NAN; - return u.i.m << 1 ? FP_NAN : FP_INFINITE; - } - if (!msb) - return FP_NAN; - return FP_NORMAL; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -int __fpclassifyl(long double x) -{ - union ldshape u = {x}; - int e = u.i.se & 0x7fff; - u.i.se = 0; - if (!e) - return u.i2.lo | u.i2.hi ? FP_SUBNORMAL : FP_ZERO; - if (e == 0x7fff) - return u.i2.lo | u.i2.hi ? FP_NAN : FP_INFINITE; - return FP_NORMAL; -} -#endif diff --git a/src/math/__invtrigl.c b/src/math/__invtrigl.c deleted file mode 100644 index 48f83aa..0000000 --- a/src/math/__invtrigl.c +++ /dev/null @@ -1,63 +0,0 @@ -#include -#include "__invtrigl.h" - -#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -static const long double -pS0 = 1.66666666666666666631e-01L, -pS1 = -4.16313987993683104320e-01L, -pS2 = 3.69068046323246813704e-01L, -pS3 = -1.36213932016738603108e-01L, -pS4 = 1.78324189708471965733e-02L, -pS5 = -2.19216428382605211588e-04L, -pS6 = -7.10526623669075243183e-06L, -qS1 = -2.94788392796209867269e+00L, -qS2 = 3.27309890266528636716e+00L, -qS3 = -1.68285799854822427013e+00L, -qS4 = 3.90699412641738801874e-01L, -qS5 = -3.14365703596053263322e-02L; - -const long double pio2_hi = 1.57079632679489661926L; -const long double pio2_lo = -2.50827880633416601173e-20L; - -/* used in asinl() and acosl() */ -/* R(x^2) is a rational approximation of (asin(x)-x)/x^3 with Remez algorithm */ -long double __invtrigl_R(long double z) -{ - long double p, q; - p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*(pS5+z*pS6)))))); - q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*(qS4+z*qS5)))); - return p/q; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -static const long double -pS0 = 1.66666666666666666666666666666700314e-01L, -pS1 = -7.32816946414566252574527475428622708e-01L, -pS2 = 1.34215708714992334609030036562143589e+00L, -pS3 = -1.32483151677116409805070261790752040e+00L, -pS4 = 7.61206183613632558824485341162121989e-01L, -pS5 = -2.56165783329023486777386833928147375e-01L, -pS6 = 4.80718586374448793411019434585413855e-02L, -pS7 = -4.42523267167024279410230886239774718e-03L, -pS8 = 1.44551535183911458253205638280410064e-04L, -pS9 = -2.10558957916600254061591040482706179e-07L, -qS1 = -4.84690167848739751544716485245697428e+00L, -qS2 = 9.96619113536172610135016921140206980e+00L, -qS3 = -1.13177895428973036660836798461641458e+01L, -qS4 = 7.74004374389488266169304117714658761e+00L, -qS5 = -3.25871986053534084709023539900339905e+00L, -qS6 = 8.27830318881232209752469022352928864e-01L, -qS7 = -1.18768052702942805423330715206348004e-01L, -qS8 = 8.32600764660522313269101537926539470e-03L, -qS9 = -1.99407384882605586705979504567947007e-04L; - -const long double pio2_hi = 1.57079632679489661923132169163975140L; -const long double pio2_lo = 4.33590506506189051239852201302167613e-35L; - -long double __invtrigl_R(long double z) -{ - long double p, q; - p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*(pS5+z*(pS6+z*(pS7+z*(pS8+z*pS9))))))))); - q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*(qS4+z*(qS5+z*(qS6+z*(qS7+z*(qS8+z*qS9)))))))); - return p/q; -} -#endif diff --git a/src/math/__invtrigl.h b/src/math/__invtrigl.h deleted file mode 100644 index bee7931..0000000 --- a/src/math/__invtrigl.h +++ /dev/null @@ -1,8 +0,0 @@ -#include - -/* shared by acosl, asinl and atan2l */ -#define pio2_hi __pio2_hi -#define pio2_lo __pio2_lo -hidden extern const long double pio2_hi, pio2_lo; - -hidden long double __invtrigl_R(long double z); diff --git a/src/math/__math_divzero.c b/src/math/__math_divzero.c deleted file mode 100644 index 59d2135..0000000 --- a/src/math/__math_divzero.c +++ /dev/null @@ -1,6 +0,0 @@ -#include "libm.h" - -double __math_divzero(uint32_t sign) -{ - return fp_barrier(sign ? -1.0 : 1.0) / 0.0; -} diff --git a/src/math/__math_divzerof.c b/src/math/__math_divzerof.c deleted file mode 100644 index ce046f3..0000000 --- a/src/math/__math_divzerof.c +++ /dev/null @@ -1,6 +0,0 @@ -#include "libm.h" - -float __math_divzerof(uint32_t sign) -{ - return fp_barrierf(sign ? -1.0f : 1.0f) / 0.0f; -} diff --git a/src/math/__math_invalid.c b/src/math/__math_invalid.c deleted file mode 100644 index 1774049..0000000 --- a/src/math/__math_invalid.c +++ /dev/null @@ -1,6 +0,0 @@ -#include "libm.h" - -double __math_invalid(double x) -{ - return (x - x) / (x - x); -} diff --git a/src/math/__math_invalidf.c b/src/math/__math_invalidf.c deleted file mode 100644 index 357d4b1..0000000 --- a/src/math/__math_invalidf.c +++ /dev/null @@ -1,6 +0,0 @@ -#include "libm.h" - -float __math_invalidf(float x) -{ - return (x - x) / (x - x); -} diff --git a/src/math/__math_invalidl.c b/src/math/__math_invalidl.c deleted file mode 100644 index 1fca99d..0000000 --- a/src/math/__math_invalidl.c +++ /dev/null @@ -1,9 +0,0 @@ -#include -#include "libm.h" - -#if LDBL_MANT_DIG != DBL_MANT_DIG -long double __math_invalidl(long double x) -{ - return (x - x) / (x - x); -} -#endif diff --git a/src/math/__math_oflow.c b/src/math/__math_oflow.c deleted file mode 100644 index c85dbf9..0000000 --- a/src/math/__math_oflow.c +++ /dev/null @@ -1,6 +0,0 @@ -#include "libm.h" - -double __math_oflow(uint32_t sign) -{ - return __math_xflow(sign, 0x1p769); -} diff --git a/src/math/__math_oflowf.c b/src/math/__math_oflowf.c deleted file mode 100644 index fa7d062..0000000 --- a/src/math/__math_oflowf.c +++ /dev/null @@ -1,6 +0,0 @@ -#include "libm.h" - -float __math_oflowf(uint32_t sign) -{ - return __math_xflowf(sign, 0x1p97f); -} diff --git a/src/math/__math_uflow.c b/src/math/__math_uflow.c deleted file mode 100644 index b90594a..0000000 --- a/src/math/__math_uflow.c +++ /dev/null @@ -1,6 +0,0 @@ -#include "libm.h" - -double __math_uflow(uint32_t sign) -{ - return __math_xflow(sign, 0x1p-767); -} diff --git a/src/math/__math_uflowf.c b/src/math/__math_uflowf.c deleted file mode 100644 index 94d50f2..0000000 --- a/src/math/__math_uflowf.c +++ /dev/null @@ -1,6 +0,0 @@ -#include "libm.h" - -float __math_uflowf(uint32_t sign) -{ - return __math_xflowf(sign, 0x1p-95f); -} diff --git a/src/math/__math_xflow.c b/src/math/__math_xflow.c deleted file mode 100644 index 744203c..0000000 --- a/src/math/__math_xflow.c +++ /dev/null @@ -1,6 +0,0 @@ -#include "libm.h" - -double __math_xflow(uint32_t sign, double y) -{ - return eval_as_double(fp_barrier(sign ? -y : y) * y); -} diff --git a/src/math/__math_xflowf.c b/src/math/__math_xflowf.c deleted file mode 100644 index f2c8478..0000000 --- a/src/math/__math_xflowf.c +++ /dev/null @@ -1,6 +0,0 @@ -#include "libm.h" - -float __math_xflowf(uint32_t sign, float y) -{ - return eval_as_float(fp_barrierf(sign ? -y : y) * y); -} diff --git a/src/math/__polevll.c b/src/math/__polevll.c deleted file mode 100644 index ce1a840..0000000 --- a/src/math/__polevll.c +++ /dev/null @@ -1,93 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/polevll.c */ -/* - * Copyright (c) 2008 Stephen L. Moshier - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. - * - * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES - * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR - * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES - * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN - * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF - * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - */ -/* - * Evaluate polynomial - * - * - * SYNOPSIS: - * - * int N; - * long double x, y, coef[N+1], polevl[]; - * - * y = polevll( x, coef, N ); - * - * - * DESCRIPTION: - * - * Evaluates polynomial of degree N: - * - * 2 N - * y = C + C x + C x +...+ C x - * 0 1 2 N - * - * Coefficients are stored in reverse order: - * - * coef[0] = C , ..., coef[N] = C . - * N 0 - * - * The function p1evll() assumes that coef[N] = 1.0 and is - * omitted from the array. Its calling arguments are - * otherwise the same as polevll(). - * - * - * SPEED: - * - * In the interest of speed, there are no checks for out - * of bounds arithmetic. This routine is used by most of - * the functions in the library. Depending on available - * equipment features, the user may wish to rewrite the - * program in microcode or assembly language. - * - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -#else -/* - * Polynomial evaluator: - * P[0] x^n + P[1] x^(n-1) + ... + P[n] - */ -long double __polevll(long double x, const long double *P, int n) -{ - long double y; - - y = *P++; - do { - y = y * x + *P++; - } while (--n); - - return y; -} - -/* - * Polynomial evaluator: - * x^n + P[0] x^(n-1) + P[1] x^(n-2) + ... + P[n] - */ -long double __p1evll(long double x, const long double *P, int n) -{ - long double y; - - n -= 1; - y = x + *P++; - do { - y = y * x + *P++; - } while (--n); - - return y; -} -#endif diff --git a/src/math/__rem_pio2.c b/src/math/__rem_pio2.c deleted file mode 100644 index dcf672f..0000000 --- a/src/math/__rem_pio2.c +++ /dev/null @@ -1,190 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - * Optimized by Bruce D. Evans. - */ -/* __rem_pio2(x,y) - * - * return the remainder of x rem pi/2 in y[0]+y[1] - * use __rem_pio2_large() for large x - */ - -#include "libm.h" - -#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 -#define EPS DBL_EPSILON -#elif FLT_EVAL_METHOD==2 -#define EPS LDBL_EPSILON -#endif - -/* - * invpio2: 53 bits of 2/pi - * pio2_1: first 33 bit of pi/2 - * pio2_1t: pi/2 - pio2_1 - * pio2_2: second 33 bit of pi/2 - * pio2_2t: pi/2 - (pio2_1+pio2_2) - * pio2_3: third 33 bit of pi/2 - * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) - */ -static const double -toint = 1.5/EPS, -pio4 = 0x1.921fb54442d18p-1, -invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ -pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ -pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ -pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ -pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ -pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ -pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ - -/* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */ -int __rem_pio2(double x, double *y) -{ - union {double f; uint64_t i;} u = {x}; - double_t z,w,t,r,fn; - double tx[3],ty[2]; - uint32_t ix; - int sign, n, ex, ey, i; - - sign = u.i>>63; - ix = u.i>>32 & 0x7fffffff; - if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ - if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ - goto medium; /* cancellation -- use medium case */ - if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ - if (!sign) { - z = x - pio2_1; /* one round good to 85 bits */ - y[0] = z - pio2_1t; - y[1] = (z-y[0]) - pio2_1t; - return 1; - } else { - z = x + pio2_1; - y[0] = z + pio2_1t; - y[1] = (z-y[0]) + pio2_1t; - return -1; - } - } else { - if (!sign) { - z = x - 2*pio2_1; - y[0] = z - 2*pio2_1t; - y[1] = (z-y[0]) - 2*pio2_1t; - return 2; - } else { - z = x + 2*pio2_1; - y[0] = z + 2*pio2_1t; - y[1] = (z-y[0]) + 2*pio2_1t; - return -2; - } - } - } - if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ - if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ - if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ - goto medium; - if (!sign) { - z = x - 3*pio2_1; - y[0] = z - 3*pio2_1t; - y[1] = (z-y[0]) - 3*pio2_1t; - return 3; - } else { - z = x + 3*pio2_1; - y[0] = z + 3*pio2_1t; - y[1] = (z-y[0]) + 3*pio2_1t; - return -3; - } - } else { - if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ - goto medium; - if (!sign) { - z = x - 4*pio2_1; - y[0] = z - 4*pio2_1t; - y[1] = (z-y[0]) - 4*pio2_1t; - return 4; - } else { - z = x + 4*pio2_1; - y[0] = z + 4*pio2_1t; - y[1] = (z-y[0]) + 4*pio2_1t; - return -4; - } - } - } - if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ -medium: - /* rint(x/(pi/2)) */ - fn = (double_t)x*invpio2 + toint - toint; - n = (int32_t)fn; - r = x - fn*pio2_1; - w = fn*pio2_1t; /* 1st round, good to 85 bits */ - /* Matters with directed rounding. */ - if (predict_false(r - w < -pio4)) { - n--; - fn--; - r = x - fn*pio2_1; - w = fn*pio2_1t; - } else if (predict_false(r - w > pio4)) { - n++; - fn++; - r = x - fn*pio2_1; - w = fn*pio2_1t; - } - y[0] = r - w; - u.f = y[0]; - ey = u.i>>52 & 0x7ff; - ex = ix>>20; - if (ex - ey > 16) { /* 2nd round, good to 118 bits */ - t = r; - w = fn*pio2_2; - r = t - w; - w = fn*pio2_2t - ((t-r)-w); - y[0] = r - w; - u.f = y[0]; - ey = u.i>>52 & 0x7ff; - if (ex - ey > 49) { /* 3rd round, good to 151 bits, covers all cases */ - t = r; - w = fn*pio2_3; - r = t - w; - w = fn*pio2_3t - ((t-r)-w); - y[0] = r - w; - } - } - y[1] = (r - y[0]) - w; - return n; - } - /* - * all other (large) arguments - */ - if (ix >= 0x7ff00000) { /* x is inf or NaN */ - y[0] = y[1] = x - x; - return 0; - } - /* set z = scalbn(|x|,-ilogb(x)+23) */ - u.f = x; - u.i &= (uint64_t)-1>>12; - u.i |= (uint64_t)(0x3ff + 23)<<52; - z = u.f; - for (i=0; i < 2; i++) { - tx[i] = (double)(int32_t)z; - z = (z-tx[i])*0x1p24; - } - tx[i] = z; - /* skip zero terms, first term is non-zero */ - while (tx[i] == 0.0) - i--; - n = __rem_pio2_large(tx,ty,(int)(ix>>20)-(0x3ff+23),i+1,1); - if (sign) { - y[0] = -ty[0]; - y[1] = -ty[1]; - return -n; - } - y[0] = ty[0]; - y[1] = ty[1]; - return n; -} diff --git a/src/math/__rem_pio2_large.c b/src/math/__rem_pio2_large.c deleted file mode 100644 index 958f28c..0000000 --- a/src/math/__rem_pio2_large.c +++ /dev/null @@ -1,442 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/k_rem_pio2.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* - * __rem_pio2_large(x,y,e0,nx,prec) - * double x[],y[]; int e0,nx,prec; - * - * __rem_pio2_large return the last three digits of N with - * y = x - N*pi/2 - * so that |y| < pi/2. - * - * The method is to compute the integer (mod 8) and fraction parts of - * (2/pi)*x without doing the full multiplication. In general we - * skip the part of the product that are known to be a huge integer ( - * more accurately, = 0 mod 8 ). Thus the number of operations are - * independent of the exponent of the input. - * - * (2/pi) is represented by an array of 24-bit integers in ipio2[]. - * - * Input parameters: - * x[] The input value (must be positive) is broken into nx - * pieces of 24-bit integers in double precision format. - * x[i] will be the i-th 24 bit of x. The scaled exponent - * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 - * match x's up to 24 bits. - * - * Example of breaking a double positive z into x[0]+x[1]+x[2]: - * e0 = ilogb(z)-23 - * z = scalbn(z,-e0) - * for i = 0,1,2 - * x[i] = floor(z) - * z = (z-x[i])*2**24 - * - * - * y[] ouput result in an array of double precision numbers. - * The dimension of y[] is: - * 24-bit precision 1 - * 53-bit precision 2 - * 64-bit precision 2 - * 113-bit precision 3 - * The actual value is the sum of them. Thus for 113-bit - * precison, one may have to do something like: - * - * long double t,w,r_head, r_tail; - * t = (long double)y[2] + (long double)y[1]; - * w = (long double)y[0]; - * r_head = t+w; - * r_tail = w - (r_head - t); - * - * e0 The exponent of x[0]. Must be <= 16360 or you need to - * expand the ipio2 table. - * - * nx dimension of x[] - * - * prec an integer indicating the precision: - * 0 24 bits (single) - * 1 53 bits (double) - * 2 64 bits (extended) - * 3 113 bits (quad) - * - * External function: - * double scalbn(), floor(); - * - * - * Here is the description of some local variables: - * - * jk jk+1 is the initial number of terms of ipio2[] needed - * in the computation. The minimum and recommended value - * for jk is 3,4,4,6 for single, double, extended, and quad. - * jk+1 must be 2 larger than you might expect so that our - * recomputation test works. (Up to 24 bits in the integer - * part (the 24 bits of it that we compute) and 23 bits in - * the fraction part may be lost to cancelation before we - * recompute.) - * - * jz local integer variable indicating the number of - * terms of ipio2[] used. - * - * jx nx - 1 - * - * jv index for pointing to the suitable ipio2[] for the - * computation. In general, we want - * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 - * is an integer. Thus - * e0-3-24*jv >= 0 or (e0-3)/24 >= jv - * Hence jv = max(0,(e0-3)/24). - * - * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. - * - * q[] double array with integral value, representing the - * 24-bits chunk of the product of x and 2/pi. - * - * q0 the corresponding exponent of q[0]. Note that the - * exponent for q[i] would be q0-24*i. - * - * PIo2[] double precision array, obtained by cutting pi/2 - * into 24 bits chunks. - * - * f[] ipio2[] in floating point - * - * iq[] integer array by breaking up q[] in 24-bits chunk. - * - * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] - * - * ih integer. If >0 it indicates q[] is >= 0.5, hence - * it also indicates the *sign* of the result. - * - */ -/* - * Constants: - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough - * to produce the hexadecimal values shown. - */ - -#include "libm.h" - -static const int init_jk[] = {3,4,4,6}; /* initial value for jk */ - -/* - * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi - * - * integer array, contains the (24*i)-th to (24*i+23)-th - * bit of 2/pi after binary point. The corresponding - * floating value is - * - * ipio2[i] * 2^(-24(i+1)). - * - * NB: This table must have at least (e0-3)/24 + jk terms. - * For quad precision (e0 <= 16360, jk = 6), this is 686. - */ -static const int32_t ipio2[] = { -0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, -0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, -0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, -0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, -0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, -0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, -0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, -0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, -0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, -0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, -0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, - -#if LDBL_MAX_EXP > 1024 -0x47C419, 0xC367CD, 0xDCE809, 0x2A8359, 0xC4768B, 0x961CA6, -0xDDAF44, 0xD15719, 0x053EA5, 0xFF0705, 0x3F7E33, 0xE832C2, -0xDE4F98, 0x327DBB, 0xC33D26, 0xEF6B1E, 0x5EF89F, 0x3A1F35, -0xCAF27F, 0x1D87F1, 0x21907C, 0x7C246A, 0xFA6ED5, 0x772D30, -0x433B15, 0xC614B5, 0x9D19C3, 0xC2C4AD, 0x414D2C, 0x5D000C, -0x467D86, 0x2D71E3, 0x9AC69B, 0x006233, 0x7CD2B4, 0x97A7B4, -0xD55537, 0xF63ED7, 0x1810A3, 0xFC764D, 0x2A9D64, 0xABD770, -0xF87C63, 0x57B07A, 0xE71517, 0x5649C0, 0xD9D63B, 0x3884A7, -0xCB2324, 0x778AD6, 0x23545A, 0xB91F00, 0x1B0AF1, 0xDFCE19, -0xFF319F, 0x6A1E66, 0x615799, 0x47FBAC, 0xD87F7E, 0xB76522, -0x89E832, 0x60BFE6, 0xCDC4EF, 0x09366C, 0xD43F5D, 0xD7DE16, -0xDE3B58, 0x929BDE, 0x2822D2, 0xE88628, 0x4D58E2, 0x32CAC6, -0x16E308, 0xCB7DE0, 0x50C017, 0xA71DF3, 0x5BE018, 0x34132E, -0x621283, 0x014883, 0x5B8EF5, 0x7FB0AD, 0xF2E91E, 0x434A48, -0xD36710, 0xD8DDAA, 0x425FAE, 0xCE616A, 0xA4280A, 0xB499D3, -0xF2A606, 0x7F775C, 0x83C2A3, 0x883C61, 0x78738A, 0x5A8CAF, -0xBDD76F, 0x63A62D, 0xCBBFF4, 0xEF818D, 0x67C126, 0x45CA55, -0x36D9CA, 0xD2A828, 0x8D61C2, 0x77C912, 0x142604, 0x9B4612, -0xC459C4, 0x44C5C8, 0x91B24D, 0xF31700, 0xAD43D4, 0xE54929, -0x10D5FD, 0xFCBE00, 0xCC941E, 0xEECE70, 0xF53E13, 0x80F1EC, -0xC3E7B3, 0x28F8C7, 0x940593, 0x3E71C1, 0xB3092E, 0xF3450B, -0x9C1288, 0x7B20AB, 0x9FB52E, 0xC29247, 0x2F327B, 0x6D550C, -0x90A772, 0x1FE76B, 0x96CB31, 0x4A1679, 0xE27941, 0x89DFF4, -0x9794E8, 0x84E6E2, 0x973199, 0x6BED88, 0x365F5F, 0x0EFDBB, -0xB49A48, 0x6CA467, 0x427271, 0x325D8D, 0xB8159F, 0x09E5BC, -0x25318D, 0x3974F7, 0x1C0530, 0x010C0D, 0x68084B, 0x58EE2C, -0x90AA47, 0x02E774, 0x24D6BD, 0xA67DF7, 0x72486E, 0xEF169F, -0xA6948E, 0xF691B4, 0x5153D1, 0xF20ACF, 0x339820, 0x7E4BF5, -0x6863B2, 0x5F3EDD, 0x035D40, 0x7F8985, 0x295255, 0xC06437, -0x10D86D, 0x324832, 0x754C5B, 0xD4714E, 0x6E5445, 0xC1090B, -0x69F52A, 0xD56614, 0x9D0727, 0x50045D, 0xDB3BB4, 0xC576EA, -0x17F987, 0x7D6B49, 0xBA271D, 0x296996, 0xACCCC6, 0x5414AD, -0x6AE290, 0x89D988, 0x50722C, 0xBEA404, 0x940777, 0x7030F3, -0x27FC00, 0xA871EA, 0x49C266, 0x3DE064, 0x83DD97, 0x973FA3, -0xFD9443, 0x8C860D, 0xDE4131, 0x9D3992, 0x8C70DD, 0xE7B717, -0x3BDF08, 0x2B3715, 0xA0805C, 0x93805A, 0x921110, 0xD8E80F, -0xAF806C, 0x4BFFDB, 0x0F9038, 0x761859, 0x15A562, 0xBBCB61, -0xB989C7, 0xBD4010, 0x04F2D2, 0x277549, 0xF6B6EB, 0xBB22DB, -0xAA140A, 0x2F2689, 0x768364, 0x333B09, 0x1A940E, 0xAA3A51, -0xC2A31D, 0xAEEDAF, 0x12265C, 0x4DC26D, 0x9C7A2D, 0x9756C0, -0x833F03, 0xF6F009, 0x8C402B, 0x99316D, 0x07B439, 0x15200C, -0x5BC3D8, 0xC492F5, 0x4BADC6, 0xA5CA4E, 0xCD37A7, 0x36A9E6, -0x9492AB, 0x6842DD, 0xDE6319, 0xEF8C76, 0x528B68, 0x37DBFC, -0xABA1AE, 0x3115DF, 0xA1AE00, 0xDAFB0C, 0x664D64, 0xB705ED, -0x306529, 0xBF5657, 0x3AFF47, 0xB9F96A, 0xF3BE75, 0xDF9328, -0x3080AB, 0xF68C66, 0x15CB04, 0x0622FA, 0x1DE4D9, 0xA4B33D, -0x8F1B57, 0x09CD36, 0xE9424E, 0xA4BE13, 0xB52333, 0x1AAAF0, -0xA8654F, 0xA5C1D2, 0x0F3F0B, 0xCD785B, 0x76F923, 0x048B7B, -0x721789, 0x53A6C6, 0xE26E6F, 0x00EBEF, 0x584A9B, 0xB7DAC4, -0xBA66AA, 0xCFCF76, 0x1D02D1, 0x2DF1B1, 0xC1998C, 0x77ADC3, -0xDA4886, 0xA05DF7, 0xF480C6, 0x2FF0AC, 0x9AECDD, 0xBC5C3F, -0x6DDED0, 0x1FC790, 0xB6DB2A, 0x3A25A3, 0x9AAF00, 0x9353AD, -0x0457B6, 0xB42D29, 0x7E804B, 0xA707DA, 0x0EAA76, 0xA1597B, -0x2A1216, 0x2DB7DC, 0xFDE5FA, 0xFEDB89, 0xFDBE89, 0x6C76E4, -0xFCA906, 0x70803E, 0x156E85, 0xFF87FD, 0x073E28, 0x336761, -0x86182A, 0xEABD4D, 0xAFE7B3, 0x6E6D8F, 0x396795, 0x5BBF31, -0x48D784, 0x16DF30, 0x432DC7, 0x356125, 0xCE70C9, 0xB8CB30, -0xFD6CBF, 0xA200A4, 0xE46C05, 0xA0DD5A, 0x476F21, 0xD21262, -0x845CB9, 0x496170, 0xE0566B, 0x015299, 0x375550, 0xB7D51E, -0xC4F133, 0x5F6E13, 0xE4305D, 0xA92E85, 0xC3B21D, 0x3632A1, -0xA4B708, 0xD4B1EA, 0x21F716, 0xE4698F, 0x77FF27, 0x80030C, -0x2D408D, 0xA0CD4F, 0x99A520, 0xD3A2B3, 0x0A5D2F, 0x42F9B4, -0xCBDA11, 0xD0BE7D, 0xC1DB9B, 0xBD17AB, 0x81A2CA, 0x5C6A08, -0x17552E, 0x550027, 0xF0147F, 0x8607E1, 0x640B14, 0x8D4196, -0xDEBE87, 0x2AFDDA, 0xB6256B, 0x34897B, 0xFEF305, 0x9EBFB9, -0x4F6A68, 0xA82A4A, 0x5AC44F, 0xBCF82D, 0x985AD7, 0x95C7F4, -0x8D4D0D, 0xA63A20, 0x5F57A4, 0xB13F14, 0x953880, 0x0120CC, -0x86DD71, 0xB6DEC9, 0xF560BF, 0x11654D, 0x6B0701, 0xACB08C, -0xD0C0B2, 0x485551, 0x0EFB1E, 0xC37295, 0x3B06A3, 0x3540C0, -0x7BDC06, 0xCC45E0, 0xFA294E, 0xC8CAD6, 0x41F3E8, 0xDE647C, -0xD8649B, 0x31BED9, 0xC397A4, 0xD45877, 0xC5E369, 0x13DAF0, -0x3C3ABA, 0x461846, 0x5F7555, 0xF5BDD2, 0xC6926E, 0x5D2EAC, -0xED440E, 0x423E1C, 0x87C461, 0xE9FD29, 0xF3D6E7, 0xCA7C22, -0x35916F, 0xC5E008, 0x8DD7FF, 0xE26A6E, 0xC6FDB0, 0xC10893, -0x745D7C, 0xB2AD6B, 0x9D6ECD, 0x7B723E, 0x6A11C6, 0xA9CFF7, -0xDF7329, 0xBAC9B5, 0x5100B7, 0x0DB2E2, 0x24BA74, 0x607DE5, -0x8AD874, 0x2C150D, 0x0C1881, 0x94667E, 0x162901, 0x767A9F, -0xBEFDFD, 0xEF4556, 0x367ED9, 0x13D9EC, 0xB9BA8B, 0xFC97C4, -0x27A831, 0xC36EF1, 0x36C594, 0x56A8D8, 0xB5A8B4, 0x0ECCCF, -0x2D8912, 0x34576F, 0x89562C, 0xE3CE99, 0xB920D6, 0xAA5E6B, -0x9C2A3E, 0xCC5F11, 0x4A0BFD, 0xFBF4E1, 0x6D3B8E, 0x2C86E2, -0x84D4E9, 0xA9B4FC, 0xD1EEEF, 0xC9352E, 0x61392F, 0x442138, -0xC8D91B, 0x0AFC81, 0x6A4AFB, 0xD81C2F, 0x84B453, 0x8C994E, -0xCC2254, 0xDC552A, 0xD6C6C0, 0x96190B, 0xB8701A, 0x649569, -0x605A26, 0xEE523F, 0x0F117F, 0x11B5F4, 0xF5CBFC, 0x2DBC34, -0xEEBC34, 0xCC5DE8, 0x605EDD, 0x9B8E67, 0xEF3392, 0xB817C9, -0x9B5861, 0xBC57E1, 0xC68351, 0x103ED8, 0x4871DD, 0xDD1C2D, -0xA118AF, 0x462C21, 0xD7F359, 0x987AD9, 0xC0549E, 0xFA864F, -0xFC0656, 0xAE79E5, 0x362289, 0x22AD38, 0xDC9367, 0xAAE855, -0x382682, 0x9BE7CA, 0xA40D51, 0xB13399, 0x0ED7A9, 0x480569, -0xF0B265, 0xA7887F, 0x974C88, 0x36D1F9, 0xB39221, 0x4A827B, -0x21CF98, 0xDC9F40, 0x5547DC, 0x3A74E1, 0x42EB67, 0xDF9DFE, -0x5FD45E, 0xA4677B, 0x7AACBA, 0xA2F655, 0x23882B, 0x55BA41, -0x086E59, 0x862A21, 0x834739, 0xE6E389, 0xD49EE5, 0x40FB49, -0xE956FF, 0xCA0F1C, 0x8A59C5, 0x2BFA94, 0xC5C1D3, 0xCFC50F, -0xAE5ADB, 0x86C547, 0x624385, 0x3B8621, 0x94792C, 0x876110, -0x7B4C2A, 0x1A2C80, 0x12BF43, 0x902688, 0x893C78, 0xE4C4A8, -0x7BDBE5, 0xC23AC4, 0xEAF426, 0x8A67F7, 0xBF920D, 0x2BA365, -0xB1933D, 0x0B7CBD, 0xDC51A4, 0x63DD27, 0xDDE169, 0x19949A, -0x9529A8, 0x28CE68, 0xB4ED09, 0x209F44, 0xCA984E, 0x638270, -0x237C7E, 0x32B90F, 0x8EF5A7, 0xE75614, 0x08F121, 0x2A9DB5, -0x4D7E6F, 0x5119A5, 0xABF9B5, 0xD6DF82, 0x61DD96, 0x023616, -0x9F3AC4, 0xA1A283, 0x6DED72, 0x7A8D39, 0xA9B882, 0x5C326B, -0x5B2746, 0xED3400, 0x7700D2, 0x55F4FC, 0x4D5901, 0x8071E0, -#endif -}; - -static const double PIo2[] = { - 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ - 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ - 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ - 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ - 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ - 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ - 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ - 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ -}; - -int __rem_pio2_large(double *x, double *y, int e0, int nx, int prec) -{ - int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; - double z,fw,f[20],fq[20],q[20]; - - /* initialize jk*/ - jk = init_jk[prec]; - jp = jk; - - /* determine jx,jv,q0, note that 3>q0 */ - jx = nx-1; - jv = (e0-3)/24; if(jv<0) jv=0; - q0 = e0-24*(jv+1); - - /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ - j = jv-jx; m = jx+jk; - for (i=0; i<=m; i++,j++) - f[i] = j<0 ? 0.0 : (double)ipio2[j]; - - /* compute q[0],q[1],...q[jk] */ - for (i=0; i<=jk; i++) { - for (j=0,fw=0.0; j<=jx; j++) - fw += x[j]*f[jx+i-j]; - q[i] = fw; - } - - jz = jk; -recompute: - /* distill q[] into iq[] reversingly */ - for (i=0,j=jz,z=q[jz]; j>0; i++,j--) { - fw = (double)(int32_t)(0x1p-24*z); - iq[i] = (int32_t)(z - 0x1p24*fw); - z = q[j-1]+fw; - } - - /* compute n */ - z = scalbn(z,q0); /* actual value of z */ - z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ - n = (int32_t)z; - z -= (double)n; - ih = 0; - if (q0 > 0) { /* need iq[jz-1] to determine n */ - i = iq[jz-1]>>(24-q0); n += i; - iq[jz-1] -= i<<(24-q0); - ih = iq[jz-1]>>(23-q0); - } - else if (q0 == 0) ih = iq[jz-1]>>23; - else if (z >= 0.5) ih = 2; - - if (ih > 0) { /* q > 0.5 */ - n += 1; carry = 0; - for (i=0; i 0) { /* rare case: chance is 1 in 12 */ - switch(q0) { - case 1: - iq[jz-1] &= 0x7fffff; break; - case 2: - iq[jz-1] &= 0x3fffff; break; - } - } - if (ih == 2) { - z = 1.0 - z; - if (carry != 0) - z -= scalbn(1.0,q0); - } - } - - /* check if recomputation is needed */ - if (z == 0.0) { - j = 0; - for (i=jz-1; i>=jk; i--) j |= iq[i]; - if (j == 0) { /* need recomputation */ - for (k=1; iq[jk-k]==0; k++); /* k = no. of terms needed */ - - for (i=jz+1; i<=jz+k; i++) { /* add q[jz+1] to q[jz+k] */ - f[jx+i] = (double)ipio2[jv+i]; - for (j=0,fw=0.0; j<=jx; j++) - fw += x[j]*f[jx+i-j]; - q[i] = fw; - } - jz += k; - goto recompute; - } - } - - /* chop off zero terms */ - if (z == 0.0) { - jz -= 1; - q0 -= 24; - while (iq[jz] == 0) { - jz--; - q0 -= 24; - } - } else { /* break z into 24-bit if necessary */ - z = scalbn(z,-q0); - if (z >= 0x1p24) { - fw = (double)(int32_t)(0x1p-24*z); - iq[jz] = (int32_t)(z - 0x1p24*fw); - jz += 1; - q0 += 24; - iq[jz] = (int32_t)fw; - } else - iq[jz] = (int32_t)z; - } - - /* convert integer "bit" chunk to floating-point value */ - fw = scalbn(1.0,q0); - for (i=jz; i>=0; i--) { - q[i] = fw*(double)iq[i]; - fw *= 0x1p-24; - } - - /* compute PIo2[0,...,jp]*q[jz,...,0] */ - for(i=jz; i>=0; i--) { - for (fw=0.0,k=0; k<=jp && k<=jz-i; k++) - fw += PIo2[k]*q[i+k]; - fq[jz-i] = fw; - } - - /* compress fq[] into y[] */ - switch(prec) { - case 0: - fw = 0.0; - for (i=jz; i>=0; i--) - fw += fq[i]; - y[0] = ih==0 ? fw : -fw; - break; - case 1: - case 2: - fw = 0.0; - for (i=jz; i>=0; i--) - fw += fq[i]; - // TODO: drop excess precision here once double_t is used - fw = (double)fw; - y[0] = ih==0 ? fw : -fw; - fw = fq[0]-fw; - for (i=1; i<=jz; i++) - fw += fq[i]; - y[1] = ih==0 ? fw : -fw; - break; - case 3: /* painful */ - for (i=jz; i>0; i--) { - fw = fq[i-1]+fq[i]; - fq[i] += fq[i-1]-fw; - fq[i-1] = fw; - } - for (i=jz; i>1; i--) { - fw = fq[i-1]+fq[i]; - fq[i] += fq[i-1]-fw; - fq[i-1] = fw; - } - for (fw=0.0,i=jz; i>=2; i--) - fw += fq[i]; - if (ih==0) { - y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; - } else { - y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; - } - } - return n&7; -} diff --git a/src/math/__rem_pio2f.c b/src/math/__rem_pio2f.c deleted file mode 100644 index e676564..0000000 --- a/src/math/__rem_pio2f.c +++ /dev/null @@ -1,86 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - * Debugged and optimized by Bruce D. Evans. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* __rem_pio2f(x,y) - * - * return the remainder of x rem pi/2 in *y - * use double precision for everything except passing x - * use __rem_pio2_large() for large x - */ - -#include "libm.h" - -#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 -#define EPS DBL_EPSILON -#elif FLT_EVAL_METHOD==2 -#define EPS LDBL_EPSILON -#endif - -/* - * invpio2: 53 bits of 2/pi - * pio2_1: first 25 bits of pi/2 - * pio2_1t: pi/2 - pio2_1 - */ -static const double -toint = 1.5/EPS, -pio4 = 0x1.921fb6p-1, -invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ -pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */ -pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */ - -int __rem_pio2f(float x, double *y) -{ - union {float f; uint32_t i;} u = {x}; - double tx[1],ty[1]; - double_t fn; - uint32_t ix; - int n, sign, e0; - - ix = u.i & 0x7fffffff; - /* 25+53 bit pi is good enough for medium size */ - if (ix < 0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */ - /* Use a specialized rint() to get fn. */ - fn = (double_t)x*invpio2 + toint - toint; - n = (int32_t)fn; - *y = x - fn*pio2_1 - fn*pio2_1t; - /* Matters with directed rounding. */ - if (predict_false(*y < -pio4)) { - n--; - fn--; - *y = x - fn*pio2_1 - fn*pio2_1t; - } else if (predict_false(*y > pio4)) { - n++; - fn++; - *y = x - fn*pio2_1 - fn*pio2_1t; - } - return n; - } - if(ix>=0x7f800000) { /* x is inf or NaN */ - *y = x-x; - return 0; - } - /* scale x into [2^23, 2^24-1] */ - sign = u.i>>31; - e0 = (ix>>23) - (0x7f+23); /* e0 = ilogb(|x|)-23, positive */ - u.i = ix - (e0<<23); - tx[0] = u.f; - n = __rem_pio2_large(tx,ty,e0,1,0); - if (sign) { - *y = -ty[0]; - return -n; - } - *y = ty[0]; - return n; -} diff --git a/src/math/__rem_pio2l.c b/src/math/__rem_pio2l.c deleted file mode 100644 index 236b2de..0000000 --- a/src/math/__rem_pio2l.c +++ /dev/null @@ -1,155 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/ld80/e_rem_pio2.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - * Optimized by Bruce D. Evans. - */ -#include "libm.h" -#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -/* ld80 and ld128 version of __rem_pio2(x,y) - * - * return the remainder of x rem pi/2 in y[0]+y[1] - * use __rem_pio2_large() for large x - */ - -static const long double toint = 1.5/LDBL_EPSILON; - -#if LDBL_MANT_DIG == 64 -/* u ~< 0x1p25*pi/2 */ -#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.m>>48) < ((0x3fff + 25)<<16 | 0x921f>>1 | 0x8000)) -#define QUOBITS(x) ((uint32_t)(int32_t)x & 0x7fffffff) -#define ROUND1 22 -#define ROUND2 61 -#define NX 3 -#define NY 2 -/* - * invpio2: 64 bits of 2/pi - * pio2_1: first 39 bits of pi/2 - * pio2_1t: pi/2 - pio2_1 - * pio2_2: second 39 bits of pi/2 - * pio2_2t: pi/2 - (pio2_1+pio2_2) - * pio2_3: third 39 bits of pi/2 - * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) - */ -static const double -pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */ -pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */ -pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */ -static const long double -pio4 = 0x1.921fb54442d1846ap-1L, -invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */ -pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */ -pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */ -pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */ -#elif LDBL_MANT_DIG == 113 -/* u ~< 0x1p45*pi/2 */ -#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.top) < ((0x3fff + 45)<<16 | 0x921f)) -#define QUOBITS(x) ((uint32_t)(int64_t)x & 0x7fffffff) -#define ROUND1 51 -#define ROUND2 119 -#define NX 5 -#define NY 3 -static const long double -pio4 = 0x1.921fb54442d18469898cc51701b8p-1L, -invpio2 = 6.3661977236758134307553505349005747e-01L, /* 0x145f306dc9c882a53f84eafa3ea6a.0p-113 */ -pio2_1 = 1.5707963267948966192292994253909555e+00L, /* 0x1921fb54442d18469800000000000.0p-112 */ -pio2_1t = 2.0222662487959507323996846200947577e-21L, /* 0x13198a2e03707344a4093822299f3.0p-181 */ -pio2_2 = 2.0222662487959507323994779168837751e-21L, /* 0x13198a2e03707344a400000000000.0p-181 */ -pio2_2t = 2.0670321098263988236496903051604844e-43L, /* 0x127044533e63a0105df531d89cd91.0p-254 */ -pio2_3 = 2.0670321098263988236499468110329591e-43L, /* 0x127044533e63a0105e00000000000.0p-254 */ -pio2_3t = -2.5650587247459238361625433492959285e-65L; /* -0x159c4ec64ddaeb5f78671cbfb2210.0p-327 */ -#endif - -int __rem_pio2l(long double x, long double *y) -{ - union ldshape u,uz; - long double z,w,t,r,fn; - double tx[NX],ty[NY]; - int ex,ey,n,i; - - u.f = x; - ex = u.i.se & 0x7fff; - if (SMALL(u)) { - /* rint(x/(pi/2)) */ - fn = x*invpio2 + toint - toint; - n = QUOBITS(fn); - r = x-fn*pio2_1; - w = fn*pio2_1t; /* 1st round good to 102/180 bits (ld80/ld128) */ - /* Matters with directed rounding. */ - if (predict_false(r - w < -pio4)) { - n--; - fn--; - r = x - fn*pio2_1; - w = fn*pio2_1t; - } else if (predict_false(r - w > pio4)) { - n++; - fn++; - r = x - fn*pio2_1; - w = fn*pio2_1t; - } - y[0] = r-w; - u.f = y[0]; - ey = u.i.se & 0x7fff; - if (ex - ey > ROUND1) { /* 2nd iteration needed, good to 141/248 (ld80/ld128) */ - t = r; - w = fn*pio2_2; - r = t-w; - w = fn*pio2_2t-((t-r)-w); - y[0] = r-w; - u.f = y[0]; - ey = u.i.se & 0x7fff; - if (ex - ey > ROUND2) { /* 3rd iteration, good to 180/316 bits */ - t = r; /* will cover all possible cases (not verified for ld128) */ - w = fn*pio2_3; - r = t-w; - w = fn*pio2_3t-((t-r)-w); - y[0] = r-w; - } - } - y[1] = (r - y[0]) - w; - return n; - } - /* - * all other (large) arguments - */ - if (ex == 0x7fff) { /* x is inf or NaN */ - y[0] = y[1] = x - x; - return 0; - } - /* set z = scalbn(|x|,-ilogb(x)+23) */ - uz.f = x; - uz.i.se = 0x3fff + 23; - z = uz.f; - for (i=0; i < NX - 1; i++) { - tx[i] = (double)(int32_t)z; - z = (z-tx[i])*0x1p24; - } - tx[i] = z; - while (tx[i] == 0) - i--; - n = __rem_pio2_large(tx, ty, ex-0x3fff-23, i+1, NY); - w = ty[1]; - if (NY == 3) - w += ty[2]; - r = ty[0] + w; - /* TODO: for ld128 this does not follow the recommendation of the - comments of __rem_pio2_large which seem wrong if |ty[0]| > |ty[1]+ty[2]| */ - w -= r - ty[0]; - if (u.i.se >> 15) { - y[0] = -r; - y[1] = -w; - return -n; - } - y[0] = r; - y[1] = w; - return n; -} -#endif diff --git a/src/math/__signbit.c b/src/math/__signbit.c deleted file mode 100644 index e700b6b..0000000 --- a/src/math/__signbit.c +++ /dev/null @@ -1,13 +0,0 @@ -#include "libm.h" - -// FIXME: macro in math.h -int __signbit(double x) -{ - union { - double d; - uint64_t i; - } y = { x }; - return y.i>>63; -} - - diff --git a/src/math/__signbitf.c b/src/math/__signbitf.c deleted file mode 100644 index 40ad3cf..0000000 --- a/src/math/__signbitf.c +++ /dev/null @@ -1,11 +0,0 @@ -#include "libm.h" - -// FIXME: macro in math.h -int __signbitf(float x) -{ - union { - float f; - uint32_t i; - } y = { x }; - return y.i>>31; -} diff --git a/src/math/__signbitl.c b/src/math/__signbitl.c deleted file mode 100644 index 63b3dc5..0000000 --- a/src/math/__signbitl.c +++ /dev/null @@ -1,14 +0,0 @@ -#include "libm.h" - -#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -int __signbitl(long double x) -{ - union ldshape u = {x}; - return u.i.se >> 15; -} -#elif LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -int __signbitl(long double x) -{ - return __signbit(x); -} -#endif diff --git a/src/math/__sin.c b/src/math/__sin.c deleted file mode 100644 index 4030949..0000000 --- a/src/math/__sin.c +++ /dev/null @@ -1,64 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/k_sin.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* __sin( x, y, iy) - * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 - * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. - * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). - * - * Algorithm - * 1. Since sin(-x) = -sin(x), we need only to consider positive x. - * 2. Callers must return sin(-0) = -0 without calling here since our - * odd polynomial is not evaluated in a way that preserves -0. - * Callers may do the optimization sin(x) ~ x for tiny x. - * 3. sin(x) is approximated by a polynomial of degree 13 on - * [0,pi/4] - * 3 13 - * sin(x) ~ x + S1*x + ... + S6*x - * where - * - * |sin(x) 2 4 6 8 10 12 | -58 - * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 - * | x | - * - * 4. sin(x+y) = sin(x) + sin'(x')*y - * ~ sin(x) + (1-x*x/2)*y - * For better accuracy, let - * 3 2 2 2 2 - * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) - * then 3 2 - * sin(x) = x + (S1*x + (x *(r-y/2)+y)) - */ - -#include "libm.h" - -static const double -S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ -S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ -S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ -S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ -S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ -S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ - -double __sin(double x, double y, int iy) -{ - double_t z,r,v,w; - - z = x*x; - w = z*z; - r = S2 + z*(S3 + z*S4) + z*w*(S5 + z*S6); - v = z*x; - if (iy == 0) - return x + v*(S1 + z*r); - else - return x - ((z*(0.5*y - v*r) - y) - v*S1); -} diff --git a/src/math/__sindf.c b/src/math/__sindf.c deleted file mode 100644 index 8fec2a3..0000000 --- a/src/math/__sindf.c +++ /dev/null @@ -1,36 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/k_sinf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - * Optimized by Bruce D. Evans. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -/* |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]). */ -static const double -S1 = -0x15555554cbac77.0p-55, /* -0.166666666416265235595 */ -S2 = 0x111110896efbb2.0p-59, /* 0.0083333293858894631756 */ -S3 = -0x1a00f9e2cae774.0p-65, /* -0.000198393348360966317347 */ -S4 = 0x16cd878c3b46a7.0p-71; /* 0.0000027183114939898219064 */ - -float __sindf(double x) -{ - double_t r, s, w, z; - - /* Try to optimize for parallel evaluation as in __tandf.c. */ - z = x*x; - w = z*z; - r = S3 + z*S4; - s = z*x; - return (x + s*(S1 + z*S2)) + s*w*r; -} diff --git a/src/math/__sinl.c b/src/math/__sinl.c deleted file mode 100644 index 2525bbe..0000000 --- a/src/math/__sinl.c +++ /dev/null @@ -1,78 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/ld80/k_sinl.c */ -/* origin: FreeBSD /usr/src/lib/msun/ld128/k_sinl.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -#if LDBL_MANT_DIG == 64 -/* - * ld80 version of __sin.c. See __sin.c for most comments. - */ -/* - * Domain [-0.7854, 0.7854], range ~[-1.89e-22, 1.915e-22] - * |sin(x)/x - s(x)| < 2**-72.1 - * - * See __cosl.c for more details about the polynomial. - */ -static const long double -S1 = -0.166666666666666666671L; /* -0xaaaaaaaaaaaaaaab.0p-66 */ -static const double -S2 = 0.0083333333333333332, /* 0x11111111111111.0p-59 */ -S3 = -0.00019841269841269427, /* -0x1a01a01a019f81.0p-65 */ -S4 = 0.0000027557319223597490, /* 0x171de3a55560f7.0p-71 */ -S5 = -0.000000025052108218074604, /* -0x1ae64564f16cad.0p-78 */ -S6 = 1.6059006598854211e-10, /* 0x161242b90243b5.0p-85 */ -S7 = -7.6429779983024564e-13, /* -0x1ae42ebd1b2e00.0p-93 */ -S8 = 2.6174587166648325e-15; /* 0x179372ea0b3f64.0p-101 */ -#define POLY(z) (S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*S8)))))) -#elif LDBL_MANT_DIG == 113 -/* - * ld128 version of __sin.c. See __sin.c for most comments. - */ -/* - * Domain [-0.7854, 0.7854], range ~[-1.53e-37, 1.659e-37] - * |sin(x)/x - s(x)| < 2**-122.1 - * - * See __cosl.c for more details about the polynomial. - */ -static const long double -S1 = -0.16666666666666666666666666666666666606732416116558L, -S2 = 0.0083333333333333333333333333333331135404851288270047L, -S3 = -0.00019841269841269841269841269839935785325638310428717L, -S4 = 0.27557319223985890652557316053039946268333231205686e-5L, -S5 = -0.25052108385441718775048214826384312253862930064745e-7L, -S6 = 0.16059043836821614596571832194524392581082444805729e-9L, -S7 = -0.76471637318198151807063387954939213287488216303768e-12L, -S8 = 0.28114572543451292625024967174638477283187397621303e-14L; -static const double -S9 = -0.82206352458348947812512122163446202498005154296863e-17, -S10 = 0.19572940011906109418080609928334380560135358385256e-19, -S11 = -0.38680813379701966970673724299207480965452616911420e-22, -S12 = 0.64038150078671872796678569586315881020659912139412e-25; -#define POLY(z) (S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*(S8+ \ - z*(S9+z*(S10+z*(S11+z*S12)))))))))) -#endif - -long double __sinl(long double x, long double y, int iy) -{ - long double z,r,v; - - z = x*x; - v = z*x; - r = POLY(z); - if (iy == 0) - return x+v*(S1+z*r); - return x-((z*(0.5*y-v*r)-y)-v*S1); -} -#endif diff --git a/src/math/__tan.c b/src/math/__tan.c deleted file mode 100644 index 8019844..0000000 --- a/src/math/__tan.c +++ /dev/null @@ -1,110 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/k_tan.c */ -/* - * ==================================================== - * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. - * - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* __tan( x, y, k ) - * kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 - * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. - * Input odd indicates whether tan (if odd = 0) or -1/tan (if odd = 1) is returned. - * - * Algorithm - * 1. Since tan(-x) = -tan(x), we need only to consider positive x. - * 2. Callers must return tan(-0) = -0 without calling here since our - * odd polynomial is not evaluated in a way that preserves -0. - * Callers may do the optimization tan(x) ~ x for tiny x. - * 3. tan(x) is approximated by a odd polynomial of degree 27 on - * [0,0.67434] - * 3 27 - * tan(x) ~ x + T1*x + ... + T13*x - * where - * - * |tan(x) 2 4 26 | -59.2 - * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 - * | x | - * - * Note: tan(x+y) = tan(x) + tan'(x)*y - * ~ tan(x) + (1+x*x)*y - * Therefore, for better accuracy in computing tan(x+y), let - * 3 2 2 2 2 - * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) - * then - * 3 2 - * tan(x+y) = x + (T1*x + (x *(r+y)+y)) - * - * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then - * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) - * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) - */ - -#include "libm.h" - -static const double T[] = { - 3.33333333333334091986e-01, /* 3FD55555, 55555563 */ - 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */ - 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */ - 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */ - 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */ - 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */ - 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */ - 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */ - 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */ - 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */ - 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */ - -1.85586374855275456654e-05, /* BEF375CB, DB605373 */ - 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */ -}, -pio4 = 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */ -pio4lo = 3.06161699786838301793e-17; /* 3C81A626, 33145C07 */ - -double __tan(double x, double y, int odd) -{ - double_t z, r, v, w, s, a; - double w0, a0; - uint32_t hx; - int big, sign; - - GET_HIGH_WORD(hx,x); - big = (hx&0x7fffffff) >= 0x3FE59428; /* |x| >= 0.6744 */ - if (big) { - sign = hx>>31; - if (sign) { - x = -x; - y = -y; - } - x = (pio4 - x) + (pio4lo - y); - y = 0.0; - } - z = x * x; - w = z * z; - /* - * Break x^5*(T[1]+x^2*T[2]+...) into - * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + - * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) - */ - r = T[1] + w*(T[3] + w*(T[5] + w*(T[7] + w*(T[9] + w*T[11])))); - v = z*(T[2] + w*(T[4] + w*(T[6] + w*(T[8] + w*(T[10] + w*T[12]))))); - s = z * x; - r = y + z*(s*(r + v) + y) + s*T[0]; - w = x + r; - if (big) { - s = 1 - 2*odd; - v = s - 2.0 * (x + (r - w*w/(w + s))); - return sign ? -v : v; - } - if (!odd) - return w; - /* -1.0/(x+r) has up to 2ulp error, so compute it accurately */ - w0 = w; - SET_LOW_WORD(w0, 0); - v = r - (w0 - x); /* w0+v = r+x */ - a0 = a = -1.0 / w; - SET_LOW_WORD(a0, 0); - return a0 + a*(1.0 + a0*w0 + a0*v); -} diff --git a/src/math/__tandf.c b/src/math/__tandf.c deleted file mode 100644 index 25047ee..0000000 --- a/src/math/__tandf.c +++ /dev/null @@ -1,54 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/k_tanf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - * Optimized by Bruce D. Evans. - */ -/* - * ==================================================== - * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. - * - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -/* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */ -static const double T[] = { - 0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */ - 0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */ - 0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */ - 0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */ - 0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */ - 0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */ -}; - -float __tandf(double x, int odd) -{ - double_t z,r,w,s,t,u; - - z = x*x; - /* - * Split up the polynomial into small independent terms to give - * opportunities for parallel evaluation. The chosen splitting is - * micro-optimized for Athlons (XP, X64). It costs 2 multiplications - * relative to Horner's method on sequential machines. - * - * We add the small terms from lowest degree up for efficiency on - * non-sequential machines (the lowest degree terms tend to be ready - * earlier). Apart from this, we don't care about order of - * operations, and don't need to to care since we have precision to - * spare. However, the chosen splitting is good for accuracy too, - * and would give results as accurate as Horner's method if the - * small terms were added from highest degree down. - */ - r = T[4] + z*T[5]; - t = T[2] + z*T[3]; - w = z*z; - s = z*x; - u = T[0] + z*T[1]; - r = (x + s*u) + (s*w)*(t + w*r); - return odd ? -1.0/r : r; -} diff --git a/src/math/__tanl.c b/src/math/__tanl.c deleted file mode 100644 index 54abc3d..0000000 --- a/src/math/__tanl.c +++ /dev/null @@ -1,143 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/ld80/k_tanl.c */ -/* origin: FreeBSD /usr/src/lib/msun/ld128/k_tanl.c */ -/* - * ==================================================== - * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. - * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. - * - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -#if LDBL_MANT_DIG == 64 -/* - * ld80 version of __tan.c. See __tan.c for most comments. - */ -/* - * Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22] - * |tan(x)/x - t(x)| < 2**-71.9 - * - * See __cosl.c for more details about the polynomial. - */ -static const long double -T3 = 0.333333333333333333180L, /* 0xaaaaaaaaaaaaaaa5.0p-65 */ -T5 = 0.133333333333333372290L, /* 0x88888888888893c3.0p-66 */ -T7 = 0.0539682539682504975744L, /* 0xdd0dd0dd0dc13ba2.0p-68 */ -pio4 = 0.785398163397448309628L, /* 0xc90fdaa22168c235.0p-64 */ -pio4lo = -1.25413940316708300586e-20L; /* -0xece675d1fc8f8cbb.0p-130 */ -static const double -T9 = 0.021869488536312216, /* 0x1664f4882cc1c2.0p-58 */ -T11 = 0.0088632355256619590, /* 0x1226e355c17612.0p-59 */ -T13 = 0.0035921281113786528, /* 0x1d6d3d185d7ff8.0p-61 */ -T15 = 0.0014558334756312418, /* 0x17da354aa3f96b.0p-62 */ -T17 = 0.00059003538700862256, /* 0x13559358685b83.0p-63 */ -T19 = 0.00023907843576635544, /* 0x1f56242026b5be.0p-65 */ -T21 = 0.000097154625656538905, /* 0x1977efc26806f4.0p-66 */ -T23 = 0.000038440165747303162, /* 0x14275a09b3ceac.0p-67 */ -T25 = 0.000018082171885432524, /* 0x12f5e563e5487e.0p-68 */ -T27 = 0.0000024196006108814377, /* 0x144c0d80cc6896.0p-71 */ -T29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */ -T31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */ -T33 = 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */ -#define RPOLY(w) (T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + \ - w * (T25 + w * (T29 + w * T33))))))) -#define VPOLY(w) (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + \ - w * (T27 + w * T31)))))) -#elif LDBL_MANT_DIG == 113 -/* - * ld128 version of __tan.c. See __tan.c for most comments. - */ -/* - * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37] - * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37) - * - * See __cosl.c for more details about the polynomial. - */ -static const long double -T3 = 0x1.5555555555555555555555555553p-2L, -T5 = 0x1.1111111111111111111111111eb5p-3L, -T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L, -T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L, -T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L, -T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L, -T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L, -T17 = 0x1.355824803674477dfcf726649efep-11L, -T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L, -T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L, -T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L, -T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L, -T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L, -T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L, -T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L, -T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L, -T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L, -T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L, -pio4 = 0x1.921fb54442d18469898cc51701b8p-1L, -pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L; -static const double -T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */ -T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */ -T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */ -T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */ -T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */ -T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */ -T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */ -T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */ -T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */ -T57 = 1.4912469681508012e-10; /* 0x147edbdba6f43a.0p-85 */ -#define RPOLY(w) (T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + \ - w * (T25 + w * (T29 + w * (T33 + w * (T37 + w * (T41 + \ - w * (T45 + w * (T49 + w * (T53 + w * T57))))))))))))) -#define VPOLY(w) (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + \ - w * (T27 + w * (T31 + w * (T35 + w * (T39 + w * (T43 + \ - w * (T47 + w * (T51 + w * T55)))))))))))) -#endif - -long double __tanl(long double x, long double y, int odd) { - long double z, r, v, w, s, a, t; - int big, sign; - - big = fabsl(x) >= 0.67434; - if (big) { - sign = 0; - if (x < 0) { - sign = 1; - x = -x; - y = -y; - } - x = (pio4 - x) + (pio4lo - y); - y = 0.0; - } - z = x * x; - w = z * z; - r = RPOLY(w); - v = z * VPOLY(w); - s = z * x; - r = y + z * (s * (r + v) + y) + T3 * s; - w = x + r; - if (big) { - s = 1 - 2*odd; - v = s - 2.0 * (x + (r - w * w / (w + s))); - return sign ? -v : v; - } - if (!odd) - return w; - /* - * if allow error up to 2 ulp, simply return - * -1.0 / (x+r) here - */ - /* compute -1.0 / (x+r) accurately */ - z = w; - z = z + 0x1p32 - 0x1p32; - v = r - (z - x); /* z+v = r+x */ - t = a = -1.0 / w; /* a = -1.0/w */ - t = t + 0x1p32 - 0x1p32; - s = 1.0 + t * z; - return t + a * (s + t * v); -} -#endif diff --git a/src/math/aarch64/ceil.c b/src/math/aarch64/ceil.c deleted file mode 100644 index ac80c1d..0000000 --- a/src/math/aarch64/ceil.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double ceil(double x) -{ - __asm__ ("frintp %d0, %d1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/ceilf.c b/src/math/aarch64/ceilf.c deleted file mode 100644 index 1ef1e9c..0000000 --- a/src/math/aarch64/ceilf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float ceilf(float x) -{ - __asm__ ("frintp %s0, %s1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/fabs.c b/src/math/aarch64/fabs.c deleted file mode 100644 index 5c3ecaf..0000000 --- a/src/math/aarch64/fabs.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double fabs(double x) -{ - __asm__ ("fabs %d0, %d1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/fabsf.c b/src/math/aarch64/fabsf.c deleted file mode 100644 index 7fde981..0000000 --- a/src/math/aarch64/fabsf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float fabsf(float x) -{ - __asm__ ("fabs %s0, %s1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/floor.c b/src/math/aarch64/floor.c deleted file mode 100644 index 50ffdb2..0000000 --- a/src/math/aarch64/floor.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double floor(double x) -{ - __asm__ ("frintm %d0, %d1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/floorf.c b/src/math/aarch64/floorf.c deleted file mode 100644 index 8d007e9..0000000 --- a/src/math/aarch64/floorf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float floorf(float x) -{ - __asm__ ("frintm %s0, %s1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/fma.c b/src/math/aarch64/fma.c deleted file mode 100644 index 2450ea7..0000000 --- a/src/math/aarch64/fma.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double fma(double x, double y, double z) -{ - __asm__ ("fmadd %d0, %d1, %d2, %d3" : "=w"(x) : "w"(x), "w"(y), "w"(z)); - return x; -} diff --git a/src/math/aarch64/fmaf.c b/src/math/aarch64/fmaf.c deleted file mode 100644 index 9a14721..0000000 --- a/src/math/aarch64/fmaf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float fmaf(float x, float y, float z) -{ - __asm__ ("fmadd %s0, %s1, %s2, %s3" : "=w"(x) : "w"(x), "w"(y), "w"(z)); - return x; -} diff --git a/src/math/aarch64/fmax.c b/src/math/aarch64/fmax.c deleted file mode 100644 index 86dcb3b..0000000 --- a/src/math/aarch64/fmax.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double fmax(double x, double y) -{ - __asm__ ("fmaxnm %d0, %d1, %d2" : "=w"(x) : "w"(x), "w"(y)); - return x; -} diff --git a/src/math/aarch64/fmaxf.c b/src/math/aarch64/fmaxf.c deleted file mode 100644 index ee5eac2..0000000 --- a/src/math/aarch64/fmaxf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float fmaxf(float x, float y) -{ - __asm__ ("fmaxnm %s0, %s1, %s2" : "=w"(x) : "w"(x), "w"(y)); - return x; -} diff --git a/src/math/aarch64/fmin.c b/src/math/aarch64/fmin.c deleted file mode 100644 index f1e9980..0000000 --- a/src/math/aarch64/fmin.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double fmin(double x, double y) -{ - __asm__ ("fminnm %d0, %d1, %d2" : "=w"(x) : "w"(x), "w"(y)); - return x; -} diff --git a/src/math/aarch64/fminf.c b/src/math/aarch64/fminf.c deleted file mode 100644 index 80468f6..0000000 --- a/src/math/aarch64/fminf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float fminf(float x, float y) -{ - __asm__ ("fminnm %s0, %s1, %s2" : "=w"(x) : "w"(x), "w"(y)); - return x; -} diff --git a/src/math/aarch64/llrint.c b/src/math/aarch64/llrint.c deleted file mode 100644 index a9e07a9..0000000 --- a/src/math/aarch64/llrint.c +++ /dev/null @@ -1,10 +0,0 @@ -#include - -long long llrint(double x) -{ - long long n; - __asm__ ( - "frintx %d1, %d1\n" - "fcvtzs %x0, %d1\n" : "=r"(n), "+w"(x)); - return n; -} diff --git a/src/math/aarch64/llrintf.c b/src/math/aarch64/llrintf.c deleted file mode 100644 index 12b6804..0000000 --- a/src/math/aarch64/llrintf.c +++ /dev/null @@ -1,10 +0,0 @@ -#include - -long long llrintf(float x) -{ - long long n; - __asm__ ( - "frintx %s1, %s1\n" - "fcvtzs %x0, %s1\n" : "=r"(n), "+w"(x)); - return n; -} diff --git a/src/math/aarch64/llround.c b/src/math/aarch64/llround.c deleted file mode 100644 index e09ddd4..0000000 --- a/src/math/aarch64/llround.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long long llround(double x) -{ - long long n; - __asm__ ("fcvtas %x0, %d1" : "=r"(n) : "w"(x)); - return n; -} diff --git a/src/math/aarch64/llroundf.c b/src/math/aarch64/llroundf.c deleted file mode 100644 index 1669959..0000000 --- a/src/math/aarch64/llroundf.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long long llroundf(float x) -{ - long long n; - __asm__ ("fcvtas %x0, %s1" : "=r"(n) : "w"(x)); - return n; -} diff --git a/src/math/aarch64/lrint.c b/src/math/aarch64/lrint.c deleted file mode 100644 index cb7785a..0000000 --- a/src/math/aarch64/lrint.c +++ /dev/null @@ -1,10 +0,0 @@ -#include - -long lrint(double x) -{ - long n; - __asm__ ( - "frintx %d1, %d1\n" - "fcvtzs %x0, %d1\n" : "=r"(n), "+w"(x)); - return n; -} diff --git a/src/math/aarch64/lrintf.c b/src/math/aarch64/lrintf.c deleted file mode 100644 index 4d750d6..0000000 --- a/src/math/aarch64/lrintf.c +++ /dev/null @@ -1,10 +0,0 @@ -#include - -long lrintf(float x) -{ - long n; - __asm__ ( - "frintx %s1, %s1\n" - "fcvtzs %x0, %s1\n" : "=r"(n), "+w"(x)); - return n; -} diff --git a/src/math/aarch64/lround.c b/src/math/aarch64/lround.c deleted file mode 100644 index 85656c7..0000000 --- a/src/math/aarch64/lround.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long lround(double x) -{ - long n; - __asm__ ("fcvtas %x0, %d1" : "=r"(n) : "w"(x)); - return n; -} diff --git a/src/math/aarch64/lroundf.c b/src/math/aarch64/lroundf.c deleted file mode 100644 index 32e51f3..0000000 --- a/src/math/aarch64/lroundf.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long lroundf(float x) -{ - long n; - __asm__ ("fcvtas %x0, %s1" : "=r"(n) : "w"(x)); - return n; -} diff --git a/src/math/aarch64/nearbyint.c b/src/math/aarch64/nearbyint.c deleted file mode 100644 index 9c3fdb4..0000000 --- a/src/math/aarch64/nearbyint.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double nearbyint(double x) -{ - __asm__ ("frinti %d0, %d1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/nearbyintf.c b/src/math/aarch64/nearbyintf.c deleted file mode 100644 index 8e7f61d..0000000 --- a/src/math/aarch64/nearbyintf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float nearbyintf(float x) -{ - __asm__ ("frinti %s0, %s1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/rint.c b/src/math/aarch64/rint.c deleted file mode 100644 index 45b194b..0000000 --- a/src/math/aarch64/rint.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double rint(double x) -{ - __asm__ ("frintx %d0, %d1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/rintf.c b/src/math/aarch64/rintf.c deleted file mode 100644 index 1ae7dd2..0000000 --- a/src/math/aarch64/rintf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float rintf(float x) -{ - __asm__ ("frintx %s0, %s1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/round.c b/src/math/aarch64/round.c deleted file mode 100644 index 897a84c..0000000 --- a/src/math/aarch64/round.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double round(double x) -{ - __asm__ ("frinta %d0, %d1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/roundf.c b/src/math/aarch64/roundf.c deleted file mode 100644 index 91637ea..0000000 --- a/src/math/aarch64/roundf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float roundf(float x) -{ - __asm__ ("frinta %s0, %s1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/sqrt.c b/src/math/aarch64/sqrt.c deleted file mode 100644 index fe93c3e..0000000 --- a/src/math/aarch64/sqrt.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double sqrt(double x) -{ - __asm__ ("fsqrt %d0, %d1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/sqrtf.c b/src/math/aarch64/sqrtf.c deleted file mode 100644 index 275c7f3..0000000 --- a/src/math/aarch64/sqrtf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float sqrtf(float x) -{ - __asm__ ("fsqrt %s0, %s1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/trunc.c b/src/math/aarch64/trunc.c deleted file mode 100644 index e592147..0000000 --- a/src/math/aarch64/trunc.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double trunc(double x) -{ - __asm__ ("frintz %d0, %d1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/aarch64/truncf.c b/src/math/aarch64/truncf.c deleted file mode 100644 index 20ef30f..0000000 --- a/src/math/aarch64/truncf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float truncf(float x) -{ - __asm__ ("frintz %s0, %s1" : "=w"(x) : "w"(x)); - return x; -} diff --git a/src/math/acos.c b/src/math/acos.c deleted file mode 100644 index ea9c87b..0000000 --- a/src/math/acos.c +++ /dev/null @@ -1,101 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* acos(x) - * Method : - * acos(x) = pi/2 - asin(x) - * acos(-x) = pi/2 + asin(x) - * For |x|<=0.5 - * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) - * For x>0.5 - * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) - * = 2asin(sqrt((1-x)/2)) - * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) - * = 2f + (2c + 2s*z*R(z)) - * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term - * for f so that f+c ~ sqrt(z). - * For x<-0.5 - * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) - * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) - * - * Special cases: - * if x is NaN, return x itself; - * if |x|>1, return NaN with invalid signal. - * - * Function needed: sqrt - */ - -#include "libm.h" - -static const double -pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ -pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ -pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ -pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ -pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ -pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ -pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ -pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ -qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ -qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ -qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ -qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ - -static double R(double z) -{ - double_t p, q; - p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); - q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4))); - return p/q; -} - -double acos(double x) -{ - double z,w,s,c,df; - uint32_t hx,ix; - - GET_HIGH_WORD(hx, x); - ix = hx & 0x7fffffff; - /* |x| >= 1 or nan */ - if (ix >= 0x3ff00000) { - uint32_t lx; - - GET_LOW_WORD(lx,x); - if ((ix-0x3ff00000 | lx) == 0) { - /* acos(1)=0, acos(-1)=pi */ - if (hx >> 31) - return 2*pio2_hi + 0x1p-120f; - return 0; - } - return 0/(x-x); - } - /* |x| < 0.5 */ - if (ix < 0x3fe00000) { - if (ix <= 0x3c600000) /* |x| < 2**-57 */ - return pio2_hi + 0x1p-120f; - return pio2_hi - (x - (pio2_lo-x*R(x*x))); - } - /* x < -0.5 */ - if (hx >> 31) { - z = (1.0+x)*0.5; - s = sqrt(z); - w = R(z)*s-pio2_lo; - return 2*(pio2_hi - (s+w)); - } - /* x > 0.5 */ - z = (1.0-x)*0.5; - s = sqrt(z); - df = s; - SET_LOW_WORD(df,0); - c = (z-df*df)/(s+df); - w = R(z)*s+c; - return 2*(df+w); -} diff --git a/src/math/acosf.c b/src/math/acosf.c deleted file mode 100644 index 8ee1a71..0000000 --- a/src/math/acosf.c +++ /dev/null @@ -1,71 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_acosf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -static const float -pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ -pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ -pS0 = 1.6666586697e-01, -pS1 = -4.2743422091e-02, -pS2 = -8.6563630030e-03, -qS1 = -7.0662963390e-01; - -static float R(float z) -{ - float_t p, q; - p = z*(pS0+z*(pS1+z*pS2)); - q = 1.0f+z*qS1; - return p/q; -} - -float acosf(float x) -{ - float z,w,s,c,df; - uint32_t hx,ix; - - GET_FLOAT_WORD(hx, x); - ix = hx & 0x7fffffff; - /* |x| >= 1 or nan */ - if (ix >= 0x3f800000) { - if (ix == 0x3f800000) { - if (hx >> 31) - return 2*pio2_hi + 0x1p-120f; - return 0; - } - return 0/(x-x); - } - /* |x| < 0.5 */ - if (ix < 0x3f000000) { - if (ix <= 0x32800000) /* |x| < 2**-26 */ - return pio2_hi + 0x1p-120f; - return pio2_hi - (x - (pio2_lo-x*R(x*x))); - } - /* x < -0.5 */ - if (hx >> 31) { - z = (1+x)*0.5f; - s = sqrtf(z); - w = R(z)*s-pio2_lo; - return 2*(pio2_hi - (s+w)); - } - /* x > 0.5 */ - z = (1-x)*0.5f; - s = sqrtf(z); - GET_FLOAT_WORD(hx,s); - SET_FLOAT_WORD(df,hx&0xfffff000); - c = (z-df*df)/(s+df); - w = R(z)*s+c; - return 2*(df+w); -} diff --git a/src/math/acosh.c b/src/math/acosh.c deleted file mode 100644 index badbf90..0000000 --- a/src/math/acosh.c +++ /dev/null @@ -1,24 +0,0 @@ -#include "libm.h" - -#if FLT_EVAL_METHOD==2 -#undef sqrt -#define sqrt sqrtl -#endif - -/* acosh(x) = log(x + sqrt(x*x-1)) */ -double acosh(double x) -{ - union {double f; uint64_t i;} u = {.f = x}; - unsigned e = u.i >> 52 & 0x7ff; - - /* x < 1 domain error is handled in the called functions */ - - if (e < 0x3ff + 1) - /* |x| < 2, up to 2ulp error in [1,1.125] */ - return log1p(x-1 + sqrt((x-1)*(x-1)+2*(x-1))); - if (e < 0x3ff + 26) - /* |x| < 0x1p26 */ - return log(2*x - 1/(x+sqrt(x*x-1))); - /* |x| >= 0x1p26 or nan */ - return log(x) + 0.693147180559945309417232121458176568; -} diff --git a/src/math/acoshf.c b/src/math/acoshf.c deleted file mode 100644 index 8a4ec4d..0000000 --- a/src/math/acoshf.c +++ /dev/null @@ -1,26 +0,0 @@ -#include "libm.h" - -#if FLT_EVAL_METHOD==2 -#undef sqrtf -#define sqrtf sqrtl -#elif FLT_EVAL_METHOD==1 -#undef sqrtf -#define sqrtf sqrt -#endif - -/* acosh(x) = log(x + sqrt(x*x-1)) */ -float acoshf(float x) -{ - union {float f; uint32_t i;} u = {x}; - uint32_t a = u.i & 0x7fffffff; - - if (a < 0x3f800000+(1<<23)) - /* |x| < 2, invalid if x < 1 or nan */ - /* up to 2ulp error in [1,1.125] */ - return log1pf(x-1 + sqrtf((x-1)*(x-1)+2*(x-1))); - if (a < 0x3f800000+(12<<23)) - /* |x| < 0x1p12 */ - return logf(2*x - 1/(x+sqrtf(x*x-1))); - /* x >= 0x1p12 */ - return logf(x) + 0.693147180559945309417232121458176568f; -} diff --git a/src/math/acoshl.c b/src/math/acoshl.c deleted file mode 100644 index 8d4b43f..0000000 --- a/src/math/acoshl.c +++ /dev/null @@ -1,29 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double acoshl(long double x) -{ - return acosh(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -/* acosh(x) = log(x + sqrt(x*x-1)) */ -long double acoshl(long double x) -{ - union ldshape u = {x}; - int e = u.i.se & 0x7fff; - - if (e < 0x3fff + 1) - /* |x| < 2, invalid if x < 1 or nan */ - return log1pl(x-1 + sqrtl((x-1)*(x-1)+2*(x-1))); - if (e < 0x3fff + 32) - /* |x| < 0x1p32 */ - return logl(2*x - 1/(x+sqrtl(x*x-1))); - return logl(x) + 0.693147180559945309417232121458176568L; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double acoshl(long double x) -{ - return acosh(x); -} -#endif diff --git a/src/math/acosl.c b/src/math/acosl.c deleted file mode 100644 index c03bdf0..0000000 --- a/src/math/acosl.c +++ /dev/null @@ -1,67 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_acosl.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* - * See comments in acos.c. - * Converted to long double by David Schultz . - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double acosl(long double x) -{ - return acos(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -#include "__invtrigl.h" -#if LDBL_MANT_DIG == 64 -#define CLEARBOTTOM(u) (u.i.m &= -1ULL << 32) -#elif LDBL_MANT_DIG == 113 -#define CLEARBOTTOM(u) (u.i.lo = 0) -#endif - -long double acosl(long double x) -{ - union ldshape u = {x}; - long double z, s, c, f; - uint16_t e = u.i.se & 0x7fff; - - /* |x| >= 1 or nan */ - if (e >= 0x3fff) { - if (x == 1) - return 0; - if (x == -1) - return 2*pio2_hi + 0x1p-120f; - return 0/(x-x); - } - /* |x| < 0.5 */ - if (e < 0x3fff - 1) { - if (e < 0x3fff - LDBL_MANT_DIG - 1) - return pio2_hi + 0x1p-120f; - return pio2_hi - (__invtrigl_R(x*x)*x - pio2_lo + x); - } - /* x < -0.5 */ - if (u.i.se >> 15) { - z = (1 + x)*0.5; - s = sqrtl(z); - return 2*(pio2_hi - (__invtrigl_R(z)*s - pio2_lo + s)); - } - /* x > 0.5 */ - z = (1 - x)*0.5; - s = sqrtl(z); - u.f = s; - CLEARBOTTOM(u); - f = u.f; - c = (z - f*f)/(s + f); - return 2*(__invtrigl_R(z)*s + c + f); -} -#endif diff --git a/src/math/arm/fabs.c b/src/math/arm/fabs.c deleted file mode 100644 index 6e1d367..0000000 --- a/src/math/arm/fabs.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __ARM_PCS_VFP && __ARM_FP&8 - -double fabs(double x) -{ - __asm__ ("vabs.f64 %P0, %P1" : "=w"(x) : "w"(x)); - return x; -} - -#else - -#include "../fabs.c" - -#endif diff --git a/src/math/arm/fabsf.c b/src/math/arm/fabsf.c deleted file mode 100644 index 4a217c9..0000000 --- a/src/math/arm/fabsf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __ARM_PCS_VFP && !BROKEN_VFP_ASM - -float fabsf(float x) -{ - __asm__ ("vabs.f32 %0, %1" : "=t"(x) : "t"(x)); - return x; -} - -#else - -#include "../fabsf.c" - -#endif diff --git a/src/math/arm/fma.c b/src/math/arm/fma.c deleted file mode 100644 index 2a9b8ef..0000000 --- a/src/math/arm/fma.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __ARM_FEATURE_FMA && __ARM_FP&8 && !__SOFTFP__ - -double fma(double x, double y, double z) -{ - __asm__ ("vfma.f64 %P0, %P1, %P2" : "+w"(z) : "w"(x), "w"(y)); - return z; -} - -#else - -#include "../fma.c" - -#endif diff --git a/src/math/arm/fmaf.c b/src/math/arm/fmaf.c deleted file mode 100644 index a1793d2..0000000 --- a/src/math/arm/fmaf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __ARM_FEATURE_FMA && __ARM_FP&4 && !__SOFTFP__ && !BROKEN_VFP_ASM - -float fmaf(float x, float y, float z) -{ - __asm__ ("vfma.f32 %0, %1, %2" : "+t"(z) : "t"(x), "t"(y)); - return z; -} - -#else - -#include "../fmaf.c" - -#endif diff --git a/src/math/arm/sqrt.c b/src/math/arm/sqrt.c deleted file mode 100644 index 567e2e9..0000000 --- a/src/math/arm/sqrt.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if (__ARM_PCS_VFP || (__VFP_FP__ && !__SOFTFP__)) && (__ARM_FP&8) - -double sqrt(double x) -{ - __asm__ ("vsqrt.f64 %P0, %P1" : "=w"(x) : "w"(x)); - return x; -} - -#else - -#include "../sqrt.c" - -#endif diff --git a/src/math/arm/sqrtf.c b/src/math/arm/sqrtf.c deleted file mode 100644 index 3269329..0000000 --- a/src/math/arm/sqrtf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if (__ARM_PCS_VFP || (__VFP_FP__ && !__SOFTFP__)) && !BROKEN_VFP_ASM - -float sqrtf(float x) -{ - __asm__ ("vsqrt.f32 %0, %1" : "=t"(x) : "t"(x)); - return x; -} - -#else - -#include "../sqrtf.c" - -#endif diff --git a/src/math/asin.c b/src/math/asin.c deleted file mode 100644 index c926b18..0000000 --- a/src/math/asin.c +++ /dev/null @@ -1,107 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_asin.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* asin(x) - * Method : - * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... - * we approximate asin(x) on [0,0.5] by - * asin(x) = x + x*x^2*R(x^2) - * where - * R(x^2) is a rational approximation of (asin(x)-x)/x^3 - * and its remez error is bounded by - * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) - * - * For x in [0.5,1] - * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) - * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; - * then for x>0.98 - * asin(x) = pi/2 - 2*(s+s*z*R(z)) - * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) - * For x<=0.98, let pio4_hi = pio2_hi/2, then - * f = hi part of s; - * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) - * and - * asin(x) = pi/2 - 2*(s+s*z*R(z)) - * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) - * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) - * - * Special cases: - * if x is NaN, return x itself; - * if |x|>1, return NaN with invalid signal. - * - */ - -#include "libm.h" - -static const double -pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ -pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ -/* coefficients for R(x^2) */ -pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ -pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ -pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ -pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ -pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ -pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ -qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ -qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ -qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ -qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ - -static double R(double z) -{ - double_t p, q; - p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); - q = 1.0+z*(qS1+z*(qS2+z*(qS3+z*qS4))); - return p/q; -} - -double asin(double x) -{ - double z,r,s; - uint32_t hx,ix; - - GET_HIGH_WORD(hx, x); - ix = hx & 0x7fffffff; - /* |x| >= 1 or nan */ - if (ix >= 0x3ff00000) { - uint32_t lx; - GET_LOW_WORD(lx, x); - if ((ix-0x3ff00000 | lx) == 0) - /* asin(1) = +-pi/2 with inexact */ - return x*pio2_hi + 0x1p-120f; - return 0/(x-x); - } - /* |x| < 0.5 */ - if (ix < 0x3fe00000) { - /* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */ - if (ix < 0x3e500000 && ix >= 0x00100000) - return x; - return x + x*R(x*x); - } - /* 1 > |x| >= 0.5 */ - z = (1 - fabs(x))*0.5; - s = sqrt(z); - r = R(z); - if (ix >= 0x3fef3333) { /* if |x| > 0.975 */ - x = pio2_hi-(2*(s+s*r)-pio2_lo); - } else { - double f,c; - /* f+c = sqrt(z) */ - f = s; - SET_LOW_WORD(f,0); - c = (z-f*f)/(s+f); - x = 0.5*pio2_hi - (2*s*r - (pio2_lo-2*c) - (0.5*pio2_hi-2*f)); - } - if (hx >> 31) - return -x; - return x; -} diff --git a/src/math/asinf.c b/src/math/asinf.c deleted file mode 100644 index bcd304a..0000000 --- a/src/math/asinf.c +++ /dev/null @@ -1,61 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_asinf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -#include "libm.h" - -static const double -pio2 = 1.570796326794896558e+00; - -static const float -/* coefficients for R(x^2) */ -pS0 = 1.6666586697e-01, -pS1 = -4.2743422091e-02, -pS2 = -8.6563630030e-03, -qS1 = -7.0662963390e-01; - -static float R(float z) -{ - float_t p, q; - p = z*(pS0+z*(pS1+z*pS2)); - q = 1.0f+z*qS1; - return p/q; -} - -float asinf(float x) -{ - double s; - float z; - uint32_t hx,ix; - - GET_FLOAT_WORD(hx, x); - ix = hx & 0x7fffffff; - if (ix >= 0x3f800000) { /* |x| >= 1 */ - if (ix == 0x3f800000) /* |x| == 1 */ - return x*pio2 + 0x1p-120f; /* asin(+-1) = +-pi/2 with inexact */ - return 0/(x-x); /* asin(|x|>1) is NaN */ - } - if (ix < 0x3f000000) { /* |x| < 0.5 */ - /* if 0x1p-126 <= |x| < 0x1p-12, avoid raising underflow */ - if (ix < 0x39800000 && ix >= 0x00800000) - return x; - return x + x*R(x*x); - } - /* 1 > |x| >= 0.5 */ - z = (1 - fabsf(x))*0.5f; - s = sqrt(z); - x = pio2 - 2*(s+s*R(z)); - if (hx >> 31) - return -x; - return x; -} diff --git a/src/math/asinh.c b/src/math/asinh.c deleted file mode 100644 index 0829f22..0000000 --- a/src/math/asinh.c +++ /dev/null @@ -1,28 +0,0 @@ -#include "libm.h" - -/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ -double asinh(double x) -{ - union {double f; uint64_t i;} u = {.f = x}; - unsigned e = u.i >> 52 & 0x7ff; - unsigned s = u.i >> 63; - - /* |x| */ - u.i &= (uint64_t)-1/2; - x = u.f; - - if (e >= 0x3ff + 26) { - /* |x| >= 0x1p26 or inf or nan */ - x = log(x) + 0.693147180559945309417232121458176568; - } else if (e >= 0x3ff + 1) { - /* |x| >= 2 */ - x = log(2*x + 1/(sqrt(x*x+1)+x)); - } else if (e >= 0x3ff - 26) { - /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */ - x = log1p(x + x*x/(sqrt(x*x+1)+1)); - } else { - /* |x| < 0x1p-26, raise inexact if x != 0 */ - FORCE_EVAL(x + 0x1p120f); - } - return s ? -x : x; -} diff --git a/src/math/asinhf.c b/src/math/asinhf.c deleted file mode 100644 index fc9f091..0000000 --- a/src/math/asinhf.c +++ /dev/null @@ -1,28 +0,0 @@ -#include "libm.h" - -/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ -float asinhf(float x) -{ - union {float f; uint32_t i;} u = {.f = x}; - uint32_t i = u.i & 0x7fffffff; - unsigned s = u.i >> 31; - - /* |x| */ - u.i = i; - x = u.f; - - if (i >= 0x3f800000 + (12<<23)) { - /* |x| >= 0x1p12 or inf or nan */ - x = logf(x) + 0.693147180559945309417232121458176568f; - } else if (i >= 0x3f800000 + (1<<23)) { - /* |x| >= 2 */ - x = logf(2*x + 1/(sqrtf(x*x+1)+x)); - } else if (i >= 0x3f800000 - (12<<23)) { - /* |x| >= 0x1p-12, up to 1.6ulp error in [0.125,0.5] */ - x = log1pf(x + x*x/(sqrtf(x*x+1)+1)); - } else { - /* |x| < 0x1p-12, raise inexact if x!=0 */ - FORCE_EVAL(x + 0x1p120f); - } - return s ? -x : x; -} diff --git a/src/math/asinhl.c b/src/math/asinhl.c deleted file mode 100644 index 8635f52..0000000 --- a/src/math/asinhl.c +++ /dev/null @@ -1,41 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double asinhl(long double x) -{ - return asinh(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ -long double asinhl(long double x) -{ - union ldshape u = {x}; - unsigned e = u.i.se & 0x7fff; - unsigned s = u.i.se >> 15; - - /* |x| */ - u.i.se = e; - x = u.f; - - if (e >= 0x3fff + 32) { - /* |x| >= 0x1p32 or inf or nan */ - x = logl(x) + 0.693147180559945309417232121458176568L; - } else if (e >= 0x3fff + 1) { - /* |x| >= 2 */ - x = logl(2*x + 1/(sqrtl(x*x+1)+x)); - } else if (e >= 0x3fff - 32) { - /* |x| >= 0x1p-32 */ - x = log1pl(x + x*x/(sqrtl(x*x+1)+1)); - } else { - /* |x| < 0x1p-32, raise inexact if x!=0 */ - FORCE_EVAL(x + 0x1p120f); - } - return s ? -x : x; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double asinhl(long double x) -{ - return asinh(x); -} -#endif diff --git a/src/math/asinl.c b/src/math/asinl.c deleted file mode 100644 index 347c535..0000000 --- a/src/math/asinl.c +++ /dev/null @@ -1,71 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_asinl.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* - * See comments in asin.c. - * Converted to long double by David Schultz . - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double asinl(long double x) -{ - return asin(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -#include "__invtrigl.h" -#if LDBL_MANT_DIG == 64 -#define CLOSETO1(u) (u.i.m>>56 >= 0xf7) -#define CLEARBOTTOM(u) (u.i.m &= -1ULL << 32) -#elif LDBL_MANT_DIG == 113 -#define CLOSETO1(u) (u.i.top >= 0xee00) -#define CLEARBOTTOM(u) (u.i.lo = 0) -#endif - -long double asinl(long double x) -{ - union ldshape u = {x}; - long double z, r, s; - uint16_t e = u.i.se & 0x7fff; - int sign = u.i.se >> 15; - - if (e >= 0x3fff) { /* |x| >= 1 or nan */ - /* asin(+-1)=+-pi/2 with inexact */ - if (x == 1 || x == -1) - return x*pio2_hi + 0x1p-120f; - return 0/(x-x); - } - if (e < 0x3fff - 1) { /* |x| < 0.5 */ - if (e < 0x3fff - (LDBL_MANT_DIG+1)/2) { - /* return x with inexact if x!=0 */ - FORCE_EVAL(x + 0x1p120f); - return x; - } - return x + x*__invtrigl_R(x*x); - } - /* 1 > |x| >= 0.5 */ - z = (1.0 - fabsl(x))*0.5; - s = sqrtl(z); - r = __invtrigl_R(z); - if (CLOSETO1(u)) { - x = pio2_hi - (2*(s+s*r)-pio2_lo); - } else { - long double f, c; - u.f = s; - CLEARBOTTOM(u); - f = u.f; - c = (z - f*f)/(s + f); - x = 0.5*pio2_hi-(2*s*r - (pio2_lo-2*c) - (0.5*pio2_hi-2*f)); - } - return sign ? -x : x; -} -#endif diff --git a/src/math/atan.c b/src/math/atan.c deleted file mode 100644 index 63b0ab2..0000000 --- a/src/math/atan.c +++ /dev/null @@ -1,116 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_atan.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* atan(x) - * Method - * 1. Reduce x to positive by atan(x) = -atan(-x). - * 2. According to the integer k=4t+0.25 chopped, t=x, the argument - * is further reduced to one of the following intervals and the - * arctangent of t is evaluated by the corresponding formula: - * - * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) - * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) - * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) - * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) - * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) - * - * Constants: - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough - * to produce the hexadecimal values shown. - */ - - -#include "libm.h" - -static const double atanhi[] = { - 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ - 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ - 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ - 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ -}; - -static const double atanlo[] = { - 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ - 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ - 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ - 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ -}; - -static const double aT[] = { - 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ - -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ - 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ - -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ - 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ - -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ - 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ - -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ - 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ - -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ - 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ -}; - -double atan(double x) -{ - double_t w,s1,s2,z; - uint32_t ix,sign; - int id; - - GET_HIGH_WORD(ix, x); - sign = ix >> 31; - ix &= 0x7fffffff; - if (ix >= 0x44100000) { /* if |x| >= 2^66 */ - if (isnan(x)) - return x; - z = atanhi[3] + 0x1p-120f; - return sign ? -z : z; - } - if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ - if (ix < 0x3e400000) { /* |x| < 2^-27 */ - if (ix < 0x00100000) - /* raise underflow for subnormal x */ - FORCE_EVAL((float)x); - return x; - } - id = -1; - } else { - x = fabs(x); - if (ix < 0x3ff30000) { /* |x| < 1.1875 */ - if (ix < 0x3fe60000) { /* 7/16 <= |x| < 11/16 */ - id = 0; - x = (2.0*x-1.0)/(2.0+x); - } else { /* 11/16 <= |x| < 19/16 */ - id = 1; - x = (x-1.0)/(x+1.0); - } - } else { - if (ix < 0x40038000) { /* |x| < 2.4375 */ - id = 2; - x = (x-1.5)/(1.0+1.5*x); - } else { /* 2.4375 <= |x| < 2^66 */ - id = 3; - x = -1.0/x; - } - } - } - /* end of argument reduction */ - z = x*x; - w = z*z; - /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ - s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); - s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); - if (id < 0) - return x - x*(s1+s2); - z = atanhi[id] - (x*(s1+s2) - atanlo[id] - x); - return sign ? -z : z; -} diff --git a/src/math/atan2.c b/src/math/atan2.c deleted file mode 100644 index 5a1903c..0000000 --- a/src/math/atan2.c +++ /dev/null @@ -1,107 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ -/* atan2(y,x) - * Method : - * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). - * 2. Reduce x to positive by (if x and y are unexceptional): - * ARG (x+iy) = arctan(y/x) ... if x > 0, - * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, - * - * Special cases: - * - * ATAN2((anything), NaN ) is NaN; - * ATAN2(NAN , (anything) ) is NaN; - * ATAN2(+-0, +(anything but NaN)) is +-0 ; - * ATAN2(+-0, -(anything but NaN)) is +-pi ; - * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; - * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; - * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; - * ATAN2(+-INF,+INF ) is +-pi/4 ; - * ATAN2(+-INF,-INF ) is +-3pi/4; - * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; - * - * Constants: - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough - * to produce the hexadecimal values shown. - */ - -#include "libm.h" - -static const double -pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ -pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ - -double atan2(double y, double x) -{ - double z; - uint32_t m,lx,ly,ix,iy; - - if (isnan(x) || isnan(y)) - return x+y; - EXTRACT_WORDS(ix, lx, x); - EXTRACT_WORDS(iy, ly, y); - if ((ix-0x3ff00000 | lx) == 0) /* x = 1.0 */ - return atan(y); - m = ((iy>>31)&1) | ((ix>>30)&2); /* 2*sign(x)+sign(y) */ - ix = ix & 0x7fffffff; - iy = iy & 0x7fffffff; - - /* when y = 0 */ - if ((iy|ly) == 0) { - switch(m) { - case 0: - case 1: return y; /* atan(+-0,+anything)=+-0 */ - case 2: return pi; /* atan(+0,-anything) = pi */ - case 3: return -pi; /* atan(-0,-anything) =-pi */ - } - } - /* when x = 0 */ - if ((ix|lx) == 0) - return m&1 ? -pi/2 : pi/2; - /* when x is INF */ - if (ix == 0x7ff00000) { - if (iy == 0x7ff00000) { - switch(m) { - case 0: return pi/4; /* atan(+INF,+INF) */ - case 1: return -pi/4; /* atan(-INF,+INF) */ - case 2: return 3*pi/4; /* atan(+INF,-INF) */ - case 3: return -3*pi/4; /* atan(-INF,-INF) */ - } - } else { - switch(m) { - case 0: return 0.0; /* atan(+...,+INF) */ - case 1: return -0.0; /* atan(-...,+INF) */ - case 2: return pi; /* atan(+...,-INF) */ - case 3: return -pi; /* atan(-...,-INF) */ - } - } - } - /* |y/x| > 0x1p64 */ - if (ix+(64<<20) < iy || iy == 0x7ff00000) - return m&1 ? -pi/2 : pi/2; - - /* z = atan(|y/x|) without spurious underflow */ - if ((m&2) && iy+(64<<20) < ix) /* |y/x| < 0x1p-64, x<0 */ - z = 0; - else - z = atan(fabs(y/x)); - switch (m) { - case 0: return z; /* atan(+,+) */ - case 1: return -z; /* atan(-,+) */ - case 2: return pi - (z-pi_lo); /* atan(+,-) */ - default: /* case 3 */ - return (z-pi_lo) - pi; /* atan(-,-) */ - } -} diff --git a/src/math/atan2f.c b/src/math/atan2f.c deleted file mode 100644 index c634d00..0000000 --- a/src/math/atan2f.c +++ /dev/null @@ -1,83 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2f.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -static const float -pi = 3.1415927410e+00, /* 0x40490fdb */ -pi_lo = -8.7422776573e-08; /* 0xb3bbbd2e */ - -float atan2f(float y, float x) -{ - float z; - uint32_t m,ix,iy; - - if (isnan(x) || isnan(y)) - return x+y; - GET_FLOAT_WORD(ix, x); - GET_FLOAT_WORD(iy, y); - if (ix == 0x3f800000) /* x=1.0 */ - return atanf(y); - m = ((iy>>31)&1) | ((ix>>30)&2); /* 2*sign(x)+sign(y) */ - ix &= 0x7fffffff; - iy &= 0x7fffffff; - - /* when y = 0 */ - if (iy == 0) { - switch (m) { - case 0: - case 1: return y; /* atan(+-0,+anything)=+-0 */ - case 2: return pi; /* atan(+0,-anything) = pi */ - case 3: return -pi; /* atan(-0,-anything) =-pi */ - } - } - /* when x = 0 */ - if (ix == 0) - return m&1 ? -pi/2 : pi/2; - /* when x is INF */ - if (ix == 0x7f800000) { - if (iy == 0x7f800000) { - switch (m) { - case 0: return pi/4; /* atan(+INF,+INF) */ - case 1: return -pi/4; /* atan(-INF,+INF) */ - case 2: return 3*pi/4; /*atan(+INF,-INF)*/ - case 3: return -3*pi/4; /*atan(-INF,-INF)*/ - } - } else { - switch (m) { - case 0: return 0.0f; /* atan(+...,+INF) */ - case 1: return -0.0f; /* atan(-...,+INF) */ - case 2: return pi; /* atan(+...,-INF) */ - case 3: return -pi; /* atan(-...,-INF) */ - } - } - } - /* |y/x| > 0x1p26 */ - if (ix+(26<<23) < iy || iy == 0x7f800000) - return m&1 ? -pi/2 : pi/2; - - /* z = atan(|y/x|) with correct underflow */ - if ((m&2) && iy+(26<<23) < ix) /*|y/x| < 0x1p-26, x < 0 */ - z = 0.0; - else - z = atanf(fabsf(y/x)); - switch (m) { - case 0: return z; /* atan(+,+) */ - case 1: return -z; /* atan(-,+) */ - case 2: return pi - (z-pi_lo); /* atan(+,-) */ - default: /* case 3 */ - return (z-pi_lo) - pi; /* atan(-,-) */ - } -} diff --git a/src/math/atan2l.c b/src/math/atan2l.c deleted file mode 100644 index f0937a9..0000000 --- a/src/math/atan2l.c +++ /dev/null @@ -1,85 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2l.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ -/* - * See comments in atan2.c. - * Converted to long double by David Schultz . - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double atan2l(long double y, long double x) -{ - return atan2(y, x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -#include "__invtrigl.h" - -long double atan2l(long double y, long double x) -{ - union ldshape ux, uy; - long double z; - int m, ex, ey; - - if (isnan(x) || isnan(y)) - return x+y; - if (x == 1) - return atanl(y); - ux.f = x; - uy.f = y; - ex = ux.i.se & 0x7fff; - ey = uy.i.se & 0x7fff; - m = 2*(ux.i.se>>15) | uy.i.se>>15; - if (y == 0) { - switch(m) { - case 0: - case 1: return y; /* atan(+-0,+anything)=+-0 */ - case 2: return 2*pio2_hi; /* atan(+0,-anything) = pi */ - case 3: return -2*pio2_hi; /* atan(-0,-anything) =-pi */ - } - } - if (x == 0) - return m&1 ? -pio2_hi : pio2_hi; - if (ex == 0x7fff) { - if (ey == 0x7fff) { - switch(m) { - case 0: return pio2_hi/2; /* atan(+INF,+INF) */ - case 1: return -pio2_hi/2; /* atan(-INF,+INF) */ - case 2: return 1.5*pio2_hi; /* atan(+INF,-INF) */ - case 3: return -1.5*pio2_hi; /* atan(-INF,-INF) */ - } - } else { - switch(m) { - case 0: return 0.0; /* atan(+...,+INF) */ - case 1: return -0.0; /* atan(-...,+INF) */ - case 2: return 2*pio2_hi; /* atan(+...,-INF) */ - case 3: return -2*pio2_hi; /* atan(-...,-INF) */ - } - } - } - if (ex+120 < ey || ey == 0x7fff) - return m&1 ? -pio2_hi : pio2_hi; - /* z = atan(|y/x|) without spurious underflow */ - if ((m&2) && ey+120 < ex) /* |y/x| < 0x1p-120, x<0 */ - z = 0.0; - else - z = atanl(fabsl(y/x)); - switch (m) { - case 0: return z; /* atan(+,+) */ - case 1: return -z; /* atan(-,+) */ - case 2: return 2*pio2_hi-(z-2*pio2_lo); /* atan(+,-) */ - default: /* case 3 */ - return (z-2*pio2_lo)-2*pio2_hi; /* atan(-,-) */ - } -} -#endif diff --git a/src/math/atanf.c b/src/math/atanf.c deleted file mode 100644 index 178341b..0000000 --- a/src/math/atanf.c +++ /dev/null @@ -1,94 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_atanf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - - -#include "libm.h" - -static const float atanhi[] = { - 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ - 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ - 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ - 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ -}; - -static const float atanlo[] = { - 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ - 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ - 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ - 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ -}; - -static const float aT[] = { - 3.3333328366e-01, - -1.9999158382e-01, - 1.4253635705e-01, - -1.0648017377e-01, - 6.1687607318e-02, -}; - -float atanf(float x) -{ - float_t w,s1,s2,z; - uint32_t ix,sign; - int id; - - GET_FLOAT_WORD(ix, x); - sign = ix>>31; - ix &= 0x7fffffff; - if (ix >= 0x4c800000) { /* if |x| >= 2**26 */ - if (isnan(x)) - return x; - z = atanhi[3] + 0x1p-120f; - return sign ? -z : z; - } - if (ix < 0x3ee00000) { /* |x| < 0.4375 */ - if (ix < 0x39800000) { /* |x| < 2**-12 */ - if (ix < 0x00800000) - /* raise underflow for subnormal x */ - FORCE_EVAL(x*x); - return x; - } - id = -1; - } else { - x = fabsf(x); - if (ix < 0x3f980000) { /* |x| < 1.1875 */ - if (ix < 0x3f300000) { /* 7/16 <= |x| < 11/16 */ - id = 0; - x = (2.0f*x - 1.0f)/(2.0f + x); - } else { /* 11/16 <= |x| < 19/16 */ - id = 1; - x = (x - 1.0f)/(x + 1.0f); - } - } else { - if (ix < 0x401c0000) { /* |x| < 2.4375 */ - id = 2; - x = (x - 1.5f)/(1.0f + 1.5f*x); - } else { /* 2.4375 <= |x| < 2**26 */ - id = 3; - x = -1.0f/x; - } - } - } - /* end of argument reduction */ - z = x*x; - w = z*z; - /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ - s1 = z*(aT[0]+w*(aT[2]+w*aT[4])); - s2 = w*(aT[1]+w*aT[3]); - if (id < 0) - return x - x*(s1+s2); - z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); - return sign ? -z : z; -} diff --git a/src/math/atanh.c b/src/math/atanh.c deleted file mode 100644 index 63a035d..0000000 --- a/src/math/atanh.c +++ /dev/null @@ -1,29 +0,0 @@ -#include "libm.h" - -/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ -double atanh(double x) -{ - union {double f; uint64_t i;} u = {.f = x}; - unsigned e = u.i >> 52 & 0x7ff; - unsigned s = u.i >> 63; - double_t y; - - /* |x| */ - u.i &= (uint64_t)-1/2; - y = u.f; - - if (e < 0x3ff - 1) { - if (e < 0x3ff - 32) { - /* handle underflow */ - if (e == 0) - FORCE_EVAL((float)y); - } else { - /* |x| < 0.5, up to 1.7ulp error */ - y = 0.5*log1p(2*y + 2*y*y/(1-y)); - } - } else { - /* avoid overflow */ - y = 0.5*log1p(2*(y/(1-y))); - } - return s ? -y : y; -} diff --git a/src/math/atanhf.c b/src/math/atanhf.c deleted file mode 100644 index 65f07c0..0000000 --- a/src/math/atanhf.c +++ /dev/null @@ -1,28 +0,0 @@ -#include "libm.h" - -/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ -float atanhf(float x) -{ - union {float f; uint32_t i;} u = {.f = x}; - unsigned s = u.i >> 31; - float_t y; - - /* |x| */ - u.i &= 0x7fffffff; - y = u.f; - - if (u.i < 0x3f800000 - (1<<23)) { - if (u.i < 0x3f800000 - (32<<23)) { - /* handle underflow */ - if (u.i < (1<<23)) - FORCE_EVAL((float)(y*y)); - } else { - /* |x| < 0.5, up to 1.7ulp error */ - y = 0.5f*log1pf(2*y + 2*y*y/(1-y)); - } - } else { - /* avoid overflow */ - y = 0.5f*log1pf(2*(y/(1-y))); - } - return s ? -y : y; -} diff --git a/src/math/atanhl.c b/src/math/atanhl.c deleted file mode 100644 index 87cd1cd..0000000 --- a/src/math/atanhl.c +++ /dev/null @@ -1,35 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double atanhl(long double x) -{ - return atanh(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ -long double atanhl(long double x) -{ - union ldshape u = {x}; - unsigned e = u.i.se & 0x7fff; - unsigned s = u.i.se >> 15; - - /* |x| */ - u.i.se = e; - x = u.f; - - if (e < 0x3ff - 1) { - if (e < 0x3ff - LDBL_MANT_DIG/2) { - /* handle underflow */ - if (e == 0) - FORCE_EVAL((float)x); - } else { - /* |x| < 0.5, up to 1.7ulp error */ - x = 0.5*log1pl(2*x + 2*x*x/(1-x)); - } - } else { - /* avoid overflow */ - x = 0.5*log1pl(2*(x/(1-x))); - } - return s ? -x : x; -} -#endif diff --git a/src/math/atanl.c b/src/math/atanl.c deleted file mode 100644 index c3b0c92..0000000 --- a/src/math/atanl.c +++ /dev/null @@ -1,184 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_atanl.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* - * See comments in atan.c. - * Converted to long double by David Schultz . - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double atanl(long double x) -{ - return atan(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 - -#if LDBL_MANT_DIG == 64 -#define EXPMAN(u) ((u.i.se & 0x7fff)<<8 | (u.i.m>>55 & 0xff)) - -static const long double atanhi[] = { - 4.63647609000806116202e-01L, - 7.85398163397448309628e-01L, - 9.82793723247329067960e-01L, - 1.57079632679489661926e+00L, -}; - -static const long double atanlo[] = { - 1.18469937025062860669e-20L, - -1.25413940316708300586e-20L, - 2.55232234165405176172e-20L, - -2.50827880633416601173e-20L, -}; - -static const long double aT[] = { - 3.33333333333333333017e-01L, - -1.99999999999999632011e-01L, - 1.42857142857046531280e-01L, - -1.11111111100562372733e-01L, - 9.09090902935647302252e-02L, - -7.69230552476207730353e-02L, - 6.66661718042406260546e-02L, - -5.88158892835030888692e-02L, - 5.25499891539726639379e-02L, - -4.70119845393155721494e-02L, - 4.03539201366454414072e-02L, - -2.91303858419364158725e-02L, - 1.24822046299269234080e-02L, -}; - -static long double T_even(long double x) -{ - return aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + - x * (aT[8] + x * (aT[10] + x * aT[12]))))); -} - -static long double T_odd(long double x) -{ - return aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + - x * (aT[9] + x * aT[11])))); -} -#elif LDBL_MANT_DIG == 113 -#define EXPMAN(u) ((u.i.se & 0x7fff)<<8 | u.i.top>>8) - -static const long double atanhi[] = { - 4.63647609000806116214256231461214397e-01L, - 7.85398163397448309615660845819875699e-01L, - 9.82793723247329067985710611014666038e-01L, - 1.57079632679489661923132169163975140e+00L, -}; - -static const long double atanlo[] = { - 4.89509642257333492668618435220297706e-36L, - 2.16795253253094525619926100651083806e-35L, - -2.31288434538183565909319952098066272e-35L, - 4.33590506506189051239852201302167613e-35L, -}; - -static const long double aT[] = { - 3.33333333333333333333333333333333125e-01L, - -1.99999999999999999999999999999180430e-01L, - 1.42857142857142857142857142125269827e-01L, - -1.11111111111111111111110834490810169e-01L, - 9.09090909090909090908522355708623681e-02L, - -7.69230769230769230696553844935357021e-02L, - 6.66666666666666660390096773046256096e-02L, - -5.88235294117646671706582985209643694e-02L, - 5.26315789473666478515847092020327506e-02L, - -4.76190476189855517021024424991436144e-02L, - 4.34782608678695085948531993458097026e-02L, - -3.99999999632663469330634215991142368e-02L, - 3.70370363987423702891250829918659723e-02L, - -3.44827496515048090726669907612335954e-02L, - 3.22579620681420149871973710852268528e-02L, - -3.03020767654269261041647570626778067e-02L, - 2.85641979882534783223403715930946138e-02L, - -2.69824879726738568189929461383741323e-02L, - 2.54194698498808542954187110873675769e-02L, - -2.35083879708189059926183138130183215e-02L, - 2.04832358998165364349957325067131428e-02L, - -1.54489555488544397858507248612362957e-02L, - 8.64492360989278761493037861575248038e-03L, - -2.58521121597609872727919154569765469e-03L, -}; - -static long double T_even(long double x) -{ - return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * (aT[8] + - x * (aT[10] + x * (aT[12] + x * (aT[14] + x * (aT[16] + - x * (aT[18] + x * (aT[20] + x * aT[22]))))))))))); -} - -static long double T_odd(long double x) -{ - return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * (aT[9] + - x * (aT[11] + x * (aT[13] + x * (aT[15] + x * (aT[17] + - x * (aT[19] + x * (aT[21] + x * aT[23]))))))))))); -} -#endif - -long double atanl(long double x) -{ - union ldshape u = {x}; - long double w, s1, s2, z; - int id; - unsigned e = u.i.se & 0x7fff; - unsigned sign = u.i.se >> 15; - unsigned expman; - - if (e >= 0x3fff + LDBL_MANT_DIG + 1) { /* if |x| is large, atan(x)~=pi/2 */ - if (isnan(x)) - return x; - return sign ? -atanhi[3] : atanhi[3]; - } - /* Extract the exponent and the first few bits of the mantissa. */ - expman = EXPMAN(u); - if (expman < ((0x3fff - 2) << 8) + 0xc0) { /* |x| < 0.4375 */ - if (e < 0x3fff - (LDBL_MANT_DIG+1)/2) { /* if |x| is small, atanl(x)~=x */ - /* raise underflow if subnormal */ - if (e == 0) - FORCE_EVAL((float)x); - return x; - } - id = -1; - } else { - x = fabsl(x); - if (expman < (0x3fff << 8) + 0x30) { /* |x| < 1.1875 */ - if (expman < ((0x3fff - 1) << 8) + 0x60) { /* 7/16 <= |x| < 11/16 */ - id = 0; - x = (2.0*x-1.0)/(2.0+x); - } else { /* 11/16 <= |x| < 19/16 */ - id = 1; - x = (x-1.0)/(x+1.0); - } - } else { - if (expman < ((0x3fff + 1) << 8) + 0x38) { /* |x| < 2.4375 */ - id = 2; - x = (x-1.5)/(1.0+1.5*x); - } else { /* 2.4375 <= |x| */ - id = 3; - x = -1.0/x; - } - } - } - /* end of argument reduction */ - z = x*x; - w = z*z; - /* break sum aT[i]z**(i+1) into odd and even poly */ - s1 = z*T_even(w); - s2 = w*T_odd(w); - if (id < 0) - return x - x*(s1+s2); - z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); - return sign ? -z : z; -} -#endif diff --git a/src/math/cbrt.c b/src/math/cbrt.c deleted file mode 100644 index 7599d3e..0000000 --- a/src/math/cbrt.c +++ /dev/null @@ -1,103 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrt.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - * Optimized by Bruce D. Evans. - */ -/* cbrt(x) - * Return cube root of x - */ - -#include -#include - -static const uint32_t -B1 = 715094163, /* B1 = (1023-1023/3-0.03306235651)*2**20 */ -B2 = 696219795; /* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */ - -/* |1/cbrt(x) - p(x)| < 2**-23.5 (~[-7.93e-8, 7.929e-8]). */ -static const double -P0 = 1.87595182427177009643, /* 0x3ffe03e6, 0x0f61e692 */ -P1 = -1.88497979543377169875, /* 0xbffe28e0, 0x92f02420 */ -P2 = 1.621429720105354466140, /* 0x3ff9f160, 0x4a49d6c2 */ -P3 = -0.758397934778766047437, /* 0xbfe844cb, 0xbee751d9 */ -P4 = 0.145996192886612446982; /* 0x3fc2b000, 0xd4e4edd7 */ - -double cbrt(double x) -{ - union {double f; uint64_t i;} u = {x}; - double_t r,s,t,w; - uint32_t hx = u.i>>32 & 0x7fffffff; - - if (hx >= 0x7ff00000) /* cbrt(NaN,INF) is itself */ - return x+x; - - /* - * Rough cbrt to 5 bits: - * cbrt(2**e*(1+m) ~= 2**(e/3)*(1+(e%3+m)/3) - * where e is integral and >= 0, m is real and in [0, 1), and "/" and - * "%" are integer division and modulus with rounding towards minus - * infinity. The RHS is always >= the LHS and has a maximum relative - * error of about 1 in 16. Adding a bias of -0.03306235651 to the - * (e%3+m)/3 term reduces the error to about 1 in 32. With the IEEE - * floating point representation, for finite positive normal values, - * ordinary integer divison of the value in bits magically gives - * almost exactly the RHS of the above provided we first subtract the - * exponent bias (1023 for doubles) and later add it back. We do the - * subtraction virtually to keep e >= 0 so that ordinary integer - * division rounds towards minus infinity; this is also efficient. - */ - if (hx < 0x00100000) { /* zero or subnormal? */ - u.f = x*0x1p54; - hx = u.i>>32 & 0x7fffffff; - if (hx == 0) - return x; /* cbrt(0) is itself */ - hx = hx/3 + B2; - } else - hx = hx/3 + B1; - u.i &= 1ULL<<63; - u.i |= (uint64_t)hx << 32; - t = u.f; - - /* - * New cbrt to 23 bits: - * cbrt(x) = t*cbrt(x/t**3) ~= t*P(t**3/x) - * where P(r) is a polynomial of degree 4 that approximates 1/cbrt(r) - * to within 2**-23.5 when |r - 1| < 1/10. The rough approximation - * has produced t such than |t/cbrt(x) - 1| ~< 1/32, and cubing this - * gives us bounds for r = t**3/x. - * - * Try to optimize for parallel evaluation as in __tanf.c. - */ - r = (t*t)*(t/x); - t = t*((P0+r*(P1+r*P2))+((r*r)*r)*(P3+r*P4)); - - /* - * Round t away from zero to 23 bits (sloppily except for ensuring that - * the result is larger in magnitude than cbrt(x) but not much more than - * 2 23-bit ulps larger). With rounding towards zero, the error bound - * would be ~5/6 instead of ~4/6. With a maximum error of 2 23-bit ulps - * in the rounded t, the infinite-precision error in the Newton - * approximation barely affects third digit in the final error - * 0.667; the error in the rounded t can be up to about 3 23-bit ulps - * before the final error is larger than 0.667 ulps. - */ - u.f = t; - u.i = (u.i + 0x80000000) & 0xffffffffc0000000ULL; - t = u.f; - - /* one step Newton iteration to 53 bits with error < 0.667 ulps */ - s = t*t; /* t*t is exact */ - r = x/s; /* error <= 0.5 ulps; |r| < |t| */ - w = t+t; /* t+t is exact */ - r = (r-t)/(w+r); /* r-t is exact; w+r ~= 3*t */ - t = t+t*r; /* error <= 0.5 + 0.5/3 + epsilon */ - return t; -} diff --git a/src/math/cbrtf.c b/src/math/cbrtf.c deleted file mode 100644 index 89c2c86..0000000 --- a/src/math/cbrtf.c +++ /dev/null @@ -1,66 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - * Debugged and optimized by Bruce D. Evans. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* cbrtf(x) - * Return cube root of x - */ - -#include -#include - -static const unsigned -B1 = 709958130, /* B1 = (127-127.0/3-0.03306235651)*2**23 */ -B2 = 642849266; /* B2 = (127-127.0/3-24/3-0.03306235651)*2**23 */ - -float cbrtf(float x) -{ - double_t r,T; - union {float f; uint32_t i;} u = {x}; - uint32_t hx = u.i & 0x7fffffff; - - if (hx >= 0x7f800000) /* cbrt(NaN,INF) is itself */ - return x + x; - - /* rough cbrt to 5 bits */ - if (hx < 0x00800000) { /* zero or subnormal? */ - if (hx == 0) - return x; /* cbrt(+-0) is itself */ - u.f = x*0x1p24f; - hx = u.i & 0x7fffffff; - hx = hx/3 + B2; - } else - hx = hx/3 + B1; - u.i &= 0x80000000; - u.i |= hx; - - /* - * First step Newton iteration (solving t*t-x/t == 0) to 16 bits. In - * double precision so that its terms can be arranged for efficiency - * without causing overflow or underflow. - */ - T = u.f; - r = T*T*T; - T = T*((double_t)x+x+r)/(x+r+r); - - /* - * Second step Newton iteration to 47 bits. In double precision for - * efficiency and accuracy. - */ - r = T*T*T; - T = T*((double_t)x+x+r)/(x+r+r); - - /* rounding to 24 bits is perfect in round-to-nearest mode */ - return T; -} diff --git a/src/math/cbrtl.c b/src/math/cbrtl.c deleted file mode 100644 index ceff913..0000000 --- a/src/math/cbrtl.c +++ /dev/null @@ -1,124 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_cbrtl.c */ -/*- - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * Copyright (c) 2009-2011, Bruce D. Evans, Steven G. Kargl, David Schultz. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - * The argument reduction and testing for exceptional cases was - * written by Steven G. Kargl with input from Bruce D. Evans - * and David A. Schultz. - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double cbrtl(long double x) -{ - return cbrt(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -static const unsigned B1 = 709958130; /* B1 = (127-127.0/3-0.03306235651)*2**23 */ - -long double cbrtl(long double x) -{ - union ldshape u = {x}, v; - union {float f; uint32_t i;} uft; - long double r, s, t, w; - double_t dr, dt, dx; - float_t ft; - int e = u.i.se & 0x7fff; - int sign = u.i.se & 0x8000; - - /* - * If x = +-Inf, then cbrt(x) = +-Inf. - * If x = NaN, then cbrt(x) = NaN. - */ - if (e == 0x7fff) - return x + x; - if (e == 0) { - /* Adjust subnormal numbers. */ - u.f *= 0x1p120; - e = u.i.se & 0x7fff; - /* If x = +-0, then cbrt(x) = +-0. */ - if (e == 0) - return x; - e -= 120; - } - e -= 0x3fff; - u.i.se = 0x3fff; - x = u.f; - switch (e % 3) { - case 1: - case -2: - x *= 2; - e--; - break; - case 2: - case -1: - x *= 4; - e -= 2; - break; - } - v.f = 1.0; - v.i.se = sign | (0x3fff + e/3); - - /* - * The following is the guts of s_cbrtf, with the handling of - * special values removed and extra care for accuracy not taken, - * but with most of the extra accuracy not discarded. - */ - - /* ~5-bit estimate: */ - uft.f = x; - uft.i = (uft.i & 0x7fffffff)/3 + B1; - ft = uft.f; - - /* ~16-bit estimate: */ - dx = x; - dt = ft; - dr = dt * dt * dt; - dt = dt * (dx + dx + dr) / (dx + dr + dr); - - /* ~47-bit estimate: */ - dr = dt * dt * dt; - dt = dt * (dx + dx + dr) / (dx + dr + dr); - -#if LDBL_MANT_DIG == 64 - /* - * dt is cbrtl(x) to ~47 bits (after x has been reduced to 1 <= x < 8). - * Round it away from zero to 32 bits (32 so that t*t is exact, and - * away from zero for technical reasons). - */ - t = dt + (0x1.0p32L + 0x1.0p-31L) - 0x1.0p32; -#elif LDBL_MANT_DIG == 113 - /* - * Round dt away from zero to 47 bits. Since we don't trust the 47, - * add 2 47-bit ulps instead of 1 to round up. Rounding is slow and - * might be avoidable in this case, since on most machines dt will - * have been evaluated in 53-bit precision and the technical reasons - * for rounding up might not apply to either case in cbrtl() since - * dt is much more accurate than needed. - */ - t = dt + 0x2.0p-46 + 0x1.0p60L - 0x1.0p60; -#endif - - /* - * Final step Newton iteration to 64 or 113 bits with - * error < 0.667 ulps - */ - s = t*t; /* t*t is exact */ - r = x/s; /* error <= 0.5 ulps; |r| < |t| */ - w = t+t; /* t+t is exact */ - r = (r-t)/(w+r); /* r-t is exact; w+r ~= 3*t */ - t = t+t*r; /* error <= 0.5 + 0.5/3 + epsilon */ - - t *= v.f; - return t; -} -#endif diff --git a/src/math/ceil.c b/src/math/ceil.c deleted file mode 100644 index b13e6f2..0000000 --- a/src/math/ceil.c +++ /dev/null @@ -1,31 +0,0 @@ -#include "libm.h" - -#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 -#define EPS DBL_EPSILON -#elif FLT_EVAL_METHOD==2 -#define EPS LDBL_EPSILON -#endif -static const double_t toint = 1/EPS; - -double ceil(double x) -{ - union {double f; uint64_t i;} u = {x}; - int e = u.i >> 52 & 0x7ff; - double_t y; - - if (e >= 0x3ff+52 || x == 0) - return x; - /* y = int(x) - x, where int(x) is an integer neighbor of x */ - if (u.i >> 63) - y = x - toint + toint - x; - else - y = x + toint - toint - x; - /* special case because of non-nearest rounding modes */ - if (e <= 0x3ff-1) { - FORCE_EVAL(y); - return u.i >> 63 ? -0.0 : 1; - } - if (y < 0) - return x + y + 1; - return x + y; -} diff --git a/src/math/ceilf.c b/src/math/ceilf.c deleted file mode 100644 index 869835f..0000000 --- a/src/math/ceilf.c +++ /dev/null @@ -1,27 +0,0 @@ -#include "libm.h" - -float ceilf(float x) -{ - union {float f; uint32_t i;} u = {x}; - int e = (int)(u.i >> 23 & 0xff) - 0x7f; - uint32_t m; - - if (e >= 23) - return x; - if (e >= 0) { - m = 0x007fffff >> e; - if ((u.i & m) == 0) - return x; - FORCE_EVAL(x + 0x1p120f); - if (u.i >> 31 == 0) - u.i += m; - u.i &= ~m; - } else { - FORCE_EVAL(x + 0x1p120f); - if (u.i >> 31) - u.f = -0.0; - else if (u.i << 1) - u.f = 1.0; - } - return u.f; -} diff --git a/src/math/ceill.c b/src/math/ceill.c deleted file mode 100644 index 60a8302..0000000 --- a/src/math/ceill.c +++ /dev/null @@ -1,34 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double ceill(long double x) -{ - return ceil(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 - -static const long double toint = 1/LDBL_EPSILON; - -long double ceill(long double x) -{ - union ldshape u = {x}; - int e = u.i.se & 0x7fff; - long double y; - - if (e >= 0x3fff+LDBL_MANT_DIG-1 || x == 0) - return x; - /* y = int(x) - x, where int(x) is an integer neighbor of x */ - if (u.i.se >> 15) - y = x - toint + toint - x; - else - y = x + toint - toint - x; - /* special case because of non-nearest rounding modes */ - if (e <= 0x3fff-1) { - FORCE_EVAL(y); - return u.i.se >> 15 ? -0.0 : 1; - } - if (y < 0) - return x + y + 1; - return x + y; -} -#endif diff --git a/src/math/copysign.c b/src/math/copysign.c deleted file mode 100644 index b09331b..0000000 --- a/src/math/copysign.c +++ /dev/null @@ -1,8 +0,0 @@ -#include "libm.h" - -double copysign(double x, double y) { - union {double f; uint64_t i;} ux={x}, uy={y}; - ux.i &= -1ULL/2; - ux.i |= uy.i & 1ULL<<63; - return ux.f; -} diff --git a/src/math/copysignf.c b/src/math/copysignf.c deleted file mode 100644 index 0af6ae9..0000000 --- a/src/math/copysignf.c +++ /dev/null @@ -1,10 +0,0 @@ -#include -#include - -float copysignf(float x, float y) -{ - union {float f; uint32_t i;} ux={x}, uy={y}; - ux.i &= 0x7fffffff; - ux.i |= uy.i & 0x80000000; - return ux.f; -} diff --git a/src/math/copysignl.c b/src/math/copysignl.c deleted file mode 100644 index 9dd933c..0000000 --- a/src/math/copysignl.c +++ /dev/null @@ -1,16 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double copysignl(long double x, long double y) -{ - return copysign(x, y); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -long double copysignl(long double x, long double y) -{ - union ldshape ux = {x}, uy = {y}; - ux.i.se &= 0x7fff; - ux.i.se |= uy.i.se & 0x8000; - return ux.f; -} -#endif diff --git a/src/math/cos.c b/src/math/cos.c deleted file mode 100644 index ee97f68..0000000 --- a/src/math/cos.c +++ /dev/null @@ -1,77 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_cos.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* cos(x) - * Return cosine function of x. - * - * kernel function: - * __sin ... sine function on [-pi/4,pi/4] - * __cos ... cosine function on [-pi/4,pi/4] - * __rem_pio2 ... argument reduction routine - * - * Method. - * Let S,C and T denote the sin, cos and tan respectively on - * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 - * in [-pi/4 , +pi/4], and let n = k mod 4. - * We have - * - * n sin(x) cos(x) tan(x) - * ---------------------------------------------------------- - * 0 S C T - * 1 C -S -1/T - * 2 -S -C T - * 3 -C S -1/T - * ---------------------------------------------------------- - * - * Special cases: - * Let trig be any of sin, cos, or tan. - * trig(+-INF) is NaN, with signals; - * trig(NaN) is that NaN; - * - * Accuracy: - * TRIG(x) returns trig(x) nearly rounded - */ - -#include "libm.h" - -double cos(double x) -{ - double y[2]; - uint32_t ix; - unsigned n; - - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; - - /* |x| ~< pi/4 */ - if (ix <= 0x3fe921fb) { - if (ix < 0x3e46a09e) { /* |x| < 2**-27 * sqrt(2) */ - /* raise inexact if x!=0 */ - FORCE_EVAL(x + 0x1p120f); - return 1.0; - } - return __cos(x, 0); - } - - /* cos(Inf or NaN) is NaN */ - if (ix >= 0x7ff00000) - return x-x; - - /* argument reduction */ - n = __rem_pio2(x, y); - switch (n&3) { - case 0: return __cos(y[0], y[1]); - case 1: return -__sin(y[0], y[1], 1); - case 2: return -__cos(y[0], y[1]); - default: - return __sin(y[0], y[1], 1); - } -} diff --git a/src/math/cosf.c b/src/math/cosf.c deleted file mode 100644 index 23f3e5b..0000000 --- a/src/math/cosf.c +++ /dev/null @@ -1,78 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_cosf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - * Optimized by Bruce D. Evans. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -/* Small multiples of pi/2 rounded to double precision. */ -static const double -c1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ -c2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ -c3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ -c4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ - -float cosf(float x) -{ - double y; - uint32_t ix; - unsigned n, sign; - - GET_FLOAT_WORD(ix, x); - sign = ix >> 31; - ix &= 0x7fffffff; - - if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ - if (ix < 0x39800000) { /* |x| < 2**-12 */ - /* raise inexact if x != 0 */ - FORCE_EVAL(x + 0x1p120f); - return 1.0f; - } - return __cosdf(x); - } - if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */ - if (ix > 0x4016cbe3) /* |x| ~> 3*pi/4 */ - return -__cosdf(sign ? x+c2pio2 : x-c2pio2); - else { - if (sign) - return __sindf(x + c1pio2); - else - return __sindf(c1pio2 - x); - } - } - if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */ - if (ix > 0x40afeddf) /* |x| ~> 7*pi/4 */ - return __cosdf(sign ? x+c4pio2 : x-c4pio2); - else { - if (sign) - return __sindf(-x - c3pio2); - else - return __sindf(x - c3pio2); - } - } - - /* cos(Inf or NaN) is NaN */ - if (ix >= 0x7f800000) - return x-x; - - /* general argument reduction needed */ - n = __rem_pio2f(x,&y); - switch (n&3) { - case 0: return __cosdf(y); - case 1: return __sindf(-y); - case 2: return -__cosdf(y); - default: - return __sindf(y); - } -} diff --git a/src/math/cosh.c b/src/math/cosh.c deleted file mode 100644 index 490c15f..0000000 --- a/src/math/cosh.c +++ /dev/null @@ -1,40 +0,0 @@ -#include "libm.h" - -/* cosh(x) = (exp(x) + 1/exp(x))/2 - * = 1 + 0.5*(exp(x)-1)*(exp(x)-1)/exp(x) - * = 1 + x*x/2 + o(x^4) - */ -double cosh(double x) -{ - union {double f; uint64_t i;} u = {.f = x}; - uint32_t w; - double t; - - /* |x| */ - u.i &= (uint64_t)-1/2; - x = u.f; - w = u.i >> 32; - - /* |x| < log(2) */ - if (w < 0x3fe62e42) { - if (w < 0x3ff00000 - (26<<20)) { - /* raise inexact if x!=0 */ - FORCE_EVAL(x + 0x1p120f); - return 1; - } - t = expm1(x); - return 1 + t*t/(2*(1+t)); - } - - /* |x| < log(DBL_MAX) */ - if (w < 0x40862e42) { - t = exp(x); - /* note: if x>log(0x1p26) then the 1/t is not needed */ - return 0.5*(t + 1/t); - } - - /* |x| > log(DBL_MAX) or nan */ - /* note: the result is stored to handle overflow */ - t = __expo2(x, 1.0); - return t; -} diff --git a/src/math/coshf.c b/src/math/coshf.c deleted file mode 100644 index e739cff..0000000 --- a/src/math/coshf.c +++ /dev/null @@ -1,33 +0,0 @@ -#include "libm.h" - -float coshf(float x) -{ - union {float f; uint32_t i;} u = {.f = x}; - uint32_t w; - float t; - - /* |x| */ - u.i &= 0x7fffffff; - x = u.f; - w = u.i; - - /* |x| < log(2) */ - if (w < 0x3f317217) { - if (w < 0x3f800000 - (12<<23)) { - FORCE_EVAL(x + 0x1p120f); - return 1; - } - t = expm1f(x); - return 1 + t*t/(2*(1+t)); - } - - /* |x| < log(FLT_MAX) */ - if (w < 0x42b17217) { - t = expf(x); - return 0.5f*(t + 1/t); - } - - /* |x| > log(FLT_MAX) or nan */ - t = __expo2f(x, 1.0f); - return t; -} diff --git a/src/math/coshl.c b/src/math/coshl.c deleted file mode 100644 index 06a56fe..0000000 --- a/src/math/coshl.c +++ /dev/null @@ -1,47 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double coshl(long double x) -{ - return cosh(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -long double coshl(long double x) -{ - union ldshape u = {x}; - unsigned ex = u.i.se & 0x7fff; - uint32_t w; - long double t; - - /* |x| */ - u.i.se = ex; - x = u.f; - w = u.i.m >> 32; - - /* |x| < log(2) */ - if (ex < 0x3fff-1 || (ex == 0x3fff-1 && w < 0xb17217f7)) { - if (ex < 0x3fff-32) { - FORCE_EVAL(x + 0x1p120f); - return 1; - } - t = expm1l(x); - return 1 + t*t/(2*(1+t)); - } - - /* |x| < log(LDBL_MAX) */ - if (ex < 0x3fff+13 || (ex == 0x3fff+13 && w < 0xb17217f7)) { - t = expl(x); - return 0.5*(t + 1/t); - } - - /* |x| > log(LDBL_MAX) or nan */ - t = expl(0.5*x); - return 0.5*t*t; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double coshl(long double x) -{ - return cosh(x); -} -#endif diff --git a/src/math/cosl.c b/src/math/cosl.c deleted file mode 100644 index 79c41c7..0000000 --- a/src/math/cosl.c +++ /dev/null @@ -1,39 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double cosl(long double x) { - return cos(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -long double cosl(long double x) -{ - union ldshape u = {x}; - unsigned n; - long double y[2], hi, lo; - - u.i.se &= 0x7fff; - if (u.i.se == 0x7fff) - return x - x; - x = u.f; - if (x < M_PI_4) { - if (u.i.se < 0x3fff - LDBL_MANT_DIG) - /* raise inexact if x!=0 */ - return 1.0 + x; - return __cosl(x, 0); - } - n = __rem_pio2l(x, y); - hi = y[0]; - lo = y[1]; - switch (n & 3) { - case 0: - return __cosl(hi, lo); - case 1: - return -__sinl(hi, lo, 1); - case 2: - return -__cosl(hi, lo); - case 3: - default: - return __sinl(hi, lo, 1); - } -} -#endif diff --git a/src/math/erf.c b/src/math/erf.c deleted file mode 100644 index 2f30a29..0000000 --- a/src/math/erf.c +++ /dev/null @@ -1,273 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_erf.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* double erf(double x) - * double erfc(double x) - * x - * 2 |\ - * erf(x) = --------- | exp(-t*t)dt - * sqrt(pi) \| - * 0 - * - * erfc(x) = 1-erf(x) - * Note that - * erf(-x) = -erf(x) - * erfc(-x) = 2 - erfc(x) - * - * Method: - * 1. For |x| in [0, 0.84375] - * erf(x) = x + x*R(x^2) - * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] - * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] - * where R = P/Q where P is an odd poly of degree 8 and - * Q is an odd poly of degree 10. - * -57.90 - * | R - (erf(x)-x)/x | <= 2 - * - * - * Remark. The formula is derived by noting - * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) - * and that - * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 - * is close to one. The interval is chosen because the fix - * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is - * near 0.6174), and by some experiment, 0.84375 is chosen to - * guarantee the error is less than one ulp for erf. - * - * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and - * c = 0.84506291151 rounded to single (24 bits) - * erf(x) = sign(x) * (c + P1(s)/Q1(s)) - * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 - * 1+(c+P1(s)/Q1(s)) if x < 0 - * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06 - * Remark: here we use the taylor series expansion at x=1. - * erf(1+s) = erf(1) + s*Poly(s) - * = 0.845.. + P1(s)/Q1(s) - * That is, we use rational approximation to approximate - * erf(1+s) - (c = (single)0.84506291151) - * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] - * where - * P1(s) = degree 6 poly in s - * Q1(s) = degree 6 poly in s - * - * 3. For x in [1.25,1/0.35(~2.857143)], - * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) - * erf(x) = 1 - erfc(x) - * where - * R1(z) = degree 7 poly in z, (z=1/x^2) - * S1(z) = degree 8 poly in z - * - * 4. For x in [1/0.35,28] - * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 - * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6 x >= 28 - * erf(x) = sign(x) *(1 - tiny) (raise inexact) - * erfc(x) = tiny*tiny (raise underflow) if x > 0 - * = 2 - tiny if x<0 - * - * 7. Special case: - * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, - * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, - * erfc/erf(NaN) is NaN - */ - -#include "libm.h" - -static const double -erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ -/* - * Coefficients for approximation to erf on [0,0.84375] - */ -efx8 = 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */ -pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ -pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ -pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ -pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ -pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */ -qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ -qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ -qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ -qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ -qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */ -/* - * Coefficients for approximation to erf in [0.84375,1.25] - */ -pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ -pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ -pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ -pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ -pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ -pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ -pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */ -qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ -qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ -qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ -qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ -qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ -qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */ -/* - * Coefficients for approximation to erfc in [1.25,1/0.35] - */ -ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ -ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ -ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ -ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ -ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ -ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ -ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ -ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */ -sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ -sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ -sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ -sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ -sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ -sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ -sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ -sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */ -/* - * Coefficients for approximation to erfc in [1/.35,28] - */ -rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ -rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ -rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ -rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ -rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ -rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ -rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */ -sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ -sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ -sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ -sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ -sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ -sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ -sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ - -static double erfc1(double x) -{ - double_t s,P,Q; - - s = fabs(x) - 1; - P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); - Q = 1+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); - return 1 - erx - P/Q; -} - -static double erfc2(uint32_t ix, double x) -{ - double_t s,R,S; - double z; - - if (ix < 0x3ff40000) /* |x| < 1.25 */ - return erfc1(x); - - x = fabs(x); - s = 1/(x*x); - if (ix < 0x4006db6d) { /* |x| < 1/.35 ~ 2.85714 */ - R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( - ra5+s*(ra6+s*ra7)))))); - S = 1.0+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( - sa5+s*(sa6+s*(sa7+s*sa8))))))); - } else { /* |x| > 1/.35 */ - R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( - rb5+s*rb6))))); - S = 1.0+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( - sb5+s*(sb6+s*sb7)))))); - } - z = x; - SET_LOW_WORD(z,0); - return exp(-z*z-0.5625)*exp((z-x)*(z+x)+R/S)/x; -} - -double erf(double x) -{ - double r,s,z,y; - uint32_t ix; - int sign; - - GET_HIGH_WORD(ix, x); - sign = ix>>31; - ix &= 0x7fffffff; - if (ix >= 0x7ff00000) { - /* erf(nan)=nan, erf(+-inf)=+-1 */ - return 1-2*sign + 1/x; - } - if (ix < 0x3feb0000) { /* |x| < 0.84375 */ - if (ix < 0x3e300000) { /* |x| < 2**-28 */ - /* avoid underflow */ - return 0.125*(8*x + efx8*x); - } - z = x*x; - r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); - s = 1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); - y = r/s; - return x + x*y; - } - if (ix < 0x40180000) /* 0.84375 <= |x| < 6 */ - y = 1 - erfc2(ix,x); - else - y = 1 - 0x1p-1022; - return sign ? -y : y; -} - -double erfc(double x) -{ - double r,s,z,y; - uint32_t ix; - int sign; - - GET_HIGH_WORD(ix, x); - sign = ix>>31; - ix &= 0x7fffffff; - if (ix >= 0x7ff00000) { - /* erfc(nan)=nan, erfc(+-inf)=0,2 */ - return 2*sign + 1/x; - } - if (ix < 0x3feb0000) { /* |x| < 0.84375 */ - if (ix < 0x3c700000) /* |x| < 2**-56 */ - return 1.0 - x; - z = x*x; - r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); - s = 1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); - y = r/s; - if (sign || ix < 0x3fd00000) { /* x < 1/4 */ - return 1.0 - (x+x*y); - } - return 0.5 - (x - 0.5 + x*y); - } - if (ix < 0x403c0000) { /* 0.84375 <= |x| < 28 */ - return sign ? 2 - erfc2(ix,x) : erfc2(ix,x); - } - return sign ? 2 - 0x1p-1022 : 0x1p-1022*0x1p-1022; -} diff --git a/src/math/erff.c b/src/math/erff.c deleted file mode 100644 index ed5f397..0000000 --- a/src/math/erff.c +++ /dev/null @@ -1,183 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_erff.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -static const float -erx = 8.4506291151e-01, /* 0x3f58560b */ -/* - * Coefficients for approximation to erf on [0,0.84375] - */ -efx8 = 1.0270333290e+00, /* 0x3f8375d4 */ -pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ -pp1 = -3.2504209876e-01, /* 0xbea66beb */ -pp2 = -2.8481749818e-02, /* 0xbce9528f */ -pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ -pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ -qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ -qq2 = 6.5022252500e-02, /* 0x3d852a63 */ -qq3 = 5.0813062117e-03, /* 0x3ba68116 */ -qq4 = 1.3249473704e-04, /* 0x390aee49 */ -qq5 = -3.9602282413e-06, /* 0xb684e21a */ -/* - * Coefficients for approximation to erf in [0.84375,1.25] - */ -pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ -pa1 = 4.1485610604e-01, /* 0x3ed46805 */ -pa2 = -3.7220788002e-01, /* 0xbebe9208 */ -pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ -pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ -pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ -pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ -qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ -qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ -qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ -qa4 = 1.2617121637e-01, /* 0x3e013307 */ -qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ -qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ -/* - * Coefficients for approximation to erfc in [1.25,1/0.35] - */ -ra0 = -9.8649440333e-03, /* 0xbc21a093 */ -ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ -ra2 = -1.0558626175e+01, /* 0xc128f022 */ -ra3 = -6.2375331879e+01, /* 0xc2798057 */ -ra4 = -1.6239666748e+02, /* 0xc322658c */ -ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ -ra6 = -8.1287437439e+01, /* 0xc2a2932b */ -ra7 = -9.8143291473e+00, /* 0xc11d077e */ -sa1 = 1.9651271820e+01, /* 0x419d35ce */ -sa2 = 1.3765776062e+02, /* 0x4309a863 */ -sa3 = 4.3456588745e+02, /* 0x43d9486f */ -sa4 = 6.4538726807e+02, /* 0x442158c9 */ -sa5 = 4.2900814819e+02, /* 0x43d6810b */ -sa6 = 1.0863500214e+02, /* 0x42d9451f */ -sa7 = 6.5702495575e+00, /* 0x40d23f7c */ -sa8 = -6.0424413532e-02, /* 0xbd777f97 */ -/* - * Coefficients for approximation to erfc in [1/.35,28] - */ -rb0 = -9.8649431020e-03, /* 0xbc21a092 */ -rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ -rb2 = -1.7757955551e+01, /* 0xc18e104b */ -rb3 = -1.6063638306e+02, /* 0xc320a2ea */ -rb4 = -6.3756646729e+02, /* 0xc41f6441 */ -rb5 = -1.0250950928e+03, /* 0xc480230b */ -rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ -sb1 = 3.0338060379e+01, /* 0x41f2b459 */ -sb2 = 3.2579251099e+02, /* 0x43a2e571 */ -sb3 = 1.5367296143e+03, /* 0x44c01759 */ -sb4 = 3.1998581543e+03, /* 0x4547fdbb */ -sb5 = 2.5530502930e+03, /* 0x451f90ce */ -sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ -sb7 = -2.2440952301e+01; /* 0xc1b38712 */ - -static float erfc1(float x) -{ - float_t s,P,Q; - - s = fabsf(x) - 1; - P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); - Q = 1+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); - return 1 - erx - P/Q; -} - -static float erfc2(uint32_t ix, float x) -{ - float_t s,R,S; - float z; - - if (ix < 0x3fa00000) /* |x| < 1.25 */ - return erfc1(x); - - x = fabsf(x); - s = 1/(x*x); - if (ix < 0x4036db6d) { /* |x| < 1/0.35 */ - R = ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( - ra5+s*(ra6+s*ra7)))))); - S = 1.0f+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( - sa5+s*(sa6+s*(sa7+s*sa8))))))); - } else { /* |x| >= 1/0.35 */ - R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( - rb5+s*rb6))))); - S = 1.0f+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( - sb5+s*(sb6+s*sb7)))))); - } - GET_FLOAT_WORD(ix, x); - SET_FLOAT_WORD(z, ix&0xffffe000); - return expf(-z*z - 0.5625f) * expf((z-x)*(z+x) + R/S)/x; -} - -float erff(float x) -{ - float r,s,z,y; - uint32_t ix; - int sign; - - GET_FLOAT_WORD(ix, x); - sign = ix>>31; - ix &= 0x7fffffff; - if (ix >= 0x7f800000) { - /* erf(nan)=nan, erf(+-inf)=+-1 */ - return 1-2*sign + 1/x; - } - if (ix < 0x3f580000) { /* |x| < 0.84375 */ - if (ix < 0x31800000) { /* |x| < 2**-28 */ - /*avoid underflow */ - return 0.125f*(8*x + efx8*x); - } - z = x*x; - r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); - s = 1+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); - y = r/s; - return x + x*y; - } - if (ix < 0x40c00000) /* |x| < 6 */ - y = 1 - erfc2(ix,x); - else - y = 1 - 0x1p-120f; - return sign ? -y : y; -} - -float erfcf(float x) -{ - float r,s,z,y; - uint32_t ix; - int sign; - - GET_FLOAT_WORD(ix, x); - sign = ix>>31; - ix &= 0x7fffffff; - if (ix >= 0x7f800000) { - /* erfc(nan)=nan, erfc(+-inf)=0,2 */ - return 2*sign + 1/x; - } - - if (ix < 0x3f580000) { /* |x| < 0.84375 */ - if (ix < 0x23800000) /* |x| < 2**-56 */ - return 1.0f - x; - z = x*x; - r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); - s = 1.0f+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); - y = r/s; - if (sign || ix < 0x3e800000) /* x < 1/4 */ - return 1.0f - (x+x*y); - return 0.5f - (x - 0.5f + x*y); - } - if (ix < 0x41e00000) { /* |x| < 28 */ - return sign ? 2 - erfc2(ix,x) : erfc2(ix,x); - } - return sign ? 2 - 0x1p-120f : 0x1p-120f*0x1p-120f; -} diff --git a/src/math/erfl.c b/src/math/erfl.c deleted file mode 100644 index e267c23..0000000 --- a/src/math/erfl.c +++ /dev/null @@ -1,353 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_erfl.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* - * Copyright (c) 2008 Stephen L. Moshier - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. - * - * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES - * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR - * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES - * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN - * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF - * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - */ -/* double erf(double x) - * double erfc(double x) - * x - * 2 |\ - * erf(x) = --------- | exp(-t*t)dt - * sqrt(pi) \| - * 0 - * - * erfc(x) = 1-erf(x) - * Note that - * erf(-x) = -erf(x) - * erfc(-x) = 2 - erfc(x) - * - * Method: - * 1. For |x| in [0, 0.84375] - * erf(x) = x + x*R(x^2) - * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] - * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] - * Remark. The formula is derived by noting - * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) - * and that - * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 - * is close to one. The interval is chosen because the fix - * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is - * near 0.6174), and by some experiment, 0.84375 is chosen to - * guarantee the error is less than one ulp for erf. - * - * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and - * c = 0.84506291151 rounded to single (24 bits) - * erf(x) = sign(x) * (c + P1(s)/Q1(s)) - * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 - * 1+(c+P1(s)/Q1(s)) if x < 0 - * Remark: here we use the taylor series expansion at x=1. - * erf(1+s) = erf(1) + s*Poly(s) - * = 0.845.. + P1(s)/Q1(s) - * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] - * - * 3. For x in [1.25,1/0.35(~2.857143)], - * erfc(x) = (1/x)*exp(-x*x-0.5625+R1(z)/S1(z)) - * z=1/x^2 - * erf(x) = 1 - erfc(x) - * - * 4. For x in [1/0.35,107] - * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 - * = 2.0 - (1/x)*exp(-x*x-0.5625+R2(z)/S2(z)) - * if -6.666 x >= 107 - * erf(x) = sign(x) *(1 - tiny) (raise inexact) - * erfc(x) = tiny*tiny (raise underflow) if x > 0 - * = 2 - tiny if x<0 - * - * 7. Special case: - * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, - * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, - * erfc/erf(NaN) is NaN - */ - - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double erfl(long double x) -{ - return erf(x); -} -long double erfcl(long double x) -{ - return erfc(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -static const long double -erx = 0.845062911510467529296875L, - -/* - * Coefficients for approximation to erf on [0,0.84375] - */ -/* 8 * (2/sqrt(pi) - 1) */ -efx8 = 1.0270333367641005911692712249723613735048E0L, -pp[6] = { - 1.122751350964552113068262337278335028553E6L, - -2.808533301997696164408397079650699163276E6L, - -3.314325479115357458197119660818768924100E5L, - -6.848684465326256109712135497895525446398E4L, - -2.657817695110739185591505062971929859314E3L, - -1.655310302737837556654146291646499062882E2L, -}, -qq[6] = { - 8.745588372054466262548908189000448124232E6L, - 3.746038264792471129367533128637019611485E6L, - 7.066358783162407559861156173539693900031E5L, - 7.448928604824620999413120955705448117056E4L, - 4.511583986730994111992253980546131408924E3L, - 1.368902937933296323345610240009071254014E2L, - /* 1.000000000000000000000000000000000000000E0 */ -}, - -/* - * Coefficients for approximation to erf in [0.84375,1.25] - */ -/* erf(x+1) = 0.845062911510467529296875 + pa(x)/qa(x) - -0.15625 <= x <= +.25 - Peak relative error 8.5e-22 */ -pa[8] = { - -1.076952146179812072156734957705102256059E0L, - 1.884814957770385593365179835059971587220E2L, - -5.339153975012804282890066622962070115606E1L, - 4.435910679869176625928504532109635632618E1L, - 1.683219516032328828278557309642929135179E1L, - -2.360236618396952560064259585299045804293E0L, - 1.852230047861891953244413872297940938041E0L, - 9.394994446747752308256773044667843200719E-2L, -}, -qa[7] = { - 4.559263722294508998149925774781887811255E2L, - 3.289248982200800575749795055149780689738E2L, - 2.846070965875643009598627918383314457912E2L, - 1.398715859064535039433275722017479994465E2L, - 6.060190733759793706299079050985358190726E1L, - 2.078695677795422351040502569964299664233E1L, - 4.641271134150895940966798357442234498546E0L, - /* 1.000000000000000000000000000000000000000E0 */ -}, - -/* - * Coefficients for approximation to erfc in [1.25,1/0.35] - */ -/* erfc(1/x) = x exp (-1/x^2 - 0.5625 + ra(x^2)/sa(x^2)) - 1/2.85711669921875 < 1/x < 1/1.25 - Peak relative error 3.1e-21 */ -ra[] = { - 1.363566591833846324191000679620738857234E-1L, - 1.018203167219873573808450274314658434507E1L, - 1.862359362334248675526472871224778045594E2L, - 1.411622588180721285284945138667933330348E3L, - 5.088538459741511988784440103218342840478E3L, - 8.928251553922176506858267311750789273656E3L, - 7.264436000148052545243018622742770549982E3L, - 2.387492459664548651671894725748959751119E3L, - 2.220916652813908085449221282808458466556E2L, -}, -sa[] = { - -1.382234625202480685182526402169222331847E1L, - -3.315638835627950255832519203687435946482E2L, - -2.949124863912936259747237164260785326692E3L, - -1.246622099070875940506391433635999693661E4L, - -2.673079795851665428695842853070996219632E4L, - -2.880269786660559337358397106518918220991E4L, - -1.450600228493968044773354186390390823713E4L, - -2.874539731125893533960680525192064277816E3L, - -1.402241261419067750237395034116942296027E2L, - /* 1.000000000000000000000000000000000000000E0 */ -}, - -/* - * Coefficients for approximation to erfc in [1/.35,107] - */ -/* erfc(1/x) = x exp (-1/x^2 - 0.5625 + rb(x^2)/sb(x^2)) - 1/6.6666259765625 < 1/x < 1/2.85711669921875 - Peak relative error 4.2e-22 */ -rb[] = { - -4.869587348270494309550558460786501252369E-5L, - -4.030199390527997378549161722412466959403E-3L, - -9.434425866377037610206443566288917589122E-2L, - -9.319032754357658601200655161585539404155E-1L, - -4.273788174307459947350256581445442062291E0L, - -8.842289940696150508373541814064198259278E0L, - -7.069215249419887403187988144752613025255E0L, - -1.401228723639514787920274427443330704764E0L, -}, -sb[] = { - 4.936254964107175160157544545879293019085E-3L, - 1.583457624037795744377163924895349412015E-1L, - 1.850647991850328356622940552450636420484E0L, - 9.927611557279019463768050710008450625415E0L, - 2.531667257649436709617165336779212114570E1L, - 2.869752886406743386458304052862814690045E1L, - 1.182059497870819562441683560749192539345E1L, - /* 1.000000000000000000000000000000000000000E0 */ -}, -/* erfc(1/x) = x exp (-1/x^2 - 0.5625 + rc(x^2)/sc(x^2)) - 1/107 <= 1/x <= 1/6.6666259765625 - Peak relative error 1.1e-21 */ -rc[] = { - -8.299617545269701963973537248996670806850E-5L, - -6.243845685115818513578933902532056244108E-3L, - -1.141667210620380223113693474478394397230E-1L, - -7.521343797212024245375240432734425789409E-1L, - -1.765321928311155824664963633786967602934E0L, - -1.029403473103215800456761180695263439188E0L, -}, -sc[] = { - 8.413244363014929493035952542677768808601E-3L, - 2.065114333816877479753334599639158060979E-1L, - 1.639064941530797583766364412782135680148E0L, - 4.936788463787115555582319302981666347450E0L, - 5.005177727208955487404729933261347679090E0L, - /* 1.000000000000000000000000000000000000000E0 */ -}; - -static long double erfc1(long double x) -{ - long double s,P,Q; - - s = fabsl(x) - 1; - P = pa[0] + s * (pa[1] + s * (pa[2] + - s * (pa[3] + s * (pa[4] + s * (pa[5] + s * (pa[6] + s * pa[7])))))); - Q = qa[0] + s * (qa[1] + s * (qa[2] + - s * (qa[3] + s * (qa[4] + s * (qa[5] + s * (qa[6] + s)))))); - return 1 - erx - P / Q; -} - -static long double erfc2(uint32_t ix, long double x) -{ - union ldshape u; - long double s,z,R,S; - - if (ix < 0x3fffa000) /* 0.84375 <= |x| < 1.25 */ - return erfc1(x); - - x = fabsl(x); - s = 1 / (x * x); - if (ix < 0x4000b6db) { /* 1.25 <= |x| < 2.857 ~ 1/.35 */ - R = ra[0] + s * (ra[1] + s * (ra[2] + s * (ra[3] + s * (ra[4] + - s * (ra[5] + s * (ra[6] + s * (ra[7] + s * ra[8]))))))); - S = sa[0] + s * (sa[1] + s * (sa[2] + s * (sa[3] + s * (sa[4] + - s * (sa[5] + s * (sa[6] + s * (sa[7] + s * (sa[8] + s)))))))); - } else if (ix < 0x4001d555) { /* 2.857 <= |x| < 6.6666259765625 */ - R = rb[0] + s * (rb[1] + s * (rb[2] + s * (rb[3] + s * (rb[4] + - s * (rb[5] + s * (rb[6] + s * rb[7])))))); - S = sb[0] + s * (sb[1] + s * (sb[2] + s * (sb[3] + s * (sb[4] + - s * (sb[5] + s * (sb[6] + s)))))); - } else { /* 6.666 <= |x| < 107 (erfc only) */ - R = rc[0] + s * (rc[1] + s * (rc[2] + s * (rc[3] + - s * (rc[4] + s * rc[5])))); - S = sc[0] + s * (sc[1] + s * (sc[2] + s * (sc[3] + - s * (sc[4] + s)))); - } - u.f = x; - u.i.m &= -1ULL << 40; - z = u.f; - return expl(-z*z - 0.5625) * expl((z - x) * (z + x) + R / S) / x; -} - -long double erfl(long double x) -{ - long double r, s, z, y; - union ldshape u = {x}; - uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48; - int sign = u.i.se >> 15; - - if (ix >= 0x7fff0000) - /* erf(nan)=nan, erf(+-inf)=+-1 */ - return 1 - 2*sign + 1/x; - if (ix < 0x3ffed800) { /* |x| < 0.84375 */ - if (ix < 0x3fde8000) { /* |x| < 2**-33 */ - return 0.125 * (8 * x + efx8 * x); /* avoid underflow */ - } - z = x * x; - r = pp[0] + z * (pp[1] + - z * (pp[2] + z * (pp[3] + z * (pp[4] + z * pp[5])))); - s = qq[0] + z * (qq[1] + - z * (qq[2] + z * (qq[3] + z * (qq[4] + z * (qq[5] + z))))); - y = r / s; - return x + x * y; - } - if (ix < 0x4001d555) /* |x| < 6.6666259765625 */ - y = 1 - erfc2(ix,x); - else - y = 1 - 0x1p-16382L; - return sign ? -y : y; -} - -long double erfcl(long double x) -{ - long double r, s, z, y; - union ldshape u = {x}; - uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48; - int sign = u.i.se >> 15; - - if (ix >= 0x7fff0000) - /* erfc(nan) = nan, erfc(+-inf) = 0,2 */ - return 2*sign + 1/x; - if (ix < 0x3ffed800) { /* |x| < 0.84375 */ - if (ix < 0x3fbe0000) /* |x| < 2**-65 */ - return 1.0 - x; - z = x * x; - r = pp[0] + z * (pp[1] + - z * (pp[2] + z * (pp[3] + z * (pp[4] + z * pp[5])))); - s = qq[0] + z * (qq[1] + - z * (qq[2] + z * (qq[3] + z * (qq[4] + z * (qq[5] + z))))); - y = r / s; - if (ix < 0x3ffd8000) /* x < 1/4 */ - return 1.0 - (x + x * y); - return 0.5 - (x - 0.5 + x * y); - } - if (ix < 0x4005d600) /* |x| < 107 */ - return sign ? 2 - erfc2(ix,x) : erfc2(ix,x); - y = 0x1p-16382L; - return sign ? 2 - y : y*y; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double erfl(long double x) -{ - return erf(x); -} -long double erfcl(long double x) -{ - return erfc(x); -} -#endif diff --git a/src/math/exp.c b/src/math/exp.c deleted file mode 100644 index b764d73..0000000 --- a/src/math/exp.c +++ /dev/null @@ -1,134 +0,0 @@ -/* - * Double-precision e^x function. - * - * Copyright (c) 2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include -#include -#include "libm.h" -#include "exp_data.h" - -#define N (1 << EXP_TABLE_BITS) -#define InvLn2N __exp_data.invln2N -#define NegLn2hiN __exp_data.negln2hiN -#define NegLn2loN __exp_data.negln2loN -#define Shift __exp_data.shift -#define T __exp_data.tab -#define C2 __exp_data.poly[5 - EXP_POLY_ORDER] -#define C3 __exp_data.poly[6 - EXP_POLY_ORDER] -#define C4 __exp_data.poly[7 - EXP_POLY_ORDER] -#define C5 __exp_data.poly[8 - EXP_POLY_ORDER] - -/* Handle cases that may overflow or underflow when computing the result that - is scale*(1+TMP) without intermediate rounding. The bit representation of - scale is in SBITS, however it has a computed exponent that may have - overflown into the sign bit so that needs to be adjusted before using it as - a double. (int32_t)KI is the k used in the argument reduction and exponent - adjustment of scale, positive k here means the result may overflow and - negative k means the result may underflow. */ -static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki) -{ - double_t scale, y; - - if ((ki & 0x80000000) == 0) { - /* k > 0, the exponent of scale might have overflowed by <= 460. */ - sbits -= 1009ull << 52; - scale = asdouble(sbits); - y = 0x1p1009 * (scale + scale * tmp); - return eval_as_double(y); - } - /* k < 0, need special care in the subnormal range. */ - sbits += 1022ull << 52; - scale = asdouble(sbits); - y = scale + scale * tmp; - if (y < 1.0) { - /* Round y to the right precision before scaling it into the subnormal - range to avoid double rounding that can cause 0.5+E/2 ulp error where - E is the worst-case ulp error outside the subnormal range. So this - is only useful if the goal is better than 1 ulp worst-case error. */ - double_t hi, lo; - lo = scale - y + scale * tmp; - hi = 1.0 + y; - lo = 1.0 - hi + y + lo; - y = eval_as_double(hi + lo) - 1.0; - /* Avoid -0.0 with downward rounding. */ - if (WANT_ROUNDING && y == 0.0) - y = 0.0; - /* The underflow exception needs to be signaled explicitly. */ - fp_force_eval(fp_barrier(0x1p-1022) * 0x1p-1022); - } - y = 0x1p-1022 * y; - return eval_as_double(y); -} - -/* Top 12 bits of a double (sign and exponent bits). */ -static inline uint32_t top12(double x) -{ - return asuint64(x) >> 52; -} - -double exp(double x) -{ - uint32_t abstop; - uint64_t ki, idx, top, sbits; - double_t kd, z, r, r2, scale, tail, tmp; - - abstop = top12(x) & 0x7ff; - if (predict_false(abstop - top12(0x1p-54) >= top12(512.0) - top12(0x1p-54))) { - if (abstop - top12(0x1p-54) >= 0x80000000) - /* Avoid spurious underflow for tiny x. */ - /* Note: 0 is common input. */ - return WANT_ROUNDING ? 1.0 + x : 1.0; - if (abstop >= top12(1024.0)) { - if (asuint64(x) == asuint64(-INFINITY)) - return 0.0; - if (abstop >= top12(INFINITY)) - return 1.0 + x; - if (asuint64(x) >> 63) - return __math_uflow(0); - else - return __math_oflow(0); - } - /* Large x is special cased below. */ - abstop = 0; - } - - /* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */ - /* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */ - z = InvLn2N * x; -#if TOINT_INTRINSICS - kd = roundtoint(z); - ki = converttoint(z); -#elif EXP_USE_TOINT_NARROW - /* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */ - kd = eval_as_double(z + Shift); - ki = asuint64(kd) >> 16; - kd = (double_t)(int32_t)ki; -#else - /* z - kd is in [-1, 1] in non-nearest rounding modes. */ - kd = eval_as_double(z + Shift); - ki = asuint64(kd); - kd -= Shift; -#endif - r = x + kd * NegLn2hiN + kd * NegLn2loN; - /* 2^(k/N) ~= scale * (1 + tail). */ - idx = 2 * (ki % N); - top = ki << (52 - EXP_TABLE_BITS); - tail = asdouble(T[idx]); - /* This is only a valid scale when -1023*N < k < 1024*N. */ - sbits = T[idx + 1] + top; - /* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1). */ - /* Evaluation is optimized assuming superscalar pipelined execution. */ - r2 = r * r; - /* Without fma the worst case error is 0.25/N ulp larger. */ - /* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp. */ - tmp = tail + r + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5); - if (predict_false(abstop == 0)) - return specialcase(tmp, sbits, ki); - scale = asdouble(sbits); - /* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there - is no spurious underflow here even without fma. */ - return eval_as_double(scale + scale * tmp); -} diff --git a/src/math/exp10.c b/src/math/exp10.c deleted file mode 100644 index 26899eb..0000000 --- a/src/math/exp10.c +++ /dev/null @@ -1,24 +0,0 @@ -#define _GNU_SOURCE -#include -#include - -double exp10(double x) -{ - static const double p10[] = { - 1e-15, 1e-14, 1e-13, 1e-12, 1e-11, 1e-10, - 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1, - 1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, - 1e10, 1e11, 1e12, 1e13, 1e14, 1e15 - }; - double n, y = modf(x, &n); - union {double f; uint64_t i;} u = {n}; - /* fabs(n) < 16 without raising invalid on nan */ - if ((u.i>>52 & 0x7ff) < 0x3ff+4) { - if (!y) return p10[(int)n+15]; - y = exp2(3.32192809488736234787031942948939 * y); - return y * p10[(int)n+15]; - } - return pow(10.0, x); -} - -weak_alias(exp10, pow10); diff --git a/src/math/exp10f.c b/src/math/exp10f.c deleted file mode 100644 index d009f0a..0000000 --- a/src/math/exp10f.c +++ /dev/null @@ -1,22 +0,0 @@ -#define _GNU_SOURCE -#include -#include - -float exp10f(float x) -{ - static const float p10[] = { - 1e-7f, 1e-6f, 1e-5f, 1e-4f, 1e-3f, 1e-2f, 1e-1f, - 1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7 - }; - float n, y = modff(x, &n); - union {float f; uint32_t i;} u = {n}; - /* fabsf(n) < 8 without raising invalid on nan */ - if ((u.i>>23 & 0xff) < 0x7f+3) { - if (!y) return p10[(int)n+7]; - y = exp2f(3.32192809488736234787031942948939f * y); - return y * p10[(int)n+7]; - } - return exp2(3.32192809488736234787031942948939 * x); -} - -weak_alias(exp10f, pow10f); diff --git a/src/math/exp10l.c b/src/math/exp10l.c deleted file mode 100644 index f3da1a0..0000000 --- a/src/math/exp10l.c +++ /dev/null @@ -1,32 +0,0 @@ -#define _GNU_SOURCE -#include -#include -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double exp10l(long double x) -{ - return exp10(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -long double exp10l(long double x) -{ - static const long double p10[] = { - 1e-15L, 1e-14L, 1e-13L, 1e-12L, 1e-11L, 1e-10L, - 1e-9L, 1e-8L, 1e-7L, 1e-6L, 1e-5L, 1e-4L, 1e-3L, 1e-2L, 1e-1L, - 1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, - 1e10, 1e11, 1e12, 1e13, 1e14, 1e15 - }; - long double n, y = modfl(x, &n); - union ldshape u = {n}; - /* fabsl(n) < 16 without raising invalid on nan */ - if ((u.i.se & 0x7fff) < 0x3fff+4) { - if (!y) return p10[(int)n+15]; - y = exp2l(3.32192809488736234787031942948939L * y); - return y * p10[(int)n+15]; - } - return powl(10.0, x); -} -#endif - -weak_alias(exp10l, pow10l); diff --git a/src/math/exp2.c b/src/math/exp2.c deleted file mode 100644 index e0ff54b..0000000 --- a/src/math/exp2.c +++ /dev/null @@ -1,121 +0,0 @@ -/* - * Double-precision 2^x function. - * - * Copyright (c) 2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include -#include -#include "libm.h" -#include "exp_data.h" - -#define N (1 << EXP_TABLE_BITS) -#define Shift __exp_data.exp2_shift -#define T __exp_data.tab -#define C1 __exp_data.exp2_poly[0] -#define C2 __exp_data.exp2_poly[1] -#define C3 __exp_data.exp2_poly[2] -#define C4 __exp_data.exp2_poly[3] -#define C5 __exp_data.exp2_poly[4] - -/* Handle cases that may overflow or underflow when computing the result that - is scale*(1+TMP) without intermediate rounding. The bit representation of - scale is in SBITS, however it has a computed exponent that may have - overflown into the sign bit so that needs to be adjusted before using it as - a double. (int32_t)KI is the k used in the argument reduction and exponent - adjustment of scale, positive k here means the result may overflow and - negative k means the result may underflow. */ -static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki) -{ - double_t scale, y; - - if ((ki & 0x80000000) == 0) { - /* k > 0, the exponent of scale might have overflowed by 1. */ - sbits -= 1ull << 52; - scale = asdouble(sbits); - y = 2 * (scale + scale * tmp); - return eval_as_double(y); - } - /* k < 0, need special care in the subnormal range. */ - sbits += 1022ull << 52; - scale = asdouble(sbits); - y = scale + scale * tmp; - if (y < 1.0) { - /* Round y to the right precision before scaling it into the subnormal - range to avoid double rounding that can cause 0.5+E/2 ulp error where - E is the worst-case ulp error outside the subnormal range. So this - is only useful if the goal is better than 1 ulp worst-case error. */ - double_t hi, lo; - lo = scale - y + scale * tmp; - hi = 1.0 + y; - lo = 1.0 - hi + y + lo; - y = eval_as_double(hi + lo) - 1.0; - /* Avoid -0.0 with downward rounding. */ - if (WANT_ROUNDING && y == 0.0) - y = 0.0; - /* The underflow exception needs to be signaled explicitly. */ - fp_force_eval(fp_barrier(0x1p-1022) * 0x1p-1022); - } - y = 0x1p-1022 * y; - return eval_as_double(y); -} - -/* Top 12 bits of a double (sign and exponent bits). */ -static inline uint32_t top12(double x) -{ - return asuint64(x) >> 52; -} - -double exp2(double x) -{ - uint32_t abstop; - uint64_t ki, idx, top, sbits; - double_t kd, r, r2, scale, tail, tmp; - - abstop = top12(x) & 0x7ff; - if (predict_false(abstop - top12(0x1p-54) >= top12(512.0) - top12(0x1p-54))) { - if (abstop - top12(0x1p-54) >= 0x80000000) - /* Avoid spurious underflow for tiny x. */ - /* Note: 0 is common input. */ - return WANT_ROUNDING ? 1.0 + x : 1.0; - if (abstop >= top12(1024.0)) { - if (asuint64(x) == asuint64(-INFINITY)) - return 0.0; - if (abstop >= top12(INFINITY)) - return 1.0 + x; - if (!(asuint64(x) >> 63)) - return __math_oflow(0); - else if (asuint64(x) >= asuint64(-1075.0)) - return __math_uflow(0); - } - if (2 * asuint64(x) > 2 * asuint64(928.0)) - /* Large x is special cased below. */ - abstop = 0; - } - - /* exp2(x) = 2^(k/N) * 2^r, with 2^r in [2^(-1/2N),2^(1/2N)]. */ - /* x = k/N + r, with int k and r in [-1/2N, 1/2N]. */ - kd = eval_as_double(x + Shift); - ki = asuint64(kd); /* k. */ - kd -= Shift; /* k/N for int k. */ - r = x - kd; - /* 2^(k/N) ~= scale * (1 + tail). */ - idx = 2 * (ki % N); - top = ki << (52 - EXP_TABLE_BITS); - tail = asdouble(T[idx]); - /* This is only a valid scale when -1023*N < k < 1024*N. */ - sbits = T[idx + 1] + top; - /* exp2(x) = 2^(k/N) * 2^r ~= scale + scale * (tail + 2^r - 1). */ - /* Evaluation is optimized assuming superscalar pipelined execution. */ - r2 = r * r; - /* Without fma the worst case error is 0.5/N ulp larger. */ - /* Worst case error is less than 0.5+0.86/N+(abs poly error * 2^53) ulp. */ - tmp = tail + r * C1 + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5); - if (predict_false(abstop == 0)) - return specialcase(tmp, sbits, ki); - scale = asdouble(sbits); - /* Note: tmp == 0 or |tmp| > 2^-65 and scale > 2^-928, so there - is no spurious underflow here even without fma. */ - return eval_as_double(scale + scale * tmp); -} diff --git a/src/math/exp2f.c b/src/math/exp2f.c deleted file mode 100644 index 0360482..0000000 --- a/src/math/exp2f.c +++ /dev/null @@ -1,69 +0,0 @@ -/* - * Single-precision 2^x function. - * - * Copyright (c) 2017-2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include -#include -#include "libm.h" -#include "exp2f_data.h" - -/* -EXP2F_TABLE_BITS = 5 -EXP2F_POLY_ORDER = 3 - -ULP error: 0.502 (nearest rounding.) -Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.) -Wrong count: 168353 (all nearest rounding wrong results with fma.) -Non-nearest ULP error: 1 (rounded ULP error) -*/ - -#define N (1 << EXP2F_TABLE_BITS) -#define T __exp2f_data.tab -#define C __exp2f_data.poly -#define SHIFT __exp2f_data.shift_scaled - -static inline uint32_t top12(float x) -{ - return asuint(x) >> 20; -} - -float exp2f(float x) -{ - uint32_t abstop; - uint64_t ki, t; - double_t kd, xd, z, r, r2, y, s; - - xd = (double_t)x; - abstop = top12(x) & 0x7ff; - if (predict_false(abstop >= top12(128.0f))) { - /* |x| >= 128 or x is nan. */ - if (asuint(x) == asuint(-INFINITY)) - return 0.0f; - if (abstop >= top12(INFINITY)) - return x + x; - if (x > 0.0f) - return __math_oflowf(0); - if (x <= -150.0f) - return __math_uflowf(0); - } - - /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */ - kd = eval_as_double(xd + SHIFT); - ki = asuint64(kd); - kd -= SHIFT; /* k/N for int k. */ - r = xd - kd; - - /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ - t = T[ki % N]; - t += ki << (52 - EXP2F_TABLE_BITS); - s = asdouble(t); - z = C[0] * r + C[1]; - r2 = r * r; - y = C[2] * r + 1; - y = z * r2 + y; - y = y * s; - return eval_as_float(y); -} diff --git a/src/math/exp2f_data.c b/src/math/exp2f_data.c deleted file mode 100644 index be32472..0000000 --- a/src/math/exp2f_data.c +++ /dev/null @@ -1,35 +0,0 @@ -/* - * Shared data between expf, exp2f and powf. - * - * Copyright (c) 2017-2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include "exp2f_data.h" - -#define N (1 << EXP2F_TABLE_BITS) - -const struct exp2f_data __exp2f_data = { - /* tab[i] = uint(2^(i/N)) - (i << 52-BITS) - used for computing 2^(k/N) for an int |k| < 150 N as - double(tab[k%N] + (k << 52-BITS)) */ - .tab = { -0x3ff0000000000000, 0x3fefd9b0d3158574, 0x3fefb5586cf9890f, 0x3fef9301d0125b51, -0x3fef72b83c7d517b, 0x3fef54873168b9aa, 0x3fef387a6e756238, 0x3fef1e9df51fdee1, -0x3fef06fe0a31b715, 0x3feef1a7373aa9cb, 0x3feedea64c123422, 0x3feece086061892d, -0x3feebfdad5362a27, 0x3feeb42b569d4f82, 0x3feeab07dd485429, 0x3feea47eb03a5585, -0x3feea09e667f3bcd, 0x3fee9f75e8ec5f74, 0x3feea11473eb0187, 0x3feea589994cce13, -0x3feeace5422aa0db, 0x3feeb737b0cdc5e5, 0x3feec49182a3f090, 0x3feed503b23e255d, -0x3feee89f995ad3ad, 0x3feeff76f2fb5e47, 0x3fef199bdd85529c, 0x3fef3720dcef9069, -0x3fef5818dcfba487, 0x3fef7c97337b9b5f, 0x3fefa4afa2a490da, 0x3fefd0765b6e4540, - }, - .shift_scaled = 0x1.8p+52 / N, - .poly = { - 0x1.c6af84b912394p-5, 0x1.ebfce50fac4f3p-3, 0x1.62e42ff0c52d6p-1, - }, - .shift = 0x1.8p+52, - .invln2_scaled = 0x1.71547652b82fep+0 * N, - .poly_scaled = { - 0x1.c6af84b912394p-5/N/N/N, 0x1.ebfce50fac4f3p-3/N/N, 0x1.62e42ff0c52d6p-1/N, - }, -}; diff --git a/src/math/exp2f_data.h b/src/math/exp2f_data.h deleted file mode 100644 index fe744f1..0000000 --- a/src/math/exp2f_data.h +++ /dev/null @@ -1,23 +0,0 @@ -/* - * Copyright (c) 2017-2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ -#ifndef _EXP2F_DATA_H -#define _EXP2F_DATA_H - -#include -#include - -/* Shared between expf, exp2f and powf. */ -#define EXP2F_TABLE_BITS 5 -#define EXP2F_POLY_ORDER 3 -extern hidden const struct exp2f_data { - uint64_t tab[1 << EXP2F_TABLE_BITS]; - double shift_scaled; - double poly[EXP2F_POLY_ORDER]; - double shift; - double invln2_scaled; - double poly_scaled[EXP2F_POLY_ORDER]; -} __exp2f_data; - -#endif diff --git a/src/math/exp2l.c b/src/math/exp2l.c deleted file mode 100644 index 3565c1e..0000000 --- a/src/math/exp2l.c +++ /dev/null @@ -1,619 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/ld80/s_exp2l.c and /usr/src/lib/msun/ld128/s_exp2l.c */ -/*- - * Copyright (c) 2005-2008 David Schultz - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double exp2l(long double x) -{ - return exp2(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -#define TBLBITS 7 -#define TBLSIZE (1 << TBLBITS) - -static const double -redux = 0x1.8p63 / TBLSIZE, -P1 = 0x1.62e42fefa39efp-1, -P2 = 0x1.ebfbdff82c58fp-3, -P3 = 0x1.c6b08d7049fap-5, -P4 = 0x1.3b2ab6fba4da5p-7, -P5 = 0x1.5d8804780a736p-10, -P6 = 0x1.430918835e33dp-13; - -static const double tbl[TBLSIZE * 2] = { - 0x1.6a09e667f3bcdp-1, -0x1.bdd3413b2648p-55, - 0x1.6c012750bdabfp-1, -0x1.2895667ff0cp-57, - 0x1.6dfb23c651a2fp-1, -0x1.bbe3a683c88p-58, - 0x1.6ff7df9519484p-1, -0x1.83c0f25860fp-56, - 0x1.71f75e8ec5f74p-1, -0x1.16e4786887bp-56, - 0x1.73f9a48a58174p-1, -0x1.0a8d96c65d5p-55, - 0x1.75feb564267c9p-1, -0x1.0245957316ep-55, - 0x1.780694fde5d3fp-1, 0x1.866b80a0216p-55, - 0x1.7a11473eb0187p-1, -0x1.41577ee0499p-56, - 0x1.7c1ed0130c132p-1, 0x1.f124cd1164ep-55, - 0x1.7e2f336cf4e62p-1, 0x1.05d02ba157ap-57, - 0x1.80427543e1a12p-1, -0x1.27c86626d97p-55, - 0x1.82589994cce13p-1, -0x1.d4c1dd41533p-55, - 0x1.8471a4623c7adp-1, -0x1.8d684a341cep-56, - 0x1.868d99b4492edp-1, -0x1.fc6f89bd4f68p-55, - 0x1.88ac7d98a6699p-1, 0x1.994c2f37cb5p-55, - 0x1.8ace5422aa0dbp-1, 0x1.6e9f156864bp-55, - 0x1.8cf3216b5448cp-1, -0x1.0d55e32e9e4p-57, - 0x1.8f1ae99157736p-1, 0x1.5cc13a2e397p-56, - 0x1.9145b0b91ffc6p-1, -0x1.dd6792e5825p-55, - 0x1.93737b0cdc5e5p-1, -0x1.75fc781b58p-58, - 0x1.95a44cbc8520fp-1, -0x1.64b7c96a5fp-57, - 0x1.97d829fde4e5p-1, -0x1.d185b7c1b86p-55, - 0x1.9a0f170ca07bap-1, -0x1.173bd91cee6p-55, - 0x1.9c49182a3f09p-1, 0x1.c7c46b071f2p-57, - 0x1.9e86319e32323p-1, 0x1.824ca78e64cp-57, - 0x1.a0c667b5de565p-1, -0x1.359495d1cd5p-55, - 0x1.a309bec4a2d33p-1, 0x1.6305c7ddc368p-55, - 0x1.a5503b23e255dp-1, -0x1.d2f6edb8d42p-55, - 0x1.a799e1330b358p-1, 0x1.bcb7ecac564p-55, - 0x1.a9e6b5579fdbfp-1, 0x1.0fac90ef7fdp-55, - 0x1.ac36bbfd3f37ap-1, -0x1.f9234cae76dp-56, - 0x1.ae89f995ad3adp-1, 0x1.7a1cd345dcc8p-55, - 0x1.b0e07298db666p-1, -0x1.bdef54c80e4p-55, - 0x1.b33a2b84f15fbp-1, -0x1.2805e3084d8p-58, - 0x1.b59728de5593ap-1, -0x1.c71dfbbba6ep-55, - 0x1.b7f76f2fb5e47p-1, -0x1.5584f7e54acp-57, - 0x1.ba5b030a1064ap-1, -0x1.efcd30e5429p-55, - 0x1.bcc1e904bc1d2p-1, 0x1.23dd07a2d9fp-56, - 0x1.bf2c25bd71e09p-1, -0x1.efdca3f6b9c8p-55, - 0x1.c199bdd85529cp-1, 0x1.11065895049p-56, - 0x1.c40ab5fffd07ap-1, 0x1.b4537e083c6p-55, - 0x1.c67f12e57d14bp-1, 0x1.2884dff483c8p-55, - 0x1.c8f6d9406e7b5p-1, 0x1.1acbc48805cp-57, - 0x1.cb720dcef9069p-1, 0x1.503cbd1e94ap-57, - 0x1.cdf0b555dc3fap-1, -0x1.dd83b53829dp-56, - 0x1.d072d4a07897cp-1, -0x1.cbc3743797a8p-55, - 0x1.d2f87080d89f2p-1, -0x1.d487b719d858p-55, - 0x1.d5818dcfba487p-1, 0x1.2ed02d75b37p-56, - 0x1.d80e316c98398p-1, -0x1.11ec18bedep-55, - 0x1.da9e603db3285p-1, 0x1.c2300696db5p-55, - 0x1.dd321f301b46p-1, 0x1.2da5778f019p-55, - 0x1.dfc97337b9b5fp-1, -0x1.1a5cd4f184b8p-55, - 0x1.e264614f5a129p-1, -0x1.7b627817a148p-55, - 0x1.e502ee78b3ff6p-1, 0x1.39e8980a9cdp-56, - 0x1.e7a51fbc74c83p-1, 0x1.2d522ca0c8ep-55, - 0x1.ea4afa2a490dap-1, -0x1.e9c23179c288p-55, - 0x1.ecf482d8e67f1p-1, -0x1.c93f3b411ad8p-55, - 0x1.efa1bee615a27p-1, 0x1.dc7f486a4b68p-55, - 0x1.f252b376bba97p-1, 0x1.3a1a5bf0d8e8p-55, - 0x1.f50765b6e454p-1, 0x1.9d3e12dd8a18p-55, - 0x1.f7bfdad9cbe14p-1, -0x1.dbb12d00635p-55, - 0x1.fa7c1819e90d8p-1, 0x1.74853f3a593p-56, - 0x1.fd3c22b8f71f1p-1, 0x1.2eb74966578p-58, - 0x1p+0, 0x0p+0, - 0x1.0163da9fb3335p+0, 0x1.b61299ab8cd8p-54, - 0x1.02c9a3e778061p+0, -0x1.19083535b08p-56, - 0x1.04315e86e7f85p+0, -0x1.0a31c1977c98p-54, - 0x1.059b0d3158574p+0, 0x1.d73e2a475b4p-55, - 0x1.0706b29ddf6dep+0, -0x1.c91dfe2b13cp-55, - 0x1.0874518759bc8p+0, 0x1.186be4bb284p-57, - 0x1.09e3ecac6f383p+0, 0x1.14878183161p-54, - 0x1.0b5586cf9890fp+0, 0x1.8a62e4adc61p-54, - 0x1.0cc922b7247f7p+0, 0x1.01edc16e24f8p-54, - 0x1.0e3ec32d3d1a2p+0, 0x1.03a1727c58p-59, - 0x1.0fb66affed31bp+0, -0x1.b9bedc44ebcp-57, - 0x1.11301d0125b51p+0, -0x1.6c51039449bp-54, - 0x1.12abdc06c31ccp+0, -0x1.1b514b36ca8p-58, - 0x1.1429aaea92dep+0, -0x1.32fbf9af1368p-54, - 0x1.15a98c8a58e51p+0, 0x1.2406ab9eeabp-55, - 0x1.172b83c7d517bp+0, -0x1.19041b9d78ap-55, - 0x1.18af9388c8deap+0, -0x1.11023d1970f8p-54, - 0x1.1a35beb6fcb75p+0, 0x1.e5b4c7b4969p-55, - 0x1.1bbe084045cd4p+0, -0x1.95386352ef6p-54, - 0x1.1d4873168b9aap+0, 0x1.e016e00a264p-54, - 0x1.1ed5022fcd91dp+0, -0x1.1df98027bb78p-54, - 0x1.2063b88628cd6p+0, 0x1.dc775814a85p-55, - 0x1.21f49917ddc96p+0, 0x1.2a97e9494a6p-55, - 0x1.2387a6e756238p+0, 0x1.9b07eb6c7058p-54, - 0x1.251ce4fb2a63fp+0, 0x1.ac155bef4f5p-55, - 0x1.26b4565e27cddp+0, 0x1.2bd339940eap-55, - 0x1.284dfe1f56381p+0, -0x1.a4c3a8c3f0d8p-54, - 0x1.29e9df51fdee1p+0, 0x1.612e8afad12p-55, - 0x1.2b87fd0dad99p+0, -0x1.10adcd6382p-59, - 0x1.2d285a6e4030bp+0, 0x1.0024754db42p-54, - 0x1.2ecafa93e2f56p+0, 0x1.1ca0f45d524p-56, - 0x1.306fe0a31b715p+0, 0x1.6f46ad23183p-55, - 0x1.32170fc4cd831p+0, 0x1.a9ce78e1804p-55, - 0x1.33c08b26416ffp+0, 0x1.327218436598p-54, - 0x1.356c55f929ff1p+0, -0x1.b5cee5c4e46p-55, - 0x1.371a7373aa9cbp+0, -0x1.63aeabf42ebp-54, - 0x1.38cae6d05d866p+0, -0x1.e958d3c99048p-54, - 0x1.3a7db34e59ff7p+0, -0x1.5e436d661f6p-56, - 0x1.3c32dc313a8e5p+0, -0x1.efff8375d2ap-54, - 0x1.3dea64c123422p+0, 0x1.ada0911f09fp-55, - 0x1.3fa4504ac801cp+0, -0x1.7d023f956fap-54, - 0x1.4160a21f72e2ap+0, -0x1.ef3691c309p-58, - 0x1.431f5d950a897p+0, -0x1.1c7dde35f7ap-55, - 0x1.44e086061892dp+0, 0x1.89b7a04ef8p-59, - 0x1.46a41ed1d0057p+0, 0x1.c944bd1648a8p-54, - 0x1.486a2b5c13cdp+0, 0x1.3c1a3b69062p-56, - 0x1.4a32af0d7d3dep+0, 0x1.9cb62f3d1be8p-54, - 0x1.4bfdad5362a27p+0, 0x1.d4397afec42p-56, - 0x1.4dcb299fddd0dp+0, 0x1.8ecdbbc6a78p-54, - 0x1.4f9b2769d2ca7p+0, -0x1.4b309d25958p-54, - 0x1.516daa2cf6642p+0, -0x1.f768569bd94p-55, - 0x1.5342b569d4f82p+0, -0x1.07abe1db13dp-55, - 0x1.551a4ca5d920fp+0, -0x1.d689cefede6p-55, - 0x1.56f4736b527dap+0, 0x1.9bb2c011d938p-54, - 0x1.58d12d497c7fdp+0, 0x1.295e15b9a1ep-55, - 0x1.5ab07dd485429p+0, 0x1.6324c0546478p-54, - 0x1.5c9268a5946b7p+0, 0x1.c4b1b81698p-60, - 0x1.5e76f15ad2148p+0, 0x1.ba6f93080e68p-54, - 0x1.605e1b976dc09p+0, -0x1.3e2429b56de8p-54, - 0x1.6247eb03a5585p+0, -0x1.383c17e40b48p-54, - 0x1.6434634ccc32p+0, -0x1.c483c759d89p-55, - 0x1.6623882552225p+0, -0x1.bb60987591cp-54, - 0x1.68155d44ca973p+0, 0x1.038ae44f74p-57, -}; - -/* - * exp2l(x): compute the base 2 exponential of x - * - * Accuracy: Peak error < 0.511 ulp. - * - * Method: (equally-spaced tables) - * - * Reduce x: - * x = 2**k + y, for integer k and |y| <= 1/2. - * Thus we have exp2l(x) = 2**k * exp2(y). - * - * Reduce y: - * y = i/TBLSIZE + z for integer i near y * TBLSIZE. - * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z), - * with |z| <= 2**-(TBLBITS+1). - * - * We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a - * degree-6 minimax polynomial with maximum error under 2**-69. - * The table entries each have 104 bits of accuracy, encoded as - * a pair of double precision values. - */ -long double exp2l(long double x) -{ - union ldshape u = {x}; - int e = u.i.se & 0x7fff; - long double r, z; - uint32_t i0; - union {uint32_t u; int32_t i;} k; - - /* Filter out exceptional cases. */ - if (e >= 0x3fff + 13) { /* |x| >= 8192 or x is NaN */ - if (u.i.se >= 0x3fff + 14 && u.i.se >> 15 == 0) - /* overflow */ - return x * 0x1p16383L; - if (e == 0x7fff) /* -inf or -nan */ - return -1/x; - if (x < -16382) { - if (x <= -16446 || x - 0x1p63 + 0x1p63 != x) - /* underflow */ - FORCE_EVAL((float)(-0x1p-149/x)); - if (x <= -16446) - return 0; - } - } else if (e < 0x3fff - 64) { - return 1 + x; - } - - /* - * Reduce x, computing z, i0, and k. The low bits of x + redux - * contain the 16-bit integer part of the exponent (k) followed by - * TBLBITS fractional bits (i0). We use bit tricks to extract these - * as integers, then set z to the remainder. - * - * Example: Suppose x is 0xabc.123456p0 and TBLBITS is 8. - * Then the low-order word of x + redux is 0x000abc12, - * We split this into k = 0xabc and i0 = 0x12 (adjusted to - * index into the table), then we compute z = 0x0.003456p0. - */ - u.f = x + redux; - i0 = u.i.m + TBLSIZE / 2; - k.u = i0 / TBLSIZE * TBLSIZE; - k.i /= TBLSIZE; - i0 %= TBLSIZE; - u.f -= redux; - z = x - u.f; - - /* Compute r = exp2l(y) = exp2lt[i0] * p(z). */ - long double t_hi = tbl[2*i0]; - long double t_lo = tbl[2*i0 + 1]; - /* XXX This gives > 1 ulp errors outside of FE_TONEAREST mode */ - r = t_lo + (t_hi + t_lo) * z * (P1 + z * (P2 + z * (P3 + z * (P4 - + z * (P5 + z * P6))))) + t_hi; - - return scalbnl(r, k.i); -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -#define TBLBITS 7 -#define TBLSIZE (1 << TBLBITS) - -static const long double - P1 = 0x1.62e42fefa39ef35793c7673007e6p-1L, - P2 = 0x1.ebfbdff82c58ea86f16b06ec9736p-3L, - P3 = 0x1.c6b08d704a0bf8b33a762bad3459p-5L, - P4 = 0x1.3b2ab6fba4e7729ccbbe0b4f3fc2p-7L, - P5 = 0x1.5d87fe78a67311071dee13fd11d9p-10L, - P6 = 0x1.430912f86c7876f4b663b23c5fe5p-13L; - -static const double - P7 = 0x1.ffcbfc588b041p-17, - P8 = 0x1.62c0223a5c7c7p-20, - P9 = 0x1.b52541ff59713p-24, - P10 = 0x1.e4cf56a391e22p-28, - redux = 0x1.8p112 / TBLSIZE; - -static const long double tbl[TBLSIZE] = { - 0x1.6a09e667f3bcc908b2fb1366dfeap-1L, - 0x1.6c012750bdabeed76a99800f4edep-1L, - 0x1.6dfb23c651a2ef220e2cbe1bc0d4p-1L, - 0x1.6ff7df9519483cf87e1b4f3e1e98p-1L, - 0x1.71f75e8ec5f73dd2370f2ef0b148p-1L, - 0x1.73f9a48a58173bd5c9a4e68ab074p-1L, - 0x1.75feb564267c8bf6e9aa33a489a8p-1L, - 0x1.780694fde5d3f619ae02808592a4p-1L, - 0x1.7a11473eb0186d7d51023f6ccb1ap-1L, - 0x1.7c1ed0130c1327c49334459378dep-1L, - 0x1.7e2f336cf4e62105d02ba1579756p-1L, - 0x1.80427543e1a11b60de67649a3842p-1L, - 0x1.82589994cce128acf88afab34928p-1L, - 0x1.8471a4623c7acce52f6b97c6444cp-1L, - 0x1.868d99b4492ec80e41d90ac2556ap-1L, - 0x1.88ac7d98a669966530bcdf2d4cc0p-1L, - 0x1.8ace5422aa0db5ba7c55a192c648p-1L, - 0x1.8cf3216b5448bef2aa1cd161c57ap-1L, - 0x1.8f1ae991577362b982745c72eddap-1L, - 0x1.9145b0b91ffc588a61b469f6b6a0p-1L, - 0x1.93737b0cdc5e4f4501c3f2540ae8p-1L, - 0x1.95a44cbc8520ee9b483695a0e7fep-1L, - 0x1.97d829fde4e4f8b9e920f91e8eb6p-1L, - 0x1.9a0f170ca07b9ba3109b8c467844p-1L, - 0x1.9c49182a3f0901c7c46b071f28dep-1L, - 0x1.9e86319e323231824ca78e64c462p-1L, - 0x1.a0c667b5de564b29ada8b8cabbacp-1L, - 0x1.a309bec4a2d3358c171f770db1f4p-1L, - 0x1.a5503b23e255c8b424491caf88ccp-1L, - 0x1.a799e1330b3586f2dfb2b158f31ep-1L, - 0x1.a9e6b5579fdbf43eb243bdff53a2p-1L, - 0x1.ac36bbfd3f379c0db966a3126988p-1L, - 0x1.ae89f995ad3ad5e8734d17731c80p-1L, - 0x1.b0e07298db66590842acdfc6fb4ep-1L, - 0x1.b33a2b84f15faf6bfd0e7bd941b0p-1L, - 0x1.b59728de559398e3881111648738p-1L, - 0x1.b7f76f2fb5e46eaa7b081ab53ff6p-1L, - 0x1.ba5b030a10649840cb3c6af5b74cp-1L, - 0x1.bcc1e904bc1d2247ba0f45b3d06cp-1L, - 0x1.bf2c25bd71e088408d7025190cd0p-1L, - 0x1.c199bdd85529c2220cb12a0916bap-1L, - 0x1.c40ab5fffd07a6d14df820f17deap-1L, - 0x1.c67f12e57d14b4a2137fd20f2a26p-1L, - 0x1.c8f6d9406e7b511acbc48805c3f6p-1L, - 0x1.cb720dcef90691503cbd1e949d0ap-1L, - 0x1.cdf0b555dc3f9c44f8958fac4f12p-1L, - 0x1.d072d4a07897b8d0f22f21a13792p-1L, - 0x1.d2f87080d89f18ade123989ea50ep-1L, - 0x1.d5818dcfba48725da05aeb66dff8p-1L, - 0x1.d80e316c98397bb84f9d048807a0p-1L, - 0x1.da9e603db3285708c01a5b6d480cp-1L, - 0x1.dd321f301b4604b695de3c0630c0p-1L, - 0x1.dfc97337b9b5eb968cac39ed284cp-1L, - 0x1.e264614f5a128a12761fa17adc74p-1L, - 0x1.e502ee78b3ff6273d130153992d0p-1L, - 0x1.e7a51fbc74c834b548b2832378a4p-1L, - 0x1.ea4afa2a490d9858f73a18f5dab4p-1L, - 0x1.ecf482d8e67f08db0312fb949d50p-1L, - 0x1.efa1bee615a27771fd21a92dabb6p-1L, - 0x1.f252b376bba974e8696fc3638f24p-1L, - 0x1.f50765b6e4540674f84b762861a6p-1L, - 0x1.f7bfdad9cbe138913b4bfe72bd78p-1L, - 0x1.fa7c1819e90d82e90a7e74b26360p-1L, - 0x1.fd3c22b8f71f10975ba4b32bd006p-1L, - 0x1.0000000000000000000000000000p+0L, - 0x1.0163da9fb33356d84a66ae336e98p+0L, - 0x1.02c9a3e778060ee6f7caca4f7a18p+0L, - 0x1.04315e86e7f84bd738f9a20da442p+0L, - 0x1.059b0d31585743ae7c548eb68c6ap+0L, - 0x1.0706b29ddf6ddc6dc403a9d87b1ep+0L, - 0x1.0874518759bc808c35f25d942856p+0L, - 0x1.09e3ecac6f3834521e060c584d5cp+0L, - 0x1.0b5586cf9890f6298b92b7184200p+0L, - 0x1.0cc922b7247f7407b705b893dbdep+0L, - 0x1.0e3ec32d3d1a2020742e4f8af794p+0L, - 0x1.0fb66affed31af232091dd8a169ep+0L, - 0x1.11301d0125b50a4ebbf1aed9321cp+0L, - 0x1.12abdc06c31cbfb92bad324d6f84p+0L, - 0x1.1429aaea92ddfb34101943b2588ep+0L, - 0x1.15a98c8a58e512480d573dd562aep+0L, - 0x1.172b83c7d517adcdf7c8c50eb162p+0L, - 0x1.18af9388c8de9bbbf70b9a3c269cp+0L, - 0x1.1a35beb6fcb753cb698f692d2038p+0L, - 0x1.1bbe084045cd39ab1e72b442810ep+0L, - 0x1.1d4873168b9aa7805b8028990be8p+0L, - 0x1.1ed5022fcd91cb8819ff61121fbep+0L, - 0x1.2063b88628cd63b8eeb0295093f6p+0L, - 0x1.21f49917ddc962552fd29294bc20p+0L, - 0x1.2387a6e75623866c1fadb1c159c0p+0L, - 0x1.251ce4fb2a63f3582ab7de9e9562p+0L, - 0x1.26b4565e27cdd257a673281d3068p+0L, - 0x1.284dfe1f5638096cf15cf03c9fa0p+0L, - 0x1.29e9df51fdee12c25d15f5a25022p+0L, - 0x1.2b87fd0dad98ffddea46538fca24p+0L, - 0x1.2d285a6e4030b40091d536d0733ep+0L, - 0x1.2ecafa93e2f5611ca0f45d5239a4p+0L, - 0x1.306fe0a31b7152de8d5a463063bep+0L, - 0x1.32170fc4cd8313539cf1c3009330p+0L, - 0x1.33c08b26416ff4c9c8610d96680ep+0L, - 0x1.356c55f929ff0c94623476373be4p+0L, - 0x1.371a7373aa9caa7145502f45452ap+0L, - 0x1.38cae6d05d86585a9cb0d9bed530p+0L, - 0x1.3a7db34e59ff6ea1bc9299e0a1fep+0L, - 0x1.3c32dc313a8e484001f228b58cf0p+0L, - 0x1.3dea64c12342235b41223e13d7eep+0L, - 0x1.3fa4504ac801ba0bf701aa417b9cp+0L, - 0x1.4160a21f72e29f84325b8f3dbacap+0L, - 0x1.431f5d950a896dc704439410b628p+0L, - 0x1.44e086061892d03136f409df0724p+0L, - 0x1.46a41ed1d005772512f459229f0ap+0L, - 0x1.486a2b5c13cd013c1a3b69062f26p+0L, - 0x1.4a32af0d7d3de672d8bcf46f99b4p+0L, - 0x1.4bfdad5362a271d4397afec42e36p+0L, - 0x1.4dcb299fddd0d63b36ef1a9e19dep+0L, - 0x1.4f9b2769d2ca6ad33d8b69aa0b8cp+0L, - 0x1.516daa2cf6641c112f52c84d6066p+0L, - 0x1.5342b569d4f81df0a83c49d86bf4p+0L, - 0x1.551a4ca5d920ec52ec620243540cp+0L, - 0x1.56f4736b527da66ecb004764e61ep+0L, - 0x1.58d12d497c7fd252bc2b7343d554p+0L, - 0x1.5ab07dd48542958c93015191e9a8p+0L, - 0x1.5c9268a5946b701c4b1b81697ed4p+0L, - 0x1.5e76f15ad21486e9be4c20399d12p+0L, - 0x1.605e1b976dc08b076f592a487066p+0L, - 0x1.6247eb03a5584b1f0fa06fd2d9eap+0L, - 0x1.6434634ccc31fc76f8714c4ee122p+0L, - 0x1.66238825522249127d9e29b92ea2p+0L, - 0x1.68155d44ca973081c57227b9f69ep+0L, -}; - -static const float eps[TBLSIZE] = { - -0x1.5c50p-101, - -0x1.5d00p-106, - 0x1.8e90p-102, - -0x1.5340p-103, - 0x1.1bd0p-102, - -0x1.4600p-105, - -0x1.7a40p-104, - 0x1.d590p-102, - -0x1.d590p-101, - 0x1.b100p-103, - -0x1.0d80p-105, - 0x1.6b00p-103, - -0x1.9f00p-105, - 0x1.c400p-103, - 0x1.e120p-103, - -0x1.c100p-104, - -0x1.9d20p-103, - 0x1.a800p-108, - 0x1.4c00p-106, - -0x1.9500p-106, - 0x1.6900p-105, - -0x1.29d0p-100, - 0x1.4c60p-103, - 0x1.13a0p-102, - -0x1.5b60p-103, - -0x1.1c40p-103, - 0x1.db80p-102, - 0x1.91a0p-102, - 0x1.dc00p-105, - 0x1.44c0p-104, - 0x1.9710p-102, - 0x1.8760p-103, - -0x1.a720p-103, - 0x1.ed20p-103, - -0x1.49c0p-102, - -0x1.e000p-111, - 0x1.86a0p-103, - 0x1.2b40p-103, - -0x1.b400p-108, - 0x1.1280p-99, - -0x1.02d8p-102, - -0x1.e3d0p-103, - -0x1.b080p-105, - -0x1.f100p-107, - -0x1.16c0p-105, - -0x1.1190p-103, - -0x1.a7d2p-100, - 0x1.3450p-103, - -0x1.67c0p-105, - 0x1.4b80p-104, - -0x1.c4e0p-103, - 0x1.6000p-108, - -0x1.3f60p-105, - 0x1.93f0p-104, - 0x1.5fe0p-105, - 0x1.6f80p-107, - -0x1.7600p-106, - 0x1.21e0p-106, - -0x1.3a40p-106, - -0x1.40c0p-104, - -0x1.9860p-105, - -0x1.5d40p-108, - -0x1.1d70p-106, - 0x1.2760p-105, - 0x0.0000p+0, - 0x1.21e2p-104, - -0x1.9520p-108, - -0x1.5720p-106, - -0x1.4810p-106, - -0x1.be00p-109, - 0x1.0080p-105, - -0x1.5780p-108, - -0x1.d460p-105, - -0x1.6140p-105, - 0x1.4630p-104, - 0x1.ad50p-103, - 0x1.82e0p-105, - 0x1.1d3cp-101, - 0x1.6100p-107, - 0x1.ec30p-104, - 0x1.f200p-108, - 0x1.0b40p-103, - 0x1.3660p-102, - 0x1.d9d0p-103, - -0x1.02d0p-102, - 0x1.b070p-103, - 0x1.b9c0p-104, - -0x1.01c0p-103, - -0x1.dfe0p-103, - 0x1.1b60p-104, - -0x1.ae94p-101, - -0x1.3340p-104, - 0x1.b3d8p-102, - -0x1.6e40p-105, - -0x1.3670p-103, - 0x1.c140p-104, - 0x1.1840p-101, - 0x1.1ab0p-102, - -0x1.a400p-104, - 0x1.1f00p-104, - -0x1.7180p-103, - 0x1.4ce0p-102, - 0x1.9200p-107, - -0x1.54c0p-103, - 0x1.1b80p-105, - -0x1.1828p-101, - 0x1.5720p-102, - -0x1.a060p-100, - 0x1.9160p-102, - 0x1.a280p-104, - 0x1.3400p-107, - 0x1.2b20p-102, - 0x1.7800p-108, - 0x1.cfd0p-101, - 0x1.2ef0p-102, - -0x1.2760p-99, - 0x1.b380p-104, - 0x1.0048p-101, - -0x1.60b0p-102, - 0x1.a1ccp-100, - -0x1.a640p-104, - -0x1.08a0p-101, - 0x1.7e60p-102, - 0x1.22c0p-103, - -0x1.7200p-106, - 0x1.f0f0p-102, - 0x1.eb4ep-99, - 0x1.c6e0p-103, -}; - -/* - * exp2l(x): compute the base 2 exponential of x - * - * Accuracy: Peak error < 0.502 ulp. - * - * Method: (accurate tables) - * - * Reduce x: - * x = 2**k + y, for integer k and |y| <= 1/2. - * Thus we have exp2(x) = 2**k * exp2(y). - * - * Reduce y: - * y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE. - * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]), - * with |z - eps[i]| <= 2**-8 + 2**-98 for the table used. - * - * We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via - * a degree-10 minimax polynomial with maximum error under 2**-120. - * The values in exp2t[] and eps[] are chosen such that - * exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such - * that exp2t[i] is accurate to 2**-122. - * - * Note that the range of i is +-TBLSIZE/2, so we actually index the tables - * by i0 = i + TBLSIZE/2. - * - * This method is due to Gal, with many details due to Gal and Bachelis: - * - * Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library - * for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991). - */ -long double -exp2l(long double x) -{ - union ldshape u = {x}; - int e = u.i.se & 0x7fff; - long double r, z, t; - uint32_t i0; - union {uint32_t u; int32_t i;} k; - - /* Filter out exceptional cases. */ - if (e >= 0x3fff + 14) { /* |x| >= 16384 or x is NaN */ - if (u.i.se >= 0x3fff + 15 && u.i.se >> 15 == 0) - /* overflow */ - return x * 0x1p16383L; - if (e == 0x7fff) /* -inf or -nan */ - return -1/x; - if (x < -16382) { - if (x <= -16495 || x - 0x1p112 + 0x1p112 != x) - /* underflow */ - FORCE_EVAL((float)(-0x1p-149/x)); - if (x <= -16446) - return 0; - } - } else if (e < 0x3fff - 114) { - return 1 + x; - } - - /* - * Reduce x, computing z, i0, and k. The low bits of x + redux - * contain the 16-bit integer part of the exponent (k) followed by - * TBLBITS fractional bits (i0). We use bit tricks to extract these - * as integers, then set z to the remainder. - * - * Example: Suppose x is 0xabc.123456p0 and TBLBITS is 8. - * Then the low-order word of x + redux is 0x000abc12, - * We split this into k = 0xabc and i0 = 0x12 (adjusted to - * index into the table), then we compute z = 0x0.003456p0. - */ - u.f = x + redux; - i0 = u.i2.lo + TBLSIZE / 2; - k.u = i0 / TBLSIZE * TBLSIZE; - k.i /= TBLSIZE; - i0 %= TBLSIZE; - u.f -= redux; - z = x - u.f; - - /* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */ - t = tbl[i0]; - z -= eps[i0]; - r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * (P5 + z * (P6 - + z * (P7 + z * (P8 + z * (P9 + z * P10))))))))); - - return scalbnl(r, k.i); -} -#endif diff --git a/src/math/exp_data.c b/src/math/exp_data.c deleted file mode 100644 index 21be014..0000000 --- a/src/math/exp_data.c +++ /dev/null @@ -1,182 +0,0 @@ -/* - * Shared data between exp, exp2 and pow. - * - * Copyright (c) 2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include "exp_data.h" - -#define N (1 << EXP_TABLE_BITS) - -const struct exp_data __exp_data = { -// N/ln2 -.invln2N = 0x1.71547652b82fep0 * N, -// -ln2/N -.negln2hiN = -0x1.62e42fefa0000p-8, -.negln2loN = -0x1.cf79abc9e3b3ap-47, -// Used for rounding when !TOINT_INTRINSICS -#if EXP_USE_TOINT_NARROW -.shift = 0x1800000000.8p0, -#else -.shift = 0x1.8p52, -#endif -// exp polynomial coefficients. -.poly = { -// abs error: 1.555*2^-66 -// ulp error: 0.509 (0.511 without fma) -// if |x| < ln2/256+eps -// abs error if |x| < ln2/256+0x1p-15: 1.09*2^-65 -// abs error if |x| < ln2/128: 1.7145*2^-56 -0x1.ffffffffffdbdp-2, -0x1.555555555543cp-3, -0x1.55555cf172b91p-5, -0x1.1111167a4d017p-7, -}, -.exp2_shift = 0x1.8p52 / N, -// exp2 polynomial coefficients. -.exp2_poly = { -// abs error: 1.2195*2^-65 -// ulp error: 0.507 (0.511 without fma) -// if |x| < 1/256 -// abs error if |x| < 1/128: 1.9941*2^-56 -0x1.62e42fefa39efp-1, -0x1.ebfbdff82c424p-3, -0x1.c6b08d70cf4b5p-5, -0x1.3b2abd24650ccp-7, -0x1.5d7e09b4e3a84p-10, -}, -// 2^(k/N) ~= H[k]*(1 + T[k]) for int k in [0,N) -// tab[2*k] = asuint64(T[k]) -// tab[2*k+1] = asuint64(H[k]) - (k << 52)/N -.tab = { -0x0, 0x3ff0000000000000, -0x3c9b3b4f1a88bf6e, 0x3feff63da9fb3335, -0xbc7160139cd8dc5d, 0x3fefec9a3e778061, -0xbc905e7a108766d1, 0x3fefe315e86e7f85, -0x3c8cd2523567f613, 0x3fefd9b0d3158574, -0xbc8bce8023f98efa, 0x3fefd06b29ddf6de, -0x3c60f74e61e6c861, 0x3fefc74518759bc8, -0x3c90a3e45b33d399, 0x3fefbe3ecac6f383, -0x3c979aa65d837b6d, 0x3fefb5586cf9890f, -0x3c8eb51a92fdeffc, 0x3fefac922b7247f7, -0x3c3ebe3d702f9cd1, 0x3fefa3ec32d3d1a2, -0xbc6a033489906e0b, 0x3fef9b66affed31b, -0xbc9556522a2fbd0e, 0x3fef9301d0125b51, -0xbc5080ef8c4eea55, 0x3fef8abdc06c31cc, -0xbc91c923b9d5f416, 0x3fef829aaea92de0, -0x3c80d3e3e95c55af, 0x3fef7a98c8a58e51, -0xbc801b15eaa59348, 0x3fef72b83c7d517b, -0xbc8f1ff055de323d, 0x3fef6af9388c8dea, -0x3c8b898c3f1353bf, 0x3fef635beb6fcb75, -0xbc96d99c7611eb26, 0x3fef5be084045cd4, -0x3c9aecf73e3a2f60, 0x3fef54873168b9aa, -0xbc8fe782cb86389d, 0x3fef4d5022fcd91d, -0x3c8a6f4144a6c38d, 0x3fef463b88628cd6, -0x3c807a05b0e4047d, 0x3fef3f49917ddc96, -0x3c968efde3a8a894, 0x3fef387a6e756238, -0x3c875e18f274487d, 0x3fef31ce4fb2a63f, -0x3c80472b981fe7f2, 0x3fef2b4565e27cdd, -0xbc96b87b3f71085e, 0x3fef24dfe1f56381, -0x3c82f7e16d09ab31, 0x3fef1e9df51fdee1, -0xbc3d219b1a6fbffa, 0x3fef187fd0dad990, -0x3c8b3782720c0ab4, 0x3fef1285a6e4030b, -0x3c6e149289cecb8f, 0x3fef0cafa93e2f56, -0x3c834d754db0abb6, 0x3fef06fe0a31b715, -0x3c864201e2ac744c, 0x3fef0170fc4cd831, -0x3c8fdd395dd3f84a, 0x3feefc08b26416ff, -0xbc86a3803b8e5b04, 0x3feef6c55f929ff1, -0xbc924aedcc4b5068, 0x3feef1a7373aa9cb, -0xbc9907f81b512d8e, 0x3feeecae6d05d866, -0xbc71d1e83e9436d2, 0x3feee7db34e59ff7, -0xbc991919b3ce1b15, 0x3feee32dc313a8e5, -0x3c859f48a72a4c6d, 0x3feedea64c123422, -0xbc9312607a28698a, 0x3feeda4504ac801c, -0xbc58a78f4817895b, 0x3feed60a21f72e2a, -0xbc7c2c9b67499a1b, 0x3feed1f5d950a897, -0x3c4363ed60c2ac11, 0x3feece086061892d, -0x3c9666093b0664ef, 0x3feeca41ed1d0057, -0x3c6ecce1daa10379, 0x3feec6a2b5c13cd0, -0x3c93ff8e3f0f1230, 0x3feec32af0d7d3de, -0x3c7690cebb7aafb0, 0x3feebfdad5362a27, -0x3c931dbdeb54e077, 0x3feebcb299fddd0d, -0xbc8f94340071a38e, 0x3feeb9b2769d2ca7, -0xbc87deccdc93a349, 0x3feeb6daa2cf6642, -0xbc78dec6bd0f385f, 0x3feeb42b569d4f82, -0xbc861246ec7b5cf6, 0x3feeb1a4ca5d920f, -0x3c93350518fdd78e, 0x3feeaf4736b527da, -0x3c7b98b72f8a9b05, 0x3feead12d497c7fd, -0x3c9063e1e21c5409, 0x3feeab07dd485429, -0x3c34c7855019c6ea, 0x3feea9268a5946b7, -0x3c9432e62b64c035, 0x3feea76f15ad2148, -0xbc8ce44a6199769f, 0x3feea5e1b976dc09, -0xbc8c33c53bef4da8, 0x3feea47eb03a5585, -0xbc845378892be9ae, 0x3feea34634ccc320, -0xbc93cedd78565858, 0x3feea23882552225, -0x3c5710aa807e1964, 0x3feea155d44ca973, -0xbc93b3efbf5e2228, 0x3feea09e667f3bcd, -0xbc6a12ad8734b982, 0x3feea012750bdabf, -0xbc6367efb86da9ee, 0x3fee9fb23c651a2f, -0xbc80dc3d54e08851, 0x3fee9f7df9519484, -0xbc781f647e5a3ecf, 0x3fee9f75e8ec5f74, -0xbc86ee4ac08b7db0, 0x3fee9f9a48a58174, -0xbc8619321e55e68a, 0x3fee9feb564267c9, -0x3c909ccb5e09d4d3, 0x3feea0694fde5d3f, -0xbc7b32dcb94da51d, 0x3feea11473eb0187, -0x3c94ecfd5467c06b, 0x3feea1ed0130c132, -0x3c65ebe1abd66c55, 0x3feea2f336cf4e62, -0xbc88a1c52fb3cf42, 0x3feea427543e1a12, -0xbc9369b6f13b3734, 0x3feea589994cce13, -0xbc805e843a19ff1e, 0x3feea71a4623c7ad, -0xbc94d450d872576e, 0x3feea8d99b4492ed, -0x3c90ad675b0e8a00, 0x3feeaac7d98a6699, -0x3c8db72fc1f0eab4, 0x3feeace5422aa0db, -0xbc65b6609cc5e7ff, 0x3feeaf3216b5448c, -0x3c7bf68359f35f44, 0x3feeb1ae99157736, -0xbc93091fa71e3d83, 0x3feeb45b0b91ffc6, -0xbc5da9b88b6c1e29, 0x3feeb737b0cdc5e5, -0xbc6c23f97c90b959, 0x3feeba44cbc8520f, -0xbc92434322f4f9aa, 0x3feebd829fde4e50, -0xbc85ca6cd7668e4b, 0x3feec0f170ca07ba, -0x3c71affc2b91ce27, 0x3feec49182a3f090, -0x3c6dd235e10a73bb, 0x3feec86319e32323, -0xbc87c50422622263, 0x3feecc667b5de565, -0x3c8b1c86e3e231d5, 0x3feed09bec4a2d33, -0xbc91bbd1d3bcbb15, 0x3feed503b23e255d, -0x3c90cc319cee31d2, 0x3feed99e1330b358, -0x3c8469846e735ab3, 0x3feede6b5579fdbf, -0xbc82dfcd978e9db4, 0x3feee36bbfd3f37a, -0x3c8c1a7792cb3387, 0x3feee89f995ad3ad, -0xbc907b8f4ad1d9fa, 0x3feeee07298db666, -0xbc55c3d956dcaeba, 0x3feef3a2b84f15fb, -0xbc90a40e3da6f640, 0x3feef9728de5593a, -0xbc68d6f438ad9334, 0x3feeff76f2fb5e47, -0xbc91eee26b588a35, 0x3fef05b030a1064a, -0x3c74ffd70a5fddcd, 0x3fef0c1e904bc1d2, -0xbc91bdfbfa9298ac, 0x3fef12c25bd71e09, -0x3c736eae30af0cb3, 0x3fef199bdd85529c, -0x3c8ee3325c9ffd94, 0x3fef20ab5fffd07a, -0x3c84e08fd10959ac, 0x3fef27f12e57d14b, -0x3c63cdaf384e1a67, 0x3fef2f6d9406e7b5, -0x3c676b2c6c921968, 0x3fef3720dcef9069, -0xbc808a1883ccb5d2, 0x3fef3f0b555dc3fa, -0xbc8fad5d3ffffa6f, 0x3fef472d4a07897c, -0xbc900dae3875a949, 0x3fef4f87080d89f2, -0x3c74a385a63d07a7, 0x3fef5818dcfba487, -0xbc82919e2040220f, 0x3fef60e316c98398, -0x3c8e5a50d5c192ac, 0x3fef69e603db3285, -0x3c843a59ac016b4b, 0x3fef7321f301b460, -0xbc82d52107b43e1f, 0x3fef7c97337b9b5f, -0xbc892ab93b470dc9, 0x3fef864614f5a129, -0x3c74b604603a88d3, 0x3fef902ee78b3ff6, -0x3c83c5ec519d7271, 0x3fef9a51fbc74c83, -0xbc8ff7128fd391f0, 0x3fefa4afa2a490da, -0xbc8dae98e223747d, 0x3fefaf482d8e67f1, -0x3c8ec3bc41aa2008, 0x3fefba1bee615a27, -0x3c842b94c3a9eb32, 0x3fefc52b376bba97, -0x3c8a64a931d185ee, 0x3fefd0765b6e4540, -0xbc8e37bae43be3ed, 0x3fefdbfdad9cbe14, -0x3c77893b4d91cd9d, 0x3fefe7c1819e90d8, -0x3c5305c14160cc89, 0x3feff3c22b8f71f1, -}, -}; diff --git a/src/math/exp_data.h b/src/math/exp_data.h deleted file mode 100644 index 3e24bac..0000000 --- a/src/math/exp_data.h +++ /dev/null @@ -1,26 +0,0 @@ -/* - * Copyright (c) 2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ -#ifndef _EXP_DATA_H -#define _EXP_DATA_H - -#include -#include - -#define EXP_TABLE_BITS 7 -#define EXP_POLY_ORDER 5 -#define EXP_USE_TOINT_NARROW 0 -#define EXP2_POLY_ORDER 5 -extern hidden const struct exp_data { - double invln2N; - double shift; - double negln2hiN; - double negln2loN; - double poly[4]; /* Last four coefficients. */ - double exp2_shift; - double exp2_poly[EXP2_POLY_ORDER]; - uint64_t tab[2*(1 << EXP_TABLE_BITS)]; -} __exp_data; - -#endif diff --git a/src/math/expf.c b/src/math/expf.c deleted file mode 100644 index f9fbf8e..0000000 --- a/src/math/expf.c +++ /dev/null @@ -1,80 +0,0 @@ -/* - * Single-precision e^x function. - * - * Copyright (c) 2017-2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include -#include -#include "libm.h" -#include "exp2f_data.h" - -/* -EXP2F_TABLE_BITS = 5 -EXP2F_POLY_ORDER = 3 - -ULP error: 0.502 (nearest rounding.) -Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.) -Wrong count: 170635 (all nearest rounding wrong results with fma.) -Non-nearest ULP error: 1 (rounded ULP error) -*/ - -#define N (1 << EXP2F_TABLE_BITS) -#define InvLn2N __exp2f_data.invln2_scaled -#define T __exp2f_data.tab -#define C __exp2f_data.poly_scaled - -static inline uint32_t top12(float x) -{ - return asuint(x) >> 20; -} - -float expf(float x) -{ - uint32_t abstop; - uint64_t ki, t; - double_t kd, xd, z, r, r2, y, s; - - xd = (double_t)x; - abstop = top12(x) & 0x7ff; - if (predict_false(abstop >= top12(88.0f))) { - /* |x| >= 88 or x is nan. */ - if (asuint(x) == asuint(-INFINITY)) - return 0.0f; - if (abstop >= top12(INFINITY)) - return x + x; - if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */ - return __math_oflowf(0); - if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */ - return __math_uflowf(0); - } - - /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */ - z = InvLn2N * xd; - - /* Round and convert z to int, the result is in [-150*N, 128*N] and - ideally ties-to-even rule is used, otherwise the magnitude of r - can be bigger which gives larger approximation error. */ -#if TOINT_INTRINSICS - kd = roundtoint(z); - ki = converttoint(z); -#else -# define SHIFT __exp2f_data.shift - kd = eval_as_double(z + SHIFT); - ki = asuint64(kd); - kd -= SHIFT; -#endif - r = z - kd; - - /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ - t = T[ki % N]; - t += ki << (52 - EXP2F_TABLE_BITS); - s = asdouble(t); - z = C[0] * r + C[1]; - r2 = r * r; - y = C[2] * r + 1; - y = z * r2 + y; - y = y * s; - return eval_as_float(y); -} diff --git a/src/math/expl.c b/src/math/expl.c deleted file mode 100644 index 0a7f44f..0000000 --- a/src/math/expl.c +++ /dev/null @@ -1,128 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expl.c */ -/* - * Copyright (c) 2008 Stephen L. Moshier - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. - * - * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES - * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR - * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES - * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN - * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF - * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - */ -/* - * Exponential function, long double precision - * - * - * SYNOPSIS: - * - * long double x, y, expl(); - * - * y = expl( x ); - * - * - * DESCRIPTION: - * - * Returns e (2.71828...) raised to the x power. - * - * Range reduction is accomplished by separating the argument - * into an integer k and fraction f such that - * - * x k f - * e = 2 e. - * - * A Pade' form of degree 5/6 is used to approximate exp(f) - 1 - * in the basic range [-0.5 ln 2, 0.5 ln 2]. - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE +-10000 50000 1.12e-19 2.81e-20 - * - * - * Error amplification in the exponential function can be - * a serious matter. The error propagation involves - * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ), - * which shows that a 1 lsb error in representing X produces - * a relative error of X times 1 lsb in the function. - * While the routine gives an accurate result for arguments - * that are exactly represented by a long double precision - * computer number, the result contains amplified roundoff - * error for large arguments not exactly represented. - * - * - * ERROR MESSAGES: - * - * message condition value returned - * exp underflow x < MINLOG 0.0 - * exp overflow x > MAXLOG MAXNUM - * - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double expl(long double x) -{ - return exp(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 - -static const long double P[3] = { - 1.2617719307481059087798E-4L, - 3.0299440770744196129956E-2L, - 9.9999999999999999991025E-1L, -}; -static const long double Q[4] = { - 3.0019850513866445504159E-6L, - 2.5244834034968410419224E-3L, - 2.2726554820815502876593E-1L, - 2.0000000000000000000897E0L, -}; -static const long double -LN2HI = 6.9314575195312500000000E-1L, -LN2LO = 1.4286068203094172321215E-6L, -LOG2E = 1.4426950408889634073599E0L; - -long double expl(long double x) -{ - long double px, xx; - int k; - - if (isnan(x)) - return x; - if (x > 11356.5234062941439488L) /* x > ln(2^16384 - 0.5) */ - return x * 0x1p16383L; - if (x < -11399.4985314888605581L) /* x < ln(2^-16446) */ - return -0x1p-16445L/x; - - /* Express e**x = e**f 2**k - * = e**(f + k ln(2)) - */ - px = floorl(LOG2E * x + 0.5); - k = px; - x -= px * LN2HI; - x -= px * LN2LO; - - /* rational approximation of the fractional part: - * e**x = 1 + 2x P(x**2)/(Q(x**2) - x P(x**2)) - */ - xx = x * x; - px = x * __polevll(xx, P, 2); - x = px/(__polevll(xx, Q, 3) - px); - x = 1.0 + 2.0 * x; - return scalbnl(x, k); -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double expl(long double x) -{ - return exp(x); -} -#endif diff --git a/src/math/expm1.c b/src/math/expm1.c deleted file mode 100644 index ac1e61e..0000000 --- a/src/math/expm1.c +++ /dev/null @@ -1,201 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* expm1(x) - * Returns exp(x)-1, the exponential of x minus 1. - * - * Method - * 1. Argument reduction: - * Given x, find r and integer k such that - * - * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 - * - * Here a correction term c will be computed to compensate - * the error in r when rounded to a floating-point number. - * - * 2. Approximating expm1(r) by a special rational function on - * the interval [0,0.34658]: - * Since - * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ... - * we define R1(r*r) by - * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r) - * That is, - * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r) - * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r)) - * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... - * We use a special Remez algorithm on [0,0.347] to generate - * a polynomial of degree 5 in r*r to approximate R1. The - * maximum error of this polynomial approximation is bounded - * by 2**-61. In other words, - * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 - * where Q1 = -1.6666666666666567384E-2, - * Q2 = 3.9682539681370365873E-4, - * Q3 = -9.9206344733435987357E-6, - * Q4 = 2.5051361420808517002E-7, - * Q5 = -6.2843505682382617102E-9; - * z = r*r, - * with error bounded by - * | 5 | -61 - * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 - * | | - * - * expm1(r) = exp(r)-1 is then computed by the following - * specific way which minimize the accumulation rounding error: - * 2 3 - * r r [ 3 - (R1 + R1*r/2) ] - * expm1(r) = r + --- + --- * [--------------------] - * 2 2 [ 6 - r*(3 - R1*r/2) ] - * - * To compensate the error in the argument reduction, we use - * expm1(r+c) = expm1(r) + c + expm1(r)*c - * ~ expm1(r) + c + r*c - * Thus c+r*c will be added in as the correction terms for - * expm1(r+c). Now rearrange the term to avoid optimization - * screw up: - * ( 2 2 ) - * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) - * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) - * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) - * ( ) - * - * = r - E - * 3. Scale back to obtain expm1(x): - * From step 1, we have - * expm1(x) = either 2^k*[expm1(r)+1] - 1 - * = or 2^k*[expm1(r) + (1-2^-k)] - * 4. Implementation notes: - * (A). To save one multiplication, we scale the coefficient Qi - * to Qi*2^i, and replace z by (x^2)/2. - * (B). To achieve maximum accuracy, we compute expm1(x) by - * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf) - * (ii) if k=0, return r-E - * (iii) if k=-1, return 0.5*(r-E)-0.5 - * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) - * else return 1.0+2.0*(r-E); - * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1) - * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else - * (vii) return 2^k(1-((E+2^-k)-r)) - * - * Special cases: - * expm1(INF) is INF, expm1(NaN) is NaN; - * expm1(-INF) is -1, and - * for finite argument, only expm1(0)=0 is exact. - * - * Accuracy: - * according to an error analysis, the error is always less than - * 1 ulp (unit in the last place). - * - * Misc. info. - * For IEEE double - * if x > 7.09782712893383973096e+02 then expm1(x) overflow - * - * Constants: - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough - * to produce the hexadecimal values shown. - */ - -#include "libm.h" - -static const double -o_threshold = 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ -ln2_hi = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ -ln2_lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ -invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ -/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */ -Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */ -Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ -Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ -Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ -Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ - -double expm1(double x) -{ - double_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk; - union {double f; uint64_t i;} u = {x}; - uint32_t hx = u.i>>32 & 0x7fffffff; - int k, sign = u.i>>63; - - /* filter out huge and non-finite argument */ - if (hx >= 0x4043687A) { /* if |x|>=56*ln2 */ - if (isnan(x)) - return x; - if (sign) - return -1; - if (x > o_threshold) { - x *= 0x1p1023; - return x; - } - } - - /* argument reduction */ - if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ - if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ - if (!sign) { - hi = x - ln2_hi; - lo = ln2_lo; - k = 1; - } else { - hi = x + ln2_hi; - lo = -ln2_lo; - k = -1; - } - } else { - k = invln2*x + (sign ? -0.5 : 0.5); - t = k; - hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ - lo = t*ln2_lo; - } - x = hi-lo; - c = (hi-x)-lo; - } else if (hx < 0x3c900000) { /* |x| < 2**-54, return x */ - if (hx < 0x00100000) - FORCE_EVAL((float)x); - return x; - } else - k = 0; - - /* x is now in primary range */ - hfx = 0.5*x; - hxs = x*hfx; - r1 = 1.0+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); - t = 3.0-r1*hfx; - e = hxs*((r1-t)/(6.0 - x*t)); - if (k == 0) /* c is 0 */ - return x - (x*e-hxs); - e = x*(e-c) - c; - e -= hxs; - /* exp(x) ~ 2^k (x_reduced - e + 1) */ - if (k == -1) - return 0.5*(x-e) - 0.5; - if (k == 1) { - if (x < -0.25) - return -2.0*(e-(x+0.5)); - return 1.0+2.0*(x-e); - } - u.i = (uint64_t)(0x3ff + k)<<52; /* 2^k */ - twopk = u.f; - if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */ - y = x - e + 1.0; - if (k == 1024) - y = y*2.0*0x1p1023; - else - y = y*twopk; - return y - 1.0; - } - u.i = (uint64_t)(0x3ff - k)<<52; /* 2^-k */ - if (k < 20) - y = (x-e+(1-u.f))*twopk; - else - y = (x-(e+u.f)+1)*twopk; - return y; -} diff --git a/src/math/expm1f.c b/src/math/expm1f.c deleted file mode 100644 index 297e0b4..0000000 --- a/src/math/expm1f.c +++ /dev/null @@ -1,111 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -static const float -o_threshold = 8.8721679688e+01, /* 0x42b17180 */ -ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ -ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ -invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ -/* - * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]: - * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04 - * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c): - */ -Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */ -Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */ - -float expm1f(float x) -{ - float_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk; - union {float f; uint32_t i;} u = {x}; - uint32_t hx = u.i & 0x7fffffff; - int k, sign = u.i >> 31; - - /* filter out huge and non-finite argument */ - if (hx >= 0x4195b844) { /* if |x|>=27*ln2 */ - if (hx > 0x7f800000) /* NaN */ - return x; - if (sign) - return -1; - if (x > o_threshold) { - x *= 0x1p127f; - return x; - } - } - - /* argument reduction */ - if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ - if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ - if (!sign) { - hi = x - ln2_hi; - lo = ln2_lo; - k = 1; - } else { - hi = x + ln2_hi; - lo = -ln2_lo; - k = -1; - } - } else { - k = invln2*x + (sign ? -0.5f : 0.5f); - t = k; - hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ - lo = t*ln2_lo; - } - x = hi-lo; - c = (hi-x)-lo; - } else if (hx < 0x33000000) { /* when |x|<2**-25, return x */ - if (hx < 0x00800000) - FORCE_EVAL(x*x); - return x; - } else - k = 0; - - /* x is now in primary range */ - hfx = 0.5f*x; - hxs = x*hfx; - r1 = 1.0f+hxs*(Q1+hxs*Q2); - t = 3.0f - r1*hfx; - e = hxs*((r1-t)/(6.0f - x*t)); - if (k == 0) /* c is 0 */ - return x - (x*e-hxs); - e = x*(e-c) - c; - e -= hxs; - /* exp(x) ~ 2^k (x_reduced - e + 1) */ - if (k == -1) - return 0.5f*(x-e) - 0.5f; - if (k == 1) { - if (x < -0.25f) - return -2.0f*(e-(x+0.5f)); - return 1.0f + 2.0f*(x-e); - } - u.i = (0x7f+k)<<23; /* 2^k */ - twopk = u.f; - if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */ - y = x - e + 1.0f; - if (k == 128) - y = y*2.0f*0x1p127f; - else - y = y*twopk; - return y - 1.0f; - } - u.i = (0x7f-k)<<23; /* 2^-k */ - if (k < 23) - y = (x-e+(1-u.f))*twopk; - else - y = (x-(e+u.f)+1)*twopk; - return y; -} diff --git a/src/math/expm1l.c b/src/math/expm1l.c deleted file mode 100644 index d171507..0000000 --- a/src/math/expm1l.c +++ /dev/null @@ -1,123 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expm1l.c */ -/* - * Copyright (c) 2008 Stephen L. Moshier - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. - * - * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES - * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR - * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES - * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN - * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF - * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - */ -/* - * Exponential function, minus 1 - * Long double precision - * - * - * SYNOPSIS: - * - * long double x, y, expm1l(); - * - * y = expm1l( x ); - * - * - * DESCRIPTION: - * - * Returns e (2.71828...) raised to the x power, minus 1. - * - * Range reduction is accomplished by separating the argument - * into an integer k and fraction f such that - * - * x k f - * e = 2 e. - * - * An expansion x + .5 x^2 + x^3 R(x) approximates exp(f) - 1 - * in the basic range [-0.5 ln 2, 0.5 ln 2]. - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE -45,+maxarg 200,000 1.2e-19 2.5e-20 - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double expm1l(long double x) -{ - return expm1(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 - -/* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x) - -.5 ln 2 < x < .5 ln 2 - Theoretical peak relative error = 3.4e-22 */ -static const long double -P0 = -1.586135578666346600772998894928250240826E4L, -P1 = 2.642771505685952966904660652518429479531E3L, -P2 = -3.423199068835684263987132888286791620673E2L, -P3 = 1.800826371455042224581246202420972737840E1L, -P4 = -5.238523121205561042771939008061958820811E-1L, -Q0 = -9.516813471998079611319047060563358064497E4L, -Q1 = 3.964866271411091674556850458227710004570E4L, -Q2 = -7.207678383830091850230366618190187434796E3L, -Q3 = 7.206038318724600171970199625081491823079E2L, -Q4 = -4.002027679107076077238836622982900945173E1L, -/* Q5 = 1.000000000000000000000000000000000000000E0 */ -/* C1 + C2 = ln 2 */ -C1 = 6.93145751953125E-1L, -C2 = 1.428606820309417232121458176568075500134E-6L, -/* ln 2^-65 */ -minarg = -4.5054566736396445112120088E1L, -/* ln 2^16384 */ -maxarg = 1.1356523406294143949492E4L; - -long double expm1l(long double x) -{ - long double px, qx, xx; - int k; - - if (isnan(x)) - return x; - if (x > maxarg) - return x*0x1p16383L; /* overflow, unless x==inf */ - if (x == 0.0) - return x; - if (x < minarg) - return -1.0; - - xx = C1 + C2; - /* Express x = ln 2 (k + remainder), remainder not exceeding 1/2. */ - px = floorl(0.5 + x / xx); - k = px; - /* remainder times ln 2 */ - x -= px * C1; - x -= px * C2; - - /* Approximate exp(remainder ln 2).*/ - px = (((( P4 * x + P3) * x + P2) * x + P1) * x + P0) * x; - qx = (((( x + Q4) * x + Q3) * x + Q2) * x + Q1) * x + Q0; - xx = x * x; - qx = x + (0.5 * xx + xx * px / qx); - - /* exp(x) = exp(k ln 2) exp(remainder ln 2) = 2^k exp(remainder ln 2). - We have qx = exp(remainder ln 2) - 1, so - exp(x) - 1 = 2^k (qx + 1) - 1 = 2^k qx + 2^k - 1. */ - px = scalbnl(1.0, k); - x = px * qx + (px - 1.0); - return x; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double expm1l(long double x) -{ - return expm1(x); -} -#endif diff --git a/src/math/fabs.c b/src/math/fabs.c deleted file mode 100644 index e8258cf..0000000 --- a/src/math/fabs.c +++ /dev/null @@ -1,9 +0,0 @@ -#include -#include - -double fabs(double x) -{ - union {double f; uint64_t i;} u = {x}; - u.i &= -1ULL/2; - return u.f; -} diff --git a/src/math/fabsf.c b/src/math/fabsf.c deleted file mode 100644 index 4efc8d6..0000000 --- a/src/math/fabsf.c +++ /dev/null @@ -1,9 +0,0 @@ -#include -#include - -float fabsf(float x) -{ - union {float f; uint32_t i;} u = {x}; - u.i &= 0x7fffffff; - return u.f; -} diff --git a/src/math/fabsl.c b/src/math/fabsl.c deleted file mode 100644 index c4f36ec..0000000 --- a/src/math/fabsl.c +++ /dev/null @@ -1,15 +0,0 @@ -#include "libm.h" -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double fabsl(long double x) -{ - return fabs(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -long double fabsl(long double x) -{ - union ldshape u = {x}; - - u.i.se &= 0x7fff; - return u.f; -} -#endif diff --git a/src/math/fdim.c b/src/math/fdim.c deleted file mode 100644 index 9585460..0000000 --- a/src/math/fdim.c +++ /dev/null @@ -1,10 +0,0 @@ -#include - -double fdim(double x, double y) -{ - if (isnan(x)) - return x; - if (isnan(y)) - return y; - return x > y ? x - y : 0; -} diff --git a/src/math/fdimf.c b/src/math/fdimf.c deleted file mode 100644 index 543c364..0000000 --- a/src/math/fdimf.c +++ /dev/null @@ -1,10 +0,0 @@ -#include - -float fdimf(float x, float y) -{ - if (isnan(x)) - return x; - if (isnan(y)) - return y; - return x > y ? x - y : 0; -} diff --git a/src/math/fdiml.c b/src/math/fdiml.c deleted file mode 100644 index 62e29b7..0000000 --- a/src/math/fdiml.c +++ /dev/null @@ -1,18 +0,0 @@ -#include -#include - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double fdiml(long double x, long double y) -{ - return fdim(x, y); -} -#else -long double fdiml(long double x, long double y) -{ - if (isnan(x)) - return x; - if (isnan(y)) - return y; - return x > y ? x - y : 0; -} -#endif diff --git a/src/math/finite.c b/src/math/finite.c deleted file mode 100644 index 25a0575..0000000 --- a/src/math/finite.c +++ /dev/null @@ -1,7 +0,0 @@ -#define _GNU_SOURCE -#include - -int finite(double x) -{ - return isfinite(x); -} diff --git a/src/math/finitef.c b/src/math/finitef.c deleted file mode 100644 index 2c4c771..0000000 --- a/src/math/finitef.c +++ /dev/null @@ -1,7 +0,0 @@ -#define _GNU_SOURCE -#include - -int finitef(float x) -{ - return isfinite(x); -} diff --git a/src/math/floor.c b/src/math/floor.c deleted file mode 100644 index 14a31cd..0000000 --- a/src/math/floor.c +++ /dev/null @@ -1,31 +0,0 @@ -#include "libm.h" - -#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 -#define EPS DBL_EPSILON -#elif FLT_EVAL_METHOD==2 -#define EPS LDBL_EPSILON -#endif -static const double_t toint = 1/EPS; - -double floor(double x) -{ - union {double f; uint64_t i;} u = {x}; - int e = u.i >> 52 & 0x7ff; - double_t y; - - if (e >= 0x3ff+52 || x == 0) - return x; - /* y = int(x) - x, where int(x) is an integer neighbor of x */ - if (u.i >> 63) - y = x - toint + toint - x; - else - y = x + toint - toint - x; - /* special case because of non-nearest rounding modes */ - if (e <= 0x3ff-1) { - FORCE_EVAL(y); - return u.i >> 63 ? -1 : 0; - } - if (y > 0) - return x + y - 1; - return x + y; -} diff --git a/src/math/floorf.c b/src/math/floorf.c deleted file mode 100644 index dceec73..0000000 --- a/src/math/floorf.c +++ /dev/null @@ -1,27 +0,0 @@ -#include "libm.h" - -float floorf(float x) -{ - union {float f; uint32_t i;} u = {x}; - int e = (int)(u.i >> 23 & 0xff) - 0x7f; - uint32_t m; - - if (e >= 23) - return x; - if (e >= 0) { - m = 0x007fffff >> e; - if ((u.i & m) == 0) - return x; - FORCE_EVAL(x + 0x1p120f); - if (u.i >> 31) - u.i += m; - u.i &= ~m; - } else { - FORCE_EVAL(x + 0x1p120f); - if (u.i >> 31 == 0) - u.i = 0; - else if (u.i << 1) - u.f = -1.0; - } - return u.f; -} diff --git a/src/math/floorl.c b/src/math/floorl.c deleted file mode 100644 index 16aaec4..0000000 --- a/src/math/floorl.c +++ /dev/null @@ -1,34 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double floorl(long double x) -{ - return floor(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 - -static const long double toint = 1/LDBL_EPSILON; - -long double floorl(long double x) -{ - union ldshape u = {x}; - int e = u.i.se & 0x7fff; - long double y; - - if (e >= 0x3fff+LDBL_MANT_DIG-1 || x == 0) - return x; - /* y = int(x) - x, where int(x) is an integer neighbor of x */ - if (u.i.se >> 15) - y = x - toint + toint - x; - else - y = x + toint - toint - x; - /* special case because of non-nearest rounding modes */ - if (e <= 0x3fff-1) { - FORCE_EVAL(y); - return u.i.se >> 15 ? -1 : 0; - } - if (y > 0) - return x + y - 1; - return x + y; -} -#endif diff --git a/src/math/fma.c b/src/math/fma.c deleted file mode 100644 index 0c6f90c..0000000 --- a/src/math/fma.c +++ /dev/null @@ -1,183 +0,0 @@ -#include -#include -#include -#include "atomic.h" - -#define ASUINT64(x) ((union {double f; uint64_t i;}){x}).i -#define ZEROINFNAN (0x7ff-0x3ff-52-1) - -struct num { uint64_t m; int e; int sign; }; - -static struct num normalize(double x) -{ - uint64_t ix = ASUINT64(x); - int e = ix>>52; - int sign = e & 0x800; - e &= 0x7ff; - if (!e) { - ix = ASUINT64(x*0x1p63); - e = ix>>52 & 0x7ff; - e = e ? e-63 : 0x800; - } - ix &= (1ull<<52)-1; - ix |= 1ull<<52; - ix <<= 1; - e -= 0x3ff + 52 + 1; - return (struct num){ix,e,sign}; -} - -static void mul(uint64_t *hi, uint64_t *lo, uint64_t x, uint64_t y) -{ - uint64_t t1,t2,t3; - uint64_t xlo = (uint32_t)x, xhi = x>>32; - uint64_t ylo = (uint32_t)y, yhi = y>>32; - - t1 = xlo*ylo; - t2 = xlo*yhi + xhi*ylo; - t3 = xhi*yhi; - *lo = t1 + (t2<<32); - *hi = t3 + (t2>>32) + (t1 > *lo); -} - -double fma(double x, double y, double z) -{ - #pragma STDC FENV_ACCESS ON - - /* normalize so top 10bits and last bit are 0 */ - struct num nx, ny, nz; - nx = normalize(x); - ny = normalize(y); - nz = normalize(z); - - if (nx.e >= ZEROINFNAN || ny.e >= ZEROINFNAN) - return x*y + z; - if (nz.e >= ZEROINFNAN) { - if (nz.e > ZEROINFNAN) /* z==0 */ - return x*y + z; - return z; - } - - /* mul: r = x*y */ - uint64_t rhi, rlo, zhi, zlo; - mul(&rhi, &rlo, nx.m, ny.m); - /* either top 20 or 21 bits of rhi and last 2 bits of rlo are 0 */ - - /* align exponents */ - int e = nx.e + ny.e; - int d = nz.e - e; - /* shift bits z<<=kz, r>>=kr, so kz+kr == d, set e = e+kr (== ez-kz) */ - if (d > 0) { - if (d < 64) { - zlo = nz.m<>64-d; - } else { - zlo = 0; - zhi = nz.m; - e = nz.e - 64; - d -= 64; - if (d == 0) { - } else if (d < 64) { - rlo = rhi<<64-d | rlo>>d | !!(rlo<<64-d); - rhi = rhi>>d; - } else { - rlo = 1; - rhi = 0; - } - } - } else { - zhi = 0; - d = -d; - if (d == 0) { - zlo = nz.m; - } else if (d < 64) { - zlo = nz.m>>d | !!(nz.m<<64-d); - } else { - zlo = 1; - } - } - - /* add */ - int sign = nx.sign^ny.sign; - int samesign = !(sign^nz.sign); - int nonzero = 1; - if (samesign) { - /* r += z */ - rlo += zlo; - rhi += zhi + (rlo < zlo); - } else { - /* r -= z */ - uint64_t t = rlo; - rlo -= zlo; - rhi = rhi - zhi - (t < rlo); - if (rhi>>63) { - rlo = -rlo; - rhi = -rhi-!!rlo; - sign = !sign; - } - nonzero = !!rhi; - } - - /* set rhi to top 63bit of the result (last bit is sticky) */ - if (nonzero) { - e += 64; - d = a_clz_64(rhi)-1; - /* note: d > 0 */ - rhi = rhi<>64-d | !!(rlo<>1 | (rlo&1); - else - rhi = rlo<>1 | (rhi&1) | 1ull<<62; - if (sign) - i = -i; - r = i; - r = 2*r - c; /* remove top bit */ - - /* raise underflow portably, such that it - cannot be optimized away */ - { - double_t tiny = DBL_MIN/FLT_MIN * r; - r += (double)(tiny*tiny) * (r-r); - } - } - } else { - /* only round once when scaled */ - d = 10; - i = ( rhi>>d | !!(rhi<<64-d) ) << d; - if (sign) - i = -i; - r = i; - } - } - return scalbn(r, e); -} diff --git a/src/math/fmaf.c b/src/math/fmaf.c deleted file mode 100644 index 80f5cd8..0000000 --- a/src/math/fmaf.c +++ /dev/null @@ -1,93 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_fmaf.c */ -/*- - * Copyright (c) 2005-2011 David Schultz - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - -#include -#include -#include - -/* - * Fused multiply-add: Compute x * y + z with a single rounding error. - * - * A double has more than twice as much precision than a float, so - * direct double-precision arithmetic suffices, except where double - * rounding occurs. - */ -float fmaf(float x, float y, float z) -{ - #pragma STDC FENV_ACCESS ON - double xy, result; - union {double f; uint64_t i;} u; - int e; - - xy = (double)x * y; - result = xy + z; - u.f = result; - e = u.i>>52 & 0x7ff; - /* Common case: The double precision result is fine. */ - if ((u.i & 0x1fffffff) != 0x10000000 || /* not a halfway case */ - e == 0x7ff || /* NaN */ - (result - xy == z && result - z == xy) || /* exact */ - fegetround() != FE_TONEAREST) /* not round-to-nearest */ - { - /* - underflow may not be raised correctly, example: - fmaf(0x1p-120f, 0x1p-120f, 0x1p-149f) - */ -#if defined(FE_INEXACT) && defined(FE_UNDERFLOW) - if (e < 0x3ff-126 && e >= 0x3ff-149 && fetestexcept(FE_INEXACT)) { - feclearexcept(FE_INEXACT); - /* TODO: gcc and clang bug workaround */ - volatile float vz = z; - result = xy + vz; - if (fetestexcept(FE_INEXACT)) - feraiseexcept(FE_UNDERFLOW); - else - feraiseexcept(FE_INEXACT); - } -#endif - z = result; - return z; - } - - /* - * If result is inexact, and exactly halfway between two float values, - * we need to adjust the low-order bit in the direction of the error. - */ -#ifdef FE_TOWARDZERO - fesetround(FE_TOWARDZERO); -#endif - volatile double vxy = xy; /* XXX work around gcc CSE bug */ - double adjusted_result = vxy + z; - fesetround(FE_TONEAREST); - if (result == adjusted_result) { - u.f = adjusted_result; - u.i++; - adjusted_result = u.f; - } - z = adjusted_result; - return z; -} diff --git a/src/math/fmal.c b/src/math/fmal.c deleted file mode 100644 index 4506aac..0000000 --- a/src/math/fmal.c +++ /dev/null @@ -1,293 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_fmal.c */ -/*- - * Copyright (c) 2005-2011 David Schultz - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - - -#include "libm.h" -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double fmal(long double x, long double y, long double z) -{ - return fma(x, y, z); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -#include -#if LDBL_MANT_DIG == 64 -#define LASTBIT(u) (u.i.m & 1) -#define SPLIT (0x1p32L + 1) -#elif LDBL_MANT_DIG == 113 -#define LASTBIT(u) (u.i.lo & 1) -#define SPLIT (0x1p57L + 1) -#endif - -/* - * A struct dd represents a floating-point number with twice the precision - * of a long double. We maintain the invariant that "hi" stores the high-order - * bits of the result. - */ -struct dd { - long double hi; - long double lo; -}; - -/* - * Compute a+b exactly, returning the exact result in a struct dd. We assume - * that both a and b are finite, but make no assumptions about their relative - * magnitudes. - */ -static inline struct dd dd_add(long double a, long double b) -{ - struct dd ret; - long double s; - - ret.hi = a + b; - s = ret.hi - a; - ret.lo = (a - (ret.hi - s)) + (b - s); - return (ret); -} - -/* - * Compute a+b, with a small tweak: The least significant bit of the - * result is adjusted into a sticky bit summarizing all the bits that - * were lost to rounding. This adjustment negates the effects of double - * rounding when the result is added to another number with a higher - * exponent. For an explanation of round and sticky bits, see any reference - * on FPU design, e.g., - * - * J. Coonen. An Implementation Guide to a Proposed Standard for - * Floating-Point Arithmetic. Computer, vol. 13, no. 1, Jan 1980. - */ -static inline long double add_adjusted(long double a, long double b) -{ - struct dd sum; - union ldshape u; - - sum = dd_add(a, b); - if (sum.lo != 0) { - u.f = sum.hi; - if (!LASTBIT(u)) - sum.hi = nextafterl(sum.hi, INFINITY * sum.lo); - } - return (sum.hi); -} - -/* - * Compute ldexp(a+b, scale) with a single rounding error. It is assumed - * that the result will be subnormal, and care is taken to ensure that - * double rounding does not occur. - */ -static inline long double add_and_denormalize(long double a, long double b, int scale) -{ - struct dd sum; - int bits_lost; - union ldshape u; - - sum = dd_add(a, b); - - /* - * If we are losing at least two bits of accuracy to denormalization, - * then the first lost bit becomes a round bit, and we adjust the - * lowest bit of sum.hi to make it a sticky bit summarizing all the - * bits in sum.lo. With the sticky bit adjusted, the hardware will - * break any ties in the correct direction. - * - * If we are losing only one bit to denormalization, however, we must - * break the ties manually. - */ - if (sum.lo != 0) { - u.f = sum.hi; - bits_lost = -u.i.se - scale + 1; - if ((bits_lost != 1) ^ LASTBIT(u)) - sum.hi = nextafterl(sum.hi, INFINITY * sum.lo); - } - return scalbnl(sum.hi, scale); -} - -/* - * Compute a*b exactly, returning the exact result in a struct dd. We assume - * that both a and b are normalized, so no underflow or overflow will occur. - * The current rounding mode must be round-to-nearest. - */ -static inline struct dd dd_mul(long double a, long double b) -{ - struct dd ret; - long double ha, hb, la, lb, p, q; - - p = a * SPLIT; - ha = a - p; - ha += p; - la = a - ha; - - p = b * SPLIT; - hb = b - p; - hb += p; - lb = b - hb; - - p = ha * hb; - q = ha * lb + la * hb; - - ret.hi = p + q; - ret.lo = p - ret.hi + q + la * lb; - return (ret); -} - -/* - * Fused multiply-add: Compute x * y + z with a single rounding error. - * - * We use scaling to avoid overflow/underflow, along with the - * canonical precision-doubling technique adapted from: - * - * Dekker, T. A Floating-Point Technique for Extending the - * Available Precision. Numer. Math. 18, 224-242 (1971). - */ -long double fmal(long double x, long double y, long double z) -{ - #pragma STDC FENV_ACCESS ON - long double xs, ys, zs, adj; - struct dd xy, r; - int oround; - int ex, ey, ez; - int spread; - - /* - * Handle special cases. The order of operations and the particular - * return values here are crucial in handling special cases involving - * infinities, NaNs, overflows, and signed zeroes correctly. - */ - if (!isfinite(x) || !isfinite(y)) - return (x * y + z); - if (!isfinite(z)) - return (z); - if (x == 0.0 || y == 0.0) - return (x * y + z); - if (z == 0.0) - return (x * y); - - xs = frexpl(x, &ex); - ys = frexpl(y, &ey); - zs = frexpl(z, &ez); - oround = fegetround(); - spread = ex + ey - ez; - - /* - * If x * y and z are many orders of magnitude apart, the scaling - * will overflow, so we handle these cases specially. Rounding - * modes other than FE_TONEAREST are painful. - */ - if (spread < -LDBL_MANT_DIG) { -#ifdef FE_INEXACT - feraiseexcept(FE_INEXACT); -#endif -#ifdef FE_UNDERFLOW - if (!isnormal(z)) - feraiseexcept(FE_UNDERFLOW); -#endif - switch (oround) { - default: /* FE_TONEAREST */ - return (z); -#ifdef FE_TOWARDZERO - case FE_TOWARDZERO: - if (x > 0.0 ^ y < 0.0 ^ z < 0.0) - return (z); - else - return (nextafterl(z, 0)); -#endif -#ifdef FE_DOWNWARD - case FE_DOWNWARD: - if (x > 0.0 ^ y < 0.0) - return (z); - else - return (nextafterl(z, -INFINITY)); -#endif -#ifdef FE_UPWARD - case FE_UPWARD: - if (x > 0.0 ^ y < 0.0) - return (nextafterl(z, INFINITY)); - else - return (z); -#endif - } - } - if (spread <= LDBL_MANT_DIG * 2) - zs = scalbnl(zs, -spread); - else - zs = copysignl(LDBL_MIN, zs); - - fesetround(FE_TONEAREST); - - /* - * Basic approach for round-to-nearest: - * - * (xy.hi, xy.lo) = x * y (exact) - * (r.hi, r.lo) = xy.hi + z (exact) - * adj = xy.lo + r.lo (inexact; low bit is sticky) - * result = r.hi + adj (correctly rounded) - */ - xy = dd_mul(xs, ys); - r = dd_add(xy.hi, zs); - - spread = ex + ey; - - if (r.hi == 0.0) { - /* - * When the addends cancel to 0, ensure that the result has - * the correct sign. - */ - fesetround(oround); - volatile long double vzs = zs; /* XXX gcc CSE bug workaround */ - return xy.hi + vzs + scalbnl(xy.lo, spread); - } - - if (oround != FE_TONEAREST) { - /* - * There is no need to worry about double rounding in directed - * rounding modes. - * But underflow may not be raised correctly, example in downward rounding: - * fmal(0x1.0000000001p-16000L, 0x1.0000000001p-400L, -0x1p-16440L) - */ - long double ret; -#if defined(FE_INEXACT) && defined(FE_UNDERFLOW) - int e = fetestexcept(FE_INEXACT); - feclearexcept(FE_INEXACT); -#endif - fesetround(oround); - adj = r.lo + xy.lo; - ret = scalbnl(r.hi + adj, spread); -#if defined(FE_INEXACT) && defined(FE_UNDERFLOW) - if (ilogbl(ret) < -16382 && fetestexcept(FE_INEXACT)) - feraiseexcept(FE_UNDERFLOW); - else if (e) - feraiseexcept(FE_INEXACT); -#endif - return ret; - } - - adj = add_adjusted(r.lo, xy.lo); - if (spread + ilogbl(r.hi) > -16383) - return scalbnl(r.hi + adj, spread); - else - return add_and_denormalize(r.hi, adj, spread); -} -#endif diff --git a/src/math/fmax.c b/src/math/fmax.c deleted file mode 100644 index 94f0caa..0000000 --- a/src/math/fmax.c +++ /dev/null @@ -1,13 +0,0 @@ -#include - -double fmax(double x, double y) -{ - if (isnan(x)) - return y; - if (isnan(y)) - return x; - /* handle signed zeros, see C99 Annex F.9.9.2 */ - if (signbit(x) != signbit(y)) - return signbit(x) ? y : x; - return x < y ? y : x; -} diff --git a/src/math/fmaxf.c b/src/math/fmaxf.c deleted file mode 100644 index 695d817..0000000 --- a/src/math/fmaxf.c +++ /dev/null @@ -1,13 +0,0 @@ -#include - -float fmaxf(float x, float y) -{ - if (isnan(x)) - return y; - if (isnan(y)) - return x; - /* handle signed zeroes, see C99 Annex F.9.9.2 */ - if (signbit(x) != signbit(y)) - return signbit(x) ? y : x; - return x < y ? y : x; -} diff --git a/src/math/fmaxl.c b/src/math/fmaxl.c deleted file mode 100644 index 4b03158..0000000 --- a/src/math/fmaxl.c +++ /dev/null @@ -1,21 +0,0 @@ -#include -#include - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double fmaxl(long double x, long double y) -{ - return fmax(x, y); -} -#else -long double fmaxl(long double x, long double y) -{ - if (isnan(x)) - return y; - if (isnan(y)) - return x; - /* handle signed zeros, see C99 Annex F.9.9.2 */ - if (signbit(x) != signbit(y)) - return signbit(x) ? y : x; - return x < y ? y : x; -} -#endif diff --git a/src/math/fmin.c b/src/math/fmin.c deleted file mode 100644 index 08a8fd1..0000000 --- a/src/math/fmin.c +++ /dev/null @@ -1,13 +0,0 @@ -#include - -double fmin(double x, double y) -{ - if (isnan(x)) - return y; - if (isnan(y)) - return x; - /* handle signed zeros, see C99 Annex F.9.9.2 */ - if (signbit(x) != signbit(y)) - return signbit(x) ? x : y; - return x < y ? x : y; -} diff --git a/src/math/fminf.c b/src/math/fminf.c deleted file mode 100644 index 3573c7d..0000000 --- a/src/math/fminf.c +++ /dev/null @@ -1,13 +0,0 @@ -#include - -float fminf(float x, float y) -{ - if (isnan(x)) - return y; - if (isnan(y)) - return x; - /* handle signed zeros, see C99 Annex F.9.9.2 */ - if (signbit(x) != signbit(y)) - return signbit(x) ? x : y; - return x < y ? x : y; -} diff --git a/src/math/fminl.c b/src/math/fminl.c deleted file mode 100644 index 69bc24a..0000000 --- a/src/math/fminl.c +++ /dev/null @@ -1,21 +0,0 @@ -#include -#include - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double fminl(long double x, long double y) -{ - return fmin(x, y); -} -#else -long double fminl(long double x, long double y) -{ - if (isnan(x)) - return y; - if (isnan(y)) - return x; - /* handle signed zeros, see C99 Annex F.9.9.2 */ - if (signbit(x) != signbit(y)) - return signbit(x) ? x : y; - return x < y ? x : y; -} -#endif diff --git a/src/math/fmod.c b/src/math/fmod.c deleted file mode 100644 index 6849722..0000000 --- a/src/math/fmod.c +++ /dev/null @@ -1,68 +0,0 @@ -#include -#include - -double fmod(double x, double y) -{ - union {double f; uint64_t i;} ux = {x}, uy = {y}; - int ex = ux.i>>52 & 0x7ff; - int ey = uy.i>>52 & 0x7ff; - int sx = ux.i>>63; - uint64_t i; - - /* in the followings uxi should be ux.i, but then gcc wrongly adds */ - /* float load/store to inner loops ruining performance and code size */ - uint64_t uxi = ux.i; - - if (uy.i<<1 == 0 || isnan(y) || ex == 0x7ff) - return (x*y)/(x*y); - if (uxi<<1 <= uy.i<<1) { - if (uxi<<1 == uy.i<<1) - return 0*x; - return x; - } - - /* normalize x and y */ - if (!ex) { - for (i = uxi<<12; i>>63 == 0; ex--, i <<= 1); - uxi <<= -ex + 1; - } else { - uxi &= -1ULL >> 12; - uxi |= 1ULL << 52; - } - if (!ey) { - for (i = uy.i<<12; i>>63 == 0; ey--, i <<= 1); - uy.i <<= -ey + 1; - } else { - uy.i &= -1ULL >> 12; - uy.i |= 1ULL << 52; - } - - /* x mod y */ - for (; ex > ey; ex--) { - i = uxi - uy.i; - if (i >> 63 == 0) { - if (i == 0) - return 0*x; - uxi = i; - } - uxi <<= 1; - } - i = uxi - uy.i; - if (i >> 63 == 0) { - if (i == 0) - return 0*x; - uxi = i; - } - for (; uxi>>52 == 0; uxi <<= 1, ex--); - - /* scale result */ - if (ex > 0) { - uxi -= 1ULL << 52; - uxi |= (uint64_t)ex << 52; - } else { - uxi >>= -ex + 1; - } - uxi |= (uint64_t)sx << 63; - ux.i = uxi; - return ux.f; -} diff --git a/src/math/fmodf.c b/src/math/fmodf.c deleted file mode 100644 index ff58f93..0000000 --- a/src/math/fmodf.c +++ /dev/null @@ -1,65 +0,0 @@ -#include -#include - -float fmodf(float x, float y) -{ - union {float f; uint32_t i;} ux = {x}, uy = {y}; - int ex = ux.i>>23 & 0xff; - int ey = uy.i>>23 & 0xff; - uint32_t sx = ux.i & 0x80000000; - uint32_t i; - uint32_t uxi = ux.i; - - if (uy.i<<1 == 0 || isnan(y) || ex == 0xff) - return (x*y)/(x*y); - if (uxi<<1 <= uy.i<<1) { - if (uxi<<1 == uy.i<<1) - return 0*x; - return x; - } - - /* normalize x and y */ - if (!ex) { - for (i = uxi<<9; i>>31 == 0; ex--, i <<= 1); - uxi <<= -ex + 1; - } else { - uxi &= -1U >> 9; - uxi |= 1U << 23; - } - if (!ey) { - for (i = uy.i<<9; i>>31 == 0; ey--, i <<= 1); - uy.i <<= -ey + 1; - } else { - uy.i &= -1U >> 9; - uy.i |= 1U << 23; - } - - /* x mod y */ - for (; ex > ey; ex--) { - i = uxi - uy.i; - if (i >> 31 == 0) { - if (i == 0) - return 0*x; - uxi = i; - } - uxi <<= 1; - } - i = uxi - uy.i; - if (i >> 31 == 0) { - if (i == 0) - return 0*x; - uxi = i; - } - for (; uxi>>23 == 0; uxi <<= 1, ex--); - - /* scale result up */ - if (ex > 0) { - uxi -= 1U << 23; - uxi |= (uint32_t)ex << 23; - } else { - uxi >>= -ex + 1; - } - uxi |= sx; - ux.i = uxi; - return ux.f; -} diff --git a/src/math/fmodl.c b/src/math/fmodl.c deleted file mode 100644 index 9f5b873..0000000 --- a/src/math/fmodl.c +++ /dev/null @@ -1,105 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double fmodl(long double x, long double y) -{ - return fmod(x, y); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -long double fmodl(long double x, long double y) -{ - union ldshape ux = {x}, uy = {y}; - int ex = ux.i.se & 0x7fff; - int ey = uy.i.se & 0x7fff; - int sx = ux.i.se & 0x8000; - - if (y == 0 || isnan(y) || ex == 0x7fff) - return (x*y)/(x*y); - ux.i.se = ex; - uy.i.se = ey; - if (ux.f <= uy.f) { - if (ux.f == uy.f) - return 0*x; - return x; - } - - /* normalize x and y */ - if (!ex) { - ux.f *= 0x1p120f; - ex = ux.i.se - 120; - } - if (!ey) { - uy.f *= 0x1p120f; - ey = uy.i.se - 120; - } - - /* x mod y */ -#if LDBL_MANT_DIG == 64 - uint64_t i, mx, my; - mx = ux.i.m; - my = uy.i.m; - for (; ex > ey; ex--) { - i = mx - my; - if (mx >= my) { - if (i == 0) - return 0*x; - mx = 2*i; - } else if (2*mx < mx) { - mx = 2*mx - my; - } else { - mx = 2*mx; - } - } - i = mx - my; - if (mx >= my) { - if (i == 0) - return 0*x; - mx = i; - } - for (; mx >> 63 == 0; mx *= 2, ex--); - ux.i.m = mx; -#elif LDBL_MANT_DIG == 113 - uint64_t hi, lo, xhi, xlo, yhi, ylo; - xhi = (ux.i2.hi & -1ULL>>16) | 1ULL<<48; - yhi = (uy.i2.hi & -1ULL>>16) | 1ULL<<48; - xlo = ux.i2.lo; - ylo = uy.i2.lo; - for (; ex > ey; ex--) { - hi = xhi - yhi; - lo = xlo - ylo; - if (xlo < ylo) - hi -= 1; - if (hi >> 63 == 0) { - if ((hi|lo) == 0) - return 0*x; - xhi = 2*hi + (lo>>63); - xlo = 2*lo; - } else { - xhi = 2*xhi + (xlo>>63); - xlo = 2*xlo; - } - } - hi = xhi - yhi; - lo = xlo - ylo; - if (xlo < ylo) - hi -= 1; - if (hi >> 63 == 0) { - if ((hi|lo) == 0) - return 0*x; - xhi = hi; - xlo = lo; - } - for (; xhi >> 48 == 0; xhi = 2*xhi + (xlo>>63), xlo = 2*xlo, ex--); - ux.i2.hi = xhi; - ux.i2.lo = xlo; -#endif - - /* scale result */ - if (ex <= 0) { - ux.i.se = (ex+120)|sx; - ux.f *= 0x1p-120f; - } else - ux.i.se = ex|sx; - return ux.f; -} -#endif diff --git a/src/math/frexp.c b/src/math/frexp.c deleted file mode 100644 index 27b6266..0000000 --- a/src/math/frexp.c +++ /dev/null @@ -1,23 +0,0 @@ -#include -#include - -double frexp(double x, int *e) -{ - union { double d; uint64_t i; } y = { x }; - int ee = y.i>>52 & 0x7ff; - - if (!ee) { - if (x) { - x = frexp(x*0x1p64, e); - *e -= 64; - } else *e = 0; - return x; - } else if (ee == 0x7ff) { - return x; - } - - *e = ee - 0x3fe; - y.i &= 0x800fffffffffffffull; - y.i |= 0x3fe0000000000000ull; - return y.d; -} diff --git a/src/math/frexpf.c b/src/math/frexpf.c deleted file mode 100644 index 0787097..0000000 --- a/src/math/frexpf.c +++ /dev/null @@ -1,23 +0,0 @@ -#include -#include - -float frexpf(float x, int *e) -{ - union { float f; uint32_t i; } y = { x }; - int ee = y.i>>23 & 0xff; - - if (!ee) { - if (x) { - x = frexpf(x*0x1p64, e); - *e -= 64; - } else *e = 0; - return x; - } else if (ee == 0xff) { - return x; - } - - *e = ee - 0x7e; - y.i &= 0x807ffffful; - y.i |= 0x3f000000ul; - return y.f; -} diff --git a/src/math/frexpl.c b/src/math/frexpl.c deleted file mode 100644 index 3c1b553..0000000 --- a/src/math/frexpl.c +++ /dev/null @@ -1,29 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double frexpl(long double x, int *e) -{ - return frexp(x, e); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -long double frexpl(long double x, int *e) -{ - union ldshape u = {x}; - int ee = u.i.se & 0x7fff; - - if (!ee) { - if (x) { - x = frexpl(x*0x1p120, e); - *e -= 120; - } else *e = 0; - return x; - } else if (ee == 0x7fff) { - return x; - } - - *e = ee - 0x3ffe; - u.i.se &= 0x8000; - u.i.se |= 0x3ffe; - return u.f; -} -#endif diff --git a/src/math/hypot.c b/src/math/hypot.c deleted file mode 100644 index 6071bf1..0000000 --- a/src/math/hypot.c +++ /dev/null @@ -1,67 +0,0 @@ -#include -#include -#include - -#if FLT_EVAL_METHOD > 1U && LDBL_MANT_DIG == 64 -#define SPLIT (0x1p32 + 1) -#else -#define SPLIT (0x1p27 + 1) -#endif - -static void sq(double_t *hi, double_t *lo, double x) -{ - double_t xh, xl, xc; - - xc = (double_t)x*SPLIT; - xh = x - xc + xc; - xl = x - xh; - *hi = (double_t)x*x; - *lo = xh*xh - *hi + 2*xh*xl + xl*xl; -} - -double hypot(double x, double y) -{ - union {double f; uint64_t i;} ux = {x}, uy = {y}, ut; - int ex, ey; - double_t hx, lx, hy, ly, z; - - /* arrange |x| >= |y| */ - ux.i &= -1ULL>>1; - uy.i &= -1ULL>>1; - if (ux.i < uy.i) { - ut = ux; - ux = uy; - uy = ut; - } - - /* special cases */ - ex = ux.i>>52; - ey = uy.i>>52; - x = ux.f; - y = uy.f; - /* note: hypot(inf,nan) == inf */ - if (ey == 0x7ff) - return y; - if (ex == 0x7ff || uy.i == 0) - return x; - /* note: hypot(x,y) ~= x + y*y/x/2 with inexact for small y/x */ - /* 64 difference is enough for ld80 double_t */ - if (ex - ey > 64) - return x + y; - - /* precise sqrt argument in nearest rounding mode without overflow */ - /* xh*xh must not overflow and xl*xl must not underflow in sq */ - z = 1; - if (ex > 0x3ff+510) { - z = 0x1p700; - x *= 0x1p-700; - y *= 0x1p-700; - } else if (ey < 0x3ff-450) { - z = 0x1p-700; - x *= 0x1p700; - y *= 0x1p700; - } - sq(&hx, &lx, x); - sq(&hy, &ly, y); - return z*sqrt(ly+lx+hy+hx); -} diff --git a/src/math/hypotf.c b/src/math/hypotf.c deleted file mode 100644 index 2fc214b..0000000 --- a/src/math/hypotf.c +++ /dev/null @@ -1,35 +0,0 @@ -#include -#include - -float hypotf(float x, float y) -{ - union {float f; uint32_t i;} ux = {x}, uy = {y}, ut; - float_t z; - - ux.i &= -1U>>1; - uy.i &= -1U>>1; - if (ux.i < uy.i) { - ut = ux; - ux = uy; - uy = ut; - } - - x = ux.f; - y = uy.f; - if (uy.i == 0xff<<23) - return y; - if (ux.i >= 0xff<<23 || uy.i == 0 || ux.i - uy.i >= 25<<23) - return x + y; - - z = 1; - if (ux.i >= (0x7f+60)<<23) { - z = 0x1p90f; - x *= 0x1p-90f; - y *= 0x1p-90f; - } else if (uy.i < (0x7f-60)<<23) { - z = 0x1p-90f; - x *= 0x1p90f; - y *= 0x1p90f; - } - return z*sqrtf((double)x*x + (double)y*y); -} diff --git a/src/math/hypotl.c b/src/math/hypotl.c deleted file mode 100644 index 479aa92..0000000 --- a/src/math/hypotl.c +++ /dev/null @@ -1,66 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double hypotl(long double x, long double y) -{ - return hypot(x, y); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -#if LDBL_MANT_DIG == 64 -#define SPLIT (0x1p32L+1) -#elif LDBL_MANT_DIG == 113 -#define SPLIT (0x1p57L+1) -#endif - -static void sq(long double *hi, long double *lo, long double x) -{ - long double xh, xl, xc; - xc = x*SPLIT; - xh = x - xc + xc; - xl = x - xh; - *hi = x*x; - *lo = xh*xh - *hi + 2*xh*xl + xl*xl; -} - -long double hypotl(long double x, long double y) -{ - union ldshape ux = {x}, uy = {y}; - int ex, ey; - long double hx, lx, hy, ly, z; - - ux.i.se &= 0x7fff; - uy.i.se &= 0x7fff; - if (ux.i.se < uy.i.se) { - ex = uy.i.se; - ey = ux.i.se; - x = uy.f; - y = ux.f; - } else { - ex = ux.i.se; - ey = uy.i.se; - x = ux.f; - y = uy.f; - } - - if (ex == 0x7fff && isinf(y)) - return y; - if (ex == 0x7fff || y == 0) - return x; - if (ex - ey > LDBL_MANT_DIG) - return x + y; - - z = 1; - if (ex > 0x3fff+8000) { - z = 0x1p10000L; - x *= 0x1p-10000L; - y *= 0x1p-10000L; - } else if (ey < 0x3fff-8000) { - z = 0x1p-10000L; - x *= 0x1p10000L; - y *= 0x1p10000L; - } - sq(&hx, &lx, x); - sq(&hy, &ly, y); - return z*sqrtl(ly+lx+hy+hx); -} -#endif diff --git a/src/math/i386/__invtrigl.s b/src/math/i386/__invtrigl.s deleted file mode 100644 index e69de29..0000000 diff --git a/src/math/i386/acos.s b/src/math/i386/acos.s deleted file mode 100644 index af423a2..0000000 --- a/src/math/i386/acos.s +++ /dev/null @@ -1,18 +0,0 @@ -# use acos(x) = atan2(fabs(sqrt((1-x)*(1+x))), x) - -.global acos -.type acos,@function -acos: - fldl 4(%esp) - fld %st(0) - fld1 - fsub %st(0),%st(1) - fadd %st(2) - fmulp - fsqrt - fabs # fix sign of zero (matters in downward rounding mode) - fxch %st(1) - fpatan - fstpl 4(%esp) - fldl 4(%esp) - ret diff --git a/src/math/i386/acosf.s b/src/math/i386/acosf.s deleted file mode 100644 index d2cdfdb..0000000 --- a/src/math/i386/acosf.s +++ /dev/null @@ -1,16 +0,0 @@ -.global acosf -.type acosf,@function -acosf: - flds 4(%esp) - fld %st(0) - fld1 - fsub %st(0),%st(1) - fadd %st(2) - fmulp - fsqrt - fabs # fix sign of zero (matters in downward rounding mode) - fxch %st(1) - fpatan - fstps 4(%esp) - flds 4(%esp) - ret diff --git a/src/math/i386/acosl.s b/src/math/i386/acosl.s deleted file mode 100644 index 599c823..0000000 --- a/src/math/i386/acosl.s +++ /dev/null @@ -1,14 +0,0 @@ -.global acosl -.type acosl,@function -acosl: - fldt 4(%esp) - fld %st(0) - fld1 - fsub %st(0),%st(1) - fadd %st(2) - fmulp - fsqrt - fabs # fix sign of zero (matters in downward rounding mode) - fxch %st(1) - fpatan - ret diff --git a/src/math/i386/asin.s b/src/math/i386/asin.s deleted file mode 100644 index 2bc8356..0000000 --- a/src/math/i386/asin.s +++ /dev/null @@ -1,21 +0,0 @@ -.global asin -.type asin,@function -asin: - fldl 4(%esp) - mov 8(%esp),%eax - add %eax,%eax - cmp $0x00200000,%eax - jb 1f - fld %st(0) - fld1 - fsub %st(0),%st(1) - fadd %st(2) - fmulp - fsqrt - fpatan - fstpl 4(%esp) - fldl 4(%esp) - ret - # subnormal x, return x with underflow -1: fsts 4(%esp) - ret diff --git a/src/math/i386/asinf.s b/src/math/i386/asinf.s deleted file mode 100644 index 0590975..0000000 --- a/src/math/i386/asinf.s +++ /dev/null @@ -1,23 +0,0 @@ -.global asinf -.type asinf,@function -asinf: - flds 4(%esp) - mov 4(%esp),%eax - add %eax,%eax - cmp $0x01000000,%eax - jb 1f - fld %st(0) - fld1 - fsub %st(0),%st(1) - fadd %st(2) - fmulp - fsqrt - fpatan - fstps 4(%esp) - flds 4(%esp) - ret - # subnormal x, return x with underflow -1: fld %st(0) - fmul %st(1) - fstps 4(%esp) - ret diff --git a/src/math/i386/asinl.s b/src/math/i386/asinl.s deleted file mode 100644 index e973fc8..0000000 --- a/src/math/i386/asinl.s +++ /dev/null @@ -1,12 +0,0 @@ -.global asinl -.type asinl,@function -asinl: - fldt 4(%esp) - fld %st(0) - fld1 - fsub %st(0),%st(1) - fadd %st(2) - fmulp - fsqrt - fpatan - ret diff --git a/src/math/i386/atan.s b/src/math/i386/atan.s deleted file mode 100644 index 2c57f6b..0000000 --- a/src/math/i386/atan.s +++ /dev/null @@ -1,16 +0,0 @@ -.global atan -.type atan,@function -atan: - fldl 4(%esp) - mov 8(%esp),%eax - add %eax,%eax - cmp $0x00200000,%eax - jb 1f - fld1 - fpatan - fstpl 4(%esp) - fldl 4(%esp) - ret - # subnormal x, return x with underflow -1: fsts 4(%esp) - ret diff --git a/src/math/i386/atan2.s b/src/math/i386/atan2.s deleted file mode 100644 index 8bc441b..0000000 --- a/src/math/i386/atan2.s +++ /dev/null @@ -1,15 +0,0 @@ -.global atan2 -.type atan2,@function -atan2: - fldl 4(%esp) - fldl 12(%esp) - fpatan - fstpl 4(%esp) - fldl 4(%esp) - mov 8(%esp),%eax - add %eax,%eax - cmp $0x00200000,%eax - jae 1f - # subnormal x, return x with underflow - fsts 4(%esp) -1: ret diff --git a/src/math/i386/atan2f.s b/src/math/i386/atan2f.s deleted file mode 100644 index 3908c86..0000000 --- a/src/math/i386/atan2f.s +++ /dev/null @@ -1,17 +0,0 @@ -.global atan2f -.type atan2f,@function -atan2f: - flds 4(%esp) - flds 8(%esp) - fpatan - fstps 4(%esp) - flds 4(%esp) - mov 4(%esp),%eax - add %eax,%eax - cmp $0x01000000,%eax - jae 1f - # subnormal x, return x with underflow - fld %st(0) - fmul %st(1) - fstps 4(%esp) -1: ret diff --git a/src/math/i386/atan2l.s b/src/math/i386/atan2l.s deleted file mode 100644 index adf6e10..0000000 --- a/src/math/i386/atan2l.s +++ /dev/null @@ -1,7 +0,0 @@ -.global atan2l -.type atan2l,@function -atan2l: - fldt 4(%esp) - fldt 16(%esp) - fpatan - ret diff --git a/src/math/i386/atanf.s b/src/math/i386/atanf.s deleted file mode 100644 index c2cbe2e..0000000 --- a/src/math/i386/atanf.s +++ /dev/null @@ -1,18 +0,0 @@ -.global atanf -.type atanf,@function -atanf: - flds 4(%esp) - mov 4(%esp),%eax - add %eax,%eax - cmp $0x01000000,%eax - jb 1f - fld1 - fpatan - fstps 4(%esp) - flds 4(%esp) - ret - # subnormal x, return x with underflow -1: fld %st(0) - fmul %st(1) - fstps 4(%esp) - ret diff --git a/src/math/i386/atanl.s b/src/math/i386/atanl.s deleted file mode 100644 index c508bc4..0000000 --- a/src/math/i386/atanl.s +++ /dev/null @@ -1,7 +0,0 @@ -.global atanl -.type atanl,@function -atanl: - fldt 4(%esp) - fld1 - fpatan - ret diff --git a/src/math/i386/ceil.s b/src/math/i386/ceil.s deleted file mode 100644 index bc29f15..0000000 --- a/src/math/i386/ceil.s +++ /dev/null @@ -1 +0,0 @@ -# see floor.s diff --git a/src/math/i386/ceilf.s b/src/math/i386/ceilf.s deleted file mode 100644 index bc29f15..0000000 --- a/src/math/i386/ceilf.s +++ /dev/null @@ -1 +0,0 @@ -# see floor.s diff --git a/src/math/i386/ceill.s b/src/math/i386/ceill.s deleted file mode 100644 index bc29f15..0000000 --- a/src/math/i386/ceill.s +++ /dev/null @@ -1 +0,0 @@ -# see floor.s diff --git a/src/math/i386/exp2l.s b/src/math/i386/exp2l.s deleted file mode 100644 index 8125761..0000000 --- a/src/math/i386/exp2l.s +++ /dev/null @@ -1 +0,0 @@ -# see exp_ld.s diff --git a/src/math/i386/exp_ld.s b/src/math/i386/exp_ld.s deleted file mode 100644 index 99cba01..0000000 --- a/src/math/i386/exp_ld.s +++ /dev/null @@ -1,93 +0,0 @@ -.global expm1l -.type expm1l,@function -expm1l: - fldt 4(%esp) - fldl2e - fmulp - mov $0xc2820000,%eax - push %eax - flds (%esp) - pop %eax - fucomp %st(1) - fnstsw %ax - sahf - fld1 - jb 1f - # x*log2e < -65, return -1 without underflow - fstp %st(1) - fchs - ret -1: fld %st(1) - fabs - fucom %st(1) - fnstsw %ax - fstp %st(0) - fstp %st(0) - sahf - ja 1f - f2xm1 - ret -1: call 1f - fld1 - fsubrp - ret - -.global exp2l -.global __exp2l -.hidden __exp2l -.type exp2l,@function -exp2l: -__exp2l: - fldt 4(%esp) -1: sub $12,%esp - fld %st(0) - fstpt (%esp) - mov 8(%esp),%ax - and $0x7fff,%ax - cmp $0x3fff+13,%ax - jb 4f # |x| < 8192 - cmp $0x3fff+15,%ax - jae 3f # |x| >= 32768 - fsts (%esp) - cmpl $0xc67ff800,(%esp) - jb 2f # x > -16382 - movl $0x5f000000,(%esp) - flds (%esp) # 0x1p63 - fld %st(1) - fsub %st(1) - faddp - fucomp %st(1) - fnstsw - sahf - je 2f # x - 0x1p63 + 0x1p63 == x - movl $1,(%esp) - flds (%esp) # 0x1p-149 - fdiv %st(1) - fstps (%esp) # raise underflow -2: fld1 - fld %st(1) - frndint - fxch %st(2) - fsub %st(2) # st(0)=x-rint(x), st(1)=1, st(2)=rint(x) - f2xm1 - faddp # 2^(x-rint(x)) -1: fscale - fstp %st(1) - add $12,%esp - ret -3: xor %eax,%eax -4: cmp $0x3fff-64,%ax - fld1 - jb 1b # |x| < 0x1p-64 - fstpt (%esp) - fistl 8(%esp) - fildl 8(%esp) - fsubrp %st(1) - addl $0x3fff,8(%esp) - f2xm1 - fld1 - faddp # 2^(x-rint(x)) - fldt (%esp) # 2^rint(x) - fmulp - add $12,%esp - ret diff --git a/src/math/i386/expl.s b/src/math/i386/expl.s deleted file mode 100644 index b5124e8..0000000 --- a/src/math/i386/expl.s +++ /dev/null @@ -1,101 +0,0 @@ -# exp(x) = 2^hi + 2^hi (2^lo - 1) -# where hi+lo = log2e*x with 128bit precision -# exact log2e*x calculation depends on nearest rounding mode -# using the exact multiplication method of Dekker and Veltkamp - -.global expl -.type expl,@function -expl: - fldt 4(%esp) - - # interesting case: 0x1p-32 <= |x| < 16384 - # check if (exponent|0x8000) is in [0xbfff-32, 0xbfff+13] - mov 12(%esp), %ax - or $0x8000, %ax - sub $0xbfdf, %ax - cmp $45, %ax - jbe 2f - test %ax, %ax - fld1 - js 1f - # if |x|>=0x1p14 or nan return 2^trunc(x) - fscale - fstp %st(1) - ret - # if |x|<0x1p-32 return 1+x -1: faddp - ret - - # should be 0x1.71547652b82fe178p0L == 0x3fff b8aa3b29 5c17f0bc - # it will be wrong on non-nearest rounding mode -2: fldl2e - subl $44, %esp - # hi = log2e_hi*x - # 2^hi = exp2l(hi) - fmul %st(1),%st - fld %st(0) - fstpt (%esp) - fstpt 16(%esp) - fstpt 32(%esp) -.hidden __exp2l - call __exp2l - # if 2^hi == inf return 2^hi - fld %st(0) - fstpt (%esp) - cmpw $0x7fff, 8(%esp) - je 1f - fldt 32(%esp) - fldt 16(%esp) - # fpu stack: 2^hi x hi - # exact mult: x*log2e - fld %st(1) - # c = 0x1p32+1 - pushl $0x41f00000 - pushl $0x00100000 - fldl (%esp) - # xh = x - c*x + c*x - # xl = x - xh - fmulp - fld %st(2) - fsub %st(1), %st - faddp - fld %st(2) - fsub %st(1), %st - # yh = log2e_hi - c*log2e_hi + c*log2e_hi - pushl $0x3ff71547 - pushl $0x65200000 - fldl (%esp) - # fpu stack: 2^hi x hi xh xl yh - # lo = hi - xh*yh + xl*yh - fld %st(2) - fmul %st(1), %st - fsubp %st, %st(4) - fmul %st(1), %st - faddp %st, %st(3) - # yl = log2e_hi - yh - pushl $0x3de705fc - pushl $0x2f000000 - fldl (%esp) - # fpu stack: 2^hi x lo xh xl yl - # lo += xh*yl + xl*yl - fmul %st, %st(2) - fmulp %st, %st(1) - fxch %st(2) - faddp - faddp - # log2e_lo - pushl $0xbfbe - pushl $0x82f0025f - pushl $0x2dc582ee - fldt (%esp) - addl $36,%esp - # fpu stack: 2^hi x lo log2e_lo - # lo += log2e_lo*x - # return 2^hi + 2^hi (2^lo - 1) - fmulp %st, %st(2) - faddp - f2xm1 - fmul %st(1), %st - faddp -1: addl $44, %esp - ret diff --git a/src/math/i386/expm1l.s b/src/math/i386/expm1l.s deleted file mode 100644 index 8125761..0000000 --- a/src/math/i386/expm1l.s +++ /dev/null @@ -1 +0,0 @@ -# see exp_ld.s diff --git a/src/math/i386/fabs.c b/src/math/i386/fabs.c deleted file mode 100644 index 3967278..0000000 --- a/src/math/i386/fabs.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double fabs(double x) -{ - __asm__ ("fabs" : "+t"(x)); - return x; -} diff --git a/src/math/i386/fabsf.c b/src/math/i386/fabsf.c deleted file mode 100644 index d882eee..0000000 --- a/src/math/i386/fabsf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float fabsf(float x) -{ - __asm__ ("fabs" : "+t"(x)); - return x; -} diff --git a/src/math/i386/fabsl.c b/src/math/i386/fabsl.c deleted file mode 100644 index cc1c9ed..0000000 --- a/src/math/i386/fabsl.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -long double fabsl(long double x) -{ - __asm__ ("fabs" : "+t"(x)); - return x; -} diff --git a/src/math/i386/floor.s b/src/math/i386/floor.s deleted file mode 100644 index 46ba88d..0000000 --- a/src/math/i386/floor.s +++ /dev/null @@ -1,67 +0,0 @@ -.global floorf -.type floorf,@function -floorf: - flds 4(%esp) - jmp 1f - -.global floorl -.type floorl,@function -floorl: - fldt 4(%esp) - jmp 1f - -.global floor -.type floor,@function -floor: - fldl 4(%esp) -1: mov $0x7,%al -1: fstcw 4(%esp) - mov 5(%esp),%ah - mov %al,5(%esp) - fldcw 4(%esp) - frndint - mov %ah,5(%esp) - fldcw 4(%esp) - ret - -.global ceil -.type ceil,@function -ceil: - fldl 4(%esp) - mov $0xb,%al - jmp 1b - -.global ceilf -.type ceilf,@function -ceilf: - flds 4(%esp) - mov $0xb,%al - jmp 1b - -.global ceill -.type ceill,@function -ceill: - fldt 4(%esp) - mov $0xb,%al - jmp 1b - -.global trunc -.type trunc,@function -trunc: - fldl 4(%esp) - mov $0xf,%al - jmp 1b - -.global truncf -.type truncf,@function -truncf: - flds 4(%esp) - mov $0xf,%al - jmp 1b - -.global truncl -.type truncl,@function -truncl: - fldt 4(%esp) - mov $0xf,%al - jmp 1b diff --git a/src/math/i386/floorf.s b/src/math/i386/floorf.s deleted file mode 100644 index bc29f15..0000000 --- a/src/math/i386/floorf.s +++ /dev/null @@ -1 +0,0 @@ -# see floor.s diff --git a/src/math/i386/floorl.s b/src/math/i386/floorl.s deleted file mode 100644 index bc29f15..0000000 --- a/src/math/i386/floorl.s +++ /dev/null @@ -1 +0,0 @@ -# see floor.s diff --git a/src/math/i386/fmod.c b/src/math/i386/fmod.c deleted file mode 100644 index ea0c58d..0000000 --- a/src/math/i386/fmod.c +++ /dev/null @@ -1,10 +0,0 @@ -#include - -double fmod(double x, double y) -{ - unsigned short fpsr; - // fprem does not introduce excess precision into x - do __asm__ ("fprem; fnstsw %%ax" : "+t"(x), "=a"(fpsr) : "u"(y)); - while (fpsr & 0x400); - return x; -} diff --git a/src/math/i386/fmodf.c b/src/math/i386/fmodf.c deleted file mode 100644 index 90b56ab..0000000 --- a/src/math/i386/fmodf.c +++ /dev/null @@ -1,10 +0,0 @@ -#include - -float fmodf(float x, float y) -{ - unsigned short fpsr; - // fprem does not introduce excess precision into x - do __asm__ ("fprem; fnstsw %%ax" : "+t"(x), "=a"(fpsr) : "u"(y)); - while (fpsr & 0x400); - return x; -} diff --git a/src/math/i386/fmodl.c b/src/math/i386/fmodl.c deleted file mode 100644 index 3daeab0..0000000 --- a/src/math/i386/fmodl.c +++ /dev/null @@ -1,9 +0,0 @@ -#include - -long double fmodl(long double x, long double y) -{ - unsigned short fpsr; - do __asm__ ("fprem; fnstsw %%ax" : "+t"(x), "=a"(fpsr) : "u"(y)); - while (fpsr & 0x400); - return x; -} diff --git a/src/math/i386/hypot.s b/src/math/i386/hypot.s deleted file mode 100644 index 299c2e1..0000000 --- a/src/math/i386/hypot.s +++ /dev/null @@ -1,45 +0,0 @@ -.global hypot -.type hypot,@function -hypot: - mov 8(%esp),%eax - mov 16(%esp),%ecx - add %eax,%eax - add %ecx,%ecx - and %eax,%ecx - cmp $0xffe00000,%ecx - jae 2f - or 4(%esp),%eax - jnz 1f - fldl 12(%esp) - fabs - ret -1: mov 16(%esp),%eax - add %eax,%eax - or 12(%esp),%eax - jnz 1f - fldl 4(%esp) - fabs - ret -1: fldl 4(%esp) - fld %st(0) - fmulp - fldl 12(%esp) - fld %st(0) - fmulp - faddp - fsqrt - ret -2: sub $0xffe00000,%eax - or 4(%esp),%eax - jnz 1f - fldl 4(%esp) - fabs - ret -1: mov 16(%esp),%eax - add %eax,%eax - sub $0xffe00000,%eax - or 12(%esp),%eax - fldl 12(%esp) - jnz 1f - fabs -1: ret diff --git a/src/math/i386/hypotf.s b/src/math/i386/hypotf.s deleted file mode 100644 index 068935e..0000000 --- a/src/math/i386/hypotf.s +++ /dev/null @@ -1,42 +0,0 @@ -.global hypotf -.type hypotf,@function -hypotf: - mov 4(%esp),%eax - mov 8(%esp),%ecx - add %eax,%eax - add %ecx,%ecx - and %eax,%ecx - cmp $0xff000000,%ecx - jae 2f - test %eax,%eax - jnz 1f - flds 8(%esp) - fabs - ret -1: mov 8(%esp),%eax - add %eax,%eax - jnz 1f - flds 4(%esp) - fabs - ret -1: flds 4(%esp) - fld %st(0) - fmulp - flds 8(%esp) - fld %st(0) - fmulp - faddp - fsqrt - ret -2: cmp $0xff000000,%eax - jnz 1f - flds 4(%esp) - fabs - ret -1: mov 8(%esp),%eax - add %eax,%eax - cmp $0xff000000,%eax - flds 8(%esp) - jnz 1f - fabs -1: ret diff --git a/src/math/i386/ldexp.s b/src/math/i386/ldexp.s deleted file mode 100644 index c430f78..0000000 --- a/src/math/i386/ldexp.s +++ /dev/null @@ -1 +0,0 @@ -# see scalbn.s diff --git a/src/math/i386/ldexpf.s b/src/math/i386/ldexpf.s deleted file mode 100644 index 3f8e4b9..0000000 --- a/src/math/i386/ldexpf.s +++ /dev/null @@ -1 +0,0 @@ -# see scalbnf.s diff --git a/src/math/i386/ldexpl.s b/src/math/i386/ldexpl.s deleted file mode 100644 index 86fe562..0000000 --- a/src/math/i386/ldexpl.s +++ /dev/null @@ -1 +0,0 @@ -# see scalbnl.s diff --git a/src/math/i386/llrint.c b/src/math/i386/llrint.c deleted file mode 100644 index aa40081..0000000 --- a/src/math/i386/llrint.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long long llrint(double x) -{ - long long r; - __asm__ ("fistpll %0" : "=m"(r) : "t"(x) : "st"); - return r; -} diff --git a/src/math/i386/llrintf.c b/src/math/i386/llrintf.c deleted file mode 100644 index c41a317..0000000 --- a/src/math/i386/llrintf.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long long llrintf(float x) -{ - long long r; - __asm__ ("fistpll %0" : "=m"(r) : "t"(x) : "st"); - return r; -} diff --git a/src/math/i386/llrintl.c b/src/math/i386/llrintl.c deleted file mode 100644 index c439ef2..0000000 --- a/src/math/i386/llrintl.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long long llrintl(long double x) -{ - long long r; - __asm__ ("fistpll %0" : "=m"(r) : "t"(x) : "st"); - return r; -} diff --git a/src/math/i386/log.s b/src/math/i386/log.s deleted file mode 100644 index 08c5992..0000000 --- a/src/math/i386/log.s +++ /dev/null @@ -1,9 +0,0 @@ -.global log -.type log,@function -log: - fldln2 - fldl 4(%esp) - fyl2x - fstpl 4(%esp) - fldl 4(%esp) - ret diff --git a/src/math/i386/log10.s b/src/math/i386/log10.s deleted file mode 100644 index 120e91e..0000000 --- a/src/math/i386/log10.s +++ /dev/null @@ -1,9 +0,0 @@ -.global log10 -.type log10,@function -log10: - fldlg2 - fldl 4(%esp) - fyl2x - fstpl 4(%esp) - fldl 4(%esp) - ret diff --git a/src/math/i386/log10f.s b/src/math/i386/log10f.s deleted file mode 100644 index b055493..0000000 --- a/src/math/i386/log10f.s +++ /dev/null @@ -1,9 +0,0 @@ -.global log10f -.type log10f,@function -log10f: - fldlg2 - flds 4(%esp) - fyl2x - fstps 4(%esp) - flds 4(%esp) - ret diff --git a/src/math/i386/log10l.s b/src/math/i386/log10l.s deleted file mode 100644 index aaa44f2..0000000 --- a/src/math/i386/log10l.s +++ /dev/null @@ -1,7 +0,0 @@ -.global log10l -.type log10l,@function -log10l: - fldlg2 - fldt 4(%esp) - fyl2x - ret diff --git a/src/math/i386/log1p.s b/src/math/i386/log1p.s deleted file mode 100644 index f3c95f8..0000000 --- a/src/math/i386/log1p.s +++ /dev/null @@ -1,25 +0,0 @@ -.global log1p -.type log1p,@function -log1p: - mov 8(%esp),%eax - fldln2 - and $0x7fffffff,%eax - fldl 4(%esp) - cmp $0x3fd28f00,%eax - ja 1f - cmp $0x00100000,%eax - jb 2f - fyl2xp1 - fstpl 4(%esp) - fldl 4(%esp) - ret -1: fld1 - faddp - fyl2x - fstpl 4(%esp) - fldl 4(%esp) - ret - # subnormal x, return x with underflow -2: fsts 4(%esp) - fstp %st(1) - ret diff --git a/src/math/i386/log1pf.s b/src/math/i386/log1pf.s deleted file mode 100644 index 9f13d95..0000000 --- a/src/math/i386/log1pf.s +++ /dev/null @@ -1,26 +0,0 @@ -.global log1pf -.type log1pf,@function -log1pf: - mov 4(%esp),%eax - fldln2 - and $0x7fffffff,%eax - flds 4(%esp) - cmp $0x3e940000,%eax - ja 1f - cmp $0x00800000,%eax - jb 2f - fyl2xp1 - fstps 4(%esp) - flds 4(%esp) - ret -1: fld1 - faddp - fyl2x - fstps 4(%esp) - flds 4(%esp) - ret - # subnormal x, return x with underflow -2: fxch - fmul %st(1) - fstps 4(%esp) - ret diff --git a/src/math/i386/log1pl.s b/src/math/i386/log1pl.s deleted file mode 100644 index a048ab6..0000000 --- a/src/math/i386/log1pl.s +++ /dev/null @@ -1,15 +0,0 @@ -.global log1pl -.type log1pl,@function -log1pl: - mov 10(%esp),%eax - fldln2 - and $0x7fffffff,%eax - fldt 4(%esp) - cmp $0x3ffd9400,%eax - ja 1f - fyl2xp1 - ret -1: fld1 - faddp - fyl2x - ret diff --git a/src/math/i386/log2.s b/src/math/i386/log2.s deleted file mode 100644 index 7eff0b6..0000000 --- a/src/math/i386/log2.s +++ /dev/null @@ -1,9 +0,0 @@ -.global log2 -.type log2,@function -log2: - fld1 - fldl 4(%esp) - fyl2x - fstpl 4(%esp) - fldl 4(%esp) - ret diff --git a/src/math/i386/log2f.s b/src/math/i386/log2f.s deleted file mode 100644 index b32fa2f..0000000 --- a/src/math/i386/log2f.s +++ /dev/null @@ -1,9 +0,0 @@ -.global log2f -.type log2f,@function -log2f: - fld1 - flds 4(%esp) - fyl2x - fstps 4(%esp) - flds 4(%esp) - ret diff --git a/src/math/i386/log2l.s b/src/math/i386/log2l.s deleted file mode 100644 index c58f56f..0000000 --- a/src/math/i386/log2l.s +++ /dev/null @@ -1,7 +0,0 @@ -.global log2l -.type log2l,@function -log2l: - fld1 - fldt 4(%esp) - fyl2x - ret diff --git a/src/math/i386/logf.s b/src/math/i386/logf.s deleted file mode 100644 index 4d0346a..0000000 --- a/src/math/i386/logf.s +++ /dev/null @@ -1,9 +0,0 @@ -.global logf -.type logf,@function -logf: - fldln2 - flds 4(%esp) - fyl2x - fstps 4(%esp) - flds 4(%esp) - ret diff --git a/src/math/i386/logl.s b/src/math/i386/logl.s deleted file mode 100644 index d4e3339..0000000 --- a/src/math/i386/logl.s +++ /dev/null @@ -1,7 +0,0 @@ -.global logl -.type logl,@function -logl: - fldln2 - fldt 4(%esp) - fyl2x - ret diff --git a/src/math/i386/lrint.c b/src/math/i386/lrint.c deleted file mode 100644 index 89563ab..0000000 --- a/src/math/i386/lrint.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long lrint(double x) -{ - long r; - __asm__ ("fistpl %0" : "=m"(r) : "t"(x) : "st"); - return r; -} diff --git a/src/math/i386/lrintf.c b/src/math/i386/lrintf.c deleted file mode 100644 index 0bbf29d..0000000 --- a/src/math/i386/lrintf.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long lrintf(float x) -{ - long r; - __asm__ ("fistpl %0" : "=m"(r) : "t"(x) : "st"); - return r; -} diff --git a/src/math/i386/lrintl.c b/src/math/i386/lrintl.c deleted file mode 100644 index eb8c090..0000000 --- a/src/math/i386/lrintl.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long lrintl(long double x) -{ - long r; - __asm__ ("fistpl %0" : "=m"(r) : "t"(x) : "st"); - return r; -} diff --git a/src/math/i386/remainder.c b/src/math/i386/remainder.c deleted file mode 100644 index c083df9..0000000 --- a/src/math/i386/remainder.c +++ /dev/null @@ -1,12 +0,0 @@ -#include - -double remainder(double x, double y) -{ - unsigned short fpsr; - // fprem1 does not introduce excess precision into x - do __asm__ ("fprem1; fnstsw %%ax" : "+t"(x), "=a"(fpsr) : "u"(y)); - while (fpsr & 0x400); - return x; -} - -weak_alias(remainder, drem); diff --git a/src/math/i386/remainderf.c b/src/math/i386/remainderf.c deleted file mode 100644 index 280207d..0000000 --- a/src/math/i386/remainderf.c +++ /dev/null @@ -1,12 +0,0 @@ -#include - -float remainderf(float x, float y) -{ - unsigned short fpsr; - // fprem1 does not introduce excess precision into x - do __asm__ ("fprem1; fnstsw %%ax" : "+t"(x), "=a"(fpsr) : "u"(y)); - while (fpsr & 0x400); - return x; -} - -weak_alias(remainderf, dremf); diff --git a/src/math/i386/remainderl.c b/src/math/i386/remainderl.c deleted file mode 100644 index 8cf7507..0000000 --- a/src/math/i386/remainderl.c +++ /dev/null @@ -1,9 +0,0 @@ -#include - -long double remainderl(long double x, long double y) -{ - unsigned short fpsr; - do __asm__ ("fprem1; fnstsw %%ax" : "+t"(x), "=a"(fpsr) : "u"(y)); - while (fpsr & 0x400); - return x; -} diff --git a/src/math/i386/remquo.s b/src/math/i386/remquo.s deleted file mode 100644 index 598e754..0000000 --- a/src/math/i386/remquo.s +++ /dev/null @@ -1,50 +0,0 @@ -.global remquof -.type remquof,@function -remquof: - mov 12(%esp),%ecx - flds 8(%esp) - flds 4(%esp) - mov 11(%esp),%dh - xor 7(%esp),%dh - jmp 1f - -.global remquol -.type remquol,@function -remquol: - mov 28(%esp),%ecx - fldt 16(%esp) - fldt 4(%esp) - mov 25(%esp),%dh - xor 13(%esp),%dh - jmp 1f - -.global remquo -.type remquo,@function -remquo: - mov 20(%esp),%ecx - fldl 12(%esp) - fldl 4(%esp) - mov 19(%esp),%dh - xor 11(%esp),%dh -1: fprem1 - fnstsw %ax - sahf - jp 1b - fstp %st(1) - mov %ah,%dl - shr %dl - and $1,%dl - mov %ah,%al - shr $5,%al - and $2,%al - or %al,%dl - mov %ah,%al - shl $2,%al - and $4,%al - or %al,%dl - test %dh,%dh - jns 1f - neg %dl -1: movsbl %dl,%edx - mov %edx,(%ecx) - ret diff --git a/src/math/i386/remquof.s b/src/math/i386/remquof.s deleted file mode 100644 index 511a6bc..0000000 --- a/src/math/i386/remquof.s +++ /dev/null @@ -1 +0,0 @@ -# see remquo.s diff --git a/src/math/i386/remquol.s b/src/math/i386/remquol.s deleted file mode 100644 index 511a6bc..0000000 --- a/src/math/i386/remquol.s +++ /dev/null @@ -1 +0,0 @@ -# see remquo.s diff --git a/src/math/i386/rint.c b/src/math/i386/rint.c deleted file mode 100644 index a5276a6..0000000 --- a/src/math/i386/rint.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double rint(double x) -{ - __asm__ ("frndint" : "+t"(x)); - return x; -} diff --git a/src/math/i386/rintf.c b/src/math/i386/rintf.c deleted file mode 100644 index bb4121a..0000000 --- a/src/math/i386/rintf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float rintf(float x) -{ - __asm__ ("frndint" : "+t"(x)); - return x; -} diff --git a/src/math/i386/rintl.c b/src/math/i386/rintl.c deleted file mode 100644 index e1a9207..0000000 --- a/src/math/i386/rintl.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -long double rintl(long double x) -{ - __asm__ ("frndint" : "+t"(x)); - return x; -} diff --git a/src/math/i386/scalbln.s b/src/math/i386/scalbln.s deleted file mode 100644 index c430f78..0000000 --- a/src/math/i386/scalbln.s +++ /dev/null @@ -1 +0,0 @@ -# see scalbn.s diff --git a/src/math/i386/scalblnf.s b/src/math/i386/scalblnf.s deleted file mode 100644 index 3f8e4b9..0000000 --- a/src/math/i386/scalblnf.s +++ /dev/null @@ -1 +0,0 @@ -# see scalbnf.s diff --git a/src/math/i386/scalblnl.s b/src/math/i386/scalblnl.s deleted file mode 100644 index 86fe562..0000000 --- a/src/math/i386/scalblnl.s +++ /dev/null @@ -1 +0,0 @@ -# see scalbnl.s diff --git a/src/math/i386/scalbn.s b/src/math/i386/scalbn.s deleted file mode 100644 index 8bf302f..0000000 --- a/src/math/i386/scalbn.s +++ /dev/null @@ -1,33 +0,0 @@ -.global ldexp -.type ldexp,@function -ldexp: - nop - -.global scalbln -.type scalbln,@function -scalbln: - nop - -.global scalbn -.type scalbn,@function -scalbn: - mov 12(%esp),%eax - add $0x3ffe,%eax - cmp $0x7ffd,%eax - jb 1f - sub $0x3ffe,%eax - sar $31,%eax - xor $0xfff,%eax - add $0x3ffe,%eax -1: inc %eax - fldl 4(%esp) - mov %eax,12(%esp) - mov $0x80000000,%eax - mov %eax,8(%esp) - xor %eax,%eax - mov %eax,4(%esp) - fldt 4(%esp) - fmulp - fstpl 4(%esp) - fldl 4(%esp) - ret diff --git a/src/math/i386/scalbnf.s b/src/math/i386/scalbnf.s deleted file mode 100644 index 9cb9ef5..0000000 --- a/src/math/i386/scalbnf.s +++ /dev/null @@ -1,32 +0,0 @@ -.global ldexpf -.type ldexpf,@function -ldexpf: - nop - -.global scalblnf -.type scalblnf,@function -scalblnf: - nop - -.global scalbnf -.type scalbnf,@function -scalbnf: - mov 8(%esp),%eax - add $0x3fe,%eax - cmp $0x7fd,%eax - jb 1f - sub $0x3fe,%eax - sar $31,%eax - xor $0x1ff,%eax - add $0x3fe,%eax -1: inc %eax - shl $20,%eax - flds 4(%esp) - mov %eax,8(%esp) - xor %eax,%eax - mov %eax,4(%esp) - fldl 4(%esp) - fmulp - fstps 4(%esp) - flds 4(%esp) - ret diff --git a/src/math/i386/scalbnl.s b/src/math/i386/scalbnl.s deleted file mode 100644 index 54414c2..0000000 --- a/src/math/i386/scalbnl.s +++ /dev/null @@ -1,32 +0,0 @@ -.global ldexpl -.type ldexpl,@function -ldexpl: - nop - -.global scalblnl -.type scalblnl,@function -scalblnl: - nop - -.global scalbnl -.type scalbnl,@function -scalbnl: - mov 16(%esp),%eax - add $0x3ffe,%eax - cmp $0x7ffd,%eax - jae 1f - inc %eax - fldt 4(%esp) - mov %eax,12(%esp) - mov $0x80000000,%eax - mov %eax,8(%esp) - xor %eax,%eax - mov %eax,4(%esp) - fldt 4(%esp) - fmulp - ret -1: fildl 16(%esp) - fldt 4(%esp) - fscale - fstp %st(1) - ret diff --git a/src/math/i386/sqrt.c b/src/math/i386/sqrt.c deleted file mode 100644 index 934fbcc..0000000 --- a/src/math/i386/sqrt.c +++ /dev/null @@ -1,15 +0,0 @@ -#include "libm.h" - -double sqrt(double x) -{ - union ldshape ux; - unsigned fpsr; - __asm__ ("fsqrt; fnstsw %%ax": "=t"(ux.f), "=a"(fpsr) : "0"(x)); - if ((ux.i.m & 0x7ff) != 0x400) - return (double)ux.f; - /* Rounding to double would have encountered an exact halfway case. - Adjust mantissa downwards if fsqrt rounded up, else upwards. - (result of fsqrt could not have been exact) */ - ux.i.m ^= (fpsr & 0x200) + 0x300; - return (double)ux.f; -} diff --git a/src/math/i386/sqrtf.c b/src/math/i386/sqrtf.c deleted file mode 100644 index 41c65c2..0000000 --- a/src/math/i386/sqrtf.c +++ /dev/null @@ -1,12 +0,0 @@ -#include - -float sqrtf(float x) -{ - long double t; - /* The long double result has sufficient precision so that - * second rounding to float still keeps the returned value - * correctly rounded, see Pierre Roux, "Innocuous Double - * Rounding of Basic Arithmetic Operations". */ - __asm__ ("fsqrt" : "=t"(t) : "0"(x)); - return (float)t; -} diff --git a/src/math/i386/sqrtl.c b/src/math/i386/sqrtl.c deleted file mode 100644 index 864cfcc..0000000 --- a/src/math/i386/sqrtl.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -long double sqrtl(long double x) -{ - __asm__ ("fsqrt" : "+t"(x)); - return x; -} diff --git a/src/math/i386/trunc.s b/src/math/i386/trunc.s deleted file mode 100644 index bc29f15..0000000 --- a/src/math/i386/trunc.s +++ /dev/null @@ -1 +0,0 @@ -# see floor.s diff --git a/src/math/i386/truncf.s b/src/math/i386/truncf.s deleted file mode 100644 index bc29f15..0000000 --- a/src/math/i386/truncf.s +++ /dev/null @@ -1 +0,0 @@ -# see floor.s diff --git a/src/math/i386/truncl.s b/src/math/i386/truncl.s deleted file mode 100644 index bc29f15..0000000 --- a/src/math/i386/truncl.s +++ /dev/null @@ -1 +0,0 @@ -# see floor.s diff --git a/src/math/ilogb.c b/src/math/ilogb.c deleted file mode 100644 index 64d4015..0000000 --- a/src/math/ilogb.c +++ /dev/null @@ -1,26 +0,0 @@ -#include -#include "libm.h" - -int ilogb(double x) -{ - #pragma STDC FENV_ACCESS ON - union {double f; uint64_t i;} u = {x}; - uint64_t i = u.i; - int e = i>>52 & 0x7ff; - - if (!e) { - i <<= 12; - if (i == 0) { - FORCE_EVAL(0/0.0f); - return FP_ILOGB0; - } - /* subnormal x */ - for (e = -0x3ff; i>>63 == 0; e--, i<<=1); - return e; - } - if (e == 0x7ff) { - FORCE_EVAL(0/0.0f); - return i<<12 ? FP_ILOGBNAN : INT_MAX; - } - return e - 0x3ff; -} diff --git a/src/math/ilogbf.c b/src/math/ilogbf.c deleted file mode 100644 index e23ba20..0000000 --- a/src/math/ilogbf.c +++ /dev/null @@ -1,26 +0,0 @@ -#include -#include "libm.h" - -int ilogbf(float x) -{ - #pragma STDC FENV_ACCESS ON - union {float f; uint32_t i;} u = {x}; - uint32_t i = u.i; - int e = i>>23 & 0xff; - - if (!e) { - i <<= 9; - if (i == 0) { - FORCE_EVAL(0/0.0f); - return FP_ILOGB0; - } - /* subnormal x */ - for (e = -0x7f; i>>31 == 0; e--, i<<=1); - return e; - } - if (e == 0xff) { - FORCE_EVAL(0/0.0f); - return i<<9 ? FP_ILOGBNAN : INT_MAX; - } - return e - 0x7f; -} diff --git a/src/math/ilogbl.c b/src/math/ilogbl.c deleted file mode 100644 index 7b1a9cf..0000000 --- a/src/math/ilogbl.c +++ /dev/null @@ -1,55 +0,0 @@ -#include -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -int ilogbl(long double x) -{ - return ilogb(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -int ilogbl(long double x) -{ - #pragma STDC FENV_ACCESS ON - union ldshape u = {x}; - uint64_t m = u.i.m; - int e = u.i.se & 0x7fff; - - if (!e) { - if (m == 0) { - FORCE_EVAL(0/0.0f); - return FP_ILOGB0; - } - /* subnormal x */ - for (e = -0x3fff+1; m>>63 == 0; e--, m<<=1); - return e; - } - if (e == 0x7fff) { - FORCE_EVAL(0/0.0f); - return m<<1 ? FP_ILOGBNAN : INT_MAX; - } - return e - 0x3fff; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -int ilogbl(long double x) -{ - #pragma STDC FENV_ACCESS ON - union ldshape u = {x}; - int e = u.i.se & 0x7fff; - - if (!e) { - if (x == 0) { - FORCE_EVAL(0/0.0f); - return FP_ILOGB0; - } - /* subnormal x */ - x *= 0x1p120; - return ilogbl(x) - 120; - } - if (e == 0x7fff) { - FORCE_EVAL(0/0.0f); - u.i.se = 0; - return u.f ? FP_ILOGBNAN : INT_MAX; - } - return e - 0x3fff; -} -#endif diff --git a/src/math/j0.c b/src/math/j0.c deleted file mode 100644 index d722d94..0000000 --- a/src/math/j0.c +++ /dev/null @@ -1,375 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_j0.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* j0(x), y0(x) - * Bessel function of the first and second kinds of order zero. - * Method -- j0(x): - * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... - * 2. Reduce x to |x| since j0(x)=j0(-x), and - * for x in (0,2) - * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; - * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) - * for x in (2,inf) - * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) - * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) - * as follow: - * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) - * = 1/sqrt(2) * (cos(x) + sin(x)) - * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) - * = 1/sqrt(2) * (sin(x) - cos(x)) - * (To avoid cancellation, use - * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - * to compute the worse one.) - * - * 3 Special cases - * j0(nan)= nan - * j0(0) = 1 - * j0(inf) = 0 - * - * Method -- y0(x): - * 1. For x<2. - * Since - * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) - * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. - * We use the following function to approximate y0, - * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 - * where - * U(z) = u00 + u01*z + ... + u06*z^6 - * V(z) = 1 + v01*z + ... + v04*z^4 - * with absolute approximation error bounded by 2**-72. - * Note: For tiny x, U/V = u0 and j0(x)~1, hence - * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) - * 2. For x>=2. - * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) - * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) - * by the method mentioned above. - * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. - */ - -#include "libm.h" - -static double pzero(double), qzero(double); - -static const double -invsqrtpi = 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ -tpi = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */ - -/* common method when |x|>=2 */ -static double common(uint32_t ix, double x, int y0) -{ - double s,c,ss,cc,z; - - /* - * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x-pi/4)-q0(x)*sin(x-pi/4)) - * y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x-pi/4)+q0(x)*cos(x-pi/4)) - * - * sin(x-pi/4) = (sin(x) - cos(x))/sqrt(2) - * cos(x-pi/4) = (sin(x) + cos(x))/sqrt(2) - * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - */ - s = sin(x); - c = cos(x); - if (y0) - c = -c; - cc = s+c; - /* avoid overflow in 2*x, big ulp error when x>=0x1p1023 */ - if (ix < 0x7fe00000) { - ss = s-c; - z = -cos(2*x); - if (s*c < 0) - cc = z/ss; - else - ss = z/cc; - if (ix < 0x48000000) { - if (y0) - ss = -ss; - cc = pzero(x)*cc-qzero(x)*ss; - } - } - return invsqrtpi*cc/sqrt(x); -} - -/* R0/S0 on [0, 2.00] */ -static const double -R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ -R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ -R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ -R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ -S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ -S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ -S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ -S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ - -double j0(double x) -{ - double z,r,s; - uint32_t ix; - - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; - - /* j0(+-inf)=0, j0(nan)=nan */ - if (ix >= 0x7ff00000) - return 1/(x*x); - x = fabs(x); - - if (ix >= 0x40000000) { /* |x| >= 2 */ - /* large ulp error near zeros: 2.4, 5.52, 8.6537,.. */ - return common(ix,x,0); - } - - /* 1 - x*x/4 + x*x*R(x^2)/S(x^2) */ - if (ix >= 0x3f200000) { /* |x| >= 2**-13 */ - /* up to 4ulp error close to 2 */ - z = x*x; - r = z*(R02+z*(R03+z*(R04+z*R05))); - s = 1+z*(S01+z*(S02+z*(S03+z*S04))); - return (1+x/2)*(1-x/2) + z*(r/s); - } - - /* 1 - x*x/4 */ - /* prevent underflow */ - /* inexact should be raised when x!=0, this is not done correctly */ - if (ix >= 0x38000000) /* |x| >= 2**-127 */ - x = 0.25*x*x; - return 1 - x; -} - -static const double -u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ -u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ -u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ -u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ -u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ -u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ -u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ -v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ -v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ -v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ -v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ - -double y0(double x) -{ - double z,u,v; - uint32_t ix,lx; - - EXTRACT_WORDS(ix, lx, x); - - /* y0(nan)=nan, y0(<0)=nan, y0(0)=-inf, y0(inf)=0 */ - if ((ix<<1 | lx) == 0) - return -1/0.0; - if (ix>>31) - return 0/0.0; - if (ix >= 0x7ff00000) - return 1/x; - - if (ix >= 0x40000000) { /* x >= 2 */ - /* large ulp errors near zeros: 3.958, 7.086,.. */ - return common(ix,x,1); - } - - /* U(x^2)/V(x^2) + (2/pi)*j0(x)*log(x) */ - if (ix >= 0x3e400000) { /* x >= 2**-27 */ - /* large ulp error near the first zero, x ~= 0.89 */ - z = x*x; - u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); - v = 1.0+z*(v01+z*(v02+z*(v03+z*v04))); - return u/v + tpi*(j0(x)*log(x)); - } - return u00 + tpi*log(x); -} - -/* The asymptotic expansions of pzero is - * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. - * For x >= 2, We approximate pzero by - * pzero(x) = 1 + (R/S) - * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 - * S = 1 + pS0*s^2 + ... + pS4*s^10 - * and - * | pzero(x)-1-R/S | <= 2 ** ( -60.26) - */ -static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ - -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ - -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ - -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ - -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ -}; -static const double pS8[5] = { - 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ - 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ - 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ - 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ - 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ -}; - -static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ - -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ - -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ - -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ - -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ - -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ - -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ -}; -static const double pS5[5] = { - 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ - 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ - 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ - 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ - 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ -}; - -static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ - -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ - -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ - -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ - -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ - -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ - -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ -}; -static const double pS3[5] = { - 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ - 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ - 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ - 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ - 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ -}; - -static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ - -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ - -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ - -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ - -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ - -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ - -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ -}; -static const double pS2[5] = { - 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ - 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ - 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ - 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ - 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ -}; - -static double pzero(double x) -{ - const double *p,*q; - double_t z,r,s; - uint32_t ix; - - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; - if (ix >= 0x40200000){p = pR8; q = pS8;} - else if (ix >= 0x40122E8B){p = pR5; q = pS5;} - else if (ix >= 0x4006DB6D){p = pR3; q = pS3;} - else /*ix >= 0x40000000*/ {p = pR2; q = pS2;} - z = 1.0/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = 1.0+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); - return 1.0 + r/s; -} - - -/* For x >= 8, the asymptotic expansions of qzero is - * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. - * We approximate pzero by - * qzero(x) = s*(-1.25 + (R/S)) - * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 - * S = 1 + qS0*s^2 + ... + qS5*s^12 - * and - * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) - */ -static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ - 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ - 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ - 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ - 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ -}; -static const double qS8[6] = { - 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ - 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ - 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ - 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ - 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ - -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ -}; - -static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ - 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ - 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ - 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ - 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ - 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ - 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ -}; -static const double qS5[6] = { - 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ - 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ - 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ - 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ - 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ - -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ -}; - -static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ - 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ - 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ - 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ - 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ - 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ - 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ -}; -static const double qS3[6] = { - 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ - 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ - 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ - 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ - 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ - -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ -}; - -static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ - 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ - 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ - 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ - 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ - 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ - 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ -}; -static const double qS2[6] = { - 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ - 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ - 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ - 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ - 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ - -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ -}; - -static double qzero(double x) -{ - const double *p,*q; - double_t s,r,z; - uint32_t ix; - - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; - if (ix >= 0x40200000){p = qR8; q = qS8;} - else if (ix >= 0x40122E8B){p = qR5; q = qS5;} - else if (ix >= 0x4006DB6D){p = qR3; q = qS3;} - else /*ix >= 0x40000000*/ {p = qR2; q = qS2;} - z = 1.0/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = 1.0+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); - return (-.125 + r/s)/x; -} diff --git a/src/math/j0f.c b/src/math/j0f.c deleted file mode 100644 index fab554a..0000000 --- a/src/math/j0f.c +++ /dev/null @@ -1,314 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_j0f.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#define _GNU_SOURCE -#include "libm.h" - -static float pzerof(float), qzerof(float); - -static const float -invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */ -tpi = 6.3661974669e-01; /* 0x3f22f983 */ - -static float common(uint32_t ix, float x, int y0) -{ - float z,s,c,ss,cc; - /* - * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) - * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) - */ - s = sinf(x); - c = cosf(x); - if (y0) - c = -c; - cc = s+c; - if (ix < 0x7f000000) { - ss = s-c; - z = -cosf(2*x); - if (s*c < 0) - cc = z/ss; - else - ss = z/cc; - if (ix < 0x58800000) { - if (y0) - ss = -ss; - cc = pzerof(x)*cc-qzerof(x)*ss; - } - } - return invsqrtpi*cc/sqrtf(x); -} - -/* R0/S0 on [0, 2.00] */ -static const float -R02 = 1.5625000000e-02, /* 0x3c800000 */ -R03 = -1.8997929874e-04, /* 0xb947352e */ -R04 = 1.8295404516e-06, /* 0x35f58e88 */ -R05 = -4.6183270541e-09, /* 0xb19eaf3c */ -S01 = 1.5619102865e-02, /* 0x3c7fe744 */ -S02 = 1.1692678527e-04, /* 0x38f53697 */ -S03 = 5.1354652442e-07, /* 0x3509daa6 */ -S04 = 1.1661400734e-09; /* 0x30a045e8 */ - -float j0f(float x) -{ - float z,r,s; - uint32_t ix; - - GET_FLOAT_WORD(ix, x); - ix &= 0x7fffffff; - if (ix >= 0x7f800000) - return 1/(x*x); - x = fabsf(x); - - if (ix >= 0x40000000) { /* |x| >= 2 */ - /* large ulp error near zeros */ - return common(ix, x, 0); - } - if (ix >= 0x3a000000) { /* |x| >= 2**-11 */ - /* up to 4ulp error near 2 */ - z = x*x; - r = z*(R02+z*(R03+z*(R04+z*R05))); - s = 1+z*(S01+z*(S02+z*(S03+z*S04))); - return (1+x/2)*(1-x/2) + z*(r/s); - } - if (ix >= 0x21800000) /* |x| >= 2**-60 */ - x = 0.25f*x*x; - return 1 - x; -} - -static const float -u00 = -7.3804296553e-02, /* 0xbd9726b5 */ -u01 = 1.7666645348e-01, /* 0x3e34e80d */ -u02 = -1.3818567619e-02, /* 0xbc626746 */ -u03 = 3.4745343146e-04, /* 0x39b62a69 */ -u04 = -3.8140706238e-06, /* 0xb67ff53c */ -u05 = 1.9559013964e-08, /* 0x32a802ba */ -u06 = -3.9820518410e-11, /* 0xae2f21eb */ -v01 = 1.2730483897e-02, /* 0x3c509385 */ -v02 = 7.6006865129e-05, /* 0x389f65e0 */ -v03 = 2.5915085189e-07, /* 0x348b216c */ -v04 = 4.4111031494e-10; /* 0x2ff280c2 */ - -float y0f(float x) -{ - float z,u,v; - uint32_t ix; - - GET_FLOAT_WORD(ix, x); - if ((ix & 0x7fffffff) == 0) - return -1/0.0f; - if (ix>>31) - return 0/0.0f; - if (ix >= 0x7f800000) - return 1/x; - if (ix >= 0x40000000) { /* |x| >= 2.0 */ - /* large ulp error near zeros */ - return common(ix,x,1); - } - if (ix >= 0x39000000) { /* x >= 2**-13 */ - /* large ulp error at x ~= 0.89 */ - z = x*x; - u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); - v = 1+z*(v01+z*(v02+z*(v03+z*v04))); - return u/v + tpi*(j0f(x)*logf(x)); - } - return u00 + tpi*logf(x); -} - -/* The asymptotic expansions of pzero is - * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. - * For x >= 2, We approximate pzero by - * pzero(x) = 1 + (R/S) - * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 - * S = 1 + pS0*s^2 + ... + pS4*s^10 - * and - * | pzero(x)-1-R/S | <= 2 ** ( -60.26) - */ -static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ - 0.0000000000e+00, /* 0x00000000 */ - -7.0312500000e-02, /* 0xbd900000 */ - -8.0816707611e+00, /* 0xc1014e86 */ - -2.5706311035e+02, /* 0xc3808814 */ - -2.4852163086e+03, /* 0xc51b5376 */ - -5.2530439453e+03, /* 0xc5a4285a */ -}; -static const float pS8[5] = { - 1.1653436279e+02, /* 0x42e91198 */ - 3.8337448730e+03, /* 0x456f9beb */ - 4.0597855469e+04, /* 0x471e95db */ - 1.1675296875e+05, /* 0x47e4087c */ - 4.7627726562e+04, /* 0x473a0bba */ -}; -static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ - -1.1412546255e-11, /* 0xad48c58a */ - -7.0312492549e-02, /* 0xbd8fffff */ - -4.1596107483e+00, /* 0xc0851b88 */ - -6.7674766541e+01, /* 0xc287597b */ - -3.3123129272e+02, /* 0xc3a59d9b */ - -3.4643338013e+02, /* 0xc3ad3779 */ -}; -static const float pS5[5] = { - 6.0753936768e+01, /* 0x42730408 */ - 1.0512523193e+03, /* 0x44836813 */ - 5.9789707031e+03, /* 0x45bad7c4 */ - 9.6254453125e+03, /* 0x461665c8 */ - 2.4060581055e+03, /* 0x451660ee */ -}; - -static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ - -2.5470459075e-09, /* 0xb12f081b */ - -7.0311963558e-02, /* 0xbd8fffb8 */ - -2.4090321064e+00, /* 0xc01a2d95 */ - -2.1965976715e+01, /* 0xc1afba52 */ - -5.8079170227e+01, /* 0xc2685112 */ - -3.1447946548e+01, /* 0xc1fb9565 */ -}; -static const float pS3[5] = { - 3.5856033325e+01, /* 0x420f6c94 */ - 3.6151397705e+02, /* 0x43b4c1ca */ - 1.1936077881e+03, /* 0x44953373 */ - 1.1279968262e+03, /* 0x448cffe6 */ - 1.7358093262e+02, /* 0x432d94b8 */ -}; - -static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ - -8.8753431271e-08, /* 0xb3be98b7 */ - -7.0303097367e-02, /* 0xbd8ffb12 */ - -1.4507384300e+00, /* 0xbfb9b1cc */ - -7.6356959343e+00, /* 0xc0f4579f */ - -1.1193166733e+01, /* 0xc1331736 */ - -3.2336456776e+00, /* 0xc04ef40d */ -}; -static const float pS2[5] = { - 2.2220300674e+01, /* 0x41b1c32d */ - 1.3620678711e+02, /* 0x430834f0 */ - 2.7047027588e+02, /* 0x43873c32 */ - 1.5387539673e+02, /* 0x4319e01a */ - 1.4657617569e+01, /* 0x416a859a */ -}; - -static float pzerof(float x) -{ - const float *p,*q; - float_t z,r,s; - uint32_t ix; - - GET_FLOAT_WORD(ix, x); - ix &= 0x7fffffff; - if (ix >= 0x41000000){p = pR8; q = pS8;} - else if (ix >= 0x409173eb){p = pR5; q = pS5;} - else if (ix >= 0x4036d917){p = pR3; q = pS3;} - else /*ix >= 0x40000000*/ {p = pR2; q = pS2;} - z = 1.0f/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); - return 1.0f + r/s; -} - - -/* For x >= 8, the asymptotic expansions of qzero is - * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. - * We approximate pzero by - * qzero(x) = s*(-1.25 + (R/S)) - * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 - * S = 1 + qS0*s^2 + ... + qS5*s^12 - * and - * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) - */ -static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ - 0.0000000000e+00, /* 0x00000000 */ - 7.3242187500e-02, /* 0x3d960000 */ - 1.1768206596e+01, /* 0x413c4a93 */ - 5.5767340088e+02, /* 0x440b6b19 */ - 8.8591972656e+03, /* 0x460a6cca */ - 3.7014625000e+04, /* 0x471096a0 */ -}; -static const float qS8[6] = { - 1.6377603149e+02, /* 0x4323c6aa */ - 8.0983447266e+03, /* 0x45fd12c2 */ - 1.4253829688e+05, /* 0x480b3293 */ - 8.0330925000e+05, /* 0x49441ed4 */ - 8.4050156250e+05, /* 0x494d3359 */ - -3.4389928125e+05, /* 0xc8a7eb69 */ -}; - -static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ - 1.8408595828e-11, /* 0x2da1ec79 */ - 7.3242180049e-02, /* 0x3d95ffff */ - 5.8356351852e+00, /* 0x40babd86 */ - 1.3511157227e+02, /* 0x43071c90 */ - 1.0272437744e+03, /* 0x448067cd */ - 1.9899779053e+03, /* 0x44f8bf4b */ -}; -static const float qS5[6] = { - 8.2776611328e+01, /* 0x42a58da0 */ - 2.0778142090e+03, /* 0x4501dd07 */ - 1.8847289062e+04, /* 0x46933e94 */ - 5.6751113281e+04, /* 0x475daf1d */ - 3.5976753906e+04, /* 0x470c88c1 */ - -5.3543427734e+03, /* 0xc5a752be */ -}; - -static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ - 4.3774099900e-09, /* 0x3196681b */ - 7.3241114616e-02, /* 0x3d95ff70 */ - 3.3442313671e+00, /* 0x405607e3 */ - 4.2621845245e+01, /* 0x422a7cc5 */ - 1.7080809021e+02, /* 0x432acedf */ - 1.6673394775e+02, /* 0x4326bbe4 */ -}; -static const float qS3[6] = { - 4.8758872986e+01, /* 0x42430916 */ - 7.0968920898e+02, /* 0x44316c1c */ - 3.7041481934e+03, /* 0x4567825f */ - 6.4604252930e+03, /* 0x45c9e367 */ - 2.5163337402e+03, /* 0x451d4557 */ - -1.4924745178e+02, /* 0xc3153f59 */ -}; - -static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ - 1.5044444979e-07, /* 0x342189db */ - 7.3223426938e-02, /* 0x3d95f62a */ - 1.9981917143e+00, /* 0x3fffc4bf */ - 1.4495602608e+01, /* 0x4167edfd */ - 3.1666231155e+01, /* 0x41fd5471 */ - 1.6252708435e+01, /* 0x4182058c */ -}; -static const float qS2[6] = { - 3.0365585327e+01, /* 0x41f2ecb8 */ - 2.6934811401e+02, /* 0x4386ac8f */ - 8.4478375244e+02, /* 0x44533229 */ - 8.8293585205e+02, /* 0x445cbbe5 */ - 2.1266638184e+02, /* 0x4354aa98 */ - -5.3109550476e+00, /* 0xc0a9f358 */ -}; - -static float qzerof(float x) -{ - const float *p,*q; - float_t s,r,z; - uint32_t ix; - - GET_FLOAT_WORD(ix, x); - ix &= 0x7fffffff; - if (ix >= 0x41000000){p = qR8; q = qS8;} - else if (ix >= 0x409173eb){p = qR5; q = qS5;} - else if (ix >= 0x4036d917){p = qR3; q = qS3;} - else /*ix >= 0x40000000*/ {p = qR2; q = qS2;} - z = 1.0f/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); - return (-.125f + r/s)/x; -} diff --git a/src/math/j1.c b/src/math/j1.c deleted file mode 100644 index df724d1..0000000 --- a/src/math/j1.c +++ /dev/null @@ -1,362 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_j1.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* j1(x), y1(x) - * Bessel function of the first and second kinds of order zero. - * Method -- j1(x): - * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... - * 2. Reduce x to |x| since j1(x)=-j1(-x), and - * for x in (0,2) - * j1(x) = x/2 + x*z*R0/S0, where z = x*x; - * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) - * for x in (2,inf) - * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) - * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) - * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) - * as follow: - * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) - * = 1/sqrt(2) * (sin(x) - cos(x)) - * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) - * = -1/sqrt(2) * (sin(x) + cos(x)) - * (To avoid cancellation, use - * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - * to compute the worse one.) - * - * 3 Special cases - * j1(nan)= nan - * j1(0) = 0 - * j1(inf) = 0 - * - * Method -- y1(x): - * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN - * 2. For x<2. - * Since - * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) - * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. - * We use the following function to approximate y1, - * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 - * where for x in [0,2] (abs err less than 2**-65.89) - * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 - * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 - * Note: For tiny x, 1/x dominate y1 and hence - * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) - * 3. For x>=2. - * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) - * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) - * by method mentioned above. - */ - -#include "libm.h" - -static double pone(double), qone(double); - -static const double -invsqrtpi = 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ -tpi = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */ - -static double common(uint32_t ix, double x, int y1, int sign) -{ - double z,s,c,ss,cc; - - /* - * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x-3pi/4)-q1(x)*sin(x-3pi/4)) - * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x-3pi/4)+q1(x)*cos(x-3pi/4)) - * - * sin(x-3pi/4) = -(sin(x) + cos(x))/sqrt(2) - * cos(x-3pi/4) = (sin(x) - cos(x))/sqrt(2) - * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - */ - s = sin(x); - if (y1) - s = -s; - c = cos(x); - cc = s-c; - if (ix < 0x7fe00000) { - /* avoid overflow in 2*x */ - ss = -s-c; - z = cos(2*x); - if (s*c > 0) - cc = z/ss; - else - ss = z/cc; - if (ix < 0x48000000) { - if (y1) - ss = -ss; - cc = pone(x)*cc-qone(x)*ss; - } - } - if (sign) - cc = -cc; - return invsqrtpi*cc/sqrt(x); -} - -/* R0/S0 on [0,2] */ -static const double -r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ -r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ -r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ -r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ -s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ -s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ -s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ -s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ -s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ - -double j1(double x) -{ - double z,r,s; - uint32_t ix; - int sign; - - GET_HIGH_WORD(ix, x); - sign = ix>>31; - ix &= 0x7fffffff; - if (ix >= 0x7ff00000) - return 1/(x*x); - if (ix >= 0x40000000) /* |x| >= 2 */ - return common(ix, fabs(x), 0, sign); - if (ix >= 0x38000000) { /* |x| >= 2**-127 */ - z = x*x; - r = z*(r00+z*(r01+z*(r02+z*r03))); - s = 1+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); - z = r/s; - } else - /* avoid underflow, raise inexact if x!=0 */ - z = x; - return (0.5 + z)*x; -} - -static const double U0[5] = { - -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ - 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ - -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ - 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ - -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ -}; -static const double V0[5] = { - 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ - 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ - 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ - 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ - 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ -}; - -double y1(double x) -{ - double z,u,v; - uint32_t ix,lx; - - EXTRACT_WORDS(ix, lx, x); - /* y1(nan)=nan, y1(<0)=nan, y1(0)=-inf, y1(inf)=0 */ - if ((ix<<1 | lx) == 0) - return -1/0.0; - if (ix>>31) - return 0/0.0; - if (ix >= 0x7ff00000) - return 1/x; - - if (ix >= 0x40000000) /* x >= 2 */ - return common(ix, x, 1, 0); - if (ix < 0x3c900000) /* x < 2**-54 */ - return -tpi/x; - z = x*x; - u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); - v = 1+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); - return x*(u/v) + tpi*(j1(x)*log(x)-1/x); -} - -/* For x >= 8, the asymptotic expansions of pone is - * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. - * We approximate pone by - * pone(x) = 1 + (R/S) - * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 - * S = 1 + ps0*s^2 + ... + ps4*s^10 - * and - * | pone(x)-1-R/S | <= 2 ** ( -60.06) - */ - -static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ - 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ - 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ - 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ - 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ -}; -static const double ps8[5] = { - 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ - 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ - 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ - 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ - 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ -}; - -static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ - 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ - 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ - 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ - 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ - 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ - 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ -}; -static const double ps5[5] = { - 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ - 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ - 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ - 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ - 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ -}; - -static const double pr3[6] = { - 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ - 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ - 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ - 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ - 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ - 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ -}; -static const double ps3[5] = { - 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ - 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ - 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ - 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ - 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ -}; - -static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ - 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ - 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ - 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ - 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ - 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ - 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ -}; -static const double ps2[5] = { - 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ - 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ - 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ - 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ - 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ -}; - -static double pone(double x) -{ - const double *p,*q; - double_t z,r,s; - uint32_t ix; - - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; - if (ix >= 0x40200000){p = pr8; q = ps8;} - else if (ix >= 0x40122E8B){p = pr5; q = ps5;} - else if (ix >= 0x4006DB6D){p = pr3; q = ps3;} - else /*ix >= 0x40000000*/ {p = pr2; q = ps2;} - z = 1.0/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = 1.0+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); - return 1.0+ r/s; -} - -/* For x >= 8, the asymptotic expansions of qone is - * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. - * We approximate pone by - * qone(x) = s*(0.375 + (R/S)) - * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 - * S = 1 + qs1*s^2 + ... + qs6*s^12 - * and - * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) - */ - -static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ - -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ - -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ - -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ - -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ -}; -static const double qs8[6] = { - 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ - 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ - 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ - 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ - 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ - -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ -}; - -static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ - -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ - -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ - -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ - -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ - -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ - -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ -}; -static const double qs5[6] = { - 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ - 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ - 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ - 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ - 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ - -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ -}; - -static const double qr3[6] = { - -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ - -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ - -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ - -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ - -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ - -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ -}; -static const double qs3[6] = { - 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ - 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ - 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ - 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ - 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ - -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ -}; - -static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ - -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ - -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ - -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ - -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ - -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ - -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ -}; -static const double qs2[6] = { - 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ - 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ - 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ - 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ - 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ - -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ -}; - -static double qone(double x) -{ - const double *p,*q; - double_t s,r,z; - uint32_t ix; - - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; - if (ix >= 0x40200000){p = qr8; q = qs8;} - else if (ix >= 0x40122E8B){p = qr5; q = qs5;} - else if (ix >= 0x4006DB6D){p = qr3; q = qs3;} - else /*ix >= 0x40000000*/ {p = qr2; q = qs2;} - z = 1.0/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = 1.0+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); - return (.375 + r/s)/x; -} diff --git a/src/math/j1f.c b/src/math/j1f.c deleted file mode 100644 index 3434c53..0000000 --- a/src/math/j1f.c +++ /dev/null @@ -1,310 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_j1f.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#define _GNU_SOURCE -#include "libm.h" - -static float ponef(float), qonef(float); - -static const float -invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */ -tpi = 6.3661974669e-01; /* 0x3f22f983 */ - -static float common(uint32_t ix, float x, int y1, int sign) -{ - double z,s,c,ss,cc; - - s = sinf(x); - if (y1) - s = -s; - c = cosf(x); - cc = s-c; - if (ix < 0x7f000000) { - ss = -s-c; - z = cosf(2*x); - if (s*c > 0) - cc = z/ss; - else - ss = z/cc; - if (ix < 0x58800000) { - if (y1) - ss = -ss; - cc = ponef(x)*cc-qonef(x)*ss; - } - } - if (sign) - cc = -cc; - return invsqrtpi*cc/sqrtf(x); -} - -/* R0/S0 on [0,2] */ -static const float -r00 = -6.2500000000e-02, /* 0xbd800000 */ -r01 = 1.4070566976e-03, /* 0x3ab86cfd */ -r02 = -1.5995563444e-05, /* 0xb7862e36 */ -r03 = 4.9672799207e-08, /* 0x335557d2 */ -s01 = 1.9153760746e-02, /* 0x3c9ce859 */ -s02 = 1.8594678841e-04, /* 0x3942fab6 */ -s03 = 1.1771846857e-06, /* 0x359dffc2 */ -s04 = 5.0463624390e-09, /* 0x31ad6446 */ -s05 = 1.2354227016e-11; /* 0x2d59567e */ - -float j1f(float x) -{ - float z,r,s; - uint32_t ix; - int sign; - - GET_FLOAT_WORD(ix, x); - sign = ix>>31; - ix &= 0x7fffffff; - if (ix >= 0x7f800000) - return 1/(x*x); - if (ix >= 0x40000000) /* |x| >= 2 */ - return common(ix, fabsf(x), 0, sign); - if (ix >= 0x39000000) { /* |x| >= 2**-13 */ - z = x*x; - r = z*(r00+z*(r01+z*(r02+z*r03))); - s = 1+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); - z = 0.5f + r/s; - } else - z = 0.5f; - return z*x; -} - -static const float U0[5] = { - -1.9605709612e-01, /* 0xbe48c331 */ - 5.0443872809e-02, /* 0x3d4e9e3c */ - -1.9125689287e-03, /* 0xbafaaf2a */ - 2.3525259166e-05, /* 0x37c5581c */ - -9.1909917899e-08, /* 0xb3c56003 */ -}; -static const float V0[5] = { - 1.9916731864e-02, /* 0x3ca3286a */ - 2.0255257550e-04, /* 0x3954644b */ - 1.3560879779e-06, /* 0x35b602d4 */ - 6.2274145840e-09, /* 0x31d5f8eb */ - 1.6655924903e-11, /* 0x2d9281cf */ -}; - -float y1f(float x) -{ - float z,u,v; - uint32_t ix; - - GET_FLOAT_WORD(ix, x); - if ((ix & 0x7fffffff) == 0) - return -1/0.0f; - if (ix>>31) - return 0/0.0f; - if (ix >= 0x7f800000) - return 1/x; - if (ix >= 0x40000000) /* |x| >= 2.0 */ - return common(ix,x,1,0); - if (ix < 0x33000000) /* x < 2**-25 */ - return -tpi/x; - z = x*x; - u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); - v = 1.0f+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); - return x*(u/v) + tpi*(j1f(x)*logf(x)-1.0f/x); -} - -/* For x >= 8, the asymptotic expansions of pone is - * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. - * We approximate pone by - * pone(x) = 1 + (R/S) - * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 - * S = 1 + ps0*s^2 + ... + ps4*s^10 - * and - * | pone(x)-1-R/S | <= 2 ** ( -60.06) - */ - -static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ - 0.0000000000e+00, /* 0x00000000 */ - 1.1718750000e-01, /* 0x3df00000 */ - 1.3239480972e+01, /* 0x4153d4ea */ - 4.1205184937e+02, /* 0x43ce06a3 */ - 3.8747453613e+03, /* 0x45722bed */ - 7.9144794922e+03, /* 0x45f753d6 */ -}; -static const float ps8[5] = { - 1.1420736694e+02, /* 0x42e46a2c */ - 3.6509309082e+03, /* 0x45642ee5 */ - 3.6956207031e+04, /* 0x47105c35 */ - 9.7602796875e+04, /* 0x47bea166 */ - 3.0804271484e+04, /* 0x46f0a88b */ -}; - -static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ - 1.3199052094e-11, /* 0x2d68333f */ - 1.1718749255e-01, /* 0x3defffff */ - 6.8027510643e+00, /* 0x40d9b023 */ - 1.0830818176e+02, /* 0x42d89dca */ - 5.1763616943e+02, /* 0x440168b7 */ - 5.2871520996e+02, /* 0x44042dc6 */ -}; -static const float ps5[5] = { - 5.9280597687e+01, /* 0x426d1f55 */ - 9.9140142822e+02, /* 0x4477d9b1 */ - 5.3532670898e+03, /* 0x45a74a23 */ - 7.8446904297e+03, /* 0x45f52586 */ - 1.5040468750e+03, /* 0x44bc0180 */ -}; - -static const float pr3[6] = { - 3.0250391081e-09, /* 0x314fe10d */ - 1.1718686670e-01, /* 0x3defffab */ - 3.9329774380e+00, /* 0x407bb5e7 */ - 3.5119403839e+01, /* 0x420c7a45 */ - 9.1055007935e+01, /* 0x42b61c2a */ - 4.8559066772e+01, /* 0x42423c7c */ -}; -static const float ps3[5] = { - 3.4791309357e+01, /* 0x420b2a4d */ - 3.3676245117e+02, /* 0x43a86198 */ - 1.0468714600e+03, /* 0x4482dbe3 */ - 8.9081134033e+02, /* 0x445eb3ed */ - 1.0378793335e+02, /* 0x42cf936c */ -}; - -static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ - 1.0771083225e-07, /* 0x33e74ea8 */ - 1.1717621982e-01, /* 0x3deffa16 */ - 2.3685150146e+00, /* 0x401795c0 */ - 1.2242610931e+01, /* 0x4143e1bc */ - 1.7693971634e+01, /* 0x418d8d41 */ - 5.0735230446e+00, /* 0x40a25a4d */ -}; -static const float ps2[5] = { - 2.1436485291e+01, /* 0x41ab7dec */ - 1.2529022980e+02, /* 0x42fa9499 */ - 2.3227647400e+02, /* 0x436846c7 */ - 1.1767937469e+02, /* 0x42eb5bd7 */ - 8.3646392822e+00, /* 0x4105d590 */ -}; - -static float ponef(float x) -{ - const float *p,*q; - float_t z,r,s; - uint32_t ix; - - GET_FLOAT_WORD(ix, x); - ix &= 0x7fffffff; - if (ix >= 0x41000000){p = pr8; q = ps8;} - else if (ix >= 0x409173eb){p = pr5; q = ps5;} - else if (ix >= 0x4036d917){p = pr3; q = ps3;} - else /*ix >= 0x40000000*/ {p = pr2; q = ps2;} - z = 1.0f/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); - return 1.0f + r/s; -} - -/* For x >= 8, the asymptotic expansions of qone is - * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. - * We approximate pone by - * qone(x) = s*(0.375 + (R/S)) - * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 - * S = 1 + qs1*s^2 + ... + qs6*s^12 - * and - * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) - */ - -static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ - 0.0000000000e+00, /* 0x00000000 */ - -1.0253906250e-01, /* 0xbdd20000 */ - -1.6271753311e+01, /* 0xc1822c8d */ - -7.5960174561e+02, /* 0xc43de683 */ - -1.1849806641e+04, /* 0xc639273a */ - -4.8438511719e+04, /* 0xc73d3683 */ -}; -static const float qs8[6] = { - 1.6139537048e+02, /* 0x43216537 */ - 7.8253862305e+03, /* 0x45f48b17 */ - 1.3387534375e+05, /* 0x4802bcd6 */ - 7.1965775000e+05, /* 0x492fb29c */ - 6.6660125000e+05, /* 0x4922be94 */ - -2.9449025000e+05, /* 0xc88fcb48 */ -}; - -static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ - -2.0897993405e-11, /* 0xadb7d219 */ - -1.0253904760e-01, /* 0xbdd1fffe */ - -8.0564479828e+00, /* 0xc100e736 */ - -1.8366960144e+02, /* 0xc337ab6b */ - -1.3731937256e+03, /* 0xc4aba633 */ - -2.6124443359e+03, /* 0xc523471c */ -}; -static const float qs5[6] = { - 8.1276550293e+01, /* 0x42a28d98 */ - 1.9917987061e+03, /* 0x44f8f98f */ - 1.7468484375e+04, /* 0x468878f8 */ - 4.9851425781e+04, /* 0x4742bb6d */ - 2.7948074219e+04, /* 0x46da5826 */ - -4.7191835938e+03, /* 0xc5937978 */ -}; - -static const float qr3[6] = { - -5.0783124372e-09, /* 0xb1ae7d4f */ - -1.0253783315e-01, /* 0xbdd1ff5b */ - -4.6101160049e+00, /* 0xc0938612 */ - -5.7847221375e+01, /* 0xc267638e */ - -2.2824453735e+02, /* 0xc3643e9a */ - -2.1921012878e+02, /* 0xc35b35cb */ -}; -static const float qs3[6] = { - 4.7665153503e+01, /* 0x423ea91e */ - 6.7386511230e+02, /* 0x4428775e */ - 3.3801528320e+03, /* 0x45534272 */ - 5.5477290039e+03, /* 0x45ad5dd5 */ - 1.9031191406e+03, /* 0x44ede3d0 */ - -1.3520118713e+02, /* 0xc3073381 */ -}; - -static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ - -1.7838172539e-07, /* 0xb43f8932 */ - -1.0251704603e-01, /* 0xbdd1f475 */ - -2.7522056103e+00, /* 0xc0302423 */ - -1.9663616180e+01, /* 0xc19d4f16 */ - -4.2325313568e+01, /* 0xc2294d1f */ - -2.1371921539e+01, /* 0xc1aaf9b2 */ -}; -static const float qs2[6] = { - 2.9533363342e+01, /* 0x41ec4454 */ - 2.5298155212e+02, /* 0x437cfb47 */ - 7.5750280762e+02, /* 0x443d602e */ - 7.3939318848e+02, /* 0x4438d92a */ - 1.5594900513e+02, /* 0x431bf2f2 */ - -4.9594988823e+00, /* 0xc09eb437 */ -}; - -static float qonef(float x) -{ - const float *p,*q; - float_t s,r,z; - uint32_t ix; - - GET_FLOAT_WORD(ix, x); - ix &= 0x7fffffff; - if (ix >= 0x41000000){p = qr8; q = qs8;} - else if (ix >= 0x409173eb){p = qr5; q = qs5;} - else if (ix >= 0x4036d917){p = qr3; q = qs3;} - else /*ix >= 0x40000000*/ {p = qr2; q = qs2;} - z = 1.0f/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); - return (.375f + r/s)/x; -} diff --git a/src/math/jn.c b/src/math/jn.c deleted file mode 100644 index 4878a54..0000000 --- a/src/math/jn.c +++ /dev/null @@ -1,280 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_jn.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* - * jn(n, x), yn(n, x) - * floating point Bessel's function of the 1st and 2nd kind - * of order n - * - * Special cases: - * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; - * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. - * Note 2. About jn(n,x), yn(n,x) - * For n=0, j0(x) is called, - * for n=1, j1(x) is called, - * for n<=x, forward recursion is used starting - * from values of j0(x) and j1(x). - * for n>x, a continued fraction approximation to - * j(n,x)/j(n-1,x) is evaluated and then backward - * recursion is used starting from a supposed value - * for j(n,x). The resulting value of j(0,x) is - * compared with the actual value to correct the - * supposed value of j(n,x). - * - * yn(n,x) is similar in all respects, except - * that forward recursion is used for all - * values of n>1. - */ - -#include "libm.h" - -static const double invsqrtpi = 5.64189583547756279280e-01; /* 0x3FE20DD7, 0x50429B6D */ - -double jn(int n, double x) -{ - uint32_t ix, lx; - int nm1, i, sign; - double a, b, temp; - - EXTRACT_WORDS(ix, lx, x); - sign = ix>>31; - ix &= 0x7fffffff; - - if ((ix | (lx|-lx)>>31) > 0x7ff00000) /* nan */ - return x; - - /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) - * Thus, J(-n,x) = J(n,-x) - */ - /* nm1 = |n|-1 is used instead of |n| to handle n==INT_MIN */ - if (n == 0) - return j0(x); - if (n < 0) { - nm1 = -(n+1); - x = -x; - sign ^= 1; - } else - nm1 = n-1; - if (nm1 == 0) - return j1(x); - - sign &= n; /* even n: 0, odd n: signbit(x) */ - x = fabs(x); - if ((ix|lx) == 0 || ix == 0x7ff00000) /* if x is 0 or inf */ - b = 0.0; - else if (nm1 < x) { - /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ - if (ix >= 0x52d00000) { /* x > 2**302 */ - /* (x >> n**2) - * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) - * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) - * Let s=sin(x), c=cos(x), - * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then - * - * n sin(xn)*sqt2 cos(xn)*sqt2 - * ---------------------------------- - * 0 s-c c+s - * 1 -s-c -c+s - * 2 -s+c -c-s - * 3 s+c c-s - */ - switch(nm1&3) { - case 0: temp = -cos(x)+sin(x); break; - case 1: temp = -cos(x)-sin(x); break; - case 2: temp = cos(x)-sin(x); break; - default: - case 3: temp = cos(x)+sin(x); break; - } - b = invsqrtpi*temp/sqrt(x); - } else { - a = j0(x); - b = j1(x); - for (i=0; i 32) /* underflow */ - b = 0.0; - else { - temp = x*0.5; - b = temp; - a = 1.0; - for (i=2; i<=nm1+1; i++) { - a *= (double)i; /* a = n! */ - b *= temp; /* b = (x/2)^n */ - } - b = b/a; - } - } else { - /* use backward recurrence */ - /* x x^2 x^2 - * J(n,x)/J(n-1,x) = ---- ------ ------ ..... - * 2n - 2(n+1) - 2(n+2) - * - * 1 1 1 - * (for large x) = ---- ------ ------ ..... - * 2n 2(n+1) 2(n+2) - * -- - ------ - ------ - - * x x x - * - * Let w = 2n/x and h=2/x, then the above quotient - * is equal to the continued fraction: - * 1 - * = ----------------------- - * 1 - * w - ----------------- - * 1 - * w+h - --------- - * w+2h - ... - * - * To determine how many terms needed, let - * Q(0) = w, Q(1) = w(w+h) - 1, - * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), - * When Q(k) > 1e4 good for single - * When Q(k) > 1e9 good for double - * When Q(k) > 1e17 good for quadruple - */ - /* determine k */ - double t,q0,q1,w,h,z,tmp,nf; - int k; - - nf = nm1 + 1.0; - w = 2*nf/x; - h = 2/x; - z = w+h; - q0 = w; - q1 = w*z - 1.0; - k = 1; - while (q1 < 1.0e9) { - k += 1; - z += h; - tmp = z*q1 - q0; - q0 = q1; - q1 = tmp; - } - for (t=0.0, i=k; i>=0; i--) - t = 1/(2*(i+nf)/x - t); - a = t; - b = 1.0; - /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) - * Hence, if n*(log(2n/x)) > ... - * single 8.8722839355e+01 - * double 7.09782712893383973096e+02 - * long double 1.1356523406294143949491931077970765006170e+04 - * then recurrent value may overflow and the result is - * likely underflow to zero - */ - tmp = nf*log(fabs(w)); - if (tmp < 7.09782712893383973096e+02) { - for (i=nm1; i>0; i--) { - temp = b; - b = b*(2.0*i)/x - a; - a = temp; - } - } else { - for (i=nm1; i>0; i--) { - temp = b; - b = b*(2.0*i)/x - a; - a = temp; - /* scale b to avoid spurious overflow */ - if (b > 0x1p500) { - a /= b; - t /= b; - b = 1.0; - } - } - } - z = j0(x); - w = j1(x); - if (fabs(z) >= fabs(w)) - b = t*z/b; - else - b = t*w/a; - } - } - return sign ? -b : b; -} - - -double yn(int n, double x) -{ - uint32_t ix, lx, ib; - int nm1, sign, i; - double a, b, temp; - - EXTRACT_WORDS(ix, lx, x); - sign = ix>>31; - ix &= 0x7fffffff; - - if ((ix | (lx|-lx)>>31) > 0x7ff00000) /* nan */ - return x; - if (sign && (ix|lx)!=0) /* x < 0 */ - return 0/0.0; - if (ix == 0x7ff00000) - return 0.0; - - if (n == 0) - return y0(x); - if (n < 0) { - nm1 = -(n+1); - sign = n&1; - } else { - nm1 = n-1; - sign = 0; - } - if (nm1 == 0) - return sign ? -y1(x) : y1(x); - - if (ix >= 0x52d00000) { /* x > 2**302 */ - /* (x >> n**2) - * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) - * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) - * Let s=sin(x), c=cos(x), - * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then - * - * n sin(xn)*sqt2 cos(xn)*sqt2 - * ---------------------------------- - * 0 s-c c+s - * 1 -s-c -c+s - * 2 -s+c -c-s - * 3 s+c c-s - */ - switch(nm1&3) { - case 0: temp = -sin(x)-cos(x); break; - case 1: temp = -sin(x)+cos(x); break; - case 2: temp = sin(x)+cos(x); break; - default: - case 3: temp = sin(x)-cos(x); break; - } - b = invsqrtpi*temp/sqrt(x); - } else { - a = y0(x); - b = y1(x); - /* quit if b is -inf */ - GET_HIGH_WORD(ib, b); - for (i=0; i>31; - ix &= 0x7fffffff; - if (ix > 0x7f800000) /* nan */ - return x; - - /* J(-n,x) = J(n,-x), use |n|-1 to avoid overflow in -n */ - if (n == 0) - return j0f(x); - if (n < 0) { - nm1 = -(n+1); - x = -x; - sign ^= 1; - } else - nm1 = n-1; - if (nm1 == 0) - return j1f(x); - - sign &= n; /* even n: 0, odd n: signbit(x) */ - x = fabsf(x); - if (ix == 0 || ix == 0x7f800000) /* if x is 0 or inf */ - b = 0.0f; - else if (nm1 < x) { - /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ - a = j0f(x); - b = j1f(x); - for (i=0; i 8) /* underflow */ - nm1 = 8; - temp = 0.5f * x; - b = temp; - a = 1.0f; - for (i=2; i<=nm1+1; i++) { - a *= (float)i; /* a = n! */ - b *= temp; /* b = (x/2)^n */ - } - b = b/a; - } else { - /* use backward recurrence */ - /* x x^2 x^2 - * J(n,x)/J(n-1,x) = ---- ------ ------ ..... - * 2n - 2(n+1) - 2(n+2) - * - * 1 1 1 - * (for large x) = ---- ------ ------ ..... - * 2n 2(n+1) 2(n+2) - * -- - ------ - ------ - - * x x x - * - * Let w = 2n/x and h=2/x, then the above quotient - * is equal to the continued fraction: - * 1 - * = ----------------------- - * 1 - * w - ----------------- - * 1 - * w+h - --------- - * w+2h - ... - * - * To determine how many terms needed, let - * Q(0) = w, Q(1) = w(w+h) - 1, - * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), - * When Q(k) > 1e4 good for single - * When Q(k) > 1e9 good for double - * When Q(k) > 1e17 good for quadruple - */ - /* determine k */ - float t,q0,q1,w,h,z,tmp,nf; - int k; - - nf = nm1+1.0f; - w = 2*nf/x; - h = 2/x; - z = w+h; - q0 = w; - q1 = w*z - 1.0f; - k = 1; - while (q1 < 1.0e4f) { - k += 1; - z += h; - tmp = z*q1 - q0; - q0 = q1; - q1 = tmp; - } - for (t=0.0f, i=k; i>=0; i--) - t = 1.0f/(2*(i+nf)/x-t); - a = t; - b = 1.0f; - /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) - * Hence, if n*(log(2n/x)) > ... - * single 8.8722839355e+01 - * double 7.09782712893383973096e+02 - * long double 1.1356523406294143949491931077970765006170e+04 - * then recurrent value may overflow and the result is - * likely underflow to zero - */ - tmp = nf*logf(fabsf(w)); - if (tmp < 88.721679688f) { - for (i=nm1; i>0; i--) { - temp = b; - b = 2.0f*i*b/x - a; - a = temp; - } - } else { - for (i=nm1; i>0; i--){ - temp = b; - b = 2.0f*i*b/x - a; - a = temp; - /* scale b to avoid spurious overflow */ - if (b > 0x1p60f) { - a /= b; - t /= b; - b = 1.0f; - } - } - } - z = j0f(x); - w = j1f(x); - if (fabsf(z) >= fabsf(w)) - b = t*z/b; - else - b = t*w/a; - } - } - return sign ? -b : b; -} - -float ynf(int n, float x) -{ - uint32_t ix, ib; - int nm1, sign, i; - float a, b, temp; - - GET_FLOAT_WORD(ix, x); - sign = ix>>31; - ix &= 0x7fffffff; - if (ix > 0x7f800000) /* nan */ - return x; - if (sign && ix != 0) /* x < 0 */ - return 0/0.0f; - if (ix == 0x7f800000) - return 0.0f; - - if (n == 0) - return y0f(x); - if (n < 0) { - nm1 = -(n+1); - sign = n&1; - } else { - nm1 = n-1; - sign = 0; - } - if (nm1 == 0) - return sign ? -y1f(x) : y1f(x); - - a = y0f(x); - b = y1f(x); - /* quit if b is -inf */ - GET_FLOAT_WORD(ib,b); - for (i = 0; i < nm1 && ib != 0xff800000; ) { - i++; - temp = b; - b = (2.0f*i/x)*b - a; - GET_FLOAT_WORD(ib, b); - a = temp; - } - return sign ? -b : b; -} diff --git a/src/math/ldexp.c b/src/math/ldexp.c deleted file mode 100644 index f4d1cd6..0000000 --- a/src/math/ldexp.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -double ldexp(double x, int n) -{ - return scalbn(x, n); -} diff --git a/src/math/ldexpf.c b/src/math/ldexpf.c deleted file mode 100644 index 3bad5f3..0000000 --- a/src/math/ldexpf.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -float ldexpf(float x, int n) -{ - return scalbnf(x, n); -} diff --git a/src/math/ldexpl.c b/src/math/ldexpl.c deleted file mode 100644 index fd145cc..0000000 --- a/src/math/ldexpl.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -long double ldexpl(long double x, int n) -{ - return scalbnl(x, n); -} diff --git a/src/math/lgamma.c b/src/math/lgamma.c deleted file mode 100644 index 2fc9b47..0000000 --- a/src/math/lgamma.c +++ /dev/null @@ -1,7 +0,0 @@ -#include -#include "libm.h" - -double lgamma(double x) -{ - return __lgamma_r(x, &__signgam); -} diff --git a/src/math/lgamma_r.c b/src/math/lgamma_r.c deleted file mode 100644 index f9984cd..0000000 --- a/src/math/lgamma_r.c +++ /dev/null @@ -1,283 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_lgamma_r.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ -/* lgamma_r(x, signgamp) - * Reentrant version of the logarithm of the Gamma function - * with user provide pointer for the sign of Gamma(x). - * - * Method: - * 1. Argument Reduction for 0 < x <= 8 - * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may - * reduce x to a number in [1.5,2.5] by - * lgamma(1+s) = log(s) + lgamma(s) - * for example, - * lgamma(7.3) = log(6.3) + lgamma(6.3) - * = log(6.3*5.3) + lgamma(5.3) - * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) - * 2. Polynomial approximation of lgamma around its - * minimun ymin=1.461632144968362245 to maintain monotonicity. - * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use - * Let z = x-ymin; - * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) - * where - * poly(z) is a 14 degree polynomial. - * 2. Rational approximation in the primary interval [2,3] - * We use the following approximation: - * s = x-2.0; - * lgamma(x) = 0.5*s + s*P(s)/Q(s) - * with accuracy - * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 - * Our algorithms are based on the following observation - * - * zeta(2)-1 2 zeta(3)-1 3 - * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... - * 2 3 - * - * where Euler = 0.5771... is the Euler constant, which is very - * close to 0.5. - * - * 3. For x>=8, we have - * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... - * (better formula: - * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) - * Let z = 1/x, then we approximation - * f(z) = lgamma(x) - (x-0.5)(log(x)-1) - * by - * 3 5 11 - * w = w0 + w1*z + w2*z + w3*z + ... + w6*z - * where - * |w - f(z)| < 2**-58.74 - * - * 4. For negative x, since (G is gamma function) - * -x*G(-x)*G(x) = pi/sin(pi*x), - * we have - * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) - * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 - * Hence, for x<0, signgam = sign(sin(pi*x)) and - * lgamma(x) = log(|Gamma(x)|) - * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); - * Note: one should avoid compute pi*(-x) directly in the - * computation of sin(pi*(-x)). - * - * 5. Special Cases - * lgamma(2+s) ~ s*(1-Euler) for tiny s - * lgamma(1) = lgamma(2) = 0 - * lgamma(x) ~ -log(|x|) for tiny x - * lgamma(0) = lgamma(neg.integer) = inf and raise divide-by-zero - * lgamma(inf) = inf - * lgamma(-inf) = inf (bug for bug compatible with C99!?) - * - */ - -#include "libm.h" - -static const double -pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ -a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */ -a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */ -a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */ -a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */ -a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */ -a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */ -a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */ -a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */ -a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */ -a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */ -a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */ -a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */ -tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */ -tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */ -/* tt = -(tail of tf) */ -tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */ -t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */ -t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */ -t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */ -t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */ -t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */ -t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */ -t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */ -t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */ -t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */ -t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */ -t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */ -t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */ -t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */ -t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */ -t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */ -u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ -u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */ -u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */ -u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */ -u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */ -u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */ -v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */ -v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */ -v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */ -v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */ -v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */ -s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ -s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */ -s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */ -s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */ -s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */ -s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */ -s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */ -r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */ -r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */ -r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */ -r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */ -r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */ -r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */ -w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */ -w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */ -w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */ -w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */ -w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */ -w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */ -w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */ - -/* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */ -static double sin_pi(double x) -{ - int n; - - /* spurious inexact if odd int */ - x = 2.0*(x*0.5 - floor(x*0.5)); /* x mod 2.0 */ - - n = (int)(x*4.0); - n = (n+1)/2; - x -= n*0.5f; - x *= pi; - - switch (n) { - default: /* case 4: */ - case 0: return __sin(x, 0.0, 0); - case 1: return __cos(x, 0.0); - case 2: return __sin(-x, 0.0, 0); - case 3: return -__cos(x, 0.0); - } -} - -double __lgamma_r(double x, int *signgamp) -{ - union {double f; uint64_t i;} u = {x}; - double_t t,y,z,nadj,p,p1,p2,p3,q,r,w; - uint32_t ix; - int sign,i; - - /* purge off +-inf, NaN, +-0, tiny and negative arguments */ - *signgamp = 1; - sign = u.i>>63; - ix = u.i>>32 & 0x7fffffff; - if (ix >= 0x7ff00000) - return x*x; - if (ix < (0x3ff-70)<<20) { /* |x|<2**-70, return -log(|x|) */ - if(sign) { - x = -x; - *signgamp = -1; - } - return -log(x); - } - if (sign) { - x = -x; - t = sin_pi(x); - if (t == 0.0) /* -integer */ - return 1.0/(x-x); - if (t > 0.0) - *signgamp = -1; - else - t = -t; - nadj = log(pi/(t*x)); - } - - /* purge off 1 and 2 */ - if ((ix == 0x3ff00000 || ix == 0x40000000) && (uint32_t)u.i == 0) - r = 0; - /* for x < 2.0 */ - else if (ix < 0x40000000) { - if (ix <= 0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */ - r = -log(x); - if (ix >= 0x3FE76944) { - y = 1.0 - x; - i = 0; - } else if (ix >= 0x3FCDA661) { - y = x - (tc-1.0); - i = 1; - } else { - y = x; - i = 2; - } - } else { - r = 0.0; - if (ix >= 0x3FFBB4C3) { /* [1.7316,2] */ - y = 2.0 - x; - i = 0; - } else if(ix >= 0x3FF3B4C4) { /* [1.23,1.73] */ - y = x - tc; - i = 1; - } else { - y = x - 1.0; - i = 2; - } - } - switch (i) { - case 0: - z = y*y; - p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); - p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); - p = y*p1+p2; - r += (p-0.5*y); - break; - case 1: - z = y*y; - w = z*y; - p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ - p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); - p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); - p = z*p1-(tt-w*(p2+y*p3)); - r += tf + p; - break; - case 2: - p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); - p2 = 1.0+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); - r += -0.5*y + p1/p2; - } - } else if (ix < 0x40200000) { /* x < 8.0 */ - i = (int)x; - y = x - (double)i; - p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); - q = 1.0+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); - r = 0.5*y+p/q; - z = 1.0; /* lgamma(1+s) = log(s) + lgamma(s) */ - switch (i) { - case 7: z *= y + 6.0; /* FALLTHRU */ - case 6: z *= y + 5.0; /* FALLTHRU */ - case 5: z *= y + 4.0; /* FALLTHRU */ - case 4: z *= y + 3.0; /* FALLTHRU */ - case 3: z *= y + 2.0; /* FALLTHRU */ - r += log(z); - break; - } - } else if (ix < 0x43900000) { /* 8.0 <= x < 2**58 */ - t = log(x); - z = 1.0/x; - y = z*z; - w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); - r = (x-0.5)*(t-1.0)+w; - } else /* 2**58 <= x <= inf */ - r = x*(log(x)-1.0); - if (sign) - r = nadj - r; - return r; -} - -weak_alias(__lgamma_r, lgamma_r); diff --git a/src/math/lgammaf.c b/src/math/lgammaf.c deleted file mode 100644 index 2ae051d..0000000 --- a/src/math/lgammaf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include -#include "libm.h" - -float lgammaf(float x) -{ - return __lgammaf_r(x, &__signgam); -} diff --git a/src/math/lgammaf_r.c b/src/math/lgammaf_r.c deleted file mode 100644 index 3f353f1..0000000 --- a/src/math/lgammaf_r.c +++ /dev/null @@ -1,218 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -static const float -pi = 3.1415927410e+00, /* 0x40490fdb */ -a0 = 7.7215664089e-02, /* 0x3d9e233f */ -a1 = 3.2246702909e-01, /* 0x3ea51a66 */ -a2 = 6.7352302372e-02, /* 0x3d89f001 */ -a3 = 2.0580807701e-02, /* 0x3ca89915 */ -a4 = 7.3855509982e-03, /* 0x3bf2027e */ -a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ -a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ -a7 = 5.1006977446e-04, /* 0x3a05b634 */ -a8 = 2.2086278477e-04, /* 0x39679767 */ -a9 = 1.0801156895e-04, /* 0x38e28445 */ -a10 = 2.5214456400e-05, /* 0x37d383a2 */ -a11 = 4.4864096708e-05, /* 0x383c2c75 */ -tc = 1.4616321325e+00, /* 0x3fbb16c3 */ -tf = -1.2148628384e-01, /* 0xbdf8cdcd */ -/* tt = -(tail of tf) */ -tt = 6.6971006518e-09, /* 0x31e61c52 */ -t0 = 4.8383611441e-01, /* 0x3ef7b95e */ -t1 = -1.4758771658e-01, /* 0xbe17213c */ -t2 = 6.4624942839e-02, /* 0x3d845a15 */ -t3 = -3.2788541168e-02, /* 0xbd064d47 */ -t4 = 1.7970675603e-02, /* 0x3c93373d */ -t5 = -1.0314224288e-02, /* 0xbc28fcfe */ -t6 = 6.1005386524e-03, /* 0x3bc7e707 */ -t7 = -3.6845202558e-03, /* 0xbb7177fe */ -t8 = 2.2596477065e-03, /* 0x3b141699 */ -t9 = -1.4034647029e-03, /* 0xbab7f476 */ -t10 = 8.8108185446e-04, /* 0x3a66f867 */ -t11 = -5.3859531181e-04, /* 0xba0d3085 */ -t12 = 3.1563205994e-04, /* 0x39a57b6b */ -t13 = -3.1275415677e-04, /* 0xb9a3f927 */ -t14 = 3.3552918467e-04, /* 0x39afe9f7 */ -u0 = -7.7215664089e-02, /* 0xbd9e233f */ -u1 = 6.3282704353e-01, /* 0x3f2200f4 */ -u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ -u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ -u4 = 2.2896373272e-01, /* 0x3e6a7578 */ -u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ -v1 = 2.4559779167e+00, /* 0x401d2ebe */ -v2 = 2.1284897327e+00, /* 0x4008392d */ -v3 = 7.6928514242e-01, /* 0x3f44efdf */ -v4 = 1.0422264785e-01, /* 0x3dd572af */ -v5 = 3.2170924824e-03, /* 0x3b52d5db */ -s0 = -7.7215664089e-02, /* 0xbd9e233f */ -s1 = 2.1498242021e-01, /* 0x3e5c245a */ -s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ -s3 = 1.4635047317e-01, /* 0x3e15dce6 */ -s4 = 2.6642270386e-02, /* 0x3cda40e4 */ -s5 = 1.8402845599e-03, /* 0x3af135b4 */ -s6 = 3.1947532989e-05, /* 0x3805ff67 */ -r1 = 1.3920053244e+00, /* 0x3fb22d3b */ -r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ -r3 = 1.7193385959e-01, /* 0x3e300f6e */ -r4 = 1.8645919859e-02, /* 0x3c98bf54 */ -r5 = 7.7794247773e-04, /* 0x3a4beed6 */ -r6 = 7.3266842264e-06, /* 0x36f5d7bd */ -w0 = 4.1893854737e-01, /* 0x3ed67f1d */ -w1 = 8.3333335817e-02, /* 0x3daaaaab */ -w2 = -2.7777778450e-03, /* 0xbb360b61 */ -w3 = 7.9365057172e-04, /* 0x3a500cfd */ -w4 = -5.9518753551e-04, /* 0xba1c065c */ -w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ -w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ - -/* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */ -static float sin_pi(float x) -{ - double_t y; - int n; - - /* spurious inexact if odd int */ - x = 2*(x*0.5f - floorf(x*0.5f)); /* x mod 2.0 */ - - n = (int)(x*4); - n = (n+1)/2; - y = x - n*0.5f; - y *= 3.14159265358979323846; - switch (n) { - default: /* case 4: */ - case 0: return __sindf(y); - case 1: return __cosdf(y); - case 2: return __sindf(-y); - case 3: return -__cosdf(y); - } -} - -float __lgammaf_r(float x, int *signgamp) -{ - union {float f; uint32_t i;} u = {x}; - float t,y,z,nadj,p,p1,p2,p3,q,r,w; - uint32_t ix; - int i,sign; - - /* purge off +-inf, NaN, +-0, tiny and negative arguments */ - *signgamp = 1; - sign = u.i>>31; - ix = u.i & 0x7fffffff; - if (ix >= 0x7f800000) - return x*x; - if (ix < 0x35000000) { /* |x| < 2**-21, return -log(|x|) */ - if (sign) { - *signgamp = -1; - x = -x; - } - return -logf(x); - } - if (sign) { - x = -x; - t = sin_pi(x); - if (t == 0.0f) /* -integer */ - return 1.0f/(x-x); - if (t > 0.0f) - *signgamp = -1; - else - t = -t; - nadj = logf(pi/(t*x)); - } - - /* purge off 1 and 2 */ - if (ix == 0x3f800000 || ix == 0x40000000) - r = 0; - /* for x < 2.0 */ - else if (ix < 0x40000000) { - if (ix <= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ - r = -logf(x); - if (ix >= 0x3f3b4a20) { - y = 1.0f - x; - i = 0; - } else if (ix >= 0x3e6d3308) { - y = x - (tc-1.0f); - i = 1; - } else { - y = x; - i = 2; - } - } else { - r = 0.0f; - if (ix >= 0x3fdda618) { /* [1.7316,2] */ - y = 2.0f - x; - i = 0; - } else if (ix >= 0x3F9da620) { /* [1.23,1.73] */ - y = x - tc; - i = 1; - } else { - y = x - 1.0f; - i = 2; - } - } - switch(i) { - case 0: - z = y*y; - p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); - p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); - p = y*p1+p2; - r += p - 0.5f*y; - break; - case 1: - z = y*y; - w = z*y; - p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ - p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); - p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); - p = z*p1-(tt-w*(p2+y*p3)); - r += (tf + p); - break; - case 2: - p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); - p2 = 1.0f+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); - r += -0.5f*y + p1/p2; - } - } else if (ix < 0x41000000) { /* x < 8.0 */ - i = (int)x; - y = x - (float)i; - p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); - q = 1.0f+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); - r = 0.5f*y+p/q; - z = 1.0f; /* lgamma(1+s) = log(s) + lgamma(s) */ - switch (i) { - case 7: z *= y + 6.0f; /* FALLTHRU */ - case 6: z *= y + 5.0f; /* FALLTHRU */ - case 5: z *= y + 4.0f; /* FALLTHRU */ - case 4: z *= y + 3.0f; /* FALLTHRU */ - case 3: z *= y + 2.0f; /* FALLTHRU */ - r += logf(z); - break; - } - } else if (ix < 0x5c800000) { /* 8.0 <= x < 2**58 */ - t = logf(x); - z = 1.0f/x; - y = z*z; - w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); - r = (x-0.5f)*(t-1.0f)+w; - } else /* 2**58 <= x <= inf */ - r = x*(logf(x)-1.0f); - if (sign) - r = nadj - r; - return r; -} - -weak_alias(__lgammaf_r, lgammaf_r); diff --git a/src/math/lgammal.c b/src/math/lgammal.c deleted file mode 100644 index abbd4fc..0000000 --- a/src/math/lgammal.c +++ /dev/null @@ -1,353 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_lgammal.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* - * Copyright (c) 2008 Stephen L. Moshier - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. - * - * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES - * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR - * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES - * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN - * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF - * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - */ -/* lgammal(x) - * Reentrant version of the logarithm of the Gamma function - * with user provide pointer for the sign of Gamma(x). - * - * Method: - * 1. Argument Reduction for 0 < x <= 8 - * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may - * reduce x to a number in [1.5,2.5] by - * lgamma(1+s) = log(s) + lgamma(s) - * for example, - * lgamma(7.3) = log(6.3) + lgamma(6.3) - * = log(6.3*5.3) + lgamma(5.3) - * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) - * 2. Polynomial approximation of lgamma around its - * minimun ymin=1.461632144968362245 to maintain monotonicity. - * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use - * Let z = x-ymin; - * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) - * 2. Rational approximation in the primary interval [2,3] - * We use the following approximation: - * s = x-2.0; - * lgamma(x) = 0.5*s + s*P(s)/Q(s) - * Our algorithms are based on the following observation - * - * zeta(2)-1 2 zeta(3)-1 3 - * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... - * 2 3 - * - * where Euler = 0.5771... is the Euler constant, which is very - * close to 0.5. - * - * 3. For x>=8, we have - * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... - * (better formula: - * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) - * Let z = 1/x, then we approximation - * f(z) = lgamma(x) - (x-0.5)(log(x)-1) - * by - * 3 5 11 - * w = w0 + w1*z + w2*z + w3*z + ... + w6*z - * - * 4. For negative x, since (G is gamma function) - * -x*G(-x)*G(x) = pi/sin(pi*x), - * we have - * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) - * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 - * Hence, for x<0, signgam = sign(sin(pi*x)) and - * lgamma(x) = log(|Gamma(x)|) - * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); - * Note: one should avoid compute pi*(-x) directly in the - * computation of sin(pi*(-x)). - * - * 5. Special Cases - * lgamma(2+s) ~ s*(1-Euler) for tiny s - * lgamma(1)=lgamma(2)=0 - * lgamma(x) ~ -log(x) for tiny x - * lgamma(0) = lgamma(inf) = inf - * lgamma(-integer) = +-inf - * - */ - -#define _GNU_SOURCE -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double __lgammal_r(long double x, int *sg) -{ - return __lgamma_r(x, sg); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -static const long double -pi = 3.14159265358979323846264L, - -/* lgam(1+x) = 0.5 x + x a(x)/b(x) - -0.268402099609375 <= x <= 0 - peak relative error 6.6e-22 */ -a0 = -6.343246574721079391729402781192128239938E2L, -a1 = 1.856560238672465796768677717168371401378E3L, -a2 = 2.404733102163746263689288466865843408429E3L, -a3 = 8.804188795790383497379532868917517596322E2L, -a4 = 1.135361354097447729740103745999661157426E2L, -a5 = 3.766956539107615557608581581190400021285E0L, - -b0 = 8.214973713960928795704317259806842490498E3L, -b1 = 1.026343508841367384879065363925870888012E4L, -b2 = 4.553337477045763320522762343132210919277E3L, -b3 = 8.506975785032585797446253359230031874803E2L, -b4 = 6.042447899703295436820744186992189445813E1L, -/* b5 = 1.000000000000000000000000000000000000000E0 */ - - -tc = 1.4616321449683623412626595423257213284682E0L, -tf = -1.2148629053584961146050602565082954242826E-1, /* double precision */ -/* tt = (tail of tf), i.e. tf + tt has extended precision. */ -tt = 3.3649914684731379602768989080467587736363E-18L, -/* lgam ( 1.4616321449683623412626595423257213284682E0 ) = --1.2148629053584960809551455717769158215135617312999903886372437313313530E-1 */ - -/* lgam (x + tc) = tf + tt + x g(x)/h(x) - -0.230003726999612341262659542325721328468 <= x - <= 0.2699962730003876587373404576742786715318 - peak relative error 2.1e-21 */ -g0 = 3.645529916721223331888305293534095553827E-18L, -g1 = 5.126654642791082497002594216163574795690E3L, -g2 = 8.828603575854624811911631336122070070327E3L, -g3 = 5.464186426932117031234820886525701595203E3L, -g4 = 1.455427403530884193180776558102868592293E3L, -g5 = 1.541735456969245924860307497029155838446E2L, -g6 = 4.335498275274822298341872707453445815118E0L, - -h0 = 1.059584930106085509696730443974495979641E4L, -h1 = 2.147921653490043010629481226937850618860E4L, -h2 = 1.643014770044524804175197151958100656728E4L, -h3 = 5.869021995186925517228323497501767586078E3L, -h4 = 9.764244777714344488787381271643502742293E2L, -h5 = 6.442485441570592541741092969581997002349E1L, -/* h6 = 1.000000000000000000000000000000000000000E0 */ - - -/* lgam (x+1) = -0.5 x + x u(x)/v(x) - -0.100006103515625 <= x <= 0.231639862060546875 - peak relative error 1.3e-21 */ -u0 = -8.886217500092090678492242071879342025627E1L, -u1 = 6.840109978129177639438792958320783599310E2L, -u2 = 2.042626104514127267855588786511809932433E3L, -u3 = 1.911723903442667422201651063009856064275E3L, -u4 = 7.447065275665887457628865263491667767695E2L, -u5 = 1.132256494121790736268471016493103952637E2L, -u6 = 4.484398885516614191003094714505960972894E0L, - -v0 = 1.150830924194461522996462401210374632929E3L, -v1 = 3.399692260848747447377972081399737098610E3L, -v2 = 3.786631705644460255229513563657226008015E3L, -v3 = 1.966450123004478374557778781564114347876E3L, -v4 = 4.741359068914069299837355438370682773122E2L, -v5 = 4.508989649747184050907206782117647852364E1L, -/* v6 = 1.000000000000000000000000000000000000000E0 */ - - -/* lgam (x+2) = .5 x + x s(x)/r(x) - 0 <= x <= 1 - peak relative error 7.2e-22 */ -s0 = 1.454726263410661942989109455292824853344E6L, -s1 = -3.901428390086348447890408306153378922752E6L, -s2 = -6.573568698209374121847873064292963089438E6L, -s3 = -3.319055881485044417245964508099095984643E6L, -s4 = -7.094891568758439227560184618114707107977E5L, -s5 = -6.263426646464505837422314539808112478303E4L, -s6 = -1.684926520999477529949915657519454051529E3L, - -r0 = -1.883978160734303518163008696712983134698E7L, -r1 = -2.815206082812062064902202753264922306830E7L, -r2 = -1.600245495251915899081846093343626358398E7L, -r3 = -4.310526301881305003489257052083370058799E6L, -r4 = -5.563807682263923279438235987186184968542E5L, -r5 = -3.027734654434169996032905158145259713083E4L, -r6 = -4.501995652861105629217250715790764371267E2L, -/* r6 = 1.000000000000000000000000000000000000000E0 */ - - -/* lgam(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x w(1/x^2) - x >= 8 - Peak relative error 1.51e-21 -w0 = LS2PI - 0.5 */ -w0 = 4.189385332046727417803e-1L, -w1 = 8.333333333333331447505E-2L, -w2 = -2.777777777750349603440E-3L, -w3 = 7.936507795855070755671E-4L, -w4 = -5.952345851765688514613E-4L, -w5 = 8.412723297322498080632E-4L, -w6 = -1.880801938119376907179E-3L, -w7 = 4.885026142432270781165E-3L; - -/* sin(pi*x) assuming x > 2^-1000, if sin(pi*x)==0 the sign is arbitrary */ -static long double sin_pi(long double x) -{ - int n; - - /* spurious inexact if odd int */ - x *= 0.5; - x = 2.0*(x - floorl(x)); /* x mod 2.0 */ - - n = (int)(x*4.0); - n = (n+1)/2; - x -= n*0.5f; - x *= pi; - - switch (n) { - default: /* case 4: */ - case 0: return __sinl(x, 0.0, 0); - case 1: return __cosl(x, 0.0); - case 2: return __sinl(-x, 0.0, 0); - case 3: return -__cosl(x, 0.0); - } -} - -long double __lgammal_r(long double x, int *sg) { - long double t, y, z, nadj, p, p1, p2, q, r, w; - union ldshape u = {x}; - uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48; - int sign = u.i.se >> 15; - int i; - - *sg = 1; - - /* purge off +-inf, NaN, +-0, tiny and negative arguments */ - if (ix >= 0x7fff0000) - return x * x; - if (ix < 0x3fc08000) { /* |x|<2**-63, return -log(|x|) */ - if (sign) { - *sg = -1; - x = -x; - } - return -logl(x); - } - if (sign) { - x = -x; - t = sin_pi(x); - if (t == 0.0) - return 1.0 / (x-x); /* -integer */ - if (t > 0.0) - *sg = -1; - else - t = -t; - nadj = logl(pi / (t * x)); - } - - /* purge off 1 and 2 (so the sign is ok with downward rounding) */ - if ((ix == 0x3fff8000 || ix == 0x40008000) && u.i.m == 0) { - r = 0; - } else if (ix < 0x40008000) { /* x < 2.0 */ - if (ix <= 0x3ffee666) { /* 8.99993896484375e-1 */ - /* lgamma(x) = lgamma(x+1) - log(x) */ - r = -logl(x); - if (ix >= 0x3ffebb4a) { /* 7.31597900390625e-1 */ - y = x - 1.0; - i = 0; - } else if (ix >= 0x3ffced33) { /* 2.31639862060546875e-1 */ - y = x - (tc - 1.0); - i = 1; - } else { /* x < 0.23 */ - y = x; - i = 2; - } - } else { - r = 0.0; - if (ix >= 0x3fffdda6) { /* 1.73162841796875 */ - /* [1.7316,2] */ - y = x - 2.0; - i = 0; - } else if (ix >= 0x3fff9da6) { /* 1.23162841796875 */ - /* [1.23,1.73] */ - y = x - tc; - i = 1; - } else { - /* [0.9, 1.23] */ - y = x - 1.0; - i = 2; - } - } - switch (i) { - case 0: - p1 = a0 + y * (a1 + y * (a2 + y * (a3 + y * (a4 + y * a5)))); - p2 = b0 + y * (b1 + y * (b2 + y * (b3 + y * (b4 + y)))); - r += 0.5 * y + y * p1/p2; - break; - case 1: - p1 = g0 + y * (g1 + y * (g2 + y * (g3 + y * (g4 + y * (g5 + y * g6))))); - p2 = h0 + y * (h1 + y * (h2 + y * (h3 + y * (h4 + y * (h5 + y))))); - p = tt + y * p1/p2; - r += (tf + p); - break; - case 2: - p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * (u5 + y * u6)))))); - p2 = v0 + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * (v5 + y))))); - r += (-0.5 * y + p1 / p2); - } - } else if (ix < 0x40028000) { /* 8.0 */ - /* x < 8.0 */ - i = (int)x; - y = x - (double)i; - p = y * (s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6)))))); - q = r0 + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * (r6 + y)))))); - r = 0.5 * y + p / q; - z = 1.0; - /* lgamma(1+s) = log(s) + lgamma(s) */ - switch (i) { - case 7: - z *= (y + 6.0); /* FALLTHRU */ - case 6: - z *= (y + 5.0); /* FALLTHRU */ - case 5: - z *= (y + 4.0); /* FALLTHRU */ - case 4: - z *= (y + 3.0); /* FALLTHRU */ - case 3: - z *= (y + 2.0); /* FALLTHRU */ - r += logl(z); - break; - } - } else if (ix < 0x40418000) { /* 2^66 */ - /* 8.0 <= x < 2**66 */ - t = logl(x); - z = 1.0 / x; - y = z * z; - w = w0 + z * (w1 + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * (w6 + y * w7)))))); - r = (x - 0.5) * (t - 1.0) + w; - } else /* 2**66 <= x <= inf */ - r = x * (logl(x) - 1.0); - if (sign) - r = nadj - r; - return r; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double __lgammal_r(long double x, int *sg) -{ - return __lgamma_r(x, sg); -} -#endif - -long double lgammal(long double x) -{ - return __lgammal_r(x, &__signgam); -} - -weak_alias(__lgammal_r, lgammal_r); diff --git a/src/math/llrint.c b/src/math/llrint.c deleted file mode 100644 index 4f583ae..0000000 --- a/src/math/llrint.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -/* uses LLONG_MAX > 2^53, see comments in lrint.c */ - -long long llrint(double x) -{ - return rint(x); -} diff --git a/src/math/llrintf.c b/src/math/llrintf.c deleted file mode 100644 index 96949a0..0000000 --- a/src/math/llrintf.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -/* uses LLONG_MAX > 2^24, see comments in lrint.c */ - -long long llrintf(float x) -{ - return rintf(x); -} diff --git a/src/math/llrintl.c b/src/math/llrintl.c deleted file mode 100644 index 3449f6f..0000000 --- a/src/math/llrintl.c +++ /dev/null @@ -1,36 +0,0 @@ -#include -#include -#include "libm.h" - - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long long llrintl(long double x) -{ - return llrint(x); -} -#elif defined(FE_INEXACT) -/* -see comments in lrint.c - -Note that if LLONG_MAX == 0x7fffffffffffffff && LDBL_MANT_DIG == 64 -then x == 2**63 - 0.5 is the only input that overflows and -raises inexact (with tonearest or upward rounding mode) -*/ -long long llrintl(long double x) -{ - #pragma STDC FENV_ACCESS ON - int e; - - e = fetestexcept(FE_INEXACT); - x = rintl(x); - if (!e && (x > LLONG_MAX || x < LLONG_MIN)) - feclearexcept(FE_INEXACT); - /* conversion */ - return x; -} -#else -long long llrintl(long double x) -{ - return rintl(x); -} -#endif diff --git a/src/math/llround.c b/src/math/llround.c deleted file mode 100644 index 4d94787..0000000 --- a/src/math/llround.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -long long llround(double x) -{ - return round(x); -} diff --git a/src/math/llroundf.c b/src/math/llroundf.c deleted file mode 100644 index 19eb77e..0000000 --- a/src/math/llroundf.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -long long llroundf(float x) -{ - return roundf(x); -} diff --git a/src/math/llroundl.c b/src/math/llroundl.c deleted file mode 100644 index 2c2ee5e..0000000 --- a/src/math/llroundl.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -long long llroundl(long double x) -{ - return roundl(x); -} diff --git a/src/math/log.c b/src/math/log.c deleted file mode 100644 index cc52585..0000000 --- a/src/math/log.c +++ /dev/null @@ -1,112 +0,0 @@ -/* - * Double-precision log(x) function. - * - * Copyright (c) 2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include -#include -#include "libm.h" -#include "log_data.h" - -#define T __log_data.tab -#define T2 __log_data.tab2 -#define B __log_data.poly1 -#define A __log_data.poly -#define Ln2hi __log_data.ln2hi -#define Ln2lo __log_data.ln2lo -#define N (1 << LOG_TABLE_BITS) -#define OFF 0x3fe6000000000000 - -/* Top 16 bits of a double. */ -static inline uint32_t top16(double x) -{ - return asuint64(x) >> 48; -} - -double log(double x) -{ - double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo; - uint64_t ix, iz, tmp; - uint32_t top; - int k, i; - - ix = asuint64(x); - top = top16(x); -#define LO asuint64(1.0 - 0x1p-4) -#define HI asuint64(1.0 + 0x1.09p-4) - if (predict_false(ix - LO < HI - LO)) { - /* Handle close to 1.0 inputs separately. */ - /* Fix sign of zero with downward rounding when x==1. */ - if (WANT_ROUNDING && predict_false(ix == asuint64(1.0))) - return 0; - r = x - 1.0; - r2 = r * r; - r3 = r * r2; - y = r3 * - (B[1] + r * B[2] + r2 * B[3] + - r3 * (B[4] + r * B[5] + r2 * B[6] + - r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10]))); - /* Worst-case error is around 0.507 ULP. */ - w = r * 0x1p27; - double_t rhi = r + w - w; - double_t rlo = r - rhi; - w = rhi * rhi * B[0]; /* B[0] == -0.5. */ - hi = r + w; - lo = r - hi + w; - lo += B[0] * rlo * (rhi + r); - y += lo; - y += hi; - return eval_as_double(y); - } - if (predict_false(top - 0x0010 >= 0x7ff0 - 0x0010)) { - /* x < 0x1p-1022 or inf or nan. */ - if (ix * 2 == 0) - return __math_divzero(1); - if (ix == asuint64(INFINITY)) /* log(inf) == inf. */ - return x; - if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0) - return __math_invalid(x); - /* x is subnormal, normalize it. */ - ix = asuint64(x * 0x1p52); - ix -= 52ULL << 52; - } - - /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. - The range is split into N subintervals. - The ith subinterval contains z and c is near its center. */ - tmp = ix - OFF; - i = (tmp >> (52 - LOG_TABLE_BITS)) % N; - k = (int64_t)tmp >> 52; /* arithmetic shift */ - iz = ix - (tmp & 0xfffULL << 52); - invc = T[i].invc; - logc = T[i].logc; - z = asdouble(iz); - - /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ - /* r ~= z/c - 1, |r| < 1/(2*N). */ -#if __FP_FAST_FMA - /* rounding error: 0x1p-55/N. */ - r = __builtin_fma(z, invc, -1.0); -#else - /* rounding error: 0x1p-55/N + 0x1p-66. */ - r = (z - T2[i].chi - T2[i].clo) * invc; -#endif - kd = (double_t)k; - - /* hi + lo = r + log(c) + k*Ln2. */ - w = kd * Ln2hi + logc; - hi = w + r; - lo = w - hi + r + kd * Ln2lo; - - /* log(x) = lo + (log1p(r) - r) + hi. */ - r2 = r * r; /* rounding error: 0x1p-54/N^2. */ - /* Worst case error if |y| > 0x1p-5: - 0.5 + 4.13/N + abs-poly-error*2^57 ULP (+ 0.002 ULP without fma) - Worst case error if |y| > 0x1p-4: - 0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma). */ - y = lo + r2 * A[0] + - r * r2 * (A[1] + r * A[2] + r2 * (A[3] + r * A[4])) + hi; - return eval_as_double(y); -} diff --git a/src/math/log10.c b/src/math/log10.c deleted file mode 100644 index 8102687..0000000 --- a/src/math/log10.c +++ /dev/null @@ -1,101 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* - * Return the base 10 logarithm of x. See log.c for most comments. - * - * Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2 - * as in log.c, then combine and scale in extra precision: - * log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2) - */ - -#include -#include - -static const double -ivln10hi = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */ -ivln10lo = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */ -log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ -log10_2lo = 3.69423907715893078616e-13, /* 0x3D59FEF3, 0x11F12B36 */ -Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ -Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ -Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ -Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ -Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ -Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ -Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ - -double log10(double x) -{ - union {double f; uint64_t i;} u = {x}; - double_t hfsq,f,s,z,R,w,t1,t2,dk,y,hi,lo,val_hi,val_lo; - uint32_t hx; - int k; - - hx = u.i>>32; - k = 0; - if (hx < 0x00100000 || hx>>31) { - if (u.i<<1 == 0) - return -1/(x*x); /* log(+-0)=-inf */ - if (hx>>31) - return (x-x)/0.0; /* log(-#) = NaN */ - /* subnormal number, scale x up */ - k -= 54; - x *= 0x1p54; - u.f = x; - hx = u.i>>32; - } else if (hx >= 0x7ff00000) { - return x; - } else if (hx == 0x3ff00000 && u.i<<32 == 0) - return 0; - - /* reduce x into [sqrt(2)/2, sqrt(2)] */ - hx += 0x3ff00000 - 0x3fe6a09e; - k += (int)(hx>>20) - 0x3ff; - hx = (hx&0x000fffff) + 0x3fe6a09e; - u.i = (uint64_t)hx<<32 | (u.i&0xffffffff); - x = u.f; - - f = x - 1.0; - hfsq = 0.5*f*f; - s = f/(2.0+f); - z = s*s; - w = z*z; - t1 = w*(Lg2+w*(Lg4+w*Lg6)); - t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); - R = t2 + t1; - - /* See log2.c for details. */ - /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */ - hi = f - hfsq; - u.f = hi; - u.i &= (uint64_t)-1<<32; - hi = u.f; - lo = f - hi - hfsq + s*(hfsq+R); - - /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */ - val_hi = hi*ivln10hi; - dk = k; - y = dk*log10_2hi; - val_lo = dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi; - - /* - * Extra precision in for adding y is not strictly needed - * since there is no very large cancellation near x = sqrt(2) or - * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs - * with some parallelism and it reduces the error for many args. - */ - w = y + val_hi; - val_lo += (y - w) + val_hi; - val_hi = w; - - return val_lo + val_hi; -} diff --git a/src/math/log10f.c b/src/math/log10f.c deleted file mode 100644 index 9ca2f01..0000000 --- a/src/math/log10f.c +++ /dev/null @@ -1,77 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* - * See comments in log10.c. - */ - -#include -#include - -static const float -ivln10hi = 4.3432617188e-01, /* 0x3ede6000 */ -ivln10lo = -3.1689971365e-05, /* 0xb804ead9 */ -log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */ -log10_2lo = 7.9034151668e-07, /* 0x355427db */ -/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ -Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ -Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ -Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ -Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ - -float log10f(float x) -{ - union {float f; uint32_t i;} u = {x}; - float_t hfsq,f,s,z,R,w,t1,t2,dk,hi,lo; - uint32_t ix; - int k; - - ix = u.i; - k = 0; - if (ix < 0x00800000 || ix>>31) { /* x < 2**-126 */ - if (ix<<1 == 0) - return -1/(x*x); /* log(+-0)=-inf */ - if (ix>>31) - return (x-x)/0.0f; /* log(-#) = NaN */ - /* subnormal number, scale up x */ - k -= 25; - x *= 0x1p25f; - u.f = x; - ix = u.i; - } else if (ix >= 0x7f800000) { - return x; - } else if (ix == 0x3f800000) - return 0; - - /* reduce x into [sqrt(2)/2, sqrt(2)] */ - ix += 0x3f800000 - 0x3f3504f3; - k += (int)(ix>>23) - 0x7f; - ix = (ix&0x007fffff) + 0x3f3504f3; - u.i = ix; - x = u.f; - - f = x - 1.0f; - s = f/(2.0f + f); - z = s*s; - w = z*z; - t1= w*(Lg2+w*Lg4); - t2= z*(Lg1+w*Lg3); - R = t2 + t1; - hfsq = 0.5f*f*f; - - hi = f - hfsq; - u.f = hi; - u.i &= 0xfffff000; - hi = u.f; - lo = f - hi - hfsq + s*(hfsq+R); - dk = k; - return dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi + hi*ivln10hi + dk*log10_2hi; -} diff --git a/src/math/log10l.c b/src/math/log10l.c deleted file mode 100644 index 63dcc28..0000000 --- a/src/math/log10l.c +++ /dev/null @@ -1,191 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_log10l.c */ -/* - * Copyright (c) 2008 Stephen L. Moshier - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. - * - * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES - * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR - * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES - * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN - * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF - * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - */ -/* - * Common logarithm, long double precision - * - * - * SYNOPSIS: - * - * long double x, y, log10l(); - * - * y = log10l( x ); - * - * - * DESCRIPTION: - * - * Returns the base 10 logarithm of x. - * - * The argument is separated into its exponent and fractional - * parts. If the exponent is between -1 and +1, the logarithm - * of the fraction is approximated by - * - * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x). - * - * Otherwise, setting z = 2(x-1)/x+1), - * - * log(x) = z + z**3 P(z)/Q(z). - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0.5, 2.0 30000 9.0e-20 2.6e-20 - * IEEE exp(+-10000) 30000 6.0e-20 2.3e-20 - * - * In the tests over the interval exp(+-10000), the logarithms - * of the random arguments were uniformly distributed over - * [-10000, +10000]. - * - * ERROR MESSAGES: - * - * log singularity: x = 0; returns MINLOG - * log domain: x < 0; returns MINLOG - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double log10l(long double x) -{ - return log10(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x) - * 1/sqrt(2) <= x < sqrt(2) - * Theoretical peak relative error = 6.2e-22 - */ -static const long double P[] = { - 4.9962495940332550844739E-1L, - 1.0767376367209449010438E1L, - 7.7671073698359539859595E1L, - 2.5620629828144409632571E2L, - 4.2401812743503691187826E2L, - 3.4258224542413922935104E2L, - 1.0747524399916215149070E2L, -}; -static const long double Q[] = { -/* 1.0000000000000000000000E0,*/ - 2.3479774160285863271658E1L, - 1.9444210022760132894510E2L, - 7.7952888181207260646090E2L, - 1.6911722418503949084863E3L, - 2.0307734695595183428202E3L, - 1.2695660352705325274404E3L, - 3.2242573199748645407652E2L, -}; - -/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), - * where z = 2(x-1)/(x+1) - * 1/sqrt(2) <= x < sqrt(2) - * Theoretical peak relative error = 6.16e-22 - */ -static const long double R[4] = { - 1.9757429581415468984296E-3L, --7.1990767473014147232598E-1L, - 1.0777257190312272158094E1L, --3.5717684488096787370998E1L, -}; -static const long double S[4] = { -/* 1.00000000000000000000E0L,*/ --2.6201045551331104417768E1L, - 1.9361891836232102174846E2L, --4.2861221385716144629696E2L, -}; -/* log10(2) */ -#define L102A 0.3125L -#define L102B -1.1470004336018804786261e-2L -/* log10(e) */ -#define L10EA 0.5L -#define L10EB -6.5705518096748172348871e-2L - -#define SQRTH 0.70710678118654752440L - -long double log10l(long double x) -{ - long double y, z; - int e; - - if (isnan(x)) - return x; - if(x <= 0.0) { - if(x == 0.0) - return -1.0 / (x*x); - return (x - x) / 0.0; - } - if (x == INFINITY) - return INFINITY; - /* separate mantissa from exponent */ - /* Note, frexp is used so that denormal numbers - * will be handled properly. - */ - x = frexpl(x, &e); - - /* logarithm using log(x) = z + z**3 P(z)/Q(z), - * where z = 2(x-1)/x+1) - */ - if (e > 2 || e < -2) { - if (x < SQRTH) { /* 2(2x-1)/(2x+1) */ - e -= 1; - z = x - 0.5; - y = 0.5 * z + 0.5; - } else { /* 2 (x-1)/(x+1) */ - z = x - 0.5; - z -= 0.5; - y = 0.5 * x + 0.5; - } - x = z / y; - z = x*x; - y = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3)); - goto done; - } - - /* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ - if (x < SQRTH) { - e -= 1; - x = 2.0*x - 1.0; - } else { - x = x - 1.0; - } - z = x*x; - y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 7)); - y = y - 0.5*z; - -done: - /* Multiply log of fraction by log10(e) - * and base 2 exponent by log10(2). - * - * ***CAUTION*** - * - * This sequence of operations is critical and it may - * be horribly defeated by some compiler optimizers. - */ - z = y * (L10EB); - z += x * (L10EB); - z += e * (L102B); - z += y * (L10EA); - z += x * (L10EA); - z += e * (L102A); - return z; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double log10l(long double x) -{ - return log10(x); -} -#endif diff --git a/src/math/log1p.c b/src/math/log1p.c deleted file mode 100644 index 0097134..0000000 --- a/src/math/log1p.c +++ /dev/null @@ -1,122 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_log1p.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* double log1p(double x) - * Return the natural logarithm of 1+x. - * - * Method : - * 1. Argument Reduction: find k and f such that - * 1+x = 2^k * (1+f), - * where sqrt(2)/2 < 1+f < sqrt(2) . - * - * Note. If k=0, then f=x is exact. However, if k!=0, then f - * may not be representable exactly. In that case, a correction - * term is need. Let u=1+x rounded. Let c = (1+x)-u, then - * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), - * and add back the correction term c/u. - * (Note: when x > 2**53, one can simply return log(x)) - * - * 2. Approximation of log(1+f): See log.c - * - * 3. Finally, log1p(x) = k*ln2 + log(1+f) + c/u. See log.c - * - * Special cases: - * log1p(x) is NaN with signal if x < -1 (including -INF) ; - * log1p(+INF) is +INF; log1p(-1) is -INF with signal; - * log1p(NaN) is that NaN with no signal. - * - * Accuracy: - * according to an error analysis, the error is always less than - * 1 ulp (unit in the last place). - * - * Constants: - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough - * to produce the hexadecimal values shown. - * - * Note: Assuming log() return accurate answer, the following - * algorithm can be used to compute log1p(x) to within a few ULP: - * - * u = 1+x; - * if(u==1.0) return x ; else - * return log(u)*(x/(u-1.0)); - * - * See HP-15C Advanced Functions Handbook, p.193. - */ - -#include "libm.h" - -static const double -ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ -ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ -Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ -Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ -Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ -Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ -Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ -Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ -Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ - -double log1p(double x) -{ - union {double f; uint64_t i;} u = {x}; - double_t hfsq,f,c,s,z,R,w,t1,t2,dk; - uint32_t hx,hu; - int k; - - hx = u.i>>32; - k = 1; - if (hx < 0x3fda827a || hx>>31) { /* 1+x < sqrt(2)+ */ - if (hx >= 0xbff00000) { /* x <= -1.0 */ - if (x == -1) - return x/0.0; /* log1p(-1) = -inf */ - return (x-x)/0.0; /* log1p(x<-1) = NaN */ - } - if (hx<<1 < 0x3ca00000<<1) { /* |x| < 2**-53 */ - /* underflow if subnormal */ - if ((hx&0x7ff00000) == 0) - FORCE_EVAL((float)x); - return x; - } - if (hx <= 0xbfd2bec4) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ - k = 0; - c = 0; - f = x; - } - } else if (hx >= 0x7ff00000) - return x; - if (k) { - u.f = 1 + x; - hu = u.i>>32; - hu += 0x3ff00000 - 0x3fe6a09e; - k = (int)(hu>>20) - 0x3ff; - /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */ - if (k < 54) { - c = k >= 2 ? 1-(u.f-x) : x-(u.f-1); - c /= u.f; - } else - c = 0; - /* reduce u into [sqrt(2)/2, sqrt(2)] */ - hu = (hu&0x000fffff) + 0x3fe6a09e; - u.i = (uint64_t)hu<<32 | (u.i&0xffffffff); - f = u.f - 1; - } - hfsq = 0.5*f*f; - s = f/(2.0+f); - z = s*s; - w = z*z; - t1 = w*(Lg2+w*(Lg4+w*Lg6)); - t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); - R = t2 + t1; - dk = k; - return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi; -} diff --git a/src/math/log1pf.c b/src/math/log1pf.c deleted file mode 100644 index 23985c3..0000000 --- a/src/math/log1pf.c +++ /dev/null @@ -1,77 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -static const float -ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ -ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ -/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ -Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ -Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ -Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ -Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ - -float log1pf(float x) -{ - union {float f; uint32_t i;} u = {x}; - float_t hfsq,f,c,s,z,R,w,t1,t2,dk; - uint32_t ix,iu; - int k; - - ix = u.i; - k = 1; - if (ix < 0x3ed413d0 || ix>>31) { /* 1+x < sqrt(2)+ */ - if (ix >= 0xbf800000) { /* x <= -1.0 */ - if (x == -1) - return x/0.0f; /* log1p(-1)=+inf */ - return (x-x)/0.0f; /* log1p(x<-1)=NaN */ - } - if (ix<<1 < 0x33800000<<1) { /* |x| < 2**-24 */ - /* underflow if subnormal */ - if ((ix&0x7f800000) == 0) - FORCE_EVAL(x*x); - return x; - } - if (ix <= 0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ - k = 0; - c = 0; - f = x; - } - } else if (ix >= 0x7f800000) - return x; - if (k) { - u.f = 1 + x; - iu = u.i; - iu += 0x3f800000 - 0x3f3504f3; - k = (int)(iu>>23) - 0x7f; - /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */ - if (k < 25) { - c = k >= 2 ? 1-(u.f-x) : x-(u.f-1); - c /= u.f; - } else - c = 0; - /* reduce u into [sqrt(2)/2, sqrt(2)] */ - iu = (iu&0x007fffff) + 0x3f3504f3; - u.i = iu; - f = u.f - 1; - } - s = f/(2.0f + f); - z = s*s; - w = z*z; - t1= w*(Lg2+w*Lg4); - t2= z*(Lg1+w*Lg3); - R = t2 + t1; - hfsq = 0.5f*f*f; - dk = k; - return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi; -} diff --git a/src/math/log1pl.c b/src/math/log1pl.c deleted file mode 100644 index 141b5f0..0000000 --- a/src/math/log1pl.c +++ /dev/null @@ -1,177 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_log1pl.c */ -/* - * Copyright (c) 2008 Stephen L. Moshier - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. - * - * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES - * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR - * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES - * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN - * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF - * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - */ -/* - * Relative error logarithm - * Natural logarithm of 1+x, long double precision - * - * - * SYNOPSIS: - * - * long double x, y, log1pl(); - * - * y = log1pl( x ); - * - * - * DESCRIPTION: - * - * Returns the base e (2.718...) logarithm of 1+x. - * - * The argument 1+x is separated into its exponent and fractional - * parts. If the exponent is between -1 and +1, the logarithm - * of the fraction is approximated by - * - * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x). - * - * Otherwise, setting z = 2(x-1)/x+1), - * - * log(x) = z + z^3 P(z)/Q(z). - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE -1.0, 9.0 100000 8.2e-20 2.5e-20 - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double log1pl(long double x) -{ - return log1p(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x) - * 1/sqrt(2) <= x < sqrt(2) - * Theoretical peak relative error = 2.32e-20 - */ -static const long double P[] = { - 4.5270000862445199635215E-5L, - 4.9854102823193375972212E-1L, - 6.5787325942061044846969E0L, - 2.9911919328553073277375E1L, - 6.0949667980987787057556E1L, - 5.7112963590585538103336E1L, - 2.0039553499201281259648E1L, -}; -static const long double Q[] = { -/* 1.0000000000000000000000E0,*/ - 1.5062909083469192043167E1L, - 8.3047565967967209469434E1L, - 2.2176239823732856465394E2L, - 3.0909872225312059774938E2L, - 2.1642788614495947685003E2L, - 6.0118660497603843919306E1L, -}; - -/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), - * where z = 2(x-1)/(x+1) - * 1/sqrt(2) <= x < sqrt(2) - * Theoretical peak relative error = 6.16e-22 - */ -static const long double R[4] = { - 1.9757429581415468984296E-3L, --7.1990767473014147232598E-1L, - 1.0777257190312272158094E1L, --3.5717684488096787370998E1L, -}; -static const long double S[4] = { -/* 1.00000000000000000000E0L,*/ --2.6201045551331104417768E1L, - 1.9361891836232102174846E2L, --4.2861221385716144629696E2L, -}; -static const long double C1 = 6.9314575195312500000000E-1L; -static const long double C2 = 1.4286068203094172321215E-6L; - -#define SQRTH 0.70710678118654752440L - -long double log1pl(long double xm1) -{ - long double x, y, z; - int e; - - if (isnan(xm1)) - return xm1; - if (xm1 == INFINITY) - return xm1; - if (xm1 == 0.0) - return xm1; - - x = xm1 + 1.0; - - /* Test for domain errors. */ - if (x <= 0.0) { - if (x == 0.0) - return -1/(x*x); /* -inf with divbyzero */ - return 0/0.0f; /* nan with invalid */ - } - - /* Separate mantissa from exponent. - Use frexp so that denormal numbers will be handled properly. */ - x = frexpl(x, &e); - - /* logarithm using log(x) = z + z^3 P(z)/Q(z), - where z = 2(x-1)/x+1) */ - if (e > 2 || e < -2) { - if (x < SQRTH) { /* 2(2x-1)/(2x+1) */ - e -= 1; - z = x - 0.5; - y = 0.5 * z + 0.5; - } else { /* 2 (x-1)/(x+1) */ - z = x - 0.5; - z -= 0.5; - y = 0.5 * x + 0.5; - } - x = z / y; - z = x*x; - z = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3)); - z = z + e * C2; - z = z + x; - z = z + e * C1; - return z; - } - - /* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ - if (x < SQRTH) { - e -= 1; - if (e != 0) - x = 2.0 * x - 1.0; - else - x = xm1; - } else { - if (e != 0) - x = x - 1.0; - else - x = xm1; - } - z = x*x; - y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 6)); - y = y + e * C2; - z = y - 0.5 * z; - z = z + x; - z = z + e * C1; - return z; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double log1pl(long double x) -{ - return log1p(x); -} -#endif diff --git a/src/math/log2.c b/src/math/log2.c deleted file mode 100644 index 1276ed4..0000000 --- a/src/math/log2.c +++ /dev/null @@ -1,122 +0,0 @@ -/* - * Double-precision log2(x) function. - * - * Copyright (c) 2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include -#include -#include "libm.h" -#include "log2_data.h" - -#define T __log2_data.tab -#define T2 __log2_data.tab2 -#define B __log2_data.poly1 -#define A __log2_data.poly -#define InvLn2hi __log2_data.invln2hi -#define InvLn2lo __log2_data.invln2lo -#define N (1 << LOG2_TABLE_BITS) -#define OFF 0x3fe6000000000000 - -/* Top 16 bits of a double. */ -static inline uint32_t top16(double x) -{ - return asuint64(x) >> 48; -} - -double log2(double x) -{ - double_t z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p; - uint64_t ix, iz, tmp; - uint32_t top; - int k, i; - - ix = asuint64(x); - top = top16(x); -#define LO asuint64(1.0 - 0x1.5b51p-5) -#define HI asuint64(1.0 + 0x1.6ab2p-5) - if (predict_false(ix - LO < HI - LO)) { - /* Handle close to 1.0 inputs separately. */ - /* Fix sign of zero with downward rounding when x==1. */ - if (WANT_ROUNDING && predict_false(ix == asuint64(1.0))) - return 0; - r = x - 1.0; -#if __FP_FAST_FMA - hi = r * InvLn2hi; - lo = r * InvLn2lo + __builtin_fma(r, InvLn2hi, -hi); -#else - double_t rhi, rlo; - rhi = asdouble(asuint64(r) & -1ULL << 32); - rlo = r - rhi; - hi = rhi * InvLn2hi; - lo = rlo * InvLn2hi + r * InvLn2lo; -#endif - r2 = r * r; /* rounding error: 0x1p-62. */ - r4 = r2 * r2; - /* Worst-case error is less than 0.54 ULP (0.55 ULP without fma). */ - p = r2 * (B[0] + r * B[1]); - y = hi + p; - lo += hi - y + p; - lo += r4 * (B[2] + r * B[3] + r2 * (B[4] + r * B[5]) + - r4 * (B[6] + r * B[7] + r2 * (B[8] + r * B[9]))); - y += lo; - return eval_as_double(y); - } - if (predict_false(top - 0x0010 >= 0x7ff0 - 0x0010)) { - /* x < 0x1p-1022 or inf or nan. */ - if (ix * 2 == 0) - return __math_divzero(1); - if (ix == asuint64(INFINITY)) /* log(inf) == inf. */ - return x; - if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0) - return __math_invalid(x); - /* x is subnormal, normalize it. */ - ix = asuint64(x * 0x1p52); - ix -= 52ULL << 52; - } - - /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. - The range is split into N subintervals. - The ith subinterval contains z and c is near its center. */ - tmp = ix - OFF; - i = (tmp >> (52 - LOG2_TABLE_BITS)) % N; - k = (int64_t)tmp >> 52; /* arithmetic shift */ - iz = ix - (tmp & 0xfffULL << 52); - invc = T[i].invc; - logc = T[i].logc; - z = asdouble(iz); - kd = (double_t)k; - - /* log2(x) = log2(z/c) + log2(c) + k. */ - /* r ~= z/c - 1, |r| < 1/(2*N). */ -#if __FP_FAST_FMA - /* rounding error: 0x1p-55/N. */ - r = __builtin_fma(z, invc, -1.0); - t1 = r * InvLn2hi; - t2 = r * InvLn2lo + __builtin_fma(r, InvLn2hi, -t1); -#else - double_t rhi, rlo; - /* rounding error: 0x1p-55/N + 0x1p-65. */ - r = (z - T2[i].chi - T2[i].clo) * invc; - rhi = asdouble(asuint64(r) & -1ULL << 32); - rlo = r - rhi; - t1 = rhi * InvLn2hi; - t2 = rlo * InvLn2hi + r * InvLn2lo; -#endif - - /* hi + lo = r/ln2 + log2(c) + k. */ - t3 = kd + logc; - hi = t3 + t1; - lo = t3 - hi + t1 + t2; - - /* log2(r+1) = r/ln2 + r^2*poly(r). */ - /* Evaluation is optimized assuming superscalar pipelined execution. */ - r2 = r * r; /* rounding error: 0x1p-54/N^2. */ - r4 = r2 * r2; - /* Worst-case error if |y| > 0x1p-4: 0.547 ULP (0.550 ULP without fma). - ~ 0.5 + 2/N/ln2 + abs-poly-error*0x1p56 ULP (+ 0.003 ULP without fma). */ - p = A[0] + r * A[1] + r2 * (A[2] + r * A[3]) + r4 * (A[4] + r * A[5]); - y = lo + r2 * p + hi; - return eval_as_double(y); -} diff --git a/src/math/log2_data.c b/src/math/log2_data.c deleted file mode 100644 index 3dd1ca5..0000000 --- a/src/math/log2_data.c +++ /dev/null @@ -1,201 +0,0 @@ -/* - * Data for log2. - * - * Copyright (c) 2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include "log2_data.h" - -#define N (1 << LOG2_TABLE_BITS) - -const struct log2_data __log2_data = { -// First coefficient: 0x1.71547652b82fe1777d0ffda0d24p0 -.invln2hi = 0x1.7154765200000p+0, -.invln2lo = 0x1.705fc2eefa200p-33, -.poly1 = { -// relative error: 0x1.2fad8188p-63 -// in -0x1.5b51p-5 0x1.6ab2p-5 --0x1.71547652b82fep-1, -0x1.ec709dc3a03f7p-2, --0x1.71547652b7c3fp-2, -0x1.2776c50f05be4p-2, --0x1.ec709dd768fe5p-3, -0x1.a61761ec4e736p-3, --0x1.7153fbc64a79bp-3, -0x1.484d154f01b4ap-3, --0x1.289e4a72c383cp-3, -0x1.0b32f285aee66p-3, -}, -.poly = { -// relative error: 0x1.a72c2bf8p-58 -// abs error: 0x1.67a552c8p-66 -// in -0x1.f45p-8 0x1.f45p-8 --0x1.71547652b8339p-1, -0x1.ec709dc3a04bep-2, --0x1.7154764702ffbp-2, -0x1.2776c50034c48p-2, --0x1.ec7b328ea92bcp-3, -0x1.a6225e117f92ep-3, -}, -/* Algorithm: - - x = 2^k z - log2(x) = k + log2(c) + log2(z/c) - log2(z/c) = poly(z/c - 1) - -where z is in [1.6p-1; 1.6p0] which is split into N subintervals and z falls -into the ith one, then table entries are computed as - - tab[i].invc = 1/c - tab[i].logc = (double)log2(c) - tab2[i].chi = (double)c - tab2[i].clo = (double)(c - (double)c) - -where c is near the center of the subinterval and is chosen by trying +-2^29 -floating point invc candidates around 1/center and selecting one for which - - 1) the rounding error in 0x1.8p10 + logc is 0, - 2) the rounding error in z - chi - clo is < 0x1p-64 and - 3) the rounding error in (double)log2(c) is minimized (< 0x1p-68). - -Note: 1) ensures that k + logc can be computed without rounding error, 2) -ensures that z/c - 1 can be computed as (z - chi - clo)*invc with close to a -single rounding error when there is no fast fma for z*invc - 1, 3) ensures -that logc + poly(z/c - 1) has small error, however near x == 1 when -|log2(x)| < 0x1p-4, this is not enough so that is special cased. */ -.tab = { -{0x1.724286bb1acf8p+0, -0x1.1095feecdb000p-1}, -{0x1.6e1f766d2cca1p+0, -0x1.08494bd76d000p-1}, -{0x1.6a13d0e30d48ap+0, -0x1.00143aee8f800p-1}, -{0x1.661ec32d06c85p+0, -0x1.efec5360b4000p-2}, -{0x1.623fa951198f8p+0, -0x1.dfdd91ab7e000p-2}, -{0x1.5e75ba4cf026cp+0, -0x1.cffae0cc79000p-2}, -{0x1.5ac055a214fb8p+0, -0x1.c043811fda000p-2}, -{0x1.571ed0f166e1ep+0, -0x1.b0b67323ae000p-2}, -{0x1.53909590bf835p+0, -0x1.a152f5a2db000p-2}, -{0x1.5014fed61adddp+0, -0x1.9217f5af86000p-2}, -{0x1.4cab88e487bd0p+0, -0x1.8304db0719000p-2}, -{0x1.49539b4334feep+0, -0x1.74189f9a9e000p-2}, -{0x1.460cbdfafd569p+0, -0x1.6552bb5199000p-2}, -{0x1.42d664ee4b953p+0, -0x1.56b23a29b1000p-2}, -{0x1.3fb01111dd8a6p+0, -0x1.483650f5fa000p-2}, -{0x1.3c995b70c5836p+0, -0x1.39de937f6a000p-2}, -{0x1.3991c4ab6fd4ap+0, -0x1.2baa1538d6000p-2}, -{0x1.3698e0ce099b5p+0, -0x1.1d98340ca4000p-2}, -{0x1.33ae48213e7b2p+0, -0x1.0fa853a40e000p-2}, -{0x1.30d191985bdb1p+0, -0x1.01d9c32e73000p-2}, -{0x1.2e025cab271d7p+0, -0x1.e857da2fa6000p-3}, -{0x1.2b404cf13cd82p+0, -0x1.cd3c8633d8000p-3}, -{0x1.288b02c7ccb50p+0, -0x1.b26034c14a000p-3}, -{0x1.25e2263944de5p+0, -0x1.97c1c2f4fe000p-3}, -{0x1.234563d8615b1p+0, -0x1.7d6023f800000p-3}, -{0x1.20b46e33eaf38p+0, -0x1.633a71a05e000p-3}, -{0x1.1e2eefdcda3ddp+0, -0x1.494f5e9570000p-3}, -{0x1.1bb4a580b3930p+0, -0x1.2f9e424e0a000p-3}, -{0x1.19453847f2200p+0, -0x1.162595afdc000p-3}, -{0x1.16e06c0d5d73cp+0, -0x1.f9c9a75bd8000p-4}, -{0x1.1485f47b7e4c2p+0, -0x1.c7b575bf9c000p-4}, -{0x1.12358ad0085d1p+0, -0x1.960c60ff48000p-4}, -{0x1.0fef00f532227p+0, -0x1.64ce247b60000p-4}, -{0x1.0db2077d03a8fp+0, -0x1.33f78b2014000p-4}, -{0x1.0b7e6d65980d9p+0, -0x1.0387d1a42c000p-4}, -{0x1.0953efe7b408dp+0, -0x1.a6f9208b50000p-5}, -{0x1.07325cac53b83p+0, -0x1.47a954f770000p-5}, -{0x1.05197e40d1b5cp+0, -0x1.d23a8c50c0000p-6}, -{0x1.03091c1208ea2p+0, -0x1.16a2629780000p-6}, -{0x1.0101025b37e21p+0, -0x1.720f8d8e80000p-8}, -{0x1.fc07ef9caa76bp-1, 0x1.6fe53b1500000p-7}, -{0x1.f4465d3f6f184p-1, 0x1.11ccce10f8000p-5}, -{0x1.ecc079f84107fp-1, 0x1.c4dfc8c8b8000p-5}, -{0x1.e573a99975ae8p-1, 0x1.3aa321e574000p-4}, -{0x1.de5d6f0bd3de6p-1, 0x1.918a0d08b8000p-4}, -{0x1.d77b681ff38b3p-1, 0x1.e72e9da044000p-4}, -{0x1.d0cb5724de943p-1, 0x1.1dcd2507f6000p-3}, -{0x1.ca4b2dc0e7563p-1, 0x1.476ab03dea000p-3}, -{0x1.c3f8ee8d6cb51p-1, 0x1.7074377e22000p-3}, -{0x1.bdd2b4f020c4cp-1, 0x1.98ede8ba94000p-3}, -{0x1.b7d6c006015cap-1, 0x1.c0db86ad2e000p-3}, -{0x1.b20366e2e338fp-1, 0x1.e840aafcee000p-3}, -{0x1.ac57026295039p-1, 0x1.0790ab4678000p-2}, -{0x1.a6d01bc2731ddp-1, 0x1.1ac056801c000p-2}, -{0x1.a16d3bc3ff18bp-1, 0x1.2db11d4fee000p-2}, -{0x1.9c2d14967feadp-1, 0x1.406464ec58000p-2}, -{0x1.970e4f47c9902p-1, 0x1.52dbe093af000p-2}, -{0x1.920fb3982bcf2p-1, 0x1.651902050d000p-2}, -{0x1.8d30187f759f1p-1, 0x1.771d2cdeaf000p-2}, -{0x1.886e5ebb9f66dp-1, 0x1.88e9c857d9000p-2}, -{0x1.83c97b658b994p-1, 0x1.9a80155e16000p-2}, -{0x1.7f405ffc61022p-1, 0x1.abe186ed3d000p-2}, -{0x1.7ad22181415cap-1, 0x1.bd0f2aea0e000p-2}, -{0x1.767dcf99eff8cp-1, 0x1.ce0a43dbf4000p-2}, -}, -#if !__FP_FAST_FMA -.tab2 = { -{0x1.6200012b90a8ep-1, 0x1.904ab0644b605p-55}, -{0x1.66000045734a6p-1, 0x1.1ff9bea62f7a9p-57}, -{0x1.69fffc325f2c5p-1, 0x1.27ecfcb3c90bap-55}, -{0x1.6e00038b95a04p-1, 0x1.8ff8856739326p-55}, -{0x1.71fffe09994e3p-1, 0x1.afd40275f82b1p-55}, -{0x1.7600015590e1p-1, -0x1.2fd75b4238341p-56}, -{0x1.7a00012655bd5p-1, 0x1.808e67c242b76p-56}, -{0x1.7e0003259e9a6p-1, -0x1.208e426f622b7p-57}, -{0x1.81fffedb4b2d2p-1, -0x1.402461ea5c92fp-55}, -{0x1.860002dfafcc3p-1, 0x1.df7f4a2f29a1fp-57}, -{0x1.89ffff78c6b5p-1, -0x1.e0453094995fdp-55}, -{0x1.8e00039671566p-1, -0x1.a04f3bec77b45p-55}, -{0x1.91fffe2bf1745p-1, -0x1.7fa34400e203cp-56}, -{0x1.95fffcc5c9fd1p-1, -0x1.6ff8005a0695dp-56}, -{0x1.9a0003bba4767p-1, 0x1.0f8c4c4ec7e03p-56}, -{0x1.9dfffe7b92da5p-1, 0x1.e7fd9478c4602p-55}, -{0x1.a1fffd72efdafp-1, -0x1.a0c554dcdae7ep-57}, -{0x1.a5fffde04ff95p-1, 0x1.67da98ce9b26bp-55}, -{0x1.a9fffca5e8d2bp-1, -0x1.284c9b54c13dep-55}, -{0x1.adfffddad03eap-1, 0x1.812c8ea602e3cp-58}, -{0x1.b1ffff10d3d4dp-1, -0x1.efaddad27789cp-55}, -{0x1.b5fffce21165ap-1, 0x1.3cb1719c61237p-58}, -{0x1.b9fffd950e674p-1, 0x1.3f7d94194cep-56}, -{0x1.be000139ca8afp-1, 0x1.50ac4215d9bcp-56}, -{0x1.c20005b46df99p-1, 0x1.beea653e9c1c9p-57}, -{0x1.c600040b9f7aep-1, -0x1.c079f274a70d6p-56}, -{0x1.ca0006255fd8ap-1, -0x1.a0b4076e84c1fp-56}, -{0x1.cdfffd94c095dp-1, 0x1.8f933f99ab5d7p-55}, -{0x1.d1ffff975d6cfp-1, -0x1.82c08665fe1bep-58}, -{0x1.d5fffa2561c93p-1, -0x1.b04289bd295f3p-56}, -{0x1.d9fff9d228b0cp-1, 0x1.70251340fa236p-55}, -{0x1.de00065bc7e16p-1, -0x1.5011e16a4d80cp-56}, -{0x1.e200002f64791p-1, 0x1.9802f09ef62ep-55}, -{0x1.e600057d7a6d8p-1, -0x1.e0b75580cf7fap-56}, -{0x1.ea00027edc00cp-1, -0x1.c848309459811p-55}, -{0x1.ee0006cf5cb7cp-1, -0x1.f8027951576f4p-55}, -{0x1.f2000782b7dccp-1, -0x1.f81d97274538fp-55}, -{0x1.f6000260c450ap-1, -0x1.071002727ffdcp-59}, -{0x1.f9fffe88cd533p-1, -0x1.81bdce1fda8bp-58}, -{0x1.fdfffd50f8689p-1, 0x1.7f91acb918e6ep-55}, -{0x1.0200004292367p+0, 0x1.b7ff365324681p-54}, -{0x1.05fffe3e3d668p+0, 0x1.6fa08ddae957bp-55}, -{0x1.0a0000a85a757p+0, -0x1.7e2de80d3fb91p-58}, -{0x1.0e0001a5f3fccp+0, -0x1.1823305c5f014p-54}, -{0x1.11ffff8afbaf5p+0, -0x1.bfabb6680bac2p-55}, -{0x1.15fffe54d91adp+0, -0x1.d7f121737e7efp-54}, -{0x1.1a00011ac36e1p+0, 0x1.c000a0516f5ffp-54}, -{0x1.1e00019c84248p+0, -0x1.082fbe4da5dap-54}, -{0x1.220000ffe5e6ep+0, -0x1.8fdd04c9cfb43p-55}, -{0x1.26000269fd891p+0, 0x1.cfe2a7994d182p-55}, -{0x1.2a00029a6e6dap+0, -0x1.00273715e8bc5p-56}, -{0x1.2dfffe0293e39p+0, 0x1.b7c39dab2a6f9p-54}, -{0x1.31ffff7dcf082p+0, 0x1.df1336edc5254p-56}, -{0x1.35ffff05a8b6p+0, -0x1.e03564ccd31ebp-54}, -{0x1.3a0002e0eaeccp+0, 0x1.5f0e74bd3a477p-56}, -{0x1.3e000043bb236p+0, 0x1.c7dcb149d8833p-54}, -{0x1.4200002d187ffp+0, 0x1.e08afcf2d3d28p-56}, -{0x1.460000d387cb1p+0, 0x1.20837856599a6p-55}, -{0x1.4a00004569f89p+0, -0x1.9fa5c904fbcd2p-55}, -{0x1.4e000043543f3p+0, -0x1.81125ed175329p-56}, -{0x1.51fffcc027f0fp+0, 0x1.883d8847754dcp-54}, -{0x1.55ffffd87b36fp+0, -0x1.709e731d02807p-55}, -{0x1.59ffff21df7bap+0, 0x1.7f79f68727b02p-55}, -{0x1.5dfffebfc3481p+0, -0x1.180902e30e93ep-54}, -}, -#endif -}; diff --git a/src/math/log2_data.h b/src/math/log2_data.h deleted file mode 100644 index 276a786..0000000 --- a/src/math/log2_data.h +++ /dev/null @@ -1,28 +0,0 @@ -/* - * Copyright (c) 2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ -#ifndef _LOG2_DATA_H -#define _LOG2_DATA_H - -#include - -#define LOG2_TABLE_BITS 6 -#define LOG2_POLY_ORDER 7 -#define LOG2_POLY1_ORDER 11 -extern hidden const struct log2_data { - double invln2hi; - double invln2lo; - double poly[LOG2_POLY_ORDER - 1]; - double poly1[LOG2_POLY1_ORDER - 1]; - struct { - double invc, logc; - } tab[1 << LOG2_TABLE_BITS]; -#if !__FP_FAST_FMA - struct { - double chi, clo; - } tab2[1 << LOG2_TABLE_BITS]; -#endif -} __log2_data; - -#endif diff --git a/src/math/log2f.c b/src/math/log2f.c deleted file mode 100644 index c368f88..0000000 --- a/src/math/log2f.c +++ /dev/null @@ -1,72 +0,0 @@ -/* - * Single-precision log2 function. - * - * Copyright (c) 2017-2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include -#include -#include "libm.h" -#include "log2f_data.h" - -/* -LOG2F_TABLE_BITS = 4 -LOG2F_POLY_ORDER = 4 - -ULP error: 0.752 (nearest rounding.) -Relative error: 1.9 * 2^-26 (before rounding.) -*/ - -#define N (1 << LOG2F_TABLE_BITS) -#define T __log2f_data.tab -#define A __log2f_data.poly -#define OFF 0x3f330000 - -float log2f(float x) -{ - double_t z, r, r2, p, y, y0, invc, logc; - uint32_t ix, iz, top, tmp; - int k, i; - - ix = asuint(x); - /* Fix sign of zero with downward rounding when x==1. */ - if (WANT_ROUNDING && predict_false(ix == 0x3f800000)) - return 0; - if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) { - /* x < 0x1p-126 or inf or nan. */ - if (ix * 2 == 0) - return __math_divzerof(1); - if (ix == 0x7f800000) /* log2(inf) == inf. */ - return x; - if ((ix & 0x80000000) || ix * 2 >= 0xff000000) - return __math_invalidf(x); - /* x is subnormal, normalize it. */ - ix = asuint(x * 0x1p23f); - ix -= 23 << 23; - } - - /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. - The range is split into N subintervals. - The ith subinterval contains z and c is near its center. */ - tmp = ix - OFF; - i = (tmp >> (23 - LOG2F_TABLE_BITS)) % N; - top = tmp & 0xff800000; - iz = ix - top; - k = (int32_t)tmp >> 23; /* arithmetic shift */ - invc = T[i].invc; - logc = T[i].logc; - z = (double_t)asfloat(iz); - - /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */ - r = z * invc - 1; - y0 = logc + (double_t)k; - - /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */ - r2 = r * r; - y = A[1] * r + A[2]; - y = A[0] * r2 + y; - p = A[3] * r + y0; - y = y * r2 + p; - return eval_as_float(y); -} diff --git a/src/math/log2f_data.c b/src/math/log2f_data.c deleted file mode 100644 index 24e450f..0000000 --- a/src/math/log2f_data.c +++ /dev/null @@ -1,33 +0,0 @@ -/* - * Data definition for log2f. - * - * Copyright (c) 2017-2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include "log2f_data.h" - -const struct log2f_data __log2f_data = { - .tab = { - { 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 }, - { 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 }, - { 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 }, - { 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 }, - { 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 }, - { 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 }, - { 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 }, - { 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 }, - { 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 }, - { 0x1p+0, 0x0p+0 }, - { 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 }, - { 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 }, - { 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 }, - { 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 }, - { 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 }, - { 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 }, - }, - .poly = { - -0x1.712b6f70a7e4dp-2, 0x1.ecabf496832ep-2, -0x1.715479ffae3dep-1, - 0x1.715475f35c8b8p0, - } -}; diff --git a/src/math/log2f_data.h b/src/math/log2f_data.h deleted file mode 100644 index 4fa4895..0000000 --- a/src/math/log2f_data.h +++ /dev/null @@ -1,19 +0,0 @@ -/* - * Copyright (c) 2017-2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ -#ifndef _LOG2F_DATA_H -#define _LOG2F_DATA_H - -#include - -#define LOG2F_TABLE_BITS 4 -#define LOG2F_POLY_ORDER 4 -extern hidden const struct log2f_data { - struct { - double invc, logc; - } tab[1 << LOG2F_TABLE_BITS]; - double poly[LOG2F_POLY_ORDER]; -} __log2f_data; - -#endif diff --git a/src/math/log2l.c b/src/math/log2l.c deleted file mode 100644 index 722b451..0000000 --- a/src/math/log2l.c +++ /dev/null @@ -1,182 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_log2l.c */ -/* - * Copyright (c) 2008 Stephen L. Moshier - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. - * - * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES - * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR - * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES - * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN - * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF - * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - */ -/* - * Base 2 logarithm, long double precision - * - * - * SYNOPSIS: - * - * long double x, y, log2l(); - * - * y = log2l( x ); - * - * - * DESCRIPTION: - * - * Returns the base 2 logarithm of x. - * - * The argument is separated into its exponent and fractional - * parts. If the exponent is between -1 and +1, the (natural) - * logarithm of the fraction is approximated by - * - * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x). - * - * Otherwise, setting z = 2(x-1)/x+1), - * - * log(x) = z + z**3 P(z)/Q(z). - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0.5, 2.0 30000 9.8e-20 2.7e-20 - * IEEE exp(+-10000) 70000 5.4e-20 2.3e-20 - * - * In the tests over the interval exp(+-10000), the logarithms - * of the random arguments were uniformly distributed over - * [-10000, +10000]. - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double log2l(long double x) -{ - return log2(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -/* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x) - * 1/sqrt(2) <= x < sqrt(2) - * Theoretical peak relative error = 6.2e-22 - */ -static const long double P[] = { - 4.9962495940332550844739E-1L, - 1.0767376367209449010438E1L, - 7.7671073698359539859595E1L, - 2.5620629828144409632571E2L, - 4.2401812743503691187826E2L, - 3.4258224542413922935104E2L, - 1.0747524399916215149070E2L, -}; -static const long double Q[] = { -/* 1.0000000000000000000000E0,*/ - 2.3479774160285863271658E1L, - 1.9444210022760132894510E2L, - 7.7952888181207260646090E2L, - 1.6911722418503949084863E3L, - 2.0307734695595183428202E3L, - 1.2695660352705325274404E3L, - 3.2242573199748645407652E2L, -}; - -/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), - * where z = 2(x-1)/(x+1) - * 1/sqrt(2) <= x < sqrt(2) - * Theoretical peak relative error = 6.16e-22 - */ -static const long double R[4] = { - 1.9757429581415468984296E-3L, --7.1990767473014147232598E-1L, - 1.0777257190312272158094E1L, --3.5717684488096787370998E1L, -}; -static const long double S[4] = { -/* 1.00000000000000000000E0L,*/ --2.6201045551331104417768E1L, - 1.9361891836232102174846E2L, --4.2861221385716144629696E2L, -}; -/* log2(e) - 1 */ -#define LOG2EA 4.4269504088896340735992e-1L - -#define SQRTH 0.70710678118654752440L - -long double log2l(long double x) -{ - long double y, z; - int e; - - if (isnan(x)) - return x; - if (x == INFINITY) - return x; - if (x <= 0.0) { - if (x == 0.0) - return -1/(x*x); /* -inf with divbyzero */ - return 0/0.0f; /* nan with invalid */ - } - - /* separate mantissa from exponent */ - /* Note, frexp is used so that denormal numbers - * will be handled properly. - */ - x = frexpl(x, &e); - - /* logarithm using log(x) = z + z**3 P(z)/Q(z), - * where z = 2(x-1)/x+1) - */ - if (e > 2 || e < -2) { - if (x < SQRTH) { /* 2(2x-1)/(2x+1) */ - e -= 1; - z = x - 0.5; - y = 0.5 * z + 0.5; - } else { /* 2 (x-1)/(x+1) */ - z = x - 0.5; - z -= 0.5; - y = 0.5 * x + 0.5; - } - x = z / y; - z = x*x; - y = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3)); - goto done; - } - - /* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ - if (x < SQRTH) { - e -= 1; - x = 2.0*x - 1.0; - } else { - x = x - 1.0; - } - z = x*x; - y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 7)); - y = y - 0.5*z; - -done: - /* Multiply log of fraction by log2(e) - * and base 2 exponent by 1 - * - * ***CAUTION*** - * - * This sequence of operations is critical and it may - * be horribly defeated by some compiler optimizers. - */ - z = y * LOG2EA; - z += x * LOG2EA; - z += y; - z += x; - z += e; - return z; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double log2l(long double x) -{ - return log2(x); -} -#endif diff --git a/src/math/log_data.c b/src/math/log_data.c deleted file mode 100644 index 1a6ec71..0000000 --- a/src/math/log_data.c +++ /dev/null @@ -1,328 +0,0 @@ -/* - * Data for log. - * - * Copyright (c) 2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include "log_data.h" - -#define N (1 << LOG_TABLE_BITS) - -const struct log_data __log_data = { -.ln2hi = 0x1.62e42fefa3800p-1, -.ln2lo = 0x1.ef35793c76730p-45, -.poly1 = { -// relative error: 0x1.c04d76cp-63 -// in -0x1p-4 0x1.09p-4 (|log(1+x)| > 0x1p-4 outside the interval) --0x1p-1, -0x1.5555555555577p-2, --0x1.ffffffffffdcbp-3, -0x1.999999995dd0cp-3, --0x1.55555556745a7p-3, -0x1.24924a344de3p-3, --0x1.fffffa4423d65p-4, -0x1.c7184282ad6cap-4, --0x1.999eb43b068ffp-4, -0x1.78182f7afd085p-4, --0x1.5521375d145cdp-4, -}, -.poly = { -// relative error: 0x1.926199e8p-56 -// abs error: 0x1.882ff33p-65 -// in -0x1.fp-9 0x1.fp-9 --0x1.0000000000001p-1, -0x1.555555551305bp-2, --0x1.fffffffeb459p-3, -0x1.999b324f10111p-3, --0x1.55575e506c89fp-3, -}, -/* Algorithm: - - x = 2^k z - log(x) = k ln2 + log(c) + log(z/c) - log(z/c) = poly(z/c - 1) - -where z is in [1.6p-1; 1.6p0] which is split into N subintervals and z falls -into the ith one, then table entries are computed as - - tab[i].invc = 1/c - tab[i].logc = (double)log(c) - tab2[i].chi = (double)c - tab2[i].clo = (double)(c - (double)c) - -where c is near the center of the subinterval and is chosen by trying +-2^29 -floating point invc candidates around 1/center and selecting one for which - - 1) the rounding error in 0x1.8p9 + logc is 0, - 2) the rounding error in z - chi - clo is < 0x1p-66 and - 3) the rounding error in (double)log(c) is minimized (< 0x1p-66). - -Note: 1) ensures that k*ln2hi + logc can be computed without rounding error, -2) ensures that z/c - 1 can be computed as (z - chi - clo)*invc with close to -a single rounding error when there is no fast fma for z*invc - 1, 3) ensures -that logc + poly(z/c - 1) has small error, however near x == 1 when -|log(x)| < 0x1p-4, this is not enough so that is special cased. */ -.tab = { -{0x1.734f0c3e0de9fp+0, -0x1.7cc7f79e69000p-2}, -{0x1.713786a2ce91fp+0, -0x1.76feec20d0000p-2}, -{0x1.6f26008fab5a0p+0, -0x1.713e31351e000p-2}, -{0x1.6d1a61f138c7dp+0, -0x1.6b85b38287800p-2}, -{0x1.6b1490bc5b4d1p+0, -0x1.65d5590807800p-2}, -{0x1.69147332f0cbap+0, -0x1.602d076180000p-2}, -{0x1.6719f18224223p+0, -0x1.5a8ca86909000p-2}, -{0x1.6524f99a51ed9p+0, -0x1.54f4356035000p-2}, -{0x1.63356aa8f24c4p+0, -0x1.4f637c36b4000p-2}, -{0x1.614b36b9ddc14p+0, -0x1.49da7fda85000p-2}, -{0x1.5f66452c65c4cp+0, -0x1.445923989a800p-2}, -{0x1.5d867b5912c4fp+0, -0x1.3edf439b0b800p-2}, -{0x1.5babccb5b90dep+0, -0x1.396ce448f7000p-2}, -{0x1.59d61f2d91a78p+0, -0x1.3401e17bda000p-2}, -{0x1.5805612465687p+0, -0x1.2e9e2ef468000p-2}, -{0x1.56397cee76bd3p+0, -0x1.2941b3830e000p-2}, -{0x1.54725e2a77f93p+0, -0x1.23ec58cda8800p-2}, -{0x1.52aff42064583p+0, -0x1.1e9e129279000p-2}, -{0x1.50f22dbb2bddfp+0, -0x1.1956d2b48f800p-2}, -{0x1.4f38f4734ded7p+0, -0x1.141679ab9f800p-2}, -{0x1.4d843cfde2840p+0, -0x1.0edd094ef9800p-2}, -{0x1.4bd3ec078a3c8p+0, -0x1.09aa518db1000p-2}, -{0x1.4a27fc3e0258ap+0, -0x1.047e65263b800p-2}, -{0x1.4880524d48434p+0, -0x1.feb224586f000p-3}, -{0x1.46dce1b192d0bp+0, -0x1.f474a7517b000p-3}, -{0x1.453d9d3391854p+0, -0x1.ea4443d103000p-3}, -{0x1.43a2744b4845ap+0, -0x1.e020d44e9b000p-3}, -{0x1.420b54115f8fbp+0, -0x1.d60a22977f000p-3}, -{0x1.40782da3ef4b1p+0, -0x1.cc00104959000p-3}, -{0x1.3ee8f5d57fe8fp+0, -0x1.c202956891000p-3}, -{0x1.3d5d9a00b4ce9p+0, -0x1.b81178d811000p-3}, -{0x1.3bd60c010c12bp+0, -0x1.ae2c9ccd3d000p-3}, -{0x1.3a5242b75dab8p+0, -0x1.a45402e129000p-3}, -{0x1.38d22cd9fd002p+0, -0x1.9a877681df000p-3}, -{0x1.3755bc5847a1cp+0, -0x1.90c6d69483000p-3}, -{0x1.35dce49ad36e2p+0, -0x1.87120a645c000p-3}, -{0x1.34679984dd440p+0, -0x1.7d68fb4143000p-3}, -{0x1.32f5cceffcb24p+0, -0x1.73cb83c627000p-3}, -{0x1.3187775a10d49p+0, -0x1.6a39a9b376000p-3}, -{0x1.301c8373e3990p+0, -0x1.60b3154b7a000p-3}, -{0x1.2eb4ebb95f841p+0, -0x1.5737d76243000p-3}, -{0x1.2d50a0219a9d1p+0, -0x1.4dc7b8fc23000p-3}, -{0x1.2bef9a8b7fd2ap+0, -0x1.4462c51d20000p-3}, -{0x1.2a91c7a0c1babp+0, -0x1.3b08abc830000p-3}, -{0x1.293726014b530p+0, -0x1.31b996b490000p-3}, -{0x1.27dfa5757a1f5p+0, -0x1.2875490a44000p-3}, -{0x1.268b39b1d3bbfp+0, -0x1.1f3b9f879a000p-3}, -{0x1.2539d838ff5bdp+0, -0x1.160c8252ca000p-3}, -{0x1.23eb7aac9083bp+0, -0x1.0ce7f57f72000p-3}, -{0x1.22a012ba940b6p+0, -0x1.03cdc49fea000p-3}, -{0x1.2157996cc4132p+0, -0x1.f57bdbc4b8000p-4}, -{0x1.201201dd2fc9bp+0, -0x1.e370896404000p-4}, -{0x1.1ecf4494d480bp+0, -0x1.d17983ef94000p-4}, -{0x1.1d8f5528f6569p+0, -0x1.bf9674ed8a000p-4}, -{0x1.1c52311577e7cp+0, -0x1.adc79202f6000p-4}, -{0x1.1b17c74cb26e9p+0, -0x1.9c0c3e7288000p-4}, -{0x1.19e010c2c1ab6p+0, -0x1.8a646b372c000p-4}, -{0x1.18ab07bb670bdp+0, -0x1.78d01b3ac0000p-4}, -{0x1.1778a25efbcb6p+0, -0x1.674f145380000p-4}, -{0x1.1648d354c31dap+0, -0x1.55e0e6d878000p-4}, -{0x1.151b990275fddp+0, -0x1.4485cdea1e000p-4}, -{0x1.13f0ea432d24cp+0, -0x1.333d94d6aa000p-4}, -{0x1.12c8b7210f9dap+0, -0x1.22079f8c56000p-4}, -{0x1.11a3028ecb531p+0, -0x1.10e4698622000p-4}, -{0x1.107fbda8434afp+0, -0x1.ffa6c6ad20000p-5}, -{0x1.0f5ee0f4e6bb3p+0, -0x1.dda8d4a774000p-5}, -{0x1.0e4065d2a9fcep+0, -0x1.bbcece4850000p-5}, -{0x1.0d244632ca521p+0, -0x1.9a1894012c000p-5}, -{0x1.0c0a77ce2981ap+0, -0x1.788583302c000p-5}, -{0x1.0af2f83c636d1p+0, -0x1.5715e67d68000p-5}, -{0x1.09ddb98a01339p+0, -0x1.35c8a49658000p-5}, -{0x1.08cabaf52e7dfp+0, -0x1.149e364154000p-5}, -{0x1.07b9f2f4e28fbp+0, -0x1.e72c082eb8000p-6}, -{0x1.06ab58c358f19p+0, -0x1.a55f152528000p-6}, -{0x1.059eea5ecf92cp+0, -0x1.63d62cf818000p-6}, -{0x1.04949cdd12c90p+0, -0x1.228fb8caa0000p-6}, -{0x1.038c6c6f0ada9p+0, -0x1.c317b20f90000p-7}, -{0x1.02865137932a9p+0, -0x1.419355daa0000p-7}, -{0x1.0182427ea7348p+0, -0x1.81203c2ec0000p-8}, -{0x1.008040614b195p+0, -0x1.0040979240000p-9}, -{0x1.fe01ff726fa1ap-1, 0x1.feff384900000p-9}, -{0x1.fa11cc261ea74p-1, 0x1.7dc41353d0000p-7}, -{0x1.f6310b081992ep-1, 0x1.3cea3c4c28000p-6}, -{0x1.f25f63ceeadcdp-1, 0x1.b9fc114890000p-6}, -{0x1.ee9c8039113e7p-1, 0x1.1b0d8ce110000p-5}, -{0x1.eae8078cbb1abp-1, 0x1.58a5bd001c000p-5}, -{0x1.e741aa29d0c9bp-1, 0x1.95c8340d88000p-5}, -{0x1.e3a91830a99b5p-1, 0x1.d276aef578000p-5}, -{0x1.e01e009609a56p-1, 0x1.07598e598c000p-4}, -{0x1.dca01e577bb98p-1, 0x1.253f5e30d2000p-4}, -{0x1.d92f20b7c9103p-1, 0x1.42edd8b380000p-4}, -{0x1.d5cac66fb5ccep-1, 0x1.606598757c000p-4}, -{0x1.d272caa5ede9dp-1, 0x1.7da76356a0000p-4}, -{0x1.cf26e3e6b2ccdp-1, 0x1.9ab434e1c6000p-4}, -{0x1.cbe6da2a77902p-1, 0x1.b78c7bb0d6000p-4}, -{0x1.c8b266d37086dp-1, 0x1.d431332e72000p-4}, -{0x1.c5894bd5d5804p-1, 0x1.f0a3171de6000p-4}, -{0x1.c26b533bb9f8cp-1, 0x1.067152b914000p-3}, -{0x1.bf583eeece73fp-1, 0x1.147858292b000p-3}, -{0x1.bc4fd75db96c1p-1, 0x1.2266ecdca3000p-3}, -{0x1.b951e0c864a28p-1, 0x1.303d7a6c55000p-3}, -{0x1.b65e2c5ef3e2cp-1, 0x1.3dfc33c331000p-3}, -{0x1.b374867c9888bp-1, 0x1.4ba366b7a8000p-3}, -{0x1.b094b211d304ap-1, 0x1.5933928d1f000p-3}, -{0x1.adbe885f2ef7ep-1, 0x1.66acd2418f000p-3}, -{0x1.aaf1d31603da2p-1, 0x1.740f8ec669000p-3}, -{0x1.a82e63fd358a7p-1, 0x1.815c0f51af000p-3}, -{0x1.a5740ef09738bp-1, 0x1.8e92954f68000p-3}, -{0x1.a2c2a90ab4b27p-1, 0x1.9bb3602f84000p-3}, -{0x1.a01a01393f2d1p-1, 0x1.a8bed1c2c0000p-3}, -{0x1.9d79f24db3c1bp-1, 0x1.b5b515c01d000p-3}, -{0x1.9ae2505c7b190p-1, 0x1.c2967ccbcc000p-3}, -{0x1.9852ef297ce2fp-1, 0x1.cf635d5486000p-3}, -{0x1.95cbaeea44b75p-1, 0x1.dc1bd3446c000p-3}, -{0x1.934c69de74838p-1, 0x1.e8c01b8cfe000p-3}, -{0x1.90d4f2f6752e6p-1, 0x1.f5509c0179000p-3}, -{0x1.8e6528effd79dp-1, 0x1.00e6c121fb800p-2}, -{0x1.8bfce9fcc007cp-1, 0x1.071b80e93d000p-2}, -{0x1.899c0dabec30ep-1, 0x1.0d46b9e867000p-2}, -{0x1.87427aa2317fbp-1, 0x1.13687334bd000p-2}, -{0x1.84f00acb39a08p-1, 0x1.1980d67234800p-2}, -{0x1.82a49e8653e55p-1, 0x1.1f8ffe0cc8000p-2}, -{0x1.8060195f40260p-1, 0x1.2595fd7636800p-2}, -{0x1.7e22563e0a329p-1, 0x1.2b9300914a800p-2}, -{0x1.7beb377dcb5adp-1, 0x1.3187210436000p-2}, -{0x1.79baa679725c2p-1, 0x1.377266dec1800p-2}, -{0x1.77907f2170657p-1, 0x1.3d54ffbaf3000p-2}, -{0x1.756cadbd6130cp-1, 0x1.432eee32fe000p-2}, -}, -#if !__FP_FAST_FMA -.tab2 = { -{0x1.61000014fb66bp-1, 0x1.e026c91425b3cp-56}, -{0x1.63000034db495p-1, 0x1.dbfea48005d41p-55}, -{0x1.650000d94d478p-1, 0x1.e7fa786d6a5b7p-55}, -{0x1.67000074e6fadp-1, 0x1.1fcea6b54254cp-57}, -{0x1.68ffffedf0faep-1, -0x1.c7e274c590efdp-56}, -{0x1.6b0000763c5bcp-1, -0x1.ac16848dcda01p-55}, -{0x1.6d0001e5cc1f6p-1, 0x1.33f1c9d499311p-55}, -{0x1.6efffeb05f63ep-1, -0x1.e80041ae22d53p-56}, -{0x1.710000e86978p-1, 0x1.bff6671097952p-56}, -{0x1.72ffffc67e912p-1, 0x1.c00e226bd8724p-55}, -{0x1.74fffdf81116ap-1, -0x1.e02916ef101d2p-57}, -{0x1.770000f679c9p-1, -0x1.7fc71cd549c74p-57}, -{0x1.78ffffa7ec835p-1, 0x1.1bec19ef50483p-55}, -{0x1.7affffe20c2e6p-1, -0x1.07e1729cc6465p-56}, -{0x1.7cfffed3fc9p-1, -0x1.08072087b8b1cp-55}, -{0x1.7efffe9261a76p-1, 0x1.dc0286d9df9aep-55}, -{0x1.81000049ca3e8p-1, 0x1.97fd251e54c33p-55}, -{0x1.8300017932c8fp-1, -0x1.afee9b630f381p-55}, -{0x1.850000633739cp-1, 0x1.9bfbf6b6535bcp-55}, -{0x1.87000204289c6p-1, -0x1.bbf65f3117b75p-55}, -{0x1.88fffebf57904p-1, -0x1.9006ea23dcb57p-55}, -{0x1.8b00022bc04dfp-1, -0x1.d00df38e04b0ap-56}, -{0x1.8cfffe50c1b8ap-1, -0x1.8007146ff9f05p-55}, -{0x1.8effffc918e43p-1, 0x1.3817bd07a7038p-55}, -{0x1.910001efa5fc7p-1, 0x1.93e9176dfb403p-55}, -{0x1.9300013467bb9p-1, 0x1.f804e4b980276p-56}, -{0x1.94fffe6ee076fp-1, -0x1.f7ef0d9ff622ep-55}, -{0x1.96fffde3c12d1p-1, -0x1.082aa962638bap-56}, -{0x1.98ffff4458a0dp-1, -0x1.7801b9164a8efp-55}, -{0x1.9afffdd982e3ep-1, -0x1.740e08a5a9337p-55}, -{0x1.9cfffed49fb66p-1, 0x1.fce08c19bep-60}, -{0x1.9f00020f19c51p-1, -0x1.a3faa27885b0ap-55}, -{0x1.a10001145b006p-1, 0x1.4ff489958da56p-56}, -{0x1.a300007bbf6fap-1, 0x1.cbeab8a2b6d18p-55}, -{0x1.a500010971d79p-1, 0x1.8fecadd78793p-55}, -{0x1.a70001df52e48p-1, -0x1.f41763dd8abdbp-55}, -{0x1.a90001c593352p-1, -0x1.ebf0284c27612p-55}, -{0x1.ab0002a4f3e4bp-1, -0x1.9fd043cff3f5fp-57}, -{0x1.acfffd7ae1ed1p-1, -0x1.23ee7129070b4p-55}, -{0x1.aefffee510478p-1, 0x1.a063ee00edea3p-57}, -{0x1.b0fffdb650d5bp-1, 0x1.a06c8381f0ab9p-58}, -{0x1.b2ffffeaaca57p-1, -0x1.9011e74233c1dp-56}, -{0x1.b4fffd995badcp-1, -0x1.9ff1068862a9fp-56}, -{0x1.b7000249e659cp-1, 0x1.aff45d0864f3ep-55}, -{0x1.b8ffff987164p-1, 0x1.cfe7796c2c3f9p-56}, -{0x1.bafffd204cb4fp-1, -0x1.3ff27eef22bc4p-57}, -{0x1.bcfffd2415c45p-1, -0x1.cffb7ee3bea21p-57}, -{0x1.beffff86309dfp-1, -0x1.14103972e0b5cp-55}, -{0x1.c0fffe1b57653p-1, 0x1.bc16494b76a19p-55}, -{0x1.c2ffff1fa57e3p-1, -0x1.4feef8d30c6edp-57}, -{0x1.c4fffdcbfe424p-1, -0x1.43f68bcec4775p-55}, -{0x1.c6fffed54b9f7p-1, 0x1.47ea3f053e0ecp-55}, -{0x1.c8fffeb998fd5p-1, 0x1.383068df992f1p-56}, -{0x1.cb0002125219ap-1, -0x1.8fd8e64180e04p-57}, -{0x1.ccfffdd94469cp-1, 0x1.e7ebe1cc7ea72p-55}, -{0x1.cefffeafdc476p-1, 0x1.ebe39ad9f88fep-55}, -{0x1.d1000169af82bp-1, 0x1.57d91a8b95a71p-56}, -{0x1.d30000d0ff71dp-1, 0x1.9c1906970c7dap-55}, -{0x1.d4fffea790fc4p-1, -0x1.80e37c558fe0cp-58}, -{0x1.d70002edc87e5p-1, -0x1.f80d64dc10f44p-56}, -{0x1.d900021dc82aap-1, -0x1.47c8f94fd5c5cp-56}, -{0x1.dafffd86b0283p-1, 0x1.c7f1dc521617ep-55}, -{0x1.dd000296c4739p-1, 0x1.8019eb2ffb153p-55}, -{0x1.defffe54490f5p-1, 0x1.e00d2c652cc89p-57}, -{0x1.e0fffcdabf694p-1, -0x1.f8340202d69d2p-56}, -{0x1.e2fffdb52c8ddp-1, 0x1.b00c1ca1b0864p-56}, -{0x1.e4ffff24216efp-1, 0x1.2ffa8b094ab51p-56}, -{0x1.e6fffe88a5e11p-1, -0x1.7f673b1efbe59p-58}, -{0x1.e9000119eff0dp-1, -0x1.4808d5e0bc801p-55}, -{0x1.eafffdfa51744p-1, 0x1.80006d54320b5p-56}, -{0x1.ed0001a127fa1p-1, -0x1.002f860565c92p-58}, -{0x1.ef00007babcc4p-1, -0x1.540445d35e611p-55}, -{0x1.f0ffff57a8d02p-1, -0x1.ffb3139ef9105p-59}, -{0x1.f30001ee58ac7p-1, 0x1.a81acf2731155p-55}, -{0x1.f4ffff5823494p-1, 0x1.a3f41d4d7c743p-55}, -{0x1.f6ffffca94c6bp-1, -0x1.202f41c987875p-57}, -{0x1.f8fffe1f9c441p-1, 0x1.77dd1f477e74bp-56}, -{0x1.fafffd2e0e37ep-1, -0x1.f01199a7ca331p-57}, -{0x1.fd0001c77e49ep-1, 0x1.181ee4bceacb1p-56}, -{0x1.feffff7e0c331p-1, -0x1.e05370170875ap-57}, -{0x1.00ffff465606ep+0, -0x1.a7ead491c0adap-55}, -{0x1.02ffff3867a58p+0, -0x1.77f69c3fcb2ep-54}, -{0x1.04ffffdfc0d17p+0, 0x1.7bffe34cb945bp-54}, -{0x1.0700003cd4d82p+0, 0x1.20083c0e456cbp-55}, -{0x1.08ffff9f2cbe8p+0, -0x1.dffdfbe37751ap-57}, -{0x1.0b000010cda65p+0, -0x1.13f7faee626ebp-54}, -{0x1.0d00001a4d338p+0, 0x1.07dfa79489ff7p-55}, -{0x1.0effffadafdfdp+0, -0x1.7040570d66bcp-56}, -{0x1.110000bbafd96p+0, 0x1.e80d4846d0b62p-55}, -{0x1.12ffffae5f45dp+0, 0x1.dbffa64fd36efp-54}, -{0x1.150000dd59ad9p+0, 0x1.a0077701250aep-54}, -{0x1.170000f21559ap+0, 0x1.dfdf9e2e3deeep-55}, -{0x1.18ffffc275426p+0, 0x1.10030dc3b7273p-54}, -{0x1.1b000123d3c59p+0, 0x1.97f7980030188p-54}, -{0x1.1cffff8299eb7p+0, -0x1.5f932ab9f8c67p-57}, -{0x1.1effff48ad4p+0, 0x1.37fbf9da75bebp-54}, -{0x1.210000c8b86a4p+0, 0x1.f806b91fd5b22p-54}, -{0x1.2300003854303p+0, 0x1.3ffc2eb9fbf33p-54}, -{0x1.24fffffbcf684p+0, 0x1.601e77e2e2e72p-56}, -{0x1.26ffff52921d9p+0, 0x1.ffcbb767f0c61p-56}, -{0x1.2900014933a3cp+0, -0x1.202ca3c02412bp-56}, -{0x1.2b00014556313p+0, -0x1.2808233f21f02p-54}, -{0x1.2cfffebfe523bp+0, -0x1.8ff7e384fdcf2p-55}, -{0x1.2f0000bb8ad96p+0, -0x1.5ff51503041c5p-55}, -{0x1.30ffffb7ae2afp+0, -0x1.10071885e289dp-55}, -{0x1.32ffffeac5f7fp+0, -0x1.1ff5d3fb7b715p-54}, -{0x1.350000ca66756p+0, 0x1.57f82228b82bdp-54}, -{0x1.3700011fbf721p+0, 0x1.000bac40dd5ccp-55}, -{0x1.38ffff9592fb9p+0, -0x1.43f9d2db2a751p-54}, -{0x1.3b00004ddd242p+0, 0x1.57f6b707638e1p-55}, -{0x1.3cffff5b2c957p+0, 0x1.a023a10bf1231p-56}, -{0x1.3efffeab0b418p+0, 0x1.87f6d66b152bp-54}, -{0x1.410001532aff4p+0, 0x1.7f8375f198524p-57}, -{0x1.4300017478b29p+0, 0x1.301e672dc5143p-55}, -{0x1.44fffe795b463p+0, 0x1.9ff69b8b2895ap-55}, -{0x1.46fffe80475ep+0, -0x1.5c0b19bc2f254p-54}, -{0x1.48fffef6fc1e7p+0, 0x1.b4009f23a2a72p-54}, -{0x1.4afffe5bea704p+0, -0x1.4ffb7bf0d7d45p-54}, -{0x1.4d000171027dep+0, -0x1.9c06471dc6a3dp-54}, -{0x1.4f0000ff03ee2p+0, 0x1.77f890b85531cp-54}, -{0x1.5100012dc4bd1p+0, 0x1.004657166a436p-57}, -{0x1.530001605277ap+0, -0x1.6bfcece233209p-54}, -{0x1.54fffecdb704cp+0, -0x1.902720505a1d7p-55}, -{0x1.56fffef5f54a9p+0, 0x1.bbfe60ec96412p-54}, -{0x1.5900017e61012p+0, 0x1.87ec581afef9p-55}, -{0x1.5b00003c93e92p+0, -0x1.f41080abf0ccp-54}, -{0x1.5d0001d4919bcp+0, -0x1.8812afb254729p-54}, -{0x1.5efffe7b87a89p+0, -0x1.47eb780ed6904p-54}, -}, -#endif -}; diff --git a/src/math/log_data.h b/src/math/log_data.h deleted file mode 100644 index 1be22ab..0000000 --- a/src/math/log_data.h +++ /dev/null @@ -1,28 +0,0 @@ -/* - * Copyright (c) 2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ -#ifndef _LOG_DATA_H -#define _LOG_DATA_H - -#include - -#define LOG_TABLE_BITS 7 -#define LOG_POLY_ORDER 6 -#define LOG_POLY1_ORDER 12 -extern hidden const struct log_data { - double ln2hi; - double ln2lo; - double poly[LOG_POLY_ORDER - 1]; /* First coefficient is 1. */ - double poly1[LOG_POLY1_ORDER - 1]; - struct { - double invc, logc; - } tab[1 << LOG_TABLE_BITS]; -#if !__FP_FAST_FMA - struct { - double chi, clo; - } tab2[1 << LOG_TABLE_BITS]; -#endif -} __log_data; - -#endif diff --git a/src/math/logb.c b/src/math/logb.c deleted file mode 100644 index 7f8bdfa..0000000 --- a/src/math/logb.c +++ /dev/null @@ -1,17 +0,0 @@ -#include - -/* -special cases: - logb(+-0) = -inf, and raise divbyzero - logb(+-inf) = +inf - logb(nan) = nan -*/ - -double logb(double x) -{ - if (!isfinite(x)) - return x * x; - if (x == 0) - return -1/(x*x); - return ilogb(x); -} diff --git a/src/math/logbf.c b/src/math/logbf.c deleted file mode 100644 index a0a0b5e..0000000 --- a/src/math/logbf.c +++ /dev/null @@ -1,10 +0,0 @@ -#include - -float logbf(float x) -{ - if (!isfinite(x)) - return x * x; - if (x == 0) - return -1/(x*x); - return ilogbf(x); -} diff --git a/src/math/logbl.c b/src/math/logbl.c deleted file mode 100644 index 962973a..0000000 --- a/src/math/logbl.c +++ /dev/null @@ -1,16 +0,0 @@ -#include -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double logbl(long double x) -{ - return logb(x); -} -#else -long double logbl(long double x) -{ - if (!isfinite(x)) - return x * x; - if (x == 0) - return -1/(x*x); - return ilogbl(x); -} -#endif diff --git a/src/math/logf.c b/src/math/logf.c deleted file mode 100644 index 7ee5d7f..0000000 --- a/src/math/logf.c +++ /dev/null @@ -1,71 +0,0 @@ -/* - * Single-precision log function. - * - * Copyright (c) 2017-2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include -#include -#include "libm.h" -#include "logf_data.h" - -/* -LOGF_TABLE_BITS = 4 -LOGF_POLY_ORDER = 4 - -ULP error: 0.818 (nearest rounding.) -Relative error: 1.957 * 2^-26 (before rounding.) -*/ - -#define T __logf_data.tab -#define A __logf_data.poly -#define Ln2 __logf_data.ln2 -#define N (1 << LOGF_TABLE_BITS) -#define OFF 0x3f330000 - -float logf(float x) -{ - double_t z, r, r2, y, y0, invc, logc; - uint32_t ix, iz, tmp; - int k, i; - - ix = asuint(x); - /* Fix sign of zero with downward rounding when x==1. */ - if (WANT_ROUNDING && predict_false(ix == 0x3f800000)) - return 0; - if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) { - /* x < 0x1p-126 or inf or nan. */ - if (ix * 2 == 0) - return __math_divzerof(1); - if (ix == 0x7f800000) /* log(inf) == inf. */ - return x; - if ((ix & 0x80000000) || ix * 2 >= 0xff000000) - return __math_invalidf(x); - /* x is subnormal, normalize it. */ - ix = asuint(x * 0x1p23f); - ix -= 23 << 23; - } - - /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. - The range is split into N subintervals. - The ith subinterval contains z and c is near its center. */ - tmp = ix - OFF; - i = (tmp >> (23 - LOGF_TABLE_BITS)) % N; - k = (int32_t)tmp >> 23; /* arithmetic shift */ - iz = ix - (tmp & 0x1ff << 23); - invc = T[i].invc; - logc = T[i].logc; - z = (double_t)asfloat(iz); - - /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */ - r = z * invc - 1; - y0 = logc + (double_t)k * Ln2; - - /* Pipelined polynomial evaluation to approximate log1p(r). */ - r2 = r * r; - y = A[1] * r + A[2]; - y = A[0] * r2 + y; - y = y * r2 + (y0 + r); - return eval_as_float(y); -} diff --git a/src/math/logf_data.c b/src/math/logf_data.c deleted file mode 100644 index 857221f..0000000 --- a/src/math/logf_data.c +++ /dev/null @@ -1,33 +0,0 @@ -/* - * Data definition for logf. - * - * Copyright (c) 2017-2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include "logf_data.h" - -const struct logf_data __logf_data = { - .tab = { - { 0x1.661ec79f8f3bep+0, -0x1.57bf7808caadep-2 }, - { 0x1.571ed4aaf883dp+0, -0x1.2bef0a7c06ddbp-2 }, - { 0x1.49539f0f010bp+0, -0x1.01eae7f513a67p-2 }, - { 0x1.3c995b0b80385p+0, -0x1.b31d8a68224e9p-3 }, - { 0x1.30d190c8864a5p+0, -0x1.6574f0ac07758p-3 }, - { 0x1.25e227b0b8eap+0, -0x1.1aa2bc79c81p-3 }, - { 0x1.1bb4a4a1a343fp+0, -0x1.a4e76ce8c0e5ep-4 }, - { 0x1.12358f08ae5bap+0, -0x1.1973c5a611cccp-4 }, - { 0x1.0953f419900a7p+0, -0x1.252f438e10c1ep-5 }, - { 0x1p+0, 0x0p+0 }, - { 0x1.e608cfd9a47acp-1, 0x1.aa5aa5df25984p-5 }, - { 0x1.ca4b31f026aap-1, 0x1.c5e53aa362eb4p-4 }, - { 0x1.b2036576afce6p-1, 0x1.526e57720db08p-3 }, - { 0x1.9c2d163a1aa2dp-1, 0x1.bc2860d22477p-3 }, - { 0x1.886e6037841edp-1, 0x1.1058bc8a07ee1p-2 }, - { 0x1.767dcf5534862p-1, 0x1.4043057b6ee09p-2 }, - }, - .ln2 = 0x1.62e42fefa39efp-1, - .poly = { - -0x1.00ea348b88334p-2, 0x1.5575b0be00b6ap-2, -0x1.ffffef20a4123p-2, - } -}; diff --git a/src/math/logf_data.h b/src/math/logf_data.h deleted file mode 100644 index 00cff6f..0000000 --- a/src/math/logf_data.h +++ /dev/null @@ -1,20 +0,0 @@ -/* - * Copyright (c) 2017-2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ -#ifndef _LOGF_DATA_H -#define _LOGF_DATA_H - -#include - -#define LOGF_TABLE_BITS 4 -#define LOGF_POLY_ORDER 4 -extern hidden const struct logf_data { - struct { - double invc, logc; - } tab[1 << LOGF_TABLE_BITS]; - double ln2; - double poly[LOGF_POLY_ORDER - 1]; /* First order coefficient is 1. */ -} __logf_data; - -#endif diff --git a/src/math/logl.c b/src/math/logl.c deleted file mode 100644 index 5d53659..0000000 --- a/src/math/logl.c +++ /dev/null @@ -1,175 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_logl.c */ -/* - * Copyright (c) 2008 Stephen L. Moshier - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. - * - * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES - * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR - * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES - * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN - * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF - * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - */ -/* - * Natural logarithm, long double precision - * - * - * SYNOPSIS: - * - * long double x, y, logl(); - * - * y = logl( x ); - * - * - * DESCRIPTION: - * - * Returns the base e (2.718...) logarithm of x. - * - * The argument is separated into its exponent and fractional - * parts. If the exponent is between -1 and +1, the logarithm - * of the fraction is approximated by - * - * log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x). - * - * Otherwise, setting z = 2(x-1)/(x+1), - * - * log(x) = log(1+z/2) - log(1-z/2) = z + z**3 P(z)/Q(z). - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE 0.5, 2.0 150000 8.71e-20 2.75e-20 - * IEEE exp(+-10000) 100000 5.39e-20 2.34e-20 - * - * In the tests over the interval exp(+-10000), the logarithms - * of the random arguments were uniformly distributed over - * [-10000, +10000]. - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double logl(long double x) -{ - return log(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x) - * 1/sqrt(2) <= x < sqrt(2) - * Theoretical peak relative error = 2.32e-20 - */ -static const long double P[] = { - 4.5270000862445199635215E-5L, - 4.9854102823193375972212E-1L, - 6.5787325942061044846969E0L, - 2.9911919328553073277375E1L, - 6.0949667980987787057556E1L, - 5.7112963590585538103336E1L, - 2.0039553499201281259648E1L, -}; -static const long double Q[] = { -/* 1.0000000000000000000000E0,*/ - 1.5062909083469192043167E1L, - 8.3047565967967209469434E1L, - 2.2176239823732856465394E2L, - 3.0909872225312059774938E2L, - 2.1642788614495947685003E2L, - 6.0118660497603843919306E1L, -}; - -/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), - * where z = 2(x-1)/(x+1) - * 1/sqrt(2) <= x < sqrt(2) - * Theoretical peak relative error = 6.16e-22 - */ -static const long double R[4] = { - 1.9757429581415468984296E-3L, --7.1990767473014147232598E-1L, - 1.0777257190312272158094E1L, --3.5717684488096787370998E1L, -}; -static const long double S[4] = { -/* 1.00000000000000000000E0L,*/ --2.6201045551331104417768E1L, - 1.9361891836232102174846E2L, --4.2861221385716144629696E2L, -}; -static const long double C1 = 6.9314575195312500000000E-1L; -static const long double C2 = 1.4286068203094172321215E-6L; - -#define SQRTH 0.70710678118654752440L - -long double logl(long double x) -{ - long double y, z; - int e; - - if (isnan(x)) - return x; - if (x == INFINITY) - return x; - if (x <= 0.0) { - if (x == 0.0) - return -1/(x*x); /* -inf with divbyzero */ - return 0/0.0f; /* nan with invalid */ - } - - /* separate mantissa from exponent */ - /* Note, frexp is used so that denormal numbers - * will be handled properly. - */ - x = frexpl(x, &e); - - /* logarithm using log(x) = z + z**3 P(z)/Q(z), - * where z = 2(x-1)/(x+1) - */ - if (e > 2 || e < -2) { - if (x < SQRTH) { /* 2(2x-1)/(2x+1) */ - e -= 1; - z = x - 0.5; - y = 0.5 * z + 0.5; - } else { /* 2 (x-1)/(x+1) */ - z = x - 0.5; - z -= 0.5; - y = 0.5 * x + 0.5; - } - x = z / y; - z = x*x; - z = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3)); - z = z + e * C2; - z = z + x; - z = z + e * C1; - return z; - } - - /* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */ - if (x < SQRTH) { - e -= 1; - x = 2.0*x - 1.0; - } else { - x = x - 1.0; - } - z = x*x; - y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 6)); - y = y + e * C2; - z = y - 0.5*z; - /* Note, the sum of above terms does not exceed x/4, - * so it contributes at most about 1/4 lsb to the error. - */ - z = z + x; - z = z + e * C1; /* This sum has an error of 1/2 lsb. */ - return z; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double logl(long double x) -{ - return log(x); -} -#endif diff --git a/src/math/lrint.c b/src/math/lrint.c deleted file mode 100644 index ddee7a0..0000000 --- a/src/math/lrint.c +++ /dev/null @@ -1,72 +0,0 @@ -#include -#include -#include -#include "libm.h" - -/* -If the result cannot be represented (overflow, nan), then -lrint raises the invalid exception. - -Otherwise if the input was not an integer then the inexact -exception is raised. - -C99 is a bit vague about whether inexact exception is -allowed to be raised when invalid is raised. -(F.9 explicitly allows spurious inexact exceptions, F.9.6.5 -does not make it clear if that rule applies to lrint, but -IEEE 754r 7.8 seems to forbid spurious inexact exception in -the ineger conversion functions) - -So we try to make sure that no spurious inexact exception is -raised in case of an overflow. - -If the bit size of long > precision of double, then there -cannot be inexact rounding in case the result overflows, -otherwise LONG_MAX and LONG_MIN can be represented exactly -as a double. -*/ - -#if LONG_MAX < 1U<<53 && defined(FE_INEXACT) -#include -#include -#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 -#define EPS DBL_EPSILON -#elif FLT_EVAL_METHOD==2 -#define EPS LDBL_EPSILON -#endif -#ifdef __GNUC__ -/* avoid stack frame in lrint */ -__attribute__((noinline)) -#endif -static long lrint_slow(double x) -{ - #pragma STDC FENV_ACCESS ON - int e; - - e = fetestexcept(FE_INEXACT); - x = rint(x); - if (!e && (x > LONG_MAX || x < LONG_MIN)) - feclearexcept(FE_INEXACT); - /* conversion */ - return x; -} - -long lrint(double x) -{ - uint32_t abstop = asuint64(x)>>32 & 0x7fffffff; - uint64_t sign = asuint64(x) & (1ULL << 63); - - if (abstop < 0x41dfffff) { - /* |x| < 0x7ffffc00, no overflow */ - double_t toint = asdouble(asuint64(1/EPS) | sign); - double_t y = x + toint - toint; - return (long)y; - } - return lrint_slow(x); -} -#else -long lrint(double x) -{ - return rint(x); -} -#endif diff --git a/src/math/lrintf.c b/src/math/lrintf.c deleted file mode 100644 index ca0b6a4..0000000 --- a/src/math/lrintf.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -/* uses LONG_MAX > 2^24, see comments in lrint.c */ - -long lrintf(float x) -{ - return rintf(x); -} diff --git a/src/math/lrintl.c b/src/math/lrintl.c deleted file mode 100644 index b2a8106..0000000 --- a/src/math/lrintl.c +++ /dev/null @@ -1,36 +0,0 @@ -#include -#include -#include "libm.h" - - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long lrintl(long double x) -{ - return lrint(x); -} -#elif defined(FE_INEXACT) -/* -see comments in lrint.c - -Note that if LONG_MAX == 0x7fffffffffffffff && LDBL_MANT_DIG == 64 -then x == 2**63 - 0.5 is the only input that overflows and -raises inexact (with tonearest or upward rounding mode) -*/ -long lrintl(long double x) -{ - #pragma STDC FENV_ACCESS ON - int e; - - e = fetestexcept(FE_INEXACT); - x = rintl(x); - if (!e && (x > LONG_MAX || x < LONG_MIN)) - feclearexcept(FE_INEXACT); - /* conversion */ - return x; -} -#else -long lrintl(long double x) -{ - return rintl(x); -} -#endif diff --git a/src/math/lround.c b/src/math/lround.c deleted file mode 100644 index b8b7954..0000000 --- a/src/math/lround.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -long lround(double x) -{ - return round(x); -} diff --git a/src/math/lroundf.c b/src/math/lroundf.c deleted file mode 100644 index c4707e7..0000000 --- a/src/math/lroundf.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -long lroundf(float x) -{ - return roundf(x); -} diff --git a/src/math/lroundl.c b/src/math/lroundl.c deleted file mode 100644 index 094fdf6..0000000 --- a/src/math/lroundl.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -long lroundl(long double x) -{ - return roundl(x); -} diff --git a/src/math/m68k/sqrtl.c b/src/math/m68k/sqrtl.c deleted file mode 100644 index b1c303c..0000000 --- a/src/math/m68k/sqrtl.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __HAVE_68881__ - -long double sqrtl(long double x) -{ - __asm__ ("fsqrt.x %1,%0" : "=f"(x) : "fm"(x)); - return x; -} - -#else - -#include "../sqrtl.c" - -#endif diff --git a/src/math/mips/fabs.c b/src/math/mips/fabs.c deleted file mode 100644 index 0a5aa3b..0000000 --- a/src/math/mips/fabs.c +++ /dev/null @@ -1,16 +0,0 @@ -#if !defined(__mips_soft_float) && defined(__mips_abs2008) - -#include - -double fabs(double x) -{ - double r; - __asm__("abs.d %0,%1" : "=f"(r) : "f"(x)); - return r; -} - -#else - -#include "../fabs.c" - -#endif diff --git a/src/math/mips/fabsf.c b/src/math/mips/fabsf.c deleted file mode 100644 index 35307be..0000000 --- a/src/math/mips/fabsf.c +++ /dev/null @@ -1,16 +0,0 @@ -#if !defined(__mips_soft_float) && defined(__mips_abs2008) - -#include - -float fabsf(float x) -{ - float r; - __asm__("abs.s %0,%1" : "=f"(r) : "f"(x)); - return r; -} - -#else - -#include "../fabsf.c" - -#endif diff --git a/src/math/mips/sqrt.c b/src/math/mips/sqrt.c deleted file mode 100644 index 595c9db..0000000 --- a/src/math/mips/sqrt.c +++ /dev/null @@ -1,16 +0,0 @@ -#if !defined(__mips_soft_float) && __mips >= 3 - -#include - -double sqrt(double x) -{ - double r; - __asm__("sqrt.d %0,%1" : "=f"(r) : "f"(x)); - return r; -} - -#else - -#include "../sqrt.c" - -#endif diff --git a/src/math/mips/sqrtf.c b/src/math/mips/sqrtf.c deleted file mode 100644 index 84090d2..0000000 --- a/src/math/mips/sqrtf.c +++ /dev/null @@ -1,16 +0,0 @@ -#if !defined(__mips_soft_float) && __mips >= 2 - -#include - -float sqrtf(float x) -{ - float r; - __asm__("sqrt.s %0,%1" : "=f"(r) : "f"(x)); - return r; -} - -#else - -#include "../sqrtf.c" - -#endif diff --git a/src/math/modf.c b/src/math/modf.c deleted file mode 100644 index 1c8a1db..0000000 --- a/src/math/modf.c +++ /dev/null @@ -1,34 +0,0 @@ -#include "libm.h" - -double modf(double x, double *iptr) -{ - union {double f; uint64_t i;} u = {x}; - uint64_t mask; - int e = (int)(u.i>>52 & 0x7ff) - 0x3ff; - - /* no fractional part */ - if (e >= 52) { - *iptr = x; - if (e == 0x400 && u.i<<12 != 0) /* nan */ - return x; - u.i &= 1ULL<<63; - return u.f; - } - - /* no integral part*/ - if (e < 0) { - u.i &= 1ULL<<63; - *iptr = u.f; - return x; - } - - mask = -1ULL>>12>>e; - if ((u.i & mask) == 0) { - *iptr = x; - u.i &= 1ULL<<63; - return u.f; - } - u.i &= ~mask; - *iptr = u.f; - return x - u.f; -} diff --git a/src/math/modff.c b/src/math/modff.c deleted file mode 100644 index 639514e..0000000 --- a/src/math/modff.c +++ /dev/null @@ -1,34 +0,0 @@ -#include "libm.h" - -float modff(float x, float *iptr) -{ - union {float f; uint32_t i;} u = {x}; - uint32_t mask; - int e = (int)(u.i>>23 & 0xff) - 0x7f; - - /* no fractional part */ - if (e >= 23) { - *iptr = x; - if (e == 0x80 && u.i<<9 != 0) { /* nan */ - return x; - } - u.i &= 0x80000000; - return u.f; - } - /* no integral part */ - if (e < 0) { - u.i &= 0x80000000; - *iptr = u.f; - return x; - } - - mask = 0x007fffff>>e; - if ((u.i & mask) == 0) { - *iptr = x; - u.i &= 0x80000000; - return u.f; - } - u.i &= ~mask; - *iptr = u.f; - return x - u.f; -} diff --git a/src/math/modfl.c b/src/math/modfl.c deleted file mode 100644 index a47b192..0000000 --- a/src/math/modfl.c +++ /dev/null @@ -1,53 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double modfl(long double x, long double *iptr) -{ - double d; - long double r; - - r = modf(x, &d); - *iptr = d; - return r; -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 - -static const long double toint = 1/LDBL_EPSILON; - -long double modfl(long double x, long double *iptr) -{ - union ldshape u = {x}; - int e = (u.i.se & 0x7fff) - 0x3fff; - int s = u.i.se >> 15; - long double absx; - long double y; - - /* no fractional part */ - if (e >= LDBL_MANT_DIG-1) { - *iptr = x; - if (isnan(x)) - return x; - return s ? -0.0 : 0.0; - } - - /* no integral part*/ - if (e < 0) { - *iptr = s ? -0.0 : 0.0; - return x; - } - - /* raises spurious inexact */ - absx = s ? -x : x; - y = absx + toint - toint - absx; - if (y == 0) { - *iptr = x; - return s ? -0.0 : 0.0; - } - if (y > 0) - y -= 1; - if (s) - y = -y; - *iptr = x + y; - return -y; -} -#endif diff --git a/src/math/nan.c b/src/math/nan.c deleted file mode 100644 index 9e0826c..0000000 --- a/src/math/nan.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -double nan(const char *s) -{ - return NAN; -} diff --git a/src/math/nanf.c b/src/math/nanf.c deleted file mode 100644 index 752ce54..0000000 --- a/src/math/nanf.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -float nanf(const char *s) -{ - return NAN; -} diff --git a/src/math/nanl.c b/src/math/nanl.c deleted file mode 100644 index 969af56..0000000 --- a/src/math/nanl.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -long double nanl(const char *s) -{ - return NAN; -} diff --git a/src/math/nearbyint.c b/src/math/nearbyint.c deleted file mode 100644 index f4e8aac..0000000 --- a/src/math/nearbyint.c +++ /dev/null @@ -1,20 +0,0 @@ -#include -#include - -/* nearbyint is the same as rint, but it must not raise the inexact exception */ - -double nearbyint(double x) -{ -#ifdef FE_INEXACT - #pragma STDC FENV_ACCESS ON - int e; - - e = fetestexcept(FE_INEXACT); -#endif - x = rint(x); -#ifdef FE_INEXACT - if (!e) - feclearexcept(FE_INEXACT); -#endif - return x; -} diff --git a/src/math/nearbyintf.c b/src/math/nearbyintf.c deleted file mode 100644 index 092e9ff..0000000 --- a/src/math/nearbyintf.c +++ /dev/null @@ -1,18 +0,0 @@ -#include -#include - -float nearbyintf(float x) -{ -#ifdef FE_INEXACT - #pragma STDC FENV_ACCESS ON - int e; - - e = fetestexcept(FE_INEXACT); -#endif - x = rintf(x); -#ifdef FE_INEXACT - if (!e) - feclearexcept(FE_INEXACT); -#endif - return x; -} diff --git a/src/math/nearbyintl.c b/src/math/nearbyintl.c deleted file mode 100644 index 8285249..0000000 --- a/src/math/nearbyintl.c +++ /dev/null @@ -1,26 +0,0 @@ -#include -#include - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double nearbyintl(long double x) -{ - return nearbyint(x); -} -#else -#include -long double nearbyintl(long double x) -{ -#ifdef FE_INEXACT - #pragma STDC FENV_ACCESS ON - int e; - - e = fetestexcept(FE_INEXACT); -#endif - x = rintl(x); -#ifdef FE_INEXACT - if (!e) - feclearexcept(FE_INEXACT); -#endif - return x; -} -#endif diff --git a/src/math/nextafter.c b/src/math/nextafter.c deleted file mode 100644 index ab5795a..0000000 --- a/src/math/nextafter.c +++ /dev/null @@ -1,31 +0,0 @@ -#include "libm.h" - -double nextafter(double x, double y) -{ - union {double f; uint64_t i;} ux={x}, uy={y}; - uint64_t ax, ay; - int e; - - if (isnan(x) || isnan(y)) - return x + y; - if (ux.i == uy.i) - return y; - ax = ux.i & -1ULL/2; - ay = uy.i & -1ULL/2; - if (ax == 0) { - if (ay == 0) - return y; - ux.i = (uy.i & 1ULL<<63) | 1; - } else if (ax > ay || ((ux.i ^ uy.i) & 1ULL<<63)) - ux.i--; - else - ux.i++; - e = ux.i >> 52 & 0x7ff; - /* raise overflow if ux.f is infinite and x is finite */ - if (e == 0x7ff) - FORCE_EVAL(x+x); - /* raise underflow if ux.f is subnormal or zero */ - if (e == 0) - FORCE_EVAL(x*x + ux.f*ux.f); - return ux.f; -} diff --git a/src/math/nextafterf.c b/src/math/nextafterf.c deleted file mode 100644 index 75a09f7..0000000 --- a/src/math/nextafterf.c +++ /dev/null @@ -1,30 +0,0 @@ -#include "libm.h" - -float nextafterf(float x, float y) -{ - union {float f; uint32_t i;} ux={x}, uy={y}; - uint32_t ax, ay, e; - - if (isnan(x) || isnan(y)) - return x + y; - if (ux.i == uy.i) - return y; - ax = ux.i & 0x7fffffff; - ay = uy.i & 0x7fffffff; - if (ax == 0) { - if (ay == 0) - return y; - ux.i = (uy.i & 0x80000000) | 1; - } else if (ax > ay || ((ux.i ^ uy.i) & 0x80000000)) - ux.i--; - else - ux.i++; - e = ux.i & 0x7f800000; - /* raise overflow if ux.f is infinite and x is finite */ - if (e == 0x7f800000) - FORCE_EVAL(x+x); - /* raise underflow if ux.f is subnormal or zero */ - if (e == 0) - FORCE_EVAL(x*x + ux.f*ux.f); - return ux.f; -} diff --git a/src/math/nextafterl.c b/src/math/nextafterl.c deleted file mode 100644 index 37e858f..0000000 --- a/src/math/nextafterl.c +++ /dev/null @@ -1,75 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double nextafterl(long double x, long double y) -{ - return nextafter(x, y); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -long double nextafterl(long double x, long double y) -{ - union ldshape ux, uy; - - if (isnan(x) || isnan(y)) - return x + y; - if (x == y) - return y; - ux.f = x; - if (x == 0) { - uy.f = y; - ux.i.m = 1; - ux.i.se = uy.i.se & 0x8000; - } else if ((x < y) == !(ux.i.se & 0x8000)) { - ux.i.m++; - if (ux.i.m << 1 == 0) { - ux.i.m = 1ULL << 63; - ux.i.se++; - } - } else { - if (ux.i.m << 1 == 0) { - ux.i.se--; - if (ux.i.se) - ux.i.m = 0; - } - ux.i.m--; - } - /* raise overflow if ux is infinite and x is finite */ - if ((ux.i.se & 0x7fff) == 0x7fff) - return x + x; - /* raise underflow if ux is subnormal or zero */ - if ((ux.i.se & 0x7fff) == 0) - FORCE_EVAL(x*x + ux.f*ux.f); - return ux.f; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -long double nextafterl(long double x, long double y) -{ - union ldshape ux, uy; - - if (isnan(x) || isnan(y)) - return x + y; - if (x == y) - return y; - ux.f = x; - if (x == 0) { - uy.f = y; - ux.i.lo = 1; - ux.i.se = uy.i.se & 0x8000; - } else if ((x < y) == !(ux.i.se & 0x8000)) { - ux.i2.lo++; - if (ux.i2.lo == 0) - ux.i2.hi++; - } else { - if (ux.i2.lo == 0) - ux.i2.hi--; - ux.i2.lo--; - } - /* raise overflow if ux is infinite and x is finite */ - if ((ux.i.se & 0x7fff) == 0x7fff) - return x + x; - /* raise underflow if ux is subnormal or zero */ - if ((ux.i.se & 0x7fff) == 0) - FORCE_EVAL(x*x + ux.f*ux.f); - return ux.f; -} -#endif diff --git a/src/math/nexttoward.c b/src/math/nexttoward.c deleted file mode 100644 index 827ee5c..0000000 --- a/src/math/nexttoward.c +++ /dev/null @@ -1,42 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -double nexttoward(double x, long double y) -{ - return nextafter(x, y); -} -#else -double nexttoward(double x, long double y) -{ - union {double f; uint64_t i;} ux = {x}; - int e; - - if (isnan(x) || isnan(y)) - return x + y; - if (x == y) - return y; - if (x == 0) { - ux.i = 1; - if (signbit(y)) - ux.i |= 1ULL<<63; - } else if (x < y) { - if (signbit(x)) - ux.i--; - else - ux.i++; - } else { - if (signbit(x)) - ux.i++; - else - ux.i--; - } - e = ux.i>>52 & 0x7ff; - /* raise overflow if ux.f is infinite and x is finite */ - if (e == 0x7ff) - FORCE_EVAL(x+x); - /* raise underflow if ux.f is subnormal or zero */ - if (e == 0) - FORCE_EVAL(x*x + ux.f*ux.f); - return ux.f; -} -#endif diff --git a/src/math/nexttowardf.c b/src/math/nexttowardf.c deleted file mode 100644 index bbf172f..0000000 --- a/src/math/nexttowardf.c +++ /dev/null @@ -1,35 +0,0 @@ -#include "libm.h" - -float nexttowardf(float x, long double y) -{ - union {float f; uint32_t i;} ux = {x}; - uint32_t e; - - if (isnan(x) || isnan(y)) - return x + y; - if (x == y) - return y; - if (x == 0) { - ux.i = 1; - if (signbit(y)) - ux.i |= 0x80000000; - } else if (x < y) { - if (signbit(x)) - ux.i--; - else - ux.i++; - } else { - if (signbit(x)) - ux.i++; - else - ux.i--; - } - e = ux.i & 0x7f800000; - /* raise overflow if ux.f is infinite and x is finite */ - if (e == 0x7f800000) - FORCE_EVAL(x+x); - /* raise underflow if ux.f is subnormal or zero */ - if (e == 0) - FORCE_EVAL(x*x + ux.f*ux.f); - return ux.f; -} diff --git a/src/math/nexttowardl.c b/src/math/nexttowardl.c deleted file mode 100644 index 67a6340..0000000 --- a/src/math/nexttowardl.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -long double nexttowardl(long double x, long double y) -{ - return nextafterl(x, y); -} diff --git a/src/math/pow.c b/src/math/pow.c deleted file mode 100644 index 694c2ef..0000000 --- a/src/math/pow.c +++ /dev/null @@ -1,343 +0,0 @@ -/* - * Double-precision x^y function. - * - * Copyright (c) 2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include -#include -#include "libm.h" -#include "exp_data.h" -#include "pow_data.h" - -/* -Worst-case error: 0.54 ULP (~= ulperr_exp + 1024*Ln2*relerr_log*2^53) -relerr_log: 1.3 * 2^-68 (Relative error of log, 1.5 * 2^-68 without fma) -ulperr_exp: 0.509 ULP (ULP error of exp, 0.511 ULP without fma) -*/ - -#define T __pow_log_data.tab -#define A __pow_log_data.poly -#define Ln2hi __pow_log_data.ln2hi -#define Ln2lo __pow_log_data.ln2lo -#define N (1 << POW_LOG_TABLE_BITS) -#define OFF 0x3fe6955500000000 - -/* Top 12 bits of a double (sign and exponent bits). */ -static inline uint32_t top12(double x) -{ - return asuint64(x) >> 52; -} - -/* Compute y+TAIL = log(x) where the rounded result is y and TAIL has about - additional 15 bits precision. IX is the bit representation of x, but - normalized in the subnormal range using the sign bit for the exponent. */ -static inline double_t log_inline(uint64_t ix, double_t *tail) -{ - /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ - double_t z, r, y, invc, logc, logctail, kd, hi, t1, t2, lo, lo1, lo2, p; - uint64_t iz, tmp; - int k, i; - - /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. - The range is split into N subintervals. - The ith subinterval contains z and c is near its center. */ - tmp = ix - OFF; - i = (tmp >> (52 - POW_LOG_TABLE_BITS)) % N; - k = (int64_t)tmp >> 52; /* arithmetic shift */ - iz = ix - (tmp & 0xfffULL << 52); - z = asdouble(iz); - kd = (double_t)k; - - /* log(x) = k*Ln2 + log(c) + log1p(z/c-1). */ - invc = T[i].invc; - logc = T[i].logc; - logctail = T[i].logctail; - - /* Note: 1/c is j/N or j/N/2 where j is an integer in [N,2N) and - |z/c - 1| < 1/N, so r = z/c - 1 is exactly representible. */ -#if __FP_FAST_FMA - r = __builtin_fma(z, invc, -1.0); -#else - /* Split z such that rhi, rlo and rhi*rhi are exact and |rlo| <= |r|. */ - double_t zhi = asdouble((iz + (1ULL << 31)) & (-1ULL << 32)); - double_t zlo = z - zhi; - double_t rhi = zhi * invc - 1.0; - double_t rlo = zlo * invc; - r = rhi + rlo; -#endif - - /* k*Ln2 + log(c) + r. */ - t1 = kd * Ln2hi + logc; - t2 = t1 + r; - lo1 = kd * Ln2lo + logctail; - lo2 = t1 - t2 + r; - - /* Evaluation is optimized assuming superscalar pipelined execution. */ - double_t ar, ar2, ar3, lo3, lo4; - ar = A[0] * r; /* A[0] = -0.5. */ - ar2 = r * ar; - ar3 = r * ar2; - /* k*Ln2 + log(c) + r + A[0]*r*r. */ -#if __FP_FAST_FMA - hi = t2 + ar2; - lo3 = __builtin_fma(ar, r, -ar2); - lo4 = t2 - hi + ar2; -#else - double_t arhi = A[0] * rhi; - double_t arhi2 = rhi * arhi; - hi = t2 + arhi2; - lo3 = rlo * (ar + arhi); - lo4 = t2 - hi + arhi2; -#endif - /* p = log1p(r) - r - A[0]*r*r. */ - p = (ar3 * (A[1] + r * A[2] + - ar2 * (A[3] + r * A[4] + ar2 * (A[5] + r * A[6])))); - lo = lo1 + lo2 + lo3 + lo4 + p; - y = hi + lo; - *tail = hi - y + lo; - return y; -} - -#undef N -#undef T -#define N (1 << EXP_TABLE_BITS) -#define InvLn2N __exp_data.invln2N -#define NegLn2hiN __exp_data.negln2hiN -#define NegLn2loN __exp_data.negln2loN -#define Shift __exp_data.shift -#define T __exp_data.tab -#define C2 __exp_data.poly[5 - EXP_POLY_ORDER] -#define C3 __exp_data.poly[6 - EXP_POLY_ORDER] -#define C4 __exp_data.poly[7 - EXP_POLY_ORDER] -#define C5 __exp_data.poly[8 - EXP_POLY_ORDER] -#define C6 __exp_data.poly[9 - EXP_POLY_ORDER] - -/* Handle cases that may overflow or underflow when computing the result that - is scale*(1+TMP) without intermediate rounding. The bit representation of - scale is in SBITS, however it has a computed exponent that may have - overflown into the sign bit so that needs to be adjusted before using it as - a double. (int32_t)KI is the k used in the argument reduction and exponent - adjustment of scale, positive k here means the result may overflow and - negative k means the result may underflow. */ -static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki) -{ - double_t scale, y; - - if ((ki & 0x80000000) == 0) { - /* k > 0, the exponent of scale might have overflowed by <= 460. */ - sbits -= 1009ull << 52; - scale = asdouble(sbits); - y = 0x1p1009 * (scale + scale * tmp); - return eval_as_double(y); - } - /* k < 0, need special care in the subnormal range. */ - sbits += 1022ull << 52; - /* Note: sbits is signed scale. */ - scale = asdouble(sbits); - y = scale + scale * tmp; - if (fabs(y) < 1.0) { - /* Round y to the right precision before scaling it into the subnormal - range to avoid double rounding that can cause 0.5+E/2 ulp error where - E is the worst-case ulp error outside the subnormal range. So this - is only useful if the goal is better than 1 ulp worst-case error. */ - double_t hi, lo, one = 1.0; - if (y < 0.0) - one = -1.0; - lo = scale - y + scale * tmp; - hi = one + y; - lo = one - hi + y + lo; - y = eval_as_double(hi + lo) - one; - /* Fix the sign of 0. */ - if (y == 0.0) - y = asdouble(sbits & 0x8000000000000000); - /* The underflow exception needs to be signaled explicitly. */ - fp_force_eval(fp_barrier(0x1p-1022) * 0x1p-1022); - } - y = 0x1p-1022 * y; - return eval_as_double(y); -} - -#define SIGN_BIAS (0x800 << EXP_TABLE_BITS) - -/* Computes sign*exp(x+xtail) where |xtail| < 2^-8/N and |xtail| <= |x|. - The sign_bias argument is SIGN_BIAS or 0 and sets the sign to -1 or 1. */ -static inline double exp_inline(double_t x, double_t xtail, uint32_t sign_bias) -{ - uint32_t abstop; - uint64_t ki, idx, top, sbits; - /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ - double_t kd, z, r, r2, scale, tail, tmp; - - abstop = top12(x) & 0x7ff; - if (predict_false(abstop - top12(0x1p-54) >= - top12(512.0) - top12(0x1p-54))) { - if (abstop - top12(0x1p-54) >= 0x80000000) { - /* Avoid spurious underflow for tiny x. */ - /* Note: 0 is common input. */ - double_t one = WANT_ROUNDING ? 1.0 + x : 1.0; - return sign_bias ? -one : one; - } - if (abstop >= top12(1024.0)) { - /* Note: inf and nan are already handled. */ - if (asuint64(x) >> 63) - return __math_uflow(sign_bias); - else - return __math_oflow(sign_bias); - } - /* Large x is special cased below. */ - abstop = 0; - } - - /* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */ - /* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */ - z = InvLn2N * x; -#if TOINT_INTRINSICS - kd = roundtoint(z); - ki = converttoint(z); -#elif EXP_USE_TOINT_NARROW - /* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes. */ - kd = eval_as_double(z + Shift); - ki = asuint64(kd) >> 16; - kd = (double_t)(int32_t)ki; -#else - /* z - kd is in [-1, 1] in non-nearest rounding modes. */ - kd = eval_as_double(z + Shift); - ki = asuint64(kd); - kd -= Shift; -#endif - r = x + kd * NegLn2hiN + kd * NegLn2loN; - /* The code assumes 2^-200 < |xtail| < 2^-8/N. */ - r += xtail; - /* 2^(k/N) ~= scale * (1 + tail). */ - idx = 2 * (ki % N); - top = (ki + sign_bias) << (52 - EXP_TABLE_BITS); - tail = asdouble(T[idx]); - /* This is only a valid scale when -1023*N < k < 1024*N. */ - sbits = T[idx + 1] + top; - /* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1). */ - /* Evaluation is optimized assuming superscalar pipelined execution. */ - r2 = r * r; - /* Without fma the worst case error is 0.25/N ulp larger. */ - /* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp. */ - tmp = tail + r + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5); - if (predict_false(abstop == 0)) - return specialcase(tmp, sbits, ki); - scale = asdouble(sbits); - /* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there - is no spurious underflow here even without fma. */ - return eval_as_double(scale + scale * tmp); -} - -/* Returns 0 if not int, 1 if odd int, 2 if even int. The argument is - the bit representation of a non-zero finite floating-point value. */ -static inline int checkint(uint64_t iy) -{ - int e = iy >> 52 & 0x7ff; - if (e < 0x3ff) - return 0; - if (e > 0x3ff + 52) - return 2; - if (iy & ((1ULL << (0x3ff + 52 - e)) - 1)) - return 0; - if (iy & (1ULL << (0x3ff + 52 - e))) - return 1; - return 2; -} - -/* Returns 1 if input is the bit representation of 0, infinity or nan. */ -static inline int zeroinfnan(uint64_t i) -{ - return 2 * i - 1 >= 2 * asuint64(INFINITY) - 1; -} - -double pow(double x, double y) -{ - uint32_t sign_bias = 0; - uint64_t ix, iy; - uint32_t topx, topy; - - ix = asuint64(x); - iy = asuint64(y); - topx = top12(x); - topy = top12(y); - if (predict_false(topx - 0x001 >= 0x7ff - 0x001 || - (topy & 0x7ff) - 0x3be >= 0x43e - 0x3be)) { - /* Note: if |y| > 1075 * ln2 * 2^53 ~= 0x1.749p62 then pow(x,y) = inf/0 - and if |y| < 2^-54 / 1075 ~= 0x1.e7b6p-65 then pow(x,y) = +-1. */ - /* Special cases: (x < 0x1p-126 or inf or nan) or - (|y| < 0x1p-65 or |y| >= 0x1p63 or nan). */ - if (predict_false(zeroinfnan(iy))) { - if (2 * iy == 0) - return issignaling_inline(x) ? x + y : 1.0; - if (ix == asuint64(1.0)) - return issignaling_inline(y) ? x + y : 1.0; - if (2 * ix > 2 * asuint64(INFINITY) || - 2 * iy > 2 * asuint64(INFINITY)) - return x + y; - if (2 * ix == 2 * asuint64(1.0)) - return 1.0; - if ((2 * ix < 2 * asuint64(1.0)) == !(iy >> 63)) - return 0.0; /* |x|<1 && y==inf or |x|>1 && y==-inf. */ - return y * y; - } - if (predict_false(zeroinfnan(ix))) { - double_t x2 = x * x; - if (ix >> 63 && checkint(iy) == 1) - x2 = -x2; - /* Without the barrier some versions of clang hoist the 1/x2 and - thus division by zero exception can be signaled spuriously. */ - return iy >> 63 ? fp_barrier(1 / x2) : x2; - } - /* Here x and y are non-zero finite. */ - if (ix >> 63) { - /* Finite x < 0. */ - int yint = checkint(iy); - if (yint == 0) - return __math_invalid(x); - if (yint == 1) - sign_bias = SIGN_BIAS; - ix &= 0x7fffffffffffffff; - topx &= 0x7ff; - } - if ((topy & 0x7ff) - 0x3be >= 0x43e - 0x3be) { - /* Note: sign_bias == 0 here because y is not odd. */ - if (ix == asuint64(1.0)) - return 1.0; - if ((topy & 0x7ff) < 0x3be) { - /* |y| < 2^-65, x^y ~= 1 + y*log(x). */ - if (WANT_ROUNDING) - return ix > asuint64(1.0) ? 1.0 + y : - 1.0 - y; - else - return 1.0; - } - return (ix > asuint64(1.0)) == (topy < 0x800) ? - __math_oflow(0) : - __math_uflow(0); - } - if (topx == 0) { - /* Normalize subnormal x so exponent becomes negative. */ - ix = asuint64(x * 0x1p52); - ix &= 0x7fffffffffffffff; - ix -= 52ULL << 52; - } - } - - double_t lo; - double_t hi = log_inline(ix, &lo); - double_t ehi, elo; -#if __FP_FAST_FMA - ehi = y * hi; - elo = y * lo + __builtin_fma(y, hi, -ehi); -#else - double_t yhi = asdouble(iy & -1ULL << 27); - double_t ylo = y - yhi; - double_t lhi = asdouble(asuint64(hi) & -1ULL << 27); - double_t llo = hi - lhi + lo; - ehi = yhi * lhi; - elo = ylo * lhi + y * llo; /* |elo| < |ehi| * 2^-25. */ -#endif - return exp_inline(ehi, elo, sign_bias); -} diff --git a/src/math/pow_data.c b/src/math/pow_data.c deleted file mode 100644 index 81e760d..0000000 --- a/src/math/pow_data.c +++ /dev/null @@ -1,180 +0,0 @@ -/* - * Data for the log part of pow. - * - * Copyright (c) 2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include "pow_data.h" - -#define N (1 << POW_LOG_TABLE_BITS) - -const struct pow_log_data __pow_log_data = { -.ln2hi = 0x1.62e42fefa3800p-1, -.ln2lo = 0x1.ef35793c76730p-45, -.poly = { -// relative error: 0x1.11922ap-70 -// in -0x1.6bp-8 0x1.6bp-8 -// Coefficients are scaled to match the scaling during evaluation. --0x1p-1, -0x1.555555555556p-2 * -2, --0x1.0000000000006p-2 * -2, -0x1.999999959554ep-3 * 4, --0x1.555555529a47ap-3 * 4, -0x1.2495b9b4845e9p-3 * -8, --0x1.0002b8b263fc3p-3 * -8, -}, -/* Algorithm: - - x = 2^k z - log(x) = k ln2 + log(c) + log(z/c) - log(z/c) = poly(z/c - 1) - -where z is in [0x1.69555p-1; 0x1.69555p0] which is split into N subintervals -and z falls into the ith one, then table entries are computed as - - tab[i].invc = 1/c - tab[i].logc = round(0x1p43*log(c))/0x1p43 - tab[i].logctail = (double)(log(c) - logc) - -where c is chosen near the center of the subinterval such that 1/c has only a -few precision bits so z/c - 1 is exactly representible as double: - - 1/c = center < 1 ? round(N/center)/N : round(2*N/center)/N/2 - -Note: |z/c - 1| < 1/N for the chosen c, |log(c) - logc - logctail| < 0x1p-97, -the last few bits of logc are rounded away so k*ln2hi + logc has no rounding -error and the interval for z is selected such that near x == 1, where log(x) -is tiny, large cancellation error is avoided in logc + poly(z/c - 1). */ -.tab = { -#define A(a, b, c) {a, 0, b, c}, -A(0x1.6a00000000000p+0, -0x1.62c82f2b9c800p-2, 0x1.ab42428375680p-48) -A(0x1.6800000000000p+0, -0x1.5d1bdbf580800p-2, -0x1.ca508d8e0f720p-46) -A(0x1.6600000000000p+0, -0x1.5767717455800p-2, -0x1.362a4d5b6506dp-45) -A(0x1.6400000000000p+0, -0x1.51aad872df800p-2, -0x1.684e49eb067d5p-49) -A(0x1.6200000000000p+0, -0x1.4be5f95777800p-2, -0x1.41b6993293ee0p-47) -A(0x1.6000000000000p+0, -0x1.4618bc21c6000p-2, 0x1.3d82f484c84ccp-46) -A(0x1.5e00000000000p+0, -0x1.404308686a800p-2, 0x1.c42f3ed820b3ap-50) -A(0x1.5c00000000000p+0, -0x1.3a64c55694800p-2, 0x1.0b1c686519460p-45) -A(0x1.5a00000000000p+0, -0x1.347dd9a988000p-2, 0x1.5594dd4c58092p-45) -A(0x1.5800000000000p+0, -0x1.2e8e2bae12000p-2, 0x1.67b1e99b72bd8p-45) -A(0x1.5600000000000p+0, -0x1.2895a13de8800p-2, 0x1.5ca14b6cfb03fp-46) -A(0x1.5600000000000p+0, -0x1.2895a13de8800p-2, 0x1.5ca14b6cfb03fp-46) -A(0x1.5400000000000p+0, -0x1.22941fbcf7800p-2, -0x1.65a242853da76p-46) -A(0x1.5200000000000p+0, -0x1.1c898c1699800p-2, -0x1.fafbc68e75404p-46) -A(0x1.5000000000000p+0, -0x1.1675cababa800p-2, 0x1.f1fc63382a8f0p-46) -A(0x1.4e00000000000p+0, -0x1.1058bf9ae4800p-2, -0x1.6a8c4fd055a66p-45) -A(0x1.4c00000000000p+0, -0x1.0a324e2739000p-2, -0x1.c6bee7ef4030ep-47) -A(0x1.4a00000000000p+0, -0x1.0402594b4d000p-2, -0x1.036b89ef42d7fp-48) -A(0x1.4a00000000000p+0, -0x1.0402594b4d000p-2, -0x1.036b89ef42d7fp-48) -A(0x1.4800000000000p+0, -0x1.fb9186d5e4000p-3, 0x1.d572aab993c87p-47) -A(0x1.4600000000000p+0, -0x1.ef0adcbdc6000p-3, 0x1.b26b79c86af24p-45) -A(0x1.4400000000000p+0, -0x1.e27076e2af000p-3, -0x1.72f4f543fff10p-46) -A(0x1.4200000000000p+0, -0x1.d5c216b4fc000p-3, 0x1.1ba91bbca681bp-45) -A(0x1.4000000000000p+0, -0x1.c8ff7c79aa000p-3, 0x1.7794f689f8434p-45) -A(0x1.4000000000000p+0, -0x1.c8ff7c79aa000p-3, 0x1.7794f689f8434p-45) -A(0x1.3e00000000000p+0, -0x1.bc286742d9000p-3, 0x1.94eb0318bb78fp-46) -A(0x1.3c00000000000p+0, -0x1.af3c94e80c000p-3, 0x1.a4e633fcd9066p-52) -A(0x1.3a00000000000p+0, -0x1.a23bc1fe2b000p-3, -0x1.58c64dc46c1eap-45) -A(0x1.3a00000000000p+0, -0x1.a23bc1fe2b000p-3, -0x1.58c64dc46c1eap-45) -A(0x1.3800000000000p+0, -0x1.9525a9cf45000p-3, -0x1.ad1d904c1d4e3p-45) -A(0x1.3600000000000p+0, -0x1.87fa06520d000p-3, 0x1.bbdbf7fdbfa09p-45) -A(0x1.3400000000000p+0, -0x1.7ab890210e000p-3, 0x1.bdb9072534a58p-45) -A(0x1.3400000000000p+0, -0x1.7ab890210e000p-3, 0x1.bdb9072534a58p-45) -A(0x1.3200000000000p+0, -0x1.6d60fe719d000p-3, -0x1.0e46aa3b2e266p-46) -A(0x1.3000000000000p+0, -0x1.5ff3070a79000p-3, -0x1.e9e439f105039p-46) -A(0x1.3000000000000p+0, -0x1.5ff3070a79000p-3, -0x1.e9e439f105039p-46) -A(0x1.2e00000000000p+0, -0x1.526e5e3a1b000p-3, -0x1.0de8b90075b8fp-45) -A(0x1.2c00000000000p+0, -0x1.44d2b6ccb8000p-3, 0x1.70cc16135783cp-46) -A(0x1.2c00000000000p+0, -0x1.44d2b6ccb8000p-3, 0x1.70cc16135783cp-46) -A(0x1.2a00000000000p+0, -0x1.371fc201e9000p-3, 0x1.178864d27543ap-48) -A(0x1.2800000000000p+0, -0x1.29552f81ff000p-3, -0x1.48d301771c408p-45) -A(0x1.2600000000000p+0, -0x1.1b72ad52f6000p-3, -0x1.e80a41811a396p-45) -A(0x1.2600000000000p+0, -0x1.1b72ad52f6000p-3, -0x1.e80a41811a396p-45) -A(0x1.2400000000000p+0, -0x1.0d77e7cd09000p-3, 0x1.a699688e85bf4p-47) -A(0x1.2400000000000p+0, -0x1.0d77e7cd09000p-3, 0x1.a699688e85bf4p-47) -A(0x1.2200000000000p+0, -0x1.fec9131dbe000p-4, -0x1.575545ca333f2p-45) -A(0x1.2000000000000p+0, -0x1.e27076e2b0000p-4, 0x1.a342c2af0003cp-45) -A(0x1.2000000000000p+0, -0x1.e27076e2b0000p-4, 0x1.a342c2af0003cp-45) -A(0x1.1e00000000000p+0, -0x1.c5e548f5bc000p-4, -0x1.d0c57585fbe06p-46) -A(0x1.1c00000000000p+0, -0x1.a926d3a4ae000p-4, 0x1.53935e85baac8p-45) -A(0x1.1c00000000000p+0, -0x1.a926d3a4ae000p-4, 0x1.53935e85baac8p-45) -A(0x1.1a00000000000p+0, -0x1.8c345d631a000p-4, 0x1.37c294d2f5668p-46) -A(0x1.1a00000000000p+0, -0x1.8c345d631a000p-4, 0x1.37c294d2f5668p-46) -A(0x1.1800000000000p+0, -0x1.6f0d28ae56000p-4, -0x1.69737c93373dap-45) -A(0x1.1600000000000p+0, -0x1.51b073f062000p-4, 0x1.f025b61c65e57p-46) -A(0x1.1600000000000p+0, -0x1.51b073f062000p-4, 0x1.f025b61c65e57p-46) -A(0x1.1400000000000p+0, -0x1.341d7961be000p-4, 0x1.c5edaccf913dfp-45) -A(0x1.1400000000000p+0, -0x1.341d7961be000p-4, 0x1.c5edaccf913dfp-45) -A(0x1.1200000000000p+0, -0x1.16536eea38000p-4, 0x1.47c5e768fa309p-46) -A(0x1.1000000000000p+0, -0x1.f0a30c0118000p-5, 0x1.d599e83368e91p-45) -A(0x1.1000000000000p+0, -0x1.f0a30c0118000p-5, 0x1.d599e83368e91p-45) -A(0x1.0e00000000000p+0, -0x1.b42dd71198000p-5, 0x1.c827ae5d6704cp-46) -A(0x1.0e00000000000p+0, -0x1.b42dd71198000p-5, 0x1.c827ae5d6704cp-46) -A(0x1.0c00000000000p+0, -0x1.77458f632c000p-5, -0x1.cfc4634f2a1eep-45) -A(0x1.0c00000000000p+0, -0x1.77458f632c000p-5, -0x1.cfc4634f2a1eep-45) -A(0x1.0a00000000000p+0, -0x1.39e87b9fec000p-5, 0x1.502b7f526feaap-48) -A(0x1.0a00000000000p+0, -0x1.39e87b9fec000p-5, 0x1.502b7f526feaap-48) -A(0x1.0800000000000p+0, -0x1.f829b0e780000p-6, -0x1.980267c7e09e4p-45) -A(0x1.0800000000000p+0, -0x1.f829b0e780000p-6, -0x1.980267c7e09e4p-45) -A(0x1.0600000000000p+0, -0x1.7b91b07d58000p-6, -0x1.88d5493faa639p-45) -A(0x1.0400000000000p+0, -0x1.fc0a8b0fc0000p-7, -0x1.f1e7cf6d3a69cp-50) -A(0x1.0400000000000p+0, -0x1.fc0a8b0fc0000p-7, -0x1.f1e7cf6d3a69cp-50) -A(0x1.0200000000000p+0, -0x1.fe02a6b100000p-8, -0x1.9e23f0dda40e4p-46) -A(0x1.0200000000000p+0, -0x1.fe02a6b100000p-8, -0x1.9e23f0dda40e4p-46) -A(0x1.0000000000000p+0, 0x0.0000000000000p+0, 0x0.0000000000000p+0) -A(0x1.0000000000000p+0, 0x0.0000000000000p+0, 0x0.0000000000000p+0) -A(0x1.fc00000000000p-1, 0x1.0101575890000p-7, -0x1.0c76b999d2be8p-46) -A(0x1.f800000000000p-1, 0x1.0205658938000p-6, -0x1.3dc5b06e2f7d2p-45) -A(0x1.f400000000000p-1, 0x1.8492528c90000p-6, -0x1.aa0ba325a0c34p-45) -A(0x1.f000000000000p-1, 0x1.0415d89e74000p-5, 0x1.111c05cf1d753p-47) -A(0x1.ec00000000000p-1, 0x1.466aed42e0000p-5, -0x1.c167375bdfd28p-45) -A(0x1.e800000000000p-1, 0x1.894aa149fc000p-5, -0x1.97995d05a267dp-46) -A(0x1.e400000000000p-1, 0x1.ccb73cdddc000p-5, -0x1.a68f247d82807p-46) -A(0x1.e200000000000p-1, 0x1.eea31c006c000p-5, -0x1.e113e4fc93b7bp-47) -A(0x1.de00000000000p-1, 0x1.1973bd1466000p-4, -0x1.5325d560d9e9bp-45) -A(0x1.da00000000000p-1, 0x1.3bdf5a7d1e000p-4, 0x1.cc85ea5db4ed7p-45) -A(0x1.d600000000000p-1, 0x1.5e95a4d97a000p-4, -0x1.c69063c5d1d1ep-45) -A(0x1.d400000000000p-1, 0x1.700d30aeac000p-4, 0x1.c1e8da99ded32p-49) -A(0x1.d000000000000p-1, 0x1.9335e5d594000p-4, 0x1.3115c3abd47dap-45) -A(0x1.cc00000000000p-1, 0x1.b6ac88dad6000p-4, -0x1.390802bf768e5p-46) -A(0x1.ca00000000000p-1, 0x1.c885801bc4000p-4, 0x1.646d1c65aacd3p-45) -A(0x1.c600000000000p-1, 0x1.ec739830a2000p-4, -0x1.dc068afe645e0p-45) -A(0x1.c400000000000p-1, 0x1.fe89139dbe000p-4, -0x1.534d64fa10afdp-45) -A(0x1.c000000000000p-1, 0x1.1178e8227e000p-3, 0x1.1ef78ce2d07f2p-45) -A(0x1.be00000000000p-1, 0x1.1aa2b7e23f000p-3, 0x1.ca78e44389934p-45) -A(0x1.ba00000000000p-1, 0x1.2d1610c868000p-3, 0x1.39d6ccb81b4a1p-47) -A(0x1.b800000000000p-1, 0x1.365fcb0159000p-3, 0x1.62fa8234b7289p-51) -A(0x1.b400000000000p-1, 0x1.4913d8333b000p-3, 0x1.5837954fdb678p-45) -A(0x1.b200000000000p-1, 0x1.527e5e4a1b000p-3, 0x1.633e8e5697dc7p-45) -A(0x1.ae00000000000p-1, 0x1.6574ebe8c1000p-3, 0x1.9cf8b2c3c2e78p-46) -A(0x1.ac00000000000p-1, 0x1.6f0128b757000p-3, -0x1.5118de59c21e1p-45) -A(0x1.aa00000000000p-1, 0x1.7898d85445000p-3, -0x1.c661070914305p-46) -A(0x1.a600000000000p-1, 0x1.8beafeb390000p-3, -0x1.73d54aae92cd1p-47) -A(0x1.a400000000000p-1, 0x1.95a5adcf70000p-3, 0x1.7f22858a0ff6fp-47) -A(0x1.a000000000000p-1, 0x1.a93ed3c8ae000p-3, -0x1.8724350562169p-45) -A(0x1.9e00000000000p-1, 0x1.b31d8575bd000p-3, -0x1.c358d4eace1aap-47) -A(0x1.9c00000000000p-1, 0x1.bd087383be000p-3, -0x1.d4bc4595412b6p-45) -A(0x1.9a00000000000p-1, 0x1.c6ffbc6f01000p-3, -0x1.1ec72c5962bd2p-48) -A(0x1.9600000000000p-1, 0x1.db13db0d49000p-3, -0x1.aff2af715b035p-45) -A(0x1.9400000000000p-1, 0x1.e530effe71000p-3, 0x1.212276041f430p-51) -A(0x1.9200000000000p-1, 0x1.ef5ade4dd0000p-3, -0x1.a211565bb8e11p-51) -A(0x1.9000000000000p-1, 0x1.f991c6cb3b000p-3, 0x1.bcbecca0cdf30p-46) -A(0x1.8c00000000000p-1, 0x1.07138604d5800p-2, 0x1.89cdb16ed4e91p-48) -A(0x1.8a00000000000p-1, 0x1.0c42d67616000p-2, 0x1.7188b163ceae9p-45) -A(0x1.8800000000000p-1, 0x1.1178e8227e800p-2, -0x1.c210e63a5f01cp-45) -A(0x1.8600000000000p-1, 0x1.16b5ccbacf800p-2, 0x1.b9acdf7a51681p-45) -A(0x1.8400000000000p-1, 0x1.1bf99635a6800p-2, 0x1.ca6ed5147bdb7p-45) -A(0x1.8200000000000p-1, 0x1.214456d0eb800p-2, 0x1.a87deba46baeap-47) -A(0x1.7e00000000000p-1, 0x1.2bef07cdc9000p-2, 0x1.a9cfa4a5004f4p-45) -A(0x1.7c00000000000p-1, 0x1.314f1e1d36000p-2, -0x1.8e27ad3213cb8p-45) -A(0x1.7a00000000000p-1, 0x1.36b6776be1000p-2, 0x1.16ecdb0f177c8p-46) -A(0x1.7800000000000p-1, 0x1.3c25277333000p-2, 0x1.83b54b606bd5cp-46) -A(0x1.7600000000000p-1, 0x1.419b423d5e800p-2, 0x1.8e436ec90e09dp-47) -A(0x1.7400000000000p-1, 0x1.4718dc271c800p-2, -0x1.f27ce0967d675p-45) -A(0x1.7200000000000p-1, 0x1.4c9e09e173000p-2, -0x1.e20891b0ad8a4p-45) -A(0x1.7000000000000p-1, 0x1.522ae0738a000p-2, 0x1.ebe708164c759p-45) -A(0x1.6e00000000000p-1, 0x1.57bf753c8d000p-2, 0x1.fadedee5d40efp-46) -A(0x1.6c00000000000p-1, 0x1.5d5bddf596000p-2, -0x1.a0b2a08a465dcp-47) -}, -}; diff --git a/src/math/pow_data.h b/src/math/pow_data.h deleted file mode 100644 index 5d609ae..0000000 --- a/src/math/pow_data.h +++ /dev/null @@ -1,22 +0,0 @@ -/* - * Copyright (c) 2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ -#ifndef _POW_DATA_H -#define _POW_DATA_H - -#include - -#define POW_LOG_TABLE_BITS 7 -#define POW_LOG_POLY_ORDER 8 -extern hidden const struct pow_log_data { - double ln2hi; - double ln2lo; - double poly[POW_LOG_POLY_ORDER - 1]; /* First coefficient is 1. */ - /* Note: the pad field is unused, but allows slightly faster indexing. */ - struct { - double invc, pad, logc, logctail; - } tab[1 << POW_LOG_TABLE_BITS]; -} __pow_log_data; - -#endif diff --git a/src/math/powerpc/fabs.c b/src/math/powerpc/fabs.c deleted file mode 100644 index 0efc21e..0000000 --- a/src/math/powerpc/fabs.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(_SOFT_FLOAT) || defined(BROKEN_PPC_D_ASM) - -#include "../fabs.c" - -#else - -double fabs(double x) -{ - __asm__ ("fabs %0, %1" : "=d"(x) : "d"(x)); - return x; -} - -#endif diff --git a/src/math/powerpc/fabsf.c b/src/math/powerpc/fabsf.c deleted file mode 100644 index d88b591..0000000 --- a/src/math/powerpc/fabsf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef _SOFT_FLOAT - -#include "../fabsf.c" - -#else - -float fabsf(float x) -{ - __asm__ ("fabs %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#endif diff --git a/src/math/powerpc/fma.c b/src/math/powerpc/fma.c deleted file mode 100644 index 135c990..0000000 --- a/src/math/powerpc/fma.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(_SOFT_FLOAT) || defined(BROKEN_PPC_D_ASM) - -#include "../fma.c" - -#else - -double fma(double x, double y, double z) -{ - __asm__("fmadd %0, %1, %2, %3" : "=d"(x) : "d"(x), "d"(y), "d"(z)); - return x; -} - -#endif diff --git a/src/math/powerpc/fmaf.c b/src/math/powerpc/fmaf.c deleted file mode 100644 index a99a2a3..0000000 --- a/src/math/powerpc/fmaf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef _SOFT_FLOAT - -#include "../fmaf.c" - -#else - -float fmaf(float x, float y, float z) -{ - __asm__("fmadds %0, %1, %2, %3" : "=f"(x) : "f"(x), "f"(y), "f"(z)); - return x; -} - -#endif diff --git a/src/math/powerpc/sqrt.c b/src/math/powerpc/sqrt.c deleted file mode 100644 index 8718dbd..0000000 --- a/src/math/powerpc/sqrt.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if !defined _SOFT_FLOAT && defined _ARCH_PPCSQ - -double sqrt(double x) -{ - __asm__ ("fsqrt %0, %1\n" : "=d" (x) : "d" (x)); - return x; -} - -#else - -#include "../sqrt.c" - -#endif diff --git a/src/math/powerpc/sqrtf.c b/src/math/powerpc/sqrtf.c deleted file mode 100644 index 3431b67..0000000 --- a/src/math/powerpc/sqrtf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if !defined _SOFT_FLOAT && defined _ARCH_PPCSQ - -float sqrtf(float x) -{ - __asm__ ("fsqrts %0, %1\n" : "=f" (x) : "f" (x)); - return x; -} - -#else - -#include "../sqrtf.c" - -#endif diff --git a/src/math/powerpc64/ceil.c b/src/math/powerpc64/ceil.c deleted file mode 100644 index 4b01133..0000000 --- a/src/math/powerpc64/ceil.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef _ARCH_PWR5X - -double ceil(double x) -{ - __asm__ ("frip %0, %1" : "=d"(x) : "d"(x)); - return x; -} - -#else - -#include "../ceil.c" - -#endif diff --git a/src/math/powerpc64/ceilf.c b/src/math/powerpc64/ceilf.c deleted file mode 100644 index 59ba396..0000000 --- a/src/math/powerpc64/ceilf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef _ARCH_PWR5X - -float ceilf(float x) -{ - __asm__ ("frip %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../ceilf.c" - -#endif diff --git a/src/math/powerpc64/fabs.c b/src/math/powerpc64/fabs.c deleted file mode 100644 index 6123c75..0000000 --- a/src/math/powerpc64/fabs.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double fabs(double x) -{ - __asm__ ("fabs %0, %1" : "=d"(x) : "d"(x)); - return x; -} diff --git a/src/math/powerpc64/fabsf.c b/src/math/powerpc64/fabsf.c deleted file mode 100644 index e9e4564..0000000 --- a/src/math/powerpc64/fabsf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float fabsf(float x) -{ - __asm__ ("fabs %0, %1" : "=f"(x) : "f"(x)); - return x; -} diff --git a/src/math/powerpc64/floor.c b/src/math/powerpc64/floor.c deleted file mode 100644 index 4e68044..0000000 --- a/src/math/powerpc64/floor.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef _ARCH_PWR5X - -double floor(double x) -{ - __asm__ ("frim %0, %1" : "=d"(x) : "d"(x)); - return x; -} - -#else - -#include "../floor.c" - -#endif diff --git a/src/math/powerpc64/floorf.c b/src/math/powerpc64/floorf.c deleted file mode 100644 index e1031ef..0000000 --- a/src/math/powerpc64/floorf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef _ARCH_PWR5X - -float floorf(float x) -{ - __asm__ ("frim %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../floorf.c" - -#endif diff --git a/src/math/powerpc64/fma.c b/src/math/powerpc64/fma.c deleted file mode 100644 index 5aebd1a..0000000 --- a/src/math/powerpc64/fma.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double fma(double x, double y, double z) -{ - __asm__ ("fmadd %0, %1, %2, %3" : "=d"(x) : "d"(x), "d"(y), "d"(z)); - return x; -} diff --git a/src/math/powerpc64/fmaf.c b/src/math/powerpc64/fmaf.c deleted file mode 100644 index c678fef..0000000 --- a/src/math/powerpc64/fmaf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float fmaf(float x, float y, float z) -{ - __asm__ ("fmadds %0, %1, %2, %3" : "=f"(x) : "f"(x), "f"(y), "f"(z)); - return x; -} diff --git a/src/math/powerpc64/fmax.c b/src/math/powerpc64/fmax.c deleted file mode 100644 index 992df7f..0000000 --- a/src/math/powerpc64/fmax.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef __VSX__ - -double fmax(double x, double y) -{ - __asm__ ("xsmaxdp %x0, %x1, %x2" : "=ws"(x) : "ws"(x), "ws"(y)); - return x; -} - -#else - -#include "../fmax.c" - -#endif diff --git a/src/math/powerpc64/fmaxf.c b/src/math/powerpc64/fmaxf.c deleted file mode 100644 index 345a234..0000000 --- a/src/math/powerpc64/fmaxf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef __VSX__ - -float fmaxf(float x, float y) -{ - __asm__ ("xsmaxdp %x0, %x1, %x2" : "=ww"(x) : "ww"(x), "ww"(y)); - return x; -} - -#else - -#include "../fmaxf.c" - -#endif diff --git a/src/math/powerpc64/fmin.c b/src/math/powerpc64/fmin.c deleted file mode 100644 index adf71ba..0000000 --- a/src/math/powerpc64/fmin.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef __VSX__ - -double fmin(double x, double y) -{ - __asm__ ("xsmindp %x0, %x1, %x2" : "=ws"(x) : "ws"(x), "ws"(y)); - return x; -} - -#else - -#include "../fmin.c" - -#endif diff --git a/src/math/powerpc64/fminf.c b/src/math/powerpc64/fminf.c deleted file mode 100644 index faf0e47..0000000 --- a/src/math/powerpc64/fminf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef __VSX__ - -float fminf(float x, float y) -{ - __asm__ ("xsmindp %x0, %x1, %x2" : "=ww"(x) : "ww"(x), "ww"(y)); - return x; -} - -#else - -#include "../fminf.c" - -#endif diff --git a/src/math/powerpc64/lrint.c b/src/math/powerpc64/lrint.c deleted file mode 100644 index 4e4b2e0..0000000 --- a/src/math/powerpc64/lrint.c +++ /dev/null @@ -1,16 +0,0 @@ -#include - -#ifdef _ARCH_PWR5X - -long lrint(double x) -{ - long n; - __asm__ ("fctid %0, %1" : "=d"(n) : "d"(x)); - return n; -} - -#else - -#include "../lrint.c" - -#endif diff --git a/src/math/powerpc64/lrintf.c b/src/math/powerpc64/lrintf.c deleted file mode 100644 index 9070fc0..0000000 --- a/src/math/powerpc64/lrintf.c +++ /dev/null @@ -1,16 +0,0 @@ -#include - -#ifdef _ARCH_PWR5X - -long lrintf(float x) -{ - long n; - __asm__ ("fctid %0, %1" : "=d"(n) : "f"(x)); - return n; -} - -#else - -#include "../lrintf.c" - -#endif diff --git a/src/math/powerpc64/lround.c b/src/math/powerpc64/lround.c deleted file mode 100644 index ee4d114..0000000 --- a/src/math/powerpc64/lround.c +++ /dev/null @@ -1,18 +0,0 @@ -#include - -#ifdef __VSX__ - -long lround(double x) -{ - long n; - __asm__ ( - "xsrdpi %1, %1\n" - "fctid %0, %1\n" : "=d"(n), "+d"(x)); - return n; -} - -#else - -#include "../lround.c" - -#endif diff --git a/src/math/powerpc64/lroundf.c b/src/math/powerpc64/lroundf.c deleted file mode 100644 index 033094f..0000000 --- a/src/math/powerpc64/lroundf.c +++ /dev/null @@ -1,18 +0,0 @@ -#include - -#ifdef __VSX__ - -long lroundf(float x) -{ - long n; - __asm__ ( - "xsrdpi %1, %1\n" - "fctid %0, %1\n" : "=d"(n), "+f"(x)); - return n; -} - -#else - -#include "../lroundf.c" - -#endif diff --git a/src/math/powerpc64/round.c b/src/math/powerpc64/round.c deleted file mode 100644 index 4b9318e..0000000 --- a/src/math/powerpc64/round.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef _ARCH_PWR5X - -double round(double x) -{ - __asm__ ("frin %0, %1" : "=d"(x) : "d"(x)); - return x; -} - -#else - -#include "../round.c" - -#endif diff --git a/src/math/powerpc64/roundf.c b/src/math/powerpc64/roundf.c deleted file mode 100644 index ae93f99..0000000 --- a/src/math/powerpc64/roundf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef _ARCH_PWR5X - -float roundf(float x) -{ - __asm__ ("frin %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../roundf.c" - -#endif diff --git a/src/math/powerpc64/sqrt.c b/src/math/powerpc64/sqrt.c deleted file mode 100644 index 13bb98d..0000000 --- a/src/math/powerpc64/sqrt.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double sqrt(double x) -{ - __asm__ ("fsqrt %0, %1" : "=d"(x) : "d"(x)); - return x; -} diff --git a/src/math/powerpc64/sqrtf.c b/src/math/powerpc64/sqrtf.c deleted file mode 100644 index b6ecb10..0000000 --- a/src/math/powerpc64/sqrtf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float sqrtf(float x) -{ - __asm__ ("fsqrts %0, %1" : "=f"(x) : "f"(x)); - return x; -} diff --git a/src/math/powerpc64/trunc.c b/src/math/powerpc64/trunc.c deleted file mode 100644 index 5791854..0000000 --- a/src/math/powerpc64/trunc.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef _ARCH_PWR5X - -double trunc(double x) -{ - __asm__ ("friz %0, %1" : "=d"(x) : "d"(x)); - return x; -} - -#else - -#include "../trunc.c" - -#endif diff --git a/src/math/powerpc64/truncf.c b/src/math/powerpc64/truncf.c deleted file mode 100644 index 94e638f..0000000 --- a/src/math/powerpc64/truncf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#ifdef _ARCH_PWR5X - -float truncf(float x) -{ - __asm__ ("friz %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../truncf.c" - -#endif diff --git a/src/math/powf.c b/src/math/powf.c deleted file mode 100644 index de8fab5..0000000 --- a/src/math/powf.c +++ /dev/null @@ -1,185 +0,0 @@ -/* - * Copyright (c) 2017-2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include -#include -#include "libm.h" -#include "exp2f_data.h" -#include "powf_data.h" - -/* -POWF_LOG2_POLY_ORDER = 5 -EXP2F_TABLE_BITS = 5 - -ULP error: 0.82 (~ 0.5 + relerr*2^24) -relerr: 1.27 * 2^-26 (Relative error ~= 128*Ln2*relerr_log2 + relerr_exp2) -relerr_log2: 1.83 * 2^-33 (Relative error of logx.) -relerr_exp2: 1.69 * 2^-34 (Relative error of exp2(ylogx).) -*/ - -#define N (1 << POWF_LOG2_TABLE_BITS) -#define T __powf_log2_data.tab -#define A __powf_log2_data.poly -#define OFF 0x3f330000 - -/* Subnormal input is normalized so ix has negative biased exponent. - Output is multiplied by N (POWF_SCALE) if TOINT_INTRINICS is set. */ -static inline double_t log2_inline(uint32_t ix) -{ - double_t z, r, r2, r4, p, q, y, y0, invc, logc; - uint32_t iz, top, tmp; - int k, i; - - /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. - The range is split into N subintervals. - The ith subinterval contains z and c is near its center. */ - tmp = ix - OFF; - i = (tmp >> (23 - POWF_LOG2_TABLE_BITS)) % N; - top = tmp & 0xff800000; - iz = ix - top; - k = (int32_t)top >> (23 - POWF_SCALE_BITS); /* arithmetic shift */ - invc = T[i].invc; - logc = T[i].logc; - z = (double_t)asfloat(iz); - - /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */ - r = z * invc - 1; - y0 = logc + (double_t)k; - - /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */ - r2 = r * r; - y = A[0] * r + A[1]; - p = A[2] * r + A[3]; - r4 = r2 * r2; - q = A[4] * r + y0; - q = p * r2 + q; - y = y * r4 + q; - return y; -} - -#undef N -#undef T -#define N (1 << EXP2F_TABLE_BITS) -#define T __exp2f_data.tab -#define SIGN_BIAS (1 << (EXP2F_TABLE_BITS + 11)) - -/* The output of log2 and thus the input of exp2 is either scaled by N - (in case of fast toint intrinsics) or not. The unscaled xd must be - in [-1021,1023], sign_bias sets the sign of the result. */ -static inline float exp2_inline(double_t xd, uint32_t sign_bias) -{ - uint64_t ki, ski, t; - double_t kd, z, r, r2, y, s; - -#if TOINT_INTRINSICS -#define C __exp2f_data.poly_scaled - /* N*x = k + r with r in [-1/2, 1/2] */ - kd = roundtoint(xd); /* k */ - ki = converttoint(xd); -#else -#define C __exp2f_data.poly -#define SHIFT __exp2f_data.shift_scaled - /* x = k/N + r with r in [-1/(2N), 1/(2N)] */ - kd = eval_as_double(xd + SHIFT); - ki = asuint64(kd); - kd -= SHIFT; /* k/N */ -#endif - r = xd - kd; - - /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ - t = T[ki % N]; - ski = ki + sign_bias; - t += ski << (52 - EXP2F_TABLE_BITS); - s = asdouble(t); - z = C[0] * r + C[1]; - r2 = r * r; - y = C[2] * r + 1; - y = z * r2 + y; - y = y * s; - return eval_as_float(y); -} - -/* Returns 0 if not int, 1 if odd int, 2 if even int. The argument is - the bit representation of a non-zero finite floating-point value. */ -static inline int checkint(uint32_t iy) -{ - int e = iy >> 23 & 0xff; - if (e < 0x7f) - return 0; - if (e > 0x7f + 23) - return 2; - if (iy & ((1 << (0x7f + 23 - e)) - 1)) - return 0; - if (iy & (1 << (0x7f + 23 - e))) - return 1; - return 2; -} - -static inline int zeroinfnan(uint32_t ix) -{ - return 2 * ix - 1 >= 2u * 0x7f800000 - 1; -} - -float powf(float x, float y) -{ - uint32_t sign_bias = 0; - uint32_t ix, iy; - - ix = asuint(x); - iy = asuint(y); - if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000 || - zeroinfnan(iy))) { - /* Either (x < 0x1p-126 or inf or nan) or (y is 0 or inf or nan). */ - if (predict_false(zeroinfnan(iy))) { - if (2 * iy == 0) - return issignalingf_inline(x) ? x + y : 1.0f; - if (ix == 0x3f800000) - return issignalingf_inline(y) ? x + y : 1.0f; - if (2 * ix > 2u * 0x7f800000 || - 2 * iy > 2u * 0x7f800000) - return x + y; - if (2 * ix == 2 * 0x3f800000) - return 1.0f; - if ((2 * ix < 2 * 0x3f800000) == !(iy & 0x80000000)) - return 0.0f; /* |x|<1 && y==inf or |x|>1 && y==-inf. */ - return y * y; - } - if (predict_false(zeroinfnan(ix))) { - float_t x2 = x * x; - if (ix & 0x80000000 && checkint(iy) == 1) - x2 = -x2; - /* Without the barrier some versions of clang hoist the 1/x2 and - thus division by zero exception can be signaled spuriously. */ - return iy & 0x80000000 ? fp_barrierf(1 / x2) : x2; - } - /* x and y are non-zero finite. */ - if (ix & 0x80000000) { - /* Finite x < 0. */ - int yint = checkint(iy); - if (yint == 0) - return __math_invalidf(x); - if (yint == 1) - sign_bias = SIGN_BIAS; - ix &= 0x7fffffff; - } - if (ix < 0x00800000) { - /* Normalize subnormal x so exponent becomes negative. */ - ix = asuint(x * 0x1p23f); - ix &= 0x7fffffff; - ix -= 23 << 23; - } - } - double_t logx = log2_inline(ix); - double_t ylogx = y * logx; /* cannot overflow, y is single prec. */ - if (predict_false((asuint64(ylogx) >> 47 & 0xffff) >= - asuint64(126.0 * POWF_SCALE) >> 47)) { - /* |y*log(x)| >= 126. */ - if (ylogx > 0x1.fffffffd1d571p+6 * POWF_SCALE) - return __math_oflowf(sign_bias); - if (ylogx <= -150.0 * POWF_SCALE) - return __math_uflowf(sign_bias); - } - return exp2_inline(ylogx, sign_bias); -} diff --git a/src/math/powf_data.c b/src/math/powf_data.c deleted file mode 100644 index 13e1d9a..0000000 --- a/src/math/powf_data.c +++ /dev/null @@ -1,34 +0,0 @@ -/* - * Data definition for powf. - * - * Copyright (c) 2017-2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ - -#include "powf_data.h" - -const struct powf_log2_data __powf_log2_data = { - .tab = { - { 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 * POWF_SCALE }, - { 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 * POWF_SCALE }, - { 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 * POWF_SCALE }, - { 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 * POWF_SCALE }, - { 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 * POWF_SCALE }, - { 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 * POWF_SCALE }, - { 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 * POWF_SCALE }, - { 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 * POWF_SCALE }, - { 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 * POWF_SCALE }, - { 0x1p+0, 0x0p+0 * POWF_SCALE }, - { 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 * POWF_SCALE }, - { 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 * POWF_SCALE }, - { 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 * POWF_SCALE }, - { 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 * POWF_SCALE }, - { 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 * POWF_SCALE }, - { 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 * POWF_SCALE }, - }, - .poly = { - 0x1.27616c9496e0bp-2 * POWF_SCALE, -0x1.71969a075c67ap-2 * POWF_SCALE, - 0x1.ec70a6ca7baddp-2 * POWF_SCALE, -0x1.7154748bef6c8p-1 * POWF_SCALE, - 0x1.71547652ab82bp0 * POWF_SCALE, - } -}; diff --git a/src/math/powf_data.h b/src/math/powf_data.h deleted file mode 100644 index 5b136e2..0000000 --- a/src/math/powf_data.h +++ /dev/null @@ -1,26 +0,0 @@ -/* - * Copyright (c) 2017-2018, Arm Limited. - * SPDX-License-Identifier: MIT - */ -#ifndef _POWF_DATA_H -#define _POWF_DATA_H - -#include "libm.h" -#include "exp2f_data.h" - -#define POWF_LOG2_TABLE_BITS 4 -#define POWF_LOG2_POLY_ORDER 5 -#if TOINT_INTRINSICS -#define POWF_SCALE_BITS EXP2F_TABLE_BITS -#else -#define POWF_SCALE_BITS 0 -#endif -#define POWF_SCALE ((double)(1 << POWF_SCALE_BITS)) -extern hidden const struct powf_log2_data { - struct { - double invc, logc; - } tab[1 << POWF_LOG2_TABLE_BITS]; - double poly[POWF_LOG2_POLY_ORDER]; -} __powf_log2_data; - -#endif diff --git a/src/math/powl.c b/src/math/powl.c deleted file mode 100644 index 5b6da07..0000000 --- a/src/math/powl.c +++ /dev/null @@ -1,522 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_powl.c */ -/* - * Copyright (c) 2008 Stephen L. Moshier - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. - * - * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES - * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR - * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES - * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN - * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF - * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - */ -/* powl.c - * - * Power function, long double precision - * - * - * SYNOPSIS: - * - * long double x, y, z, powl(); - * - * z = powl( x, y ); - * - * - * DESCRIPTION: - * - * Computes x raised to the yth power. Analytically, - * - * x**y = exp( y log(x) ). - * - * Following Cody and Waite, this program uses a lookup table - * of 2**-i/32 and pseudo extended precision arithmetic to - * obtain several extra bits of accuracy in both the logarithm - * and the exponential. - * - * - * ACCURACY: - * - * The relative error of pow(x,y) can be estimated - * by y dl ln(2), where dl is the absolute error of - * the internally computed base 2 logarithm. At the ends - * of the approximation interval the logarithm equal 1/32 - * and its relative error is about 1 lsb = 1.1e-19. Hence - * the predicted relative error in the result is 2.3e-21 y . - * - * Relative error: - * arithmetic domain # trials peak rms - * - * IEEE +-1000 40000 2.8e-18 3.7e-19 - * .001 < x < 1000, with log(x) uniformly distributed. - * -1000 < y < 1000, y uniformly distributed. - * - * IEEE 0,8700 60000 6.5e-18 1.0e-18 - * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed. - * - * - * ERROR MESSAGES: - * - * message condition value returned - * pow overflow x**y > MAXNUM INFINITY - * pow underflow x**y < 1/MAXNUM 0.0 - * pow domain x<0 and y noninteger 0.0 - * - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double powl(long double x, long double y) -{ - return pow(x, y); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 - -/* Table size */ -#define NXT 32 - -/* log(1+x) = x - .5x^2 + x^3 * P(z)/Q(z) - * on the domain 2^(-1/32) - 1 <= x <= 2^(1/32) - 1 - */ -static const long double P[] = { - 8.3319510773868690346226E-4L, - 4.9000050881978028599627E-1L, - 1.7500123722550302671919E0L, - 1.4000100839971580279335E0L, -}; -static const long double Q[] = { -/* 1.0000000000000000000000E0L,*/ - 5.2500282295834889175431E0L, - 8.4000598057587009834666E0L, - 4.2000302519914740834728E0L, -}; -/* A[i] = 2^(-i/32), rounded to IEEE long double precision. - * If i is even, A[i] + B[i/2] gives additional accuracy. - */ -static const long double A[33] = { - 1.0000000000000000000000E0L, - 9.7857206208770013448287E-1L, - 9.5760328069857364691013E-1L, - 9.3708381705514995065011E-1L, - 9.1700404320467123175367E-1L, - 8.9735453750155359320742E-1L, - 8.7812608018664974155474E-1L, - 8.5930964906123895780165E-1L, - 8.4089641525371454301892E-1L, - 8.2287773907698242225554E-1L, - 8.0524516597462715409607E-1L, - 7.8799042255394324325455E-1L, - 7.7110541270397041179298E-1L, - 7.5458221379671136985669E-1L, - 7.3841307296974965571198E-1L, - 7.2259040348852331001267E-1L, - 7.0710678118654752438189E-1L, - 6.9195494098191597746178E-1L, - 6.7712777346844636413344E-1L, - 6.6261832157987064729696E-1L, - 6.4841977732550483296079E-1L, - 6.3452547859586661129850E-1L, - 6.2092890603674202431705E-1L, - 6.0762367999023443907803E-1L, - 5.9460355750136053334378E-1L, - 5.8186242938878875689693E-1L, - 5.6939431737834582684856E-1L, - 5.5719337129794626814472E-1L, - 5.4525386633262882960438E-1L, - 5.3357020033841180906486E-1L, - 5.2213689121370692017331E-1L, - 5.1094857432705833910408E-1L, - 5.0000000000000000000000E-1L, -}; -static const long double B[17] = { - 0.0000000000000000000000E0L, - 2.6176170809902549338711E-20L, --1.0126791927256478897086E-20L, - 1.3438228172316276937655E-21L, - 1.2207982955417546912101E-20L, --6.3084814358060867200133E-21L, - 1.3164426894366316434230E-20L, --1.8527916071632873716786E-20L, - 1.8950325588932570796551E-20L, - 1.5564775779538780478155E-20L, - 6.0859793637556860974380E-21L, --2.0208749253662532228949E-20L, - 1.4966292219224761844552E-20L, - 3.3540909728056476875639E-21L, --8.6987564101742849540743E-22L, --1.2327176863327626135542E-20L, - 0.0000000000000000000000E0L, -}; - -/* 2^x = 1 + x P(x), - * on the interval -1/32 <= x <= 0 - */ -static const long double R[] = { - 1.5089970579127659901157E-5L, - 1.5402715328927013076125E-4L, - 1.3333556028915671091390E-3L, - 9.6181291046036762031786E-3L, - 5.5504108664798463044015E-2L, - 2.4022650695910062854352E-1L, - 6.9314718055994530931447E-1L, -}; - -#define MEXP (NXT*16384.0L) -/* The following if denormal numbers are supported, else -MEXP: */ -#define MNEXP (-NXT*(16384.0L+64.0L)) -/* log2(e) - 1 */ -#define LOG2EA 0.44269504088896340735992L - -#define F W -#define Fa Wa -#define Fb Wb -#define G W -#define Ga Wa -#define Gb u -#define H W -#define Ha Wb -#define Hb Wb - -static const long double MAXLOGL = 1.1356523406294143949492E4L; -static const long double MINLOGL = -1.13994985314888605586758E4L; -static const long double LOGE2L = 6.9314718055994530941723E-1L; -static const long double huge = 0x1p10000L; -/* XXX Prevent gcc from erroneously constant folding this. */ -static const volatile long double twom10000 = 0x1p-10000L; - -static long double reducl(long double); -static long double powil(long double, int); - -long double powl(long double x, long double y) -{ - /* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */ - int i, nflg, iyflg, yoddint; - long e; - volatile long double z=0; - long double w=0, W=0, Wa=0, Wb=0, ya=0, yb=0, u=0; - - /* make sure no invalid exception is raised by nan comparision */ - if (isnan(x)) { - if (!isnan(y) && y == 0.0) - return 1.0; - return x; - } - if (isnan(y)) { - if (x == 1.0) - return 1.0; - return y; - } - if (x == 1.0) - return 1.0; /* 1**y = 1, even if y is nan */ - if (x == -1.0 && !isfinite(y)) - return 1.0; /* -1**inf = 1 */ - if (y == 0.0) - return 1.0; /* x**0 = 1, even if x is nan */ - if (y == 1.0) - return x; - if (y >= LDBL_MAX) { - if (x > 1.0 || x < -1.0) - return INFINITY; - if (x != 0.0) - return 0.0; - } - if (y <= -LDBL_MAX) { - if (x > 1.0 || x < -1.0) - return 0.0; - if (x != 0.0 || y == -INFINITY) - return INFINITY; - } - if (x >= LDBL_MAX) { - if (y > 0.0) - return INFINITY; - return 0.0; - } - - w = floorl(y); - - /* Set iyflg to 1 if y is an integer. */ - iyflg = 0; - if (w == y) - iyflg = 1; - - /* Test for odd integer y. */ - yoddint = 0; - if (iyflg) { - ya = fabsl(y); - ya = floorl(0.5 * ya); - yb = 0.5 * fabsl(w); - if( ya != yb ) - yoddint = 1; - } - - if (x <= -LDBL_MAX) { - if (y > 0.0) { - if (yoddint) - return -INFINITY; - return INFINITY; - } - if (y < 0.0) { - if (yoddint) - return -0.0; - return 0.0; - } - } - nflg = 0; /* (x<0)**(odd int) */ - if (x <= 0.0) { - if (x == 0.0) { - if (y < 0.0) { - if (signbit(x) && yoddint) - /* (-0.0)**(-odd int) = -inf, divbyzero */ - return -1.0/0.0; - /* (+-0.0)**(negative) = inf, divbyzero */ - return 1.0/0.0; - } - if (signbit(x) && yoddint) - return -0.0; - return 0.0; - } - if (iyflg == 0) - return (x - x) / (x - x); /* (x<0)**(non-int) is NaN */ - /* (x<0)**(integer) */ - if (yoddint) - nflg = 1; /* negate result */ - x = -x; - } - /* (+integer)**(integer) */ - if (iyflg && floorl(x) == x && fabsl(y) < 32768.0) { - w = powil(x, (int)y); - return nflg ? -w : w; - } - - /* separate significand from exponent */ - x = frexpl(x, &i); - e = i; - - /* find significand in antilog table A[] */ - i = 1; - if (x <= A[17]) - i = 17; - if (x <= A[i+8]) - i += 8; - if (x <= A[i+4]) - i += 4; - if (x <= A[i+2]) - i += 2; - if (x >= A[1]) - i = -1; - i += 1; - - /* Find (x - A[i])/A[i] - * in order to compute log(x/A[i]): - * - * log(x) = log( a x/a ) = log(a) + log(x/a) - * - * log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a - */ - x -= A[i]; - x -= B[i/2]; - x /= A[i]; - - /* rational approximation for log(1+v): - * - * log(1+v) = v - v**2/2 + v**3 P(v) / Q(v) - */ - z = x*x; - w = x * (z * __polevll(x, P, 3) / __p1evll(x, Q, 3)); - w = w - 0.5*z; - - /* Convert to base 2 logarithm: - * multiply by log2(e) = 1 + LOG2EA - */ - z = LOG2EA * w; - z += w; - z += LOG2EA * x; - z += x; - - /* Compute exponent term of the base 2 logarithm. */ - w = -i; - w /= NXT; - w += e; - /* Now base 2 log of x is w + z. */ - - /* Multiply base 2 log by y, in extended precision. */ - - /* separate y into large part ya - * and small part yb less than 1/NXT - */ - ya = reducl(y); - yb = y - ya; - - /* (w+z)(ya+yb) - * = w*ya + w*yb + z*y - */ - F = z * y + w * yb; - Fa = reducl(F); - Fb = F - Fa; - - G = Fa + w * ya; - Ga = reducl(G); - Gb = G - Ga; - - H = Fb + Gb; - Ha = reducl(H); - w = (Ga + Ha) * NXT; - - /* Test the power of 2 for overflow */ - if (w > MEXP) - return huge * huge; /* overflow */ - if (w < MNEXP) - return twom10000 * twom10000; /* underflow */ - - e = w; - Hb = H - Ha; - - if (Hb > 0.0) { - e += 1; - Hb -= 1.0/NXT; /*0.0625L;*/ - } - - /* Now the product y * log2(x) = Hb + e/NXT. - * - * Compute base 2 exponential of Hb, - * where -0.0625 <= Hb <= 0. - */ - z = Hb * __polevll(Hb, R, 6); /* z = 2**Hb - 1 */ - - /* Express e/NXT as an integer plus a negative number of (1/NXT)ths. - * Find lookup table entry for the fractional power of 2. - */ - if (e < 0) - i = 0; - else - i = 1; - i = e/NXT + i; - e = NXT*i - e; - w = A[e]; - z = w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */ - z = z + w; - z = scalbnl(z, i); /* multiply by integer power of 2 */ - - if (nflg) - z = -z; - return z; -} - - -/* Find a multiple of 1/NXT that is within 1/NXT of x. */ -static long double reducl(long double x) -{ - long double t; - - t = x * NXT; - t = floorl(t); - t = t / NXT; - return t; -} - -/* - * Positive real raised to integer power, long double precision - * - * - * SYNOPSIS: - * - * long double x, y, powil(); - * int n; - * - * y = powil( x, n ); - * - * - * DESCRIPTION: - * - * Returns argument x>0 raised to the nth power. - * The routine efficiently decomposes n as a sum of powers of - * two. The desired power is a product of two-to-the-kth - * powers of x. Thus to compute the 32767 power of x requires - * 28 multiplications instead of 32767 multiplications. - * - * - * ACCURACY: - * - * Relative error: - * arithmetic x domain n domain # trials peak rms - * IEEE .001,1000 -1022,1023 50000 4.3e-17 7.8e-18 - * IEEE 1,2 -1022,1023 20000 3.9e-17 7.6e-18 - * IEEE .99,1.01 0,8700 10000 3.6e-16 7.2e-17 - * - * Returns MAXNUM on overflow, zero on underflow. - */ - -static long double powil(long double x, int nn) -{ - long double ww, y; - long double s; - int n, e, sign, lx; - - if (nn == 0) - return 1.0; - - if (nn < 0) { - sign = -1; - n = -nn; - } else { - sign = 1; - n = nn; - } - - /* Overflow detection */ - - /* Calculate approximate logarithm of answer */ - s = x; - s = frexpl( s, &lx); - e = (lx - 1)*n; - if ((e == 0) || (e > 64) || (e < -64)) { - s = (s - 7.0710678118654752e-1L) / (s + 7.0710678118654752e-1L); - s = (2.9142135623730950L * s - 0.5 + lx) * nn * LOGE2L; - } else { - s = LOGE2L * e; - } - - if (s > MAXLOGL) - return huge * huge; /* overflow */ - - if (s < MINLOGL) - return twom10000 * twom10000; /* underflow */ - /* Handle tiny denormal answer, but with less accuracy - * since roundoff error in 1.0/x will be amplified. - * The precise demarcation should be the gradual underflow threshold. - */ - if (s < -MAXLOGL+2.0) { - x = 1.0/x; - sign = -sign; - } - - /* First bit of the power */ - if (n & 1) - y = x; - else - y = 1.0; - - ww = x; - n >>= 1; - while (n) { - ww = ww * ww; /* arg to the 2-to-the-kth power */ - if (n & 1) /* if that bit is set, then include in product */ - y *= ww; - n >>= 1; - } - - if (sign < 0) - y = 1.0/y; - return y; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double powl(long double x, long double y) -{ - return pow(x, y); -} -#endif diff --git a/src/math/remainder.c b/src/math/remainder.c deleted file mode 100644 index 612155f..0000000 --- a/src/math/remainder.c +++ /dev/null @@ -1,9 +0,0 @@ -#include - -double remainder(double x, double y) -{ - int q; - return remquo(x, y, &q); -} - -weak_alias(remainder, drem); diff --git a/src/math/remainderf.c b/src/math/remainderf.c deleted file mode 100644 index bf1d7b2..0000000 --- a/src/math/remainderf.c +++ /dev/null @@ -1,9 +0,0 @@ -#include - -float remainderf(float x, float y) -{ - int q; - return remquof(x, y, &q); -} - -weak_alias(remainderf, dremf); diff --git a/src/math/remainderl.c b/src/math/remainderl.c deleted file mode 100644 index 2a13c1d..0000000 --- a/src/math/remainderl.c +++ /dev/null @@ -1,15 +0,0 @@ -#include -#include - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double remainderl(long double x, long double y) -{ - return remainder(x, y); -} -#else -long double remainderl(long double x, long double y) -{ - int q; - return remquol(x, y, &q); -} -#endif diff --git a/src/math/remquo.c b/src/math/remquo.c deleted file mode 100644 index 59d5ad5..0000000 --- a/src/math/remquo.c +++ /dev/null @@ -1,82 +0,0 @@ -#include -#include - -double remquo(double x, double y, int *quo) -{ - union {double f; uint64_t i;} ux = {x}, uy = {y}; - int ex = ux.i>>52 & 0x7ff; - int ey = uy.i>>52 & 0x7ff; - int sx = ux.i>>63; - int sy = uy.i>>63; - uint32_t q; - uint64_t i; - uint64_t uxi = ux.i; - - *quo = 0; - if (uy.i<<1 == 0 || isnan(y) || ex == 0x7ff) - return (x*y)/(x*y); - if (ux.i<<1 == 0) - return x; - - /* normalize x and y */ - if (!ex) { - for (i = uxi<<12; i>>63 == 0; ex--, i <<= 1); - uxi <<= -ex + 1; - } else { - uxi &= -1ULL >> 12; - uxi |= 1ULL << 52; - } - if (!ey) { - for (i = uy.i<<12; i>>63 == 0; ey--, i <<= 1); - uy.i <<= -ey + 1; - } else { - uy.i &= -1ULL >> 12; - uy.i |= 1ULL << 52; - } - - q = 0; - if (ex < ey) { - if (ex+1 == ey) - goto end; - return x; - } - - /* x mod y */ - for (; ex > ey; ex--) { - i = uxi - uy.i; - if (i >> 63 == 0) { - uxi = i; - q++; - } - uxi <<= 1; - q <<= 1; - } - i = uxi - uy.i; - if (i >> 63 == 0) { - uxi = i; - q++; - } - if (uxi == 0) - ex = -60; - else - for (; uxi>>52 == 0; uxi <<= 1, ex--); -end: - /* scale result and decide between |x| and |x|-|y| */ - if (ex > 0) { - uxi -= 1ULL << 52; - uxi |= (uint64_t)ex << 52; - } else { - uxi >>= -ex + 1; - } - ux.i = uxi; - x = ux.f; - if (sy) - y = -y; - if (ex == ey || (ex+1 == ey && (2*x > y || (2*x == y && q%2)))) { - x -= y; - q++; - } - q &= 0x7fffffff; - *quo = sx^sy ? -(int)q : (int)q; - return sx ? -x : x; -} diff --git a/src/math/remquof.c b/src/math/remquof.c deleted file mode 100644 index 2f41ff7..0000000 --- a/src/math/remquof.c +++ /dev/null @@ -1,82 +0,0 @@ -#include -#include - -float remquof(float x, float y, int *quo) -{ - union {float f; uint32_t i;} ux = {x}, uy = {y}; - int ex = ux.i>>23 & 0xff; - int ey = uy.i>>23 & 0xff; - int sx = ux.i>>31; - int sy = uy.i>>31; - uint32_t q; - uint32_t i; - uint32_t uxi = ux.i; - - *quo = 0; - if (uy.i<<1 == 0 || isnan(y) || ex == 0xff) - return (x*y)/(x*y); - if (ux.i<<1 == 0) - return x; - - /* normalize x and y */ - if (!ex) { - for (i = uxi<<9; i>>31 == 0; ex--, i <<= 1); - uxi <<= -ex + 1; - } else { - uxi &= -1U >> 9; - uxi |= 1U << 23; - } - if (!ey) { - for (i = uy.i<<9; i>>31 == 0; ey--, i <<= 1); - uy.i <<= -ey + 1; - } else { - uy.i &= -1U >> 9; - uy.i |= 1U << 23; - } - - q = 0; - if (ex < ey) { - if (ex+1 == ey) - goto end; - return x; - } - - /* x mod y */ - for (; ex > ey; ex--) { - i = uxi - uy.i; - if (i >> 31 == 0) { - uxi = i; - q++; - } - uxi <<= 1; - q <<= 1; - } - i = uxi - uy.i; - if (i >> 31 == 0) { - uxi = i; - q++; - } - if (uxi == 0) - ex = -30; - else - for (; uxi>>23 == 0; uxi <<= 1, ex--); -end: - /* scale result and decide between |x| and |x|-|y| */ - if (ex > 0) { - uxi -= 1U << 23; - uxi |= (uint32_t)ex << 23; - } else { - uxi >>= -ex + 1; - } - ux.i = uxi; - x = ux.f; - if (sy) - y = -y; - if (ex == ey || (ex+1 == ey && (2*x > y || (2*x == y && q%2)))) { - x -= y; - q++; - } - q &= 0x7fffffff; - *quo = sx^sy ? -(int)q : (int)q; - return sx ? -x : x; -} diff --git a/src/math/remquol.c b/src/math/remquol.c deleted file mode 100644 index 9b065c0..0000000 --- a/src/math/remquol.c +++ /dev/null @@ -1,124 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double remquol(long double x, long double y, int *quo) -{ - return remquo(x, y, quo); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -long double remquol(long double x, long double y, int *quo) -{ - union ldshape ux = {x}, uy = {y}; - int ex = ux.i.se & 0x7fff; - int ey = uy.i.se & 0x7fff; - int sx = ux.i.se >> 15; - int sy = uy.i.se >> 15; - uint32_t q; - - *quo = 0; - if (y == 0 || isnan(y) || ex == 0x7fff) - return (x*y)/(x*y); - if (x == 0) - return x; - - /* normalize x and y */ - if (!ex) { - ux.i.se = ex; - ux.f *= 0x1p120f; - ex = ux.i.se - 120; - } - if (!ey) { - uy.i.se = ey; - uy.f *= 0x1p120f; - ey = uy.i.se - 120; - } - - q = 0; - if (ex >= ey) { - /* x mod y */ -#if LDBL_MANT_DIG == 64 - uint64_t i, mx, my; - mx = ux.i.m; - my = uy.i.m; - for (; ex > ey; ex--) { - i = mx - my; - if (mx >= my) { - mx = 2*i; - q++; - q <<= 1; - } else if (2*mx < mx) { - mx = 2*mx - my; - q <<= 1; - q++; - } else { - mx = 2*mx; - q <<= 1; - } - } - i = mx - my; - if (mx >= my) { - mx = i; - q++; - } - if (mx == 0) - ex = -120; - else - for (; mx >> 63 == 0; mx *= 2, ex--); - ux.i.m = mx; -#elif LDBL_MANT_DIG == 113 - uint64_t hi, lo, xhi, xlo, yhi, ylo; - xhi = (ux.i2.hi & -1ULL>>16) | 1ULL<<48; - yhi = (uy.i2.hi & -1ULL>>16) | 1ULL<<48; - xlo = ux.i2.lo; - ylo = ux.i2.lo; - for (; ex > ey; ex--) { - hi = xhi - yhi; - lo = xlo - ylo; - if (xlo < ylo) - hi -= 1; - if (hi >> 63 == 0) { - xhi = 2*hi + (lo>>63); - xlo = 2*lo; - q++; - } else { - xhi = 2*xhi + (xlo>>63); - xlo = 2*xlo; - } - q <<= 1; - } - hi = xhi - yhi; - lo = xlo - ylo; - if (xlo < ylo) - hi -= 1; - if (hi >> 63 == 0) { - xhi = hi; - xlo = lo; - q++; - } - if ((xhi|xlo) == 0) - ex = -120; - else - for (; xhi >> 48 == 0; xhi = 2*xhi + (xlo>>63), xlo = 2*xlo, ex--); - ux.i2.hi = xhi; - ux.i2.lo = xlo; -#endif - } - - /* scale result and decide between |x| and |x|-|y| */ - if (ex <= 0) { - ux.i.se = ex + 120; - ux.f *= 0x1p-120f; - } else - ux.i.se = ex; - x = ux.f; - if (sy) - y = -y; - if (ex == ey || (ex+1 == ey && (2*x > y || (2*x == y && q%2)))) { - x -= y; - q++; - } - q &= 0x7fffffff; - *quo = sx^sy ? -(int)q : (int)q; - return sx ? -x : x; -} -#endif diff --git a/src/math/rint.c b/src/math/rint.c deleted file mode 100644 index fbba390..0000000 --- a/src/math/rint.c +++ /dev/null @@ -1,28 +0,0 @@ -#include -#include -#include - -#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 -#define EPS DBL_EPSILON -#elif FLT_EVAL_METHOD==2 -#define EPS LDBL_EPSILON -#endif -static const double_t toint = 1/EPS; - -double rint(double x) -{ - union {double f; uint64_t i;} u = {x}; - int e = u.i>>52 & 0x7ff; - int s = u.i>>63; - double_t y; - - if (e >= 0x3ff+52) - return x; - if (s) - y = x - toint + toint; - else - y = x + toint - toint; - if (y == 0) - return s ? -0.0 : 0; - return y; -} diff --git a/src/math/rintf.c b/src/math/rintf.c deleted file mode 100644 index 9047688..0000000 --- a/src/math/rintf.c +++ /dev/null @@ -1,30 +0,0 @@ -#include -#include -#include - -#if FLT_EVAL_METHOD==0 -#define EPS FLT_EPSILON -#elif FLT_EVAL_METHOD==1 -#define EPS DBL_EPSILON -#elif FLT_EVAL_METHOD==2 -#define EPS LDBL_EPSILON -#endif -static const float_t toint = 1/EPS; - -float rintf(float x) -{ - union {float f; uint32_t i;} u = {x}; - int e = u.i>>23 & 0xff; - int s = u.i>>31; - float_t y; - - if (e >= 0x7f+23) - return x; - if (s) - y = x - toint + toint; - else - y = x + toint - toint; - if (y == 0) - return s ? -0.0f : 0.0f; - return y; -} diff --git a/src/math/rintl.c b/src/math/rintl.c deleted file mode 100644 index 374327d..0000000 --- a/src/math/rintl.c +++ /dev/null @@ -1,29 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double rintl(long double x) -{ - return rint(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 - -static const long double toint = 1/LDBL_EPSILON; - -long double rintl(long double x) -{ - union ldshape u = {x}; - int e = u.i.se & 0x7fff; - int s = u.i.se >> 15; - long double y; - - if (e >= 0x3fff+LDBL_MANT_DIG-1) - return x; - if (s) - y = x - toint + toint; - else - y = x + toint - toint; - if (y == 0) - return 0*x; - return y; -} -#endif diff --git a/src/math/riscv64/copysign.c b/src/math/riscv64/copysign.c deleted file mode 100644 index c785417..0000000 --- a/src/math/riscv64/copysign.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __riscv_flen >= 64 - -double copysign(double x, double y) -{ - __asm__ ("fsgnj.d %0, %1, %2" : "=f"(x) : "f"(x), "f"(y)); - return x; -} - -#else - -#include "../copysign.c" - -#endif diff --git a/src/math/riscv64/copysignf.c b/src/math/riscv64/copysignf.c deleted file mode 100644 index a125611..0000000 --- a/src/math/riscv64/copysignf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __riscv_flen >= 32 - -float copysignf(float x, float y) -{ - __asm__ ("fsgnj.s %0, %1, %2" : "=f"(x) : "f"(x), "f"(y)); - return x; -} - -#else - -#include "../copysignf.c" - -#endif diff --git a/src/math/riscv64/fabs.c b/src/math/riscv64/fabs.c deleted file mode 100644 index 5290b6f..0000000 --- a/src/math/riscv64/fabs.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __riscv_flen >= 64 - -double fabs(double x) -{ - __asm__ ("fabs.d %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../fabs.c" - -#endif diff --git a/src/math/riscv64/fabsf.c b/src/math/riscv64/fabsf.c deleted file mode 100644 index f5032e3..0000000 --- a/src/math/riscv64/fabsf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __riscv_flen >= 32 - -float fabsf(float x) -{ - __asm__ ("fabs.s %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../fabsf.c" - -#endif diff --git a/src/math/riscv64/fma.c b/src/math/riscv64/fma.c deleted file mode 100644 index 99b0571..0000000 --- a/src/math/riscv64/fma.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __riscv_flen >= 64 - -double fma(double x, double y, double z) -{ - __asm__ ("fmadd.d %0, %1, %2, %3" : "=f"(x) : "f"(x), "f"(y), "f"(z)); - return x; -} - -#else - -#include "../fma.c" - -#endif diff --git a/src/math/riscv64/fmaf.c b/src/math/riscv64/fmaf.c deleted file mode 100644 index f9dc47e..0000000 --- a/src/math/riscv64/fmaf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __riscv_flen >= 32 - -float fmaf(float x, float y, float z) -{ - __asm__ ("fmadd.s %0, %1, %2, %3" : "=f"(x) : "f"(x), "f"(y), "f"(z)); - return x; -} - -#else - -#include "../fmaf.c" - -#endif diff --git a/src/math/riscv64/fmax.c b/src/math/riscv64/fmax.c deleted file mode 100644 index 023709c..0000000 --- a/src/math/riscv64/fmax.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __riscv_flen >= 64 - -double fmax(double x, double y) -{ - __asm__ ("fmax.d %0, %1, %2" : "=f"(x) : "f"(x), "f"(y)); - return x; -} - -#else - -#include "../fmax.c" - -#endif diff --git a/src/math/riscv64/fmaxf.c b/src/math/riscv64/fmaxf.c deleted file mode 100644 index 863d2bd..0000000 --- a/src/math/riscv64/fmaxf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __riscv_flen >= 32 - -float fmaxf(float x, float y) -{ - __asm__ ("fmax.s %0, %1, %2" : "=f"(x) : "f"(x), "f"(y)); - return x; -} - -#else - -#include "../fmaxf.c" - -#endif diff --git a/src/math/riscv64/fmin.c b/src/math/riscv64/fmin.c deleted file mode 100644 index a4e3b06..0000000 --- a/src/math/riscv64/fmin.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __riscv_flen >= 64 - -double fmin(double x, double y) -{ - __asm__ ("fmin.d %0, %1, %2" : "=f"(x) : "f"(x), "f"(y)); - return x; -} - -#else - -#include "../fmin.c" - -#endif diff --git a/src/math/riscv64/fminf.c b/src/math/riscv64/fminf.c deleted file mode 100644 index 32156e8..0000000 --- a/src/math/riscv64/fminf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __riscv_flen >= 32 - -float fminf(float x, float y) -{ - __asm__ ("fmin.s %0, %1, %2" : "=f"(x) : "f"(x), "f"(y)); - return x; -} - -#else - -#include "../fminf.c" - -#endif diff --git a/src/math/riscv64/sqrt.c b/src/math/riscv64/sqrt.c deleted file mode 100644 index 867a504..0000000 --- a/src/math/riscv64/sqrt.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __riscv_flen >= 64 - -double sqrt(double x) -{ - __asm__ ("fsqrt.d %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../sqrt.c" - -#endif diff --git a/src/math/riscv64/sqrtf.c b/src/math/riscv64/sqrtf.c deleted file mode 100644 index 610c2cf..0000000 --- a/src/math/riscv64/sqrtf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if __riscv_flen >= 32 - -float sqrtf(float x) -{ - __asm__ ("fsqrt.s %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../sqrtf.c" - -#endif diff --git a/src/math/round.c b/src/math/round.c deleted file mode 100644 index 130d58d..0000000 --- a/src/math/round.c +++ /dev/null @@ -1,35 +0,0 @@ -#include "libm.h" - -#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 -#define EPS DBL_EPSILON -#elif FLT_EVAL_METHOD==2 -#define EPS LDBL_EPSILON -#endif -static const double_t toint = 1/EPS; - -double round(double x) -{ - union {double f; uint64_t i;} u = {x}; - int e = u.i >> 52 & 0x7ff; - double_t y; - - if (e >= 0x3ff+52) - return x; - if (u.i >> 63) - x = -x; - if (e < 0x3ff-1) { - /* raise inexact if x!=0 */ - FORCE_EVAL(x + toint); - return 0*u.f; - } - y = x + toint - toint - x; - if (y > 0.5) - y = y + x - 1; - else if (y <= -0.5) - y = y + x + 1; - else - y = y + x; - if (u.i >> 63) - y = -y; - return y; -} diff --git a/src/math/roundf.c b/src/math/roundf.c deleted file mode 100644 index e8210af..0000000 --- a/src/math/roundf.c +++ /dev/null @@ -1,36 +0,0 @@ -#include "libm.h" - -#if FLT_EVAL_METHOD==0 -#define EPS FLT_EPSILON -#elif FLT_EVAL_METHOD==1 -#define EPS DBL_EPSILON -#elif FLT_EVAL_METHOD==2 -#define EPS LDBL_EPSILON -#endif -static const float_t toint = 1/EPS; - -float roundf(float x) -{ - union {float f; uint32_t i;} u = {x}; - int e = u.i >> 23 & 0xff; - float_t y; - - if (e >= 0x7f+23) - return x; - if (u.i >> 31) - x = -x; - if (e < 0x7f-1) { - FORCE_EVAL(x + toint); - return 0*u.f; - } - y = x + toint - toint - x; - if (y > 0.5f) - y = y + x - 1; - else if (y <= -0.5f) - y = y + x + 1; - else - y = y + x; - if (u.i >> 31) - y = -y; - return y; -} diff --git a/src/math/roundl.c b/src/math/roundl.c deleted file mode 100644 index f4ff682..0000000 --- a/src/math/roundl.c +++ /dev/null @@ -1,37 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double roundl(long double x) -{ - return round(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 - -static const long double toint = 1/LDBL_EPSILON; - -long double roundl(long double x) -{ - union ldshape u = {x}; - int e = u.i.se & 0x7fff; - long double y; - - if (e >= 0x3fff+LDBL_MANT_DIG-1) - return x; - if (u.i.se >> 15) - x = -x; - if (e < 0x3fff-1) { - FORCE_EVAL(x + toint); - return 0*u.f; - } - y = x + toint - toint - x; - if (y > 0.5) - y = y + x - 1; - else if (y <= -0.5) - y = y + x + 1; - else - y = y + x; - if (u.i.se >> 15) - y = -y; - return y; -} -#endif diff --git a/src/math/s390x/ceil.c b/src/math/s390x/ceil.c deleted file mode 100644 index aee17df..0000000 --- a/src/math/s390x/ceil.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -double ceil(double x) -{ - __asm__ ("fidbra %0, 6, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../ceil.c" - -#endif diff --git a/src/math/s390x/ceilf.c b/src/math/s390x/ceilf.c deleted file mode 100644 index 29ba8d4..0000000 --- a/src/math/s390x/ceilf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -float ceilf(float x) -{ - __asm__ ("fiebra %0, 6, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../ceilf.c" - -#endif diff --git a/src/math/s390x/ceill.c b/src/math/s390x/ceill.c deleted file mode 100644 index b838dc1..0000000 --- a/src/math/s390x/ceill.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -long double ceill(long double x) -{ - __asm__ ("fixbra %0, 6, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../ceill.c" - -#endif diff --git a/src/math/s390x/fabs.c b/src/math/s390x/fabs.c deleted file mode 100644 index 9bb51cb..0000000 --- a/src/math/s390x/fabs.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -double fabs(double x) -{ - __asm__ ("lpdbr %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../fabs.c" - -#endif diff --git a/src/math/s390x/fabsf.c b/src/math/s390x/fabsf.c deleted file mode 100644 index 9fd96bc..0000000 --- a/src/math/s390x/fabsf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -float fabsf(float x) -{ - __asm__ ("lpebr %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../fabsf.c" - -#endif diff --git a/src/math/s390x/fabsl.c b/src/math/s390x/fabsl.c deleted file mode 100644 index 65f1005..0000000 --- a/src/math/s390x/fabsl.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -long double fabsl(long double x) -{ - __asm__ ("lpxbr %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../fabsl.c" - -#endif diff --git a/src/math/s390x/floor.c b/src/math/s390x/floor.c deleted file mode 100644 index 4c0c7f1..0000000 --- a/src/math/s390x/floor.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -double floor(double x) -{ - __asm__ ("fidbra %0, 7, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../floor.c" - -#endif diff --git a/src/math/s390x/floorf.c b/src/math/s390x/floorf.c deleted file mode 100644 index ea28ec7..0000000 --- a/src/math/s390x/floorf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -float floorf(float x) -{ - __asm__ ("fiebra %0, 7, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../floorf.c" - -#endif diff --git a/src/math/s390x/floorl.c b/src/math/s390x/floorl.c deleted file mode 100644 index 8a0e16a..0000000 --- a/src/math/s390x/floorl.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -long double floorl(long double x) -{ - __asm__ ("fixbra %0, 7, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../floorl.c" - -#endif diff --git a/src/math/s390x/fma.c b/src/math/s390x/fma.c deleted file mode 100644 index 86da0e4..0000000 --- a/src/math/s390x/fma.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double fma(double x, double y, double z) -{ - __asm__ ("madbr %0, %1, %2" : "+f"(z) : "f"(x), "f"(y)); - return z; -} diff --git a/src/math/s390x/fmaf.c b/src/math/s390x/fmaf.c deleted file mode 100644 index f1aec6a..0000000 --- a/src/math/s390x/fmaf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float fmaf(float x, float y, float z) -{ - __asm__ ("maebr %0, %1, %2" : "+f"(z) : "f"(x), "f"(y)); - return z; -} diff --git a/src/math/s390x/nearbyint.c b/src/math/s390x/nearbyint.c deleted file mode 100644 index b70da52..0000000 --- a/src/math/s390x/nearbyint.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -double nearbyint(double x) -{ - __asm__ ("fidbra %0, 0, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../nearbyint.c" - -#endif diff --git a/src/math/s390x/nearbyintf.c b/src/math/s390x/nearbyintf.c deleted file mode 100644 index 704f267..0000000 --- a/src/math/s390x/nearbyintf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -float nearbyintf(float x) -{ - __asm__ ("fiebra %0, 0, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../nearbyintf.c" - -#endif diff --git a/src/math/s390x/nearbyintl.c b/src/math/s390x/nearbyintl.c deleted file mode 100644 index b4bd552..0000000 --- a/src/math/s390x/nearbyintl.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -long double nearbyintl(long double x) -{ - __asm__ ("fixbra %0, 0, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../nearbyintl.c" - -#endif diff --git a/src/math/s390x/rint.c b/src/math/s390x/rint.c deleted file mode 100644 index b02f09e..0000000 --- a/src/math/s390x/rint.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -double rint(double x) -{ - __asm__ ("fidbr %0, 0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../rint.c" - -#endif diff --git a/src/math/s390x/rintf.c b/src/math/s390x/rintf.c deleted file mode 100644 index c9f1313..0000000 --- a/src/math/s390x/rintf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -float rintf(float x) -{ - __asm__ ("fiebr %0, 0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../rintf.c" - -#endif diff --git a/src/math/s390x/rintl.c b/src/math/s390x/rintl.c deleted file mode 100644 index bae5318..0000000 --- a/src/math/s390x/rintl.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -long double rintl(long double x) -{ - __asm__ ("fixbr %0, 0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../rintl.c" - -#endif diff --git a/src/math/s390x/round.c b/src/math/s390x/round.c deleted file mode 100644 index 71f8025..0000000 --- a/src/math/s390x/round.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -double round(double x) -{ - __asm__ ("fidbra %0, 1, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../round.c" - -#endif diff --git a/src/math/s390x/roundf.c b/src/math/s390x/roundf.c deleted file mode 100644 index 46d2e10..0000000 --- a/src/math/s390x/roundf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -float roundf(float x) -{ - __asm__ ("fiebra %0, 1, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../roundf.c" - -#endif diff --git a/src/math/s390x/roundl.c b/src/math/s390x/roundl.c deleted file mode 100644 index ce644dd..0000000 --- a/src/math/s390x/roundl.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -long double roundl(long double x) -{ - __asm__ ("fixbra %0, 1, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../roundl.c" - -#endif diff --git a/src/math/s390x/sqrt.c b/src/math/s390x/sqrt.c deleted file mode 100644 index a80dc4a..0000000 --- a/src/math/s390x/sqrt.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -double sqrt(double x) -{ - __asm__ ("sqdbr %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../sqrt.c" - -#endif diff --git a/src/math/s390x/sqrtf.c b/src/math/s390x/sqrtf.c deleted file mode 100644 index 52f57eb..0000000 --- a/src/math/s390x/sqrtf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -float sqrtf(float x) -{ - __asm__ ("sqebr %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../sqrtf.c" - -#endif diff --git a/src/math/s390x/sqrtl.c b/src/math/s390x/sqrtl.c deleted file mode 100644 index 5702d54..0000000 --- a/src/math/s390x/sqrtl.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -long double sqrtl(long double x) -{ - __asm__ ("sqxbr %0, %1" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../sqrtl.c" - -#endif diff --git a/src/math/s390x/trunc.c b/src/math/s390x/trunc.c deleted file mode 100644 index 3e5d886..0000000 --- a/src/math/s390x/trunc.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -double trunc(double x) -{ - __asm__ ("fidbra %0, 5, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../trunc.c" - -#endif diff --git a/src/math/s390x/truncf.c b/src/math/s390x/truncf.c deleted file mode 100644 index 9097bac..0000000 --- a/src/math/s390x/truncf.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -float truncf(float x) -{ - __asm__ ("fiebra %0, 5, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../truncf.c" - -#endif diff --git a/src/math/s390x/truncl.c b/src/math/s390x/truncl.c deleted file mode 100644 index 4eb920a..0000000 --- a/src/math/s390x/truncl.c +++ /dev/null @@ -1,15 +0,0 @@ -#include - -#if defined(__HTM__) || __ARCH__ >= 9 - -long double truncl(long double x) -{ - __asm__ ("fixbra %0, 5, %1, 4" : "=f"(x) : "f"(x)); - return x; -} - -#else - -#include "../truncl.c" - -#endif diff --git a/src/math/scalb.c b/src/math/scalb.c deleted file mode 100644 index efe69e6..0000000 --- a/src/math/scalb.c +++ /dev/null @@ -1,35 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_scalb.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* - * scalb(x, fn) is provide for - * passing various standard test suite. One - * should use scalbn() instead. - */ - -#define _GNU_SOURCE -#include - -double scalb(double x, double fn) -{ - if (isnan(x) || isnan(fn)) - return x*fn; - if (!isfinite(fn)) { - if (fn > 0.0) - return x*fn; - else - return x/(-fn); - } - if (rint(fn) != fn) return (fn-fn)/(fn-fn); - if ( fn > 65000.0) return scalbn(x, 65000); - if (-fn > 65000.0) return scalbn(x,-65000); - return scalbn(x,(int)fn); -} diff --git a/src/math/scalbf.c b/src/math/scalbf.c deleted file mode 100644 index f44ed5b..0000000 --- a/src/math/scalbf.c +++ /dev/null @@ -1,32 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_scalbf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#define _GNU_SOURCE -#include - -float scalbf(float x, float fn) -{ - if (isnan(x) || isnan(fn)) return x*fn; - if (!isfinite(fn)) { - if (fn > 0.0f) - return x*fn; - else - return x/(-fn); - } - if (rintf(fn) != fn) return (fn-fn)/(fn-fn); - if ( fn > 65000.0f) return scalbnf(x, 65000); - if (-fn > 65000.0f) return scalbnf(x,-65000); - return scalbnf(x,(int)fn); -} diff --git a/src/math/scalbln.c b/src/math/scalbln.c deleted file mode 100644 index e6f3f19..0000000 --- a/src/math/scalbln.c +++ /dev/null @@ -1,11 +0,0 @@ -#include -#include - -double scalbln(double x, long n) -{ - if (n > INT_MAX) - n = INT_MAX; - else if (n < INT_MIN) - n = INT_MIN; - return scalbn(x, n); -} diff --git a/src/math/scalblnf.c b/src/math/scalblnf.c deleted file mode 100644 index d8e8166..0000000 --- a/src/math/scalblnf.c +++ /dev/null @@ -1,11 +0,0 @@ -#include -#include - -float scalblnf(float x, long n) -{ - if (n > INT_MAX) - n = INT_MAX; - else if (n < INT_MIN) - n = INT_MIN; - return scalbnf(x, n); -} diff --git a/src/math/scalblnl.c b/src/math/scalblnl.c deleted file mode 100644 index 854c51c..0000000 --- a/src/math/scalblnl.c +++ /dev/null @@ -1,19 +0,0 @@ -#include -#include -#include - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double scalblnl(long double x, long n) -{ - return scalbln(x, n); -} -#else -long double scalblnl(long double x, long n) -{ - if (n > INT_MAX) - n = INT_MAX; - else if (n < INT_MIN) - n = INT_MIN; - return scalbnl(x, n); -} -#endif diff --git a/src/math/scalbn.c b/src/math/scalbn.c deleted file mode 100644 index 182f561..0000000 --- a/src/math/scalbn.c +++ /dev/null @@ -1,33 +0,0 @@ -#include -#include - -double scalbn(double x, int n) -{ - union {double f; uint64_t i;} u; - double_t y = x; - - if (n > 1023) { - y *= 0x1p1023; - n -= 1023; - if (n > 1023) { - y *= 0x1p1023; - n -= 1023; - if (n > 1023) - n = 1023; - } - } else if (n < -1022) { - /* make sure final n < -53 to avoid double - rounding in the subnormal range */ - y *= 0x1p-1022 * 0x1p53; - n += 1022 - 53; - if (n < -1022) { - y *= 0x1p-1022 * 0x1p53; - n += 1022 - 53; - if (n < -1022) - n = -1022; - } - } - u.i = (uint64_t)(0x3ff+n)<<52; - x = y * u.f; - return x; -} diff --git a/src/math/scalbnf.c b/src/math/scalbnf.c deleted file mode 100644 index a5ad208..0000000 --- a/src/math/scalbnf.c +++ /dev/null @@ -1,31 +0,0 @@ -#include -#include - -float scalbnf(float x, int n) -{ - union {float f; uint32_t i;} u; - float_t y = x; - - if (n > 127) { - y *= 0x1p127f; - n -= 127; - if (n > 127) { - y *= 0x1p127f; - n -= 127; - if (n > 127) - n = 127; - } - } else if (n < -126) { - y *= 0x1p-126f * 0x1p24f; - n += 126 - 24; - if (n < -126) { - y *= 0x1p-126f * 0x1p24f; - n += 126 - 24; - if (n < -126) - n = -126; - } - } - u.i = (uint32_t)(0x7f+n)<<23; - x = y * u.f; - return x; -} diff --git a/src/math/scalbnl.c b/src/math/scalbnl.c deleted file mode 100644 index db44dab..0000000 --- a/src/math/scalbnl.c +++ /dev/null @@ -1,36 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double scalbnl(long double x, int n) -{ - return scalbn(x, n); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -long double scalbnl(long double x, int n) -{ - union ldshape u; - - if (n > 16383) { - x *= 0x1p16383L; - n -= 16383; - if (n > 16383) { - x *= 0x1p16383L; - n -= 16383; - if (n > 16383) - n = 16383; - } - } else if (n < -16382) { - x *= 0x1p-16382L * 0x1p113L; - n += 16382 - 113; - if (n < -16382) { - x *= 0x1p-16382L * 0x1p113L; - n += 16382 - 113; - if (n < -16382) - n = -16382; - } - } - u.f = 1.0; - u.i.se = 0x3fff + n; - return x * u.f; -} -#endif diff --git a/src/math/signgam.c b/src/math/signgam.c deleted file mode 100644 index ee331b2..0000000 --- a/src/math/signgam.c +++ /dev/null @@ -1,6 +0,0 @@ -#include -#include "libm.h" - -int __signgam = 0; - -weak_alias(__signgam, signgam); diff --git a/src/math/significand.c b/src/math/significand.c deleted file mode 100644 index 40d9aa9..0000000 --- a/src/math/significand.c +++ /dev/null @@ -1,7 +0,0 @@ -#define _GNU_SOURCE -#include - -double significand(double x) -{ - return scalbn(x, -ilogb(x)); -} diff --git a/src/math/significandf.c b/src/math/significandf.c deleted file mode 100644 index 8a697e1..0000000 --- a/src/math/significandf.c +++ /dev/null @@ -1,7 +0,0 @@ -#define _GNU_SOURCE -#include - -float significandf(float x) -{ - return scalbnf(x, -ilogbf(x)); -} diff --git a/src/math/sin.c b/src/math/sin.c deleted file mode 100644 index 055e215..0000000 --- a/src/math/sin.c +++ /dev/null @@ -1,78 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_sin.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* sin(x) - * Return sine function of x. - * - * kernel function: - * __sin ... sine function on [-pi/4,pi/4] - * __cos ... cose function on [-pi/4,pi/4] - * __rem_pio2 ... argument reduction routine - * - * Method. - * Let S,C and T denote the sin, cos and tan respectively on - * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 - * in [-pi/4 , +pi/4], and let n = k mod 4. - * We have - * - * n sin(x) cos(x) tan(x) - * ---------------------------------------------------------- - * 0 S C T - * 1 C -S -1/T - * 2 -S -C T - * 3 -C S -1/T - * ---------------------------------------------------------- - * - * Special cases: - * Let trig be any of sin, cos, or tan. - * trig(+-INF) is NaN, with signals; - * trig(NaN) is that NaN; - * - * Accuracy: - * TRIG(x) returns trig(x) nearly rounded - */ - -#include "libm.h" - -double sin(double x) -{ - double y[2]; - uint32_t ix; - unsigned n; - - /* High word of x. */ - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; - - /* |x| ~< pi/4 */ - if (ix <= 0x3fe921fb) { - if (ix < 0x3e500000) { /* |x| < 2**-26 */ - /* raise inexact if x != 0 and underflow if subnormal*/ - FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f); - return x; - } - return __sin(x, 0.0, 0); - } - - /* sin(Inf or NaN) is NaN */ - if (ix >= 0x7ff00000) - return x - x; - - /* argument reduction needed */ - n = __rem_pio2(x, y); - switch (n&3) { - case 0: return __sin(y[0], y[1], 1); - case 1: return __cos(y[0], y[1]); - case 2: return -__sin(y[0], y[1], 1); - default: - return -__cos(y[0], y[1]); - } -} diff --git a/src/math/sincos.c b/src/math/sincos.c deleted file mode 100644 index 35b2d92..0000000 --- a/src/math/sincos.c +++ /dev/null @@ -1,69 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_sin.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#define _GNU_SOURCE -#include "libm.h" - -void sincos(double x, double *sin, double *cos) -{ - double y[2], s, c; - uint32_t ix; - unsigned n; - - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; - - /* |x| ~< pi/4 */ - if (ix <= 0x3fe921fb) { - /* if |x| < 2**-27 * sqrt(2) */ - if (ix < 0x3e46a09e) { - /* raise inexact if x!=0 and underflow if subnormal */ - FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f); - *sin = x; - *cos = 1.0; - return; - } - *sin = __sin(x, 0.0, 0); - *cos = __cos(x, 0.0); - return; - } - - /* sincos(Inf or NaN) is NaN */ - if (ix >= 0x7ff00000) { - *sin = *cos = x - x; - return; - } - - /* argument reduction needed */ - n = __rem_pio2(x, y); - s = __sin(y[0], y[1], 1); - c = __cos(y[0], y[1]); - switch (n&3) { - case 0: - *sin = s; - *cos = c; - break; - case 1: - *sin = c; - *cos = -s; - break; - case 2: - *sin = -s; - *cos = -c; - break; - case 3: - default: - *sin = -c; - *cos = s; - break; - } -} diff --git a/src/math/sincosf.c b/src/math/sincosf.c deleted file mode 100644 index f8ca723..0000000 --- a/src/math/sincosf.c +++ /dev/null @@ -1,117 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_sinf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - * Optimized by Bruce D. Evans. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#define _GNU_SOURCE -#include "libm.h" - -/* Small multiples of pi/2 rounded to double precision. */ -static const double -s1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ -s2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ -s3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ -s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ - -void sincosf(float x, float *sin, float *cos) -{ - double y; - float_t s, c; - uint32_t ix; - unsigned n, sign; - - GET_FLOAT_WORD(ix, x); - sign = ix >> 31; - ix &= 0x7fffffff; - - /* |x| ~<= pi/4 */ - if (ix <= 0x3f490fda) { - /* |x| < 2**-12 */ - if (ix < 0x39800000) { - /* raise inexact if x!=0 and underflow if subnormal */ - FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f); - *sin = x; - *cos = 1.0f; - return; - } - *sin = __sindf(x); - *cos = __cosdf(x); - return; - } - - /* |x| ~<= 5*pi/4 */ - if (ix <= 0x407b53d1) { - if (ix <= 0x4016cbe3) { /* |x| ~<= 3pi/4 */ - if (sign) { - *sin = -__cosdf(x + s1pio2); - *cos = __sindf(x + s1pio2); - } else { - *sin = __cosdf(s1pio2 - x); - *cos = __sindf(s1pio2 - x); - } - return; - } - /* -sin(x+c) is not correct if x+c could be 0: -0 vs +0 */ - *sin = -__sindf(sign ? x + s2pio2 : x - s2pio2); - *cos = -__cosdf(sign ? x + s2pio2 : x - s2pio2); - return; - } - - /* |x| ~<= 9*pi/4 */ - if (ix <= 0x40e231d5) { - if (ix <= 0x40afeddf) { /* |x| ~<= 7*pi/4 */ - if (sign) { - *sin = __cosdf(x + s3pio2); - *cos = -__sindf(x + s3pio2); - } else { - *sin = -__cosdf(x - s3pio2); - *cos = __sindf(x - s3pio2); - } - return; - } - *sin = __sindf(sign ? x + s4pio2 : x - s4pio2); - *cos = __cosdf(sign ? x + s4pio2 : x - s4pio2); - return; - } - - /* sin(Inf or NaN) is NaN */ - if (ix >= 0x7f800000) { - *sin = *cos = x - x; - return; - } - - /* general argument reduction needed */ - n = __rem_pio2f(x, &y); - s = __sindf(y); - c = __cosdf(y); - switch (n&3) { - case 0: - *sin = s; - *cos = c; - break; - case 1: - *sin = c; - *cos = -s; - break; - case 2: - *sin = -s; - *cos = -c; - break; - case 3: - default: - *sin = -c; - *cos = s; - break; - } -} diff --git a/src/math/sincosl.c b/src/math/sincosl.c deleted file mode 100644 index d3ac1c4..0000000 --- a/src/math/sincosl.c +++ /dev/null @@ -1,60 +0,0 @@ -#define _GNU_SOURCE -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -void sincosl(long double x, long double *sin, long double *cos) -{ - double sind, cosd; - sincos(x, &sind, &cosd); - *sin = sind; - *cos = cosd; -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -void sincosl(long double x, long double *sin, long double *cos) -{ - union ldshape u = {x}; - unsigned n; - long double y[2], s, c; - - u.i.se &= 0x7fff; - if (u.i.se == 0x7fff) { - *sin = *cos = x - x; - return; - } - if (u.f < M_PI_4) { - if (u.i.se < 0x3fff - LDBL_MANT_DIG) { - /* raise underflow if subnormal */ - if (u.i.se == 0) FORCE_EVAL(x*0x1p-120f); - *sin = x; - /* raise inexact if x!=0 */ - *cos = 1.0 + x; - return; - } - *sin = __sinl(x, 0, 0); - *cos = __cosl(x, 0); - return; - } - n = __rem_pio2l(x, y); - s = __sinl(y[0], y[1], 1); - c = __cosl(y[0], y[1]); - switch (n & 3) { - case 0: - *sin = s; - *cos = c; - break; - case 1: - *sin = c; - *cos = -s; - break; - case 2: - *sin = -s; - *cos = -c; - break; - case 3: - default: - *sin = -c; - *cos = s; - break; - } -} -#endif diff --git a/src/math/sinf.c b/src/math/sinf.c deleted file mode 100644 index 64e39f5..0000000 --- a/src/math/sinf.c +++ /dev/null @@ -1,76 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_sinf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - * Optimized by Bruce D. Evans. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -/* Small multiples of pi/2 rounded to double precision. */ -static const double -s1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ -s2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ -s3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ -s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ - -float sinf(float x) -{ - double y; - uint32_t ix; - int n, sign; - - GET_FLOAT_WORD(ix, x); - sign = ix >> 31; - ix &= 0x7fffffff; - - if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ - if (ix < 0x39800000) { /* |x| < 2**-12 */ - /* raise inexact if x!=0 and underflow if subnormal */ - FORCE_EVAL(ix < 0x00800000 ? x/0x1p120f : x+0x1p120f); - return x; - } - return __sindf(x); - } - if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */ - if (ix <= 0x4016cbe3) { /* |x| ~<= 3pi/4 */ - if (sign) - return -__cosdf(x + s1pio2); - else - return __cosdf(x - s1pio2); - } - return __sindf(sign ? -(x + s2pio2) : -(x - s2pio2)); - } - if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */ - if (ix <= 0x40afeddf) { /* |x| ~<= 7*pi/4 */ - if (sign) - return __cosdf(x + s3pio2); - else - return -__cosdf(x - s3pio2); - } - return __sindf(sign ? x + s4pio2 : x - s4pio2); - } - - /* sin(Inf or NaN) is NaN */ - if (ix >= 0x7f800000) - return x - x; - - /* general argument reduction needed */ - n = __rem_pio2f(x, &y); - switch (n&3) { - case 0: return __sindf(y); - case 1: return __cosdf(y); - case 2: return __sindf(-y); - default: - return -__cosdf(y); - } -} diff --git a/src/math/sinh.c b/src/math/sinh.c deleted file mode 100644 index a01951a..0000000 --- a/src/math/sinh.c +++ /dev/null @@ -1,39 +0,0 @@ -#include "libm.h" - -/* sinh(x) = (exp(x) - 1/exp(x))/2 - * = (exp(x)-1 + (exp(x)-1)/exp(x))/2 - * = x + x^3/6 + o(x^5) - */ -double sinh(double x) -{ - union {double f; uint64_t i;} u = {.f = x}; - uint32_t w; - double t, h, absx; - - h = 0.5; - if (u.i >> 63) - h = -h; - /* |x| */ - u.i &= (uint64_t)-1/2; - absx = u.f; - w = u.i >> 32; - - /* |x| < log(DBL_MAX) */ - if (w < 0x40862e42) { - t = expm1(absx); - if (w < 0x3ff00000) { - if (w < 0x3ff00000 - (26<<20)) - /* note: inexact and underflow are raised by expm1 */ - /* note: this branch avoids spurious underflow */ - return x; - return h*(2*t - t*t/(t+1)); - } - /* note: |x|>log(0x1p26)+eps could be just h*exp(x) */ - return h*(t + t/(t+1)); - } - - /* |x| > log(DBL_MAX) or nan */ - /* note: the result is stored to handle overflow */ - t = __expo2(absx, 2*h); - return t; -} diff --git a/src/math/sinhf.c b/src/math/sinhf.c deleted file mode 100644 index b9caa79..0000000 --- a/src/math/sinhf.c +++ /dev/null @@ -1,31 +0,0 @@ -#include "libm.h" - -float sinhf(float x) -{ - union {float f; uint32_t i;} u = {.f = x}; - uint32_t w; - float t, h, absx; - - h = 0.5; - if (u.i >> 31) - h = -h; - /* |x| */ - u.i &= 0x7fffffff; - absx = u.f; - w = u.i; - - /* |x| < log(FLT_MAX) */ - if (w < 0x42b17217) { - t = expm1f(absx); - if (w < 0x3f800000) { - if (w < 0x3f800000 - (12<<23)) - return x; - return h*(2*t - t*t/(t+1)); - } - return h*(t + t/(t+1)); - } - - /* |x| > logf(FLT_MAX) or nan */ - t = __expo2f(absx, 2*h); - return t; -} diff --git a/src/math/sinhl.c b/src/math/sinhl.c deleted file mode 100644 index b305d4d..0000000 --- a/src/math/sinhl.c +++ /dev/null @@ -1,43 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double sinhl(long double x) -{ - return sinh(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -long double sinhl(long double x) -{ - union ldshape u = {x}; - unsigned ex = u.i.se & 0x7fff; - long double h, t, absx; - - h = 0.5; - if (u.i.se & 0x8000) - h = -h; - /* |x| */ - u.i.se = ex; - absx = u.f; - - /* |x| < log(LDBL_MAX) */ - if (ex < 0x3fff+13 || (ex == 0x3fff+13 && u.i.m>>32 < 0xb17217f7)) { - t = expm1l(absx); - if (ex < 0x3fff) { - if (ex < 0x3fff-32) - return x; - return h*(2*t - t*t/(1+t)); - } - return h*(t + t/(t+1)); - } - - /* |x| > log(LDBL_MAX) or nan */ - t = expl(0.5*absx); - return h*t*t; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double sinhl(long double x) -{ - return sinh(x); -} -#endif diff --git a/src/math/sinl.c b/src/math/sinl.c deleted file mode 100644 index 9c0b16e..0000000 --- a/src/math/sinl.c +++ /dev/null @@ -1,41 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double sinl(long double x) -{ - return sin(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -long double sinl(long double x) -{ - union ldshape u = {x}; - unsigned n; - long double y[2], hi, lo; - - u.i.se &= 0x7fff; - if (u.i.se == 0x7fff) - return x - x; - if (u.f < M_PI_4) { - if (u.i.se < 0x3fff - LDBL_MANT_DIG/2) { - /* raise inexact if x!=0 and underflow if subnormal */ - FORCE_EVAL(u.i.se == 0 ? x*0x1p-120f : x+0x1p120f); - return x; - } - return __sinl(x, 0.0, 0); - } - n = __rem_pio2l(x, y); - hi = y[0]; - lo = y[1]; - switch (n & 3) { - case 0: - return __sinl(hi, lo, 1); - case 1: - return __cosl(hi, lo); - case 2: - return -__sinl(hi, lo, 1); - case 3: - default: - return -__cosl(hi, lo); - } -} -#endif diff --git a/src/math/sqrt.c b/src/math/sqrt.c deleted file mode 100644 index 5ba2655..0000000 --- a/src/math/sqrt.c +++ /dev/null @@ -1,158 +0,0 @@ -#include -#include -#include "libm.h" -#include "sqrt_data.h" - -#define FENV_SUPPORT 1 - -/* returns a*b*2^-32 - e, with error 0 <= e < 1. */ -static inline uint32_t mul32(uint32_t a, uint32_t b) -{ - return (uint64_t)a*b >> 32; -} - -/* returns a*b*2^-64 - e, with error 0 <= e < 3. */ -static inline uint64_t mul64(uint64_t a, uint64_t b) -{ - uint64_t ahi = a>>32; - uint64_t alo = a&0xffffffff; - uint64_t bhi = b>>32; - uint64_t blo = b&0xffffffff; - return ahi*bhi + (ahi*blo >> 32) + (alo*bhi >> 32); -} - -double sqrt(double x) -{ - uint64_t ix, top, m; - - /* special case handling. */ - ix = asuint64(x); - top = ix >> 52; - if (predict_false(top - 0x001 >= 0x7ff - 0x001)) { - /* x < 0x1p-1022 or inf or nan. */ - if (ix * 2 == 0) - return x; - if (ix == 0x7ff0000000000000) - return x; - if (ix > 0x7ff0000000000000) - return __math_invalid(x); - /* x is subnormal, normalize it. */ - ix = asuint64(x * 0x1p52); - top = ix >> 52; - top -= 52; - } - - /* argument reduction: - x = 4^e m; with integer e, and m in [1, 4) - m: fixed point representation [2.62] - 2^e is the exponent part of the result. */ - int even = top & 1; - m = (ix << 11) | 0x8000000000000000; - if (even) m >>= 1; - top = (top + 0x3ff) >> 1; - - /* approximate r ~ 1/sqrt(m) and s ~ sqrt(m) when m in [1,4) - - initial estimate: - 7bit table lookup (1bit exponent and 6bit significand). - - iterative approximation: - using 2 goldschmidt iterations with 32bit int arithmetics - and a final iteration with 64bit int arithmetics. - - details: - - the relative error (e = r0 sqrt(m)-1) of a linear estimate - (r0 = a m + b) is |e| < 0.085955 ~ 0x1.6p-4 at best, - a table lookup is faster and needs one less iteration - 6 bit lookup table (128b) gives |e| < 0x1.f9p-8 - 7 bit lookup table (256b) gives |e| < 0x1.fdp-9 - for single and double prec 6bit is enough but for quad - prec 7bit is needed (or modified iterations). to avoid - one more iteration >=13bit table would be needed (16k). - - a newton-raphson iteration for r is - w = r*r - u = 3 - m*w - r = r*u/2 - can use a goldschmidt iteration for s at the end or - s = m*r - - first goldschmidt iteration is - s = m*r - u = 3 - s*r - r = r*u/2 - s = s*u/2 - next goldschmidt iteration is - u = 3 - s*r - r = r*u/2 - s = s*u/2 - and at the end r is not computed only s. - - they use the same amount of operations and converge at the - same quadratic rate, i.e. if - r1 sqrt(m) - 1 = e, then - r2 sqrt(m) - 1 = -3/2 e^2 - 1/2 e^3 - the advantage of goldschmidt is that the mul for s and r - are independent (computed in parallel), however it is not - "self synchronizing": it only uses the input m in the - first iteration so rounding errors accumulate. at the end - or when switching to larger precision arithmetics rounding - errors dominate so the first iteration should be used. - - the fixed point representations are - m: 2.30 r: 0.32, s: 2.30, d: 2.30, u: 2.30, three: 2.30 - and after switching to 64 bit - m: 2.62 r: 0.64, s: 2.62, d: 2.62, u: 2.62, three: 2.62 */ - - static const uint64_t three = 0xc0000000; - uint64_t r, s, d, u, i; - - i = (ix >> 46) % 128; - r = (uint32_t)__rsqrt_tab[i] << 16; - /* |r sqrt(m) - 1| < 0x1.fdp-9 */ - s = mul32(m>>32, r); - /* |s/sqrt(m) - 1| < 0x1.fdp-9 */ - d = mul32(s, r); - u = three - d; - r = mul32(r, u) << 1; - /* |r sqrt(m) - 1| < 0x1.7bp-16 */ - s = mul32(s, u) << 1; - /* |s/sqrt(m) - 1| < 0x1.7bp-16 */ - d = mul32(s, r); - u = three - d; - r = mul32(r, u) << 1; - /* |r sqrt(m) - 1| < 0x1.3704p-29 (measured worst-case) */ - r = r << 32; - s = mul64(m, r); - d = mul64(s, r); - u = (three<<32) - d; - s = mul64(s, u); /* repr: 3.61 */ - /* -0x1p-57 < s - sqrt(m) < 0x1.8001p-61 */ - s = (s - 2) >> 9; /* repr: 12.52 */ - /* -0x1.09p-52 < s - sqrt(m) < -0x1.fffcp-63 */ - - /* s < sqrt(m) < s + 0x1.09p-52, - compute nearest rounded result: - the nearest result to 52 bits is either s or s+0x1p-52, - we can decide by comparing (2^52 s + 0.5)^2 to 2^104 m. */ - uint64_t d0, d1, d2; - double y, t; - d0 = (m << 42) - s*s; - d1 = s - d0; - d2 = d1 + s + 1; - s += d1 >> 63; - s &= 0x000fffffffffffff; - s |= top << 52; - y = asdouble(s); - if (FENV_SUPPORT) { - /* handle rounding modes and inexact exception: - only (s+1)^2 == 2^42 m case is exact otherwise - add a tiny value to cause the fenv effects. */ - uint64_t tiny = predict_false(d2==0) ? 0 : 0x0010000000000000; - tiny |= (d1^d2) & 0x8000000000000000; - t = asdouble(tiny); - y = eval_as_double(y + t); - } - return y; -} diff --git a/src/math/sqrt_data.c b/src/math/sqrt_data.c deleted file mode 100644 index 61bc22f..0000000 --- a/src/math/sqrt_data.c +++ /dev/null @@ -1,19 +0,0 @@ -#include "sqrt_data.h" -const uint16_t __rsqrt_tab[128] = { -0xb451,0xb2f0,0xb196,0xb044,0xaef9,0xadb6,0xac79,0xab43, -0xaa14,0xa8eb,0xa7c8,0xa6aa,0xa592,0xa480,0xa373,0xa26b, -0xa168,0xa06a,0x9f70,0x9e7b,0x9d8a,0x9c9d,0x9bb5,0x9ad1, -0x99f0,0x9913,0x983a,0x9765,0x9693,0x95c4,0x94f8,0x9430, -0x936b,0x92a9,0x91ea,0x912e,0x9075,0x8fbe,0x8f0a,0x8e59, -0x8daa,0x8cfe,0x8c54,0x8bac,0x8b07,0x8a64,0x89c4,0x8925, -0x8889,0x87ee,0x8756,0x86c0,0x862b,0x8599,0x8508,0x8479, -0x83ec,0x8361,0x82d8,0x8250,0x81c9,0x8145,0x80c2,0x8040, -0xff02,0xfd0e,0xfb25,0xf947,0xf773,0xf5aa,0xf3ea,0xf234, -0xf087,0xeee3,0xed47,0xebb3,0xea27,0xe8a3,0xe727,0xe5b2, -0xe443,0xe2dc,0xe17a,0xe020,0xdecb,0xdd7d,0xdc34,0xdaf1, -0xd9b3,0xd87b,0xd748,0xd61a,0xd4f1,0xd3cd,0xd2ad,0xd192, -0xd07b,0xcf69,0xce5b,0xcd51,0xcc4a,0xcb48,0xca4a,0xc94f, -0xc858,0xc764,0xc674,0xc587,0xc49d,0xc3b7,0xc2d4,0xc1f4, -0xc116,0xc03c,0xbf65,0xbe90,0xbdbe,0xbcef,0xbc23,0xbb59, -0xba91,0xb9cc,0xb90a,0xb84a,0xb78c,0xb6d0,0xb617,0xb560, -}; diff --git a/src/math/sqrt_data.h b/src/math/sqrt_data.h deleted file mode 100644 index 260c7f9..0000000 --- a/src/math/sqrt_data.h +++ /dev/null @@ -1,13 +0,0 @@ -#ifndef _SQRT_DATA_H -#define _SQRT_DATA_H - -#include -#include - -/* if x in [1,2): i = (int)(64*x); - if x in [2,4): i = (int)(32*x-64); - __rsqrt_tab[i]*2^-16 is estimating 1/sqrt(x) with small relative error: - |__rsqrt_tab[i]*0x1p-16*sqrt(x) - 1| < -0x1.fdp-9 < 2^-8 */ -extern hidden const uint16_t __rsqrt_tab[128]; - -#endif diff --git a/src/math/sqrtf.c b/src/math/sqrtf.c deleted file mode 100644 index 740d81c..0000000 --- a/src/math/sqrtf.c +++ /dev/null @@ -1,83 +0,0 @@ -#include -#include -#include "libm.h" -#include "sqrt_data.h" - -#define FENV_SUPPORT 1 - -static inline uint32_t mul32(uint32_t a, uint32_t b) -{ - return (uint64_t)a*b >> 32; -} - -/* see sqrt.c for more detailed comments. */ - -float sqrtf(float x) -{ - uint32_t ix, m, m1, m0, even, ey; - - ix = asuint(x); - if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) { - /* x < 0x1p-126 or inf or nan. */ - if (ix * 2 == 0) - return x; - if (ix == 0x7f800000) - return x; - if (ix > 0x7f800000) - return __math_invalidf(x); - /* x is subnormal, normalize it. */ - ix = asuint(x * 0x1p23f); - ix -= 23 << 23; - } - - /* x = 4^e m; with int e and m in [1, 4). */ - even = ix & 0x00800000; - m1 = (ix << 8) | 0x80000000; - m0 = (ix << 7) & 0x7fffffff; - m = even ? m0 : m1; - - /* 2^e is the exponent part of the return value. */ - ey = ix >> 1; - ey += 0x3f800000 >> 1; - ey &= 0x7f800000; - - /* compute r ~ 1/sqrt(m), s ~ sqrt(m) with 2 goldschmidt iterations. */ - static const uint32_t three = 0xc0000000; - uint32_t r, s, d, u, i; - i = (ix >> 17) % 128; - r = (uint32_t)__rsqrt_tab[i] << 16; - /* |r*sqrt(m) - 1| < 0x1p-8 */ - s = mul32(m, r); - /* |s/sqrt(m) - 1| < 0x1p-8 */ - d = mul32(s, r); - u = three - d; - r = mul32(r, u) << 1; - /* |r*sqrt(m) - 1| < 0x1.7bp-16 */ - s = mul32(s, u) << 1; - /* |s/sqrt(m) - 1| < 0x1.7bp-16 */ - d = mul32(s, r); - u = three - d; - s = mul32(s, u); - /* -0x1.03p-28 < s/sqrt(m) - 1 < 0x1.fp-31 */ - s = (s - 1)>>6; - /* s < sqrt(m) < s + 0x1.08p-23 */ - - /* compute nearest rounded result. */ - uint32_t d0, d1, d2; - float y, t; - d0 = (m << 16) - s*s; - d1 = s - d0; - d2 = d1 + s + 1; - s += d1 >> 31; - s &= 0x007fffff; - s |= ey; - y = asfloat(s); - if (FENV_SUPPORT) { - /* handle rounding and inexact exception. */ - uint32_t tiny = predict_false(d2==0) ? 0 : 0x01000000; - tiny |= (d1^d2) & 0x80000000; - t = asfloat(tiny); - y = eval_as_float(y + t); - } - return y; -} diff --git a/src/math/sqrtl.c b/src/math/sqrtl.c deleted file mode 100644 index 1b9f19c..0000000 --- a/src/math/sqrtl.c +++ /dev/null @@ -1,259 +0,0 @@ -#include -#include -#include -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double sqrtl(long double x) -{ - return sqrt(x); -} -#elif (LDBL_MANT_DIG == 113 || LDBL_MANT_DIG == 64) && LDBL_MAX_EXP == 16384 -#include "sqrt_data.h" - -#define FENV_SUPPORT 1 - -typedef struct { - uint64_t hi; - uint64_t lo; -} u128; - -/* top: 16 bit sign+exponent, x: significand. */ -static inline long double mkldbl(uint64_t top, u128 x) -{ - union ldshape u; -#if LDBL_MANT_DIG == 113 - u.i2.hi = x.hi; - u.i2.lo = x.lo; - u.i2.hi &= 0x0000ffffffffffff; - u.i2.hi |= top << 48; -#elif LDBL_MANT_DIG == 64 - u.i.se = top; - u.i.m = x.lo; - /* force the top bit on non-zero (and non-subnormal) results. */ - if (top & 0x7fff) - u.i.m |= 0x8000000000000000; -#endif - return u.f; -} - -/* return: top 16 bit is sign+exp and following bits are the significand. */ -static inline u128 asu128(long double x) -{ - union ldshape u = {.f=x}; - u128 r; -#if LDBL_MANT_DIG == 113 - r.hi = u.i2.hi; - r.lo = u.i2.lo; -#elif LDBL_MANT_DIG == 64 - r.lo = u.i.m<<49; - /* ignore the top bit: pseudo numbers are not handled. */ - r.hi = u.i.m>>15; - r.hi &= 0x0000ffffffffffff; - r.hi |= (uint64_t)u.i.se << 48; -#endif - return r; -} - -/* returns a*b*2^-32 - e, with error 0 <= e < 1. */ -static inline uint32_t mul32(uint32_t a, uint32_t b) -{ - return (uint64_t)a*b >> 32; -} - -/* returns a*b*2^-64 - e, with error 0 <= e < 3. */ -static inline uint64_t mul64(uint64_t a, uint64_t b) -{ - uint64_t ahi = a>>32; - uint64_t alo = a&0xffffffff; - uint64_t bhi = b>>32; - uint64_t blo = b&0xffffffff; - return ahi*bhi + (ahi*blo >> 32) + (alo*bhi >> 32); -} - -static inline u128 add64(u128 a, uint64_t b) -{ - u128 r; - r.lo = a.lo + b; - r.hi = a.hi; - if (r.lo < a.lo) - r.hi++; - return r; -} - -static inline u128 add128(u128 a, u128 b) -{ - u128 r; - r.lo = a.lo + b.lo; - r.hi = a.hi + b.hi; - if (r.lo < a.lo) - r.hi++; - return r; -} - -static inline u128 sub64(u128 a, uint64_t b) -{ - u128 r; - r.lo = a.lo - b; - r.hi = a.hi; - if (a.lo < b) - r.hi--; - return r; -} - -static inline u128 sub128(u128 a, u128 b) -{ - u128 r; - r.lo = a.lo - b.lo; - r.hi = a.hi - b.hi; - if (a.lo < b.lo) - r.hi--; - return r; -} - -/* a<= 64) { - a.hi = a.lo<<(n-64); - a.lo = 0; - } else { - a.hi = (a.hi<>(64-n)); - a.lo = a.lo<>n, 0 <= n <= 127 */ -static inline u128 rsh(u128 a, int n) -{ - if (n == 0) - return a; - if (n >= 64) { - a.lo = a.hi>>(n-64); - a.hi = 0; - } else { - a.lo = (a.lo>>n) | (a.hi<<(64-n)); - a.hi = a.hi>>n; - } - return a; -} - -/* returns a*b exactly. */ -static inline u128 mul64_128(uint64_t a, uint64_t b) -{ - u128 r; - uint64_t ahi = a>>32; - uint64_t alo = a&0xffffffff; - uint64_t bhi = b>>32; - uint64_t blo = b&0xffffffff; - uint64_t lo1 = ((ahi*blo)&0xffffffff) + ((alo*bhi)&0xffffffff) + (alo*blo>>32); - uint64_t lo2 = (alo*blo)&0xffffffff; - r.hi = ahi*bhi + (ahi*blo>>32) + (alo*bhi>>32) + (lo1>>32); - r.lo = (lo1<<32) + lo2; - return r; -} - -/* returns a*b*2^-128 - e, with error 0 <= e < 7. */ -static inline u128 mul128(u128 a, u128 b) -{ - u128 hi = mul64_128(a.hi, b.hi); - uint64_t m1 = mul64(a.hi, b.lo); - uint64_t m2 = mul64(a.lo, b.hi); - return add64(add64(hi, m1), m2); -} - -/* returns a*b % 2^128. */ -static inline u128 mul128_tail(u128 a, u128 b) -{ - u128 lo = mul64_128(a.lo, b.lo); - lo.hi += a.hi*b.lo + a.lo*b.hi; - return lo; -} - - -/* see sqrt.c for detailed comments. */ - -long double sqrtl(long double x) -{ - u128 ix, ml; - uint64_t top; - - ix = asu128(x); - top = ix.hi >> 48; - if (predict_false(top - 0x0001 >= 0x7fff - 0x0001)) { - /* x < 0x1p-16382 or inf or nan. */ - if (2*ix.hi == 0 && ix.lo == 0) - return x; - if (ix.hi == 0x7fff000000000000 && ix.lo == 0) - return x; - if (top >= 0x7fff) - return __math_invalidl(x); - /* x is subnormal, normalize it. */ - ix = asu128(x * 0x1p112); - top = ix.hi >> 48; - top -= 112; - } - - /* x = 4^e m; with int e and m in [1, 4) */ - int even = top & 1; - ml = lsh(ix, 15); - ml.hi |= 0x8000000000000000; - if (even) ml = rsh(ml, 1); - top = (top + 0x3fff) >> 1; - - /* r ~ 1/sqrt(m) */ - static const uint64_t three = 0xc0000000; - uint64_t r, s, d, u, i; - i = (ix.hi >> 42) % 128; - r = (uint32_t)__rsqrt_tab[i] << 16; - /* |r sqrt(m) - 1| < 0x1p-8 */ - s = mul32(ml.hi>>32, r); - d = mul32(s, r); - u = three - d; - r = mul32(u, r) << 1; - /* |r sqrt(m) - 1| < 0x1.7bp-16, switch to 64bit */ - r = r<<32; - s = mul64(ml.hi, r); - d = mul64(s, r); - u = (three<<32) - d; - r = mul64(u, r) << 1; - /* |r sqrt(m) - 1| < 0x1.a5p-31 */ - s = mul64(u, s) << 1; - d = mul64(s, r); - u = (three<<32) - d; - r = mul64(u, r) << 1; - /* |r sqrt(m) - 1| < 0x1.c001p-59, switch to 128bit */ - - static const u128 threel = {.hi=three<<32, .lo=0}; - u128 rl, sl, dl, ul; - rl.hi = r; - rl.lo = 0; - sl = mul128(ml, rl); - dl = mul128(sl, rl); - ul = sub128(threel, dl); - sl = mul128(ul, sl); /* repr: 3.125 */ - /* -0x1p-116 < s - sqrt(m) < 0x3.8001p-125 */ - sl = rsh(sub64(sl, 4), 125-(LDBL_MANT_DIG-1)); - /* s < sqrt(m) < s + 1 ULP + tiny */ - - long double y; - u128 d2, d1, d0; - d0 = sub128(lsh(ml, 2*(LDBL_MANT_DIG-1)-126), mul128_tail(sl,sl)); - d1 = sub128(sl, d0); - d2 = add128(add64(sl, 1), d1); - sl = add64(sl, d1.hi >> 63); - y = mkldbl(top, sl); - if (FENV_SUPPORT) { - /* handle rounding modes and inexact exception. */ - top = predict_false((d2.hi|d2.lo)==0) ? 0 : 1; - top |= ((d1.hi^d2.hi)&0x8000000000000000) >> 48; - y += mkldbl(top, (u128){0}); - } - return y; -} -#else -#error unsupported long double format -#endif diff --git a/src/math/tan.c b/src/math/tan.c deleted file mode 100644 index 9c724a4..0000000 --- a/src/math/tan.c +++ /dev/null @@ -1,70 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_tan.c */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* tan(x) - * Return tangent function of x. - * - * kernel function: - * __tan ... tangent function on [-pi/4,pi/4] - * __rem_pio2 ... argument reduction routine - * - * Method. - * Let S,C and T denote the sin, cos and tan respectively on - * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 - * in [-pi/4 , +pi/4], and let n = k mod 4. - * We have - * - * n sin(x) cos(x) tan(x) - * ---------------------------------------------------------- - * 0 S C T - * 1 C -S -1/T - * 2 -S -C T - * 3 -C S -1/T - * ---------------------------------------------------------- - * - * Special cases: - * Let trig be any of sin, cos, or tan. - * trig(+-INF) is NaN, with signals; - * trig(NaN) is that NaN; - * - * Accuracy: - * TRIG(x) returns trig(x) nearly rounded - */ - -#include "libm.h" - -double tan(double x) -{ - double y[2]; - uint32_t ix; - unsigned n; - - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; - - /* |x| ~< pi/4 */ - if (ix <= 0x3fe921fb) { - if (ix < 0x3e400000) { /* |x| < 2**-27 */ - /* raise inexact if x!=0 and underflow if subnormal */ - FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f); - return x; - } - return __tan(x, 0.0, 0); - } - - /* tan(Inf or NaN) is NaN */ - if (ix >= 0x7ff00000) - return x - x; - - /* argument reduction */ - n = __rem_pio2(x, y); - return __tan(y[0], y[1], n&1); -} diff --git a/src/math/tanf.c b/src/math/tanf.c deleted file mode 100644 index aba1977..0000000 --- a/src/math/tanf.c +++ /dev/null @@ -1,64 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/s_tanf.c */ -/* - * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - * Optimized by Bruce D. Evans. - */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "libm.h" - -/* Small multiples of pi/2 rounded to double precision. */ -static const double -t1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ -t2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ -t3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ -t4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ - -float tanf(float x) -{ - double y; - uint32_t ix; - unsigned n, sign; - - GET_FLOAT_WORD(ix, x); - sign = ix >> 31; - ix &= 0x7fffffff; - - if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ - if (ix < 0x39800000) { /* |x| < 2**-12 */ - /* raise inexact if x!=0 and underflow if subnormal */ - FORCE_EVAL(ix < 0x00800000 ? x/0x1p120f : x+0x1p120f); - return x; - } - return __tandf(x, 0); - } - if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */ - if (ix <= 0x4016cbe3) /* |x| ~<= 3pi/4 */ - return __tandf((sign ? x+t1pio2 : x-t1pio2), 1); - else - return __tandf((sign ? x+t2pio2 : x-t2pio2), 0); - } - if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */ - if (ix <= 0x40afeddf) /* |x| ~<= 7*pi/4 */ - return __tandf((sign ? x+t3pio2 : x-t3pio2), 1); - else - return __tandf((sign ? x+t4pio2 : x-t4pio2), 0); - } - - /* tan(Inf or NaN) is NaN */ - if (ix >= 0x7f800000) - return x - x; - - /* argument reduction */ - n = __rem_pio2f(x, &y); - return __tandf(y, n&1); -} diff --git a/src/math/tanh.c b/src/math/tanh.c deleted file mode 100644 index 20d6dbc..0000000 --- a/src/math/tanh.c +++ /dev/null @@ -1,45 +0,0 @@ -#include "libm.h" - -/* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x)) - * = (exp(2*x) - 1)/(exp(2*x) - 1 + 2) - * = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2) - */ -double tanh(double x) -{ - union {double f; uint64_t i;} u = {.f = x}; - uint32_t w; - int sign; - double_t t; - - /* x = |x| */ - sign = u.i >> 63; - u.i &= (uint64_t)-1/2; - x = u.f; - w = u.i >> 32; - - if (w > 0x3fe193ea) { - /* |x| > log(3)/2 ~= 0.5493 or nan */ - if (w > 0x40340000) { - /* |x| > 20 or nan */ - /* note: this branch avoids raising overflow */ - t = 1 - 0/x; - } else { - t = expm1(2*x); - t = 1 - 2/(t+2); - } - } else if (w > 0x3fd058ae) { - /* |x| > log(5/3)/2 ~= 0.2554 */ - t = expm1(2*x); - t = t/(t+2); - } else if (w >= 0x00100000) { - /* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */ - t = expm1(-2*x); - t = -t/(t+2); - } else { - /* |x| is subnormal */ - /* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */ - FORCE_EVAL((float)x); - t = x; - } - return sign ? -t : t; -} diff --git a/src/math/tanhf.c b/src/math/tanhf.c deleted file mode 100644 index 10636fb..0000000 --- a/src/math/tanhf.c +++ /dev/null @@ -1,39 +0,0 @@ -#include "libm.h" - -float tanhf(float x) -{ - union {float f; uint32_t i;} u = {.f = x}; - uint32_t w; - int sign; - float t; - - /* x = |x| */ - sign = u.i >> 31; - u.i &= 0x7fffffff; - x = u.f; - w = u.i; - - if (w > 0x3f0c9f54) { - /* |x| > log(3)/2 ~= 0.5493 or nan */ - if (w > 0x41200000) { - /* |x| > 10 */ - t = 1 + 0/x; - } else { - t = expm1f(2*x); - t = 1 - 2/(t+2); - } - } else if (w > 0x3e82c578) { - /* |x| > log(5/3)/2 ~= 0.2554 */ - t = expm1f(2*x); - t = t/(t+2); - } else if (w >= 0x00800000) { - /* |x| >= 0x1p-126 */ - t = expm1f(-2*x); - t = -t/(t+2); - } else { - /* |x| is subnormal */ - FORCE_EVAL(x*x); - t = x; - } - return sign ? -t : t; -} diff --git a/src/math/tanhl.c b/src/math/tanhl.c deleted file mode 100644 index 4e1aa9f..0000000 --- a/src/math/tanhl.c +++ /dev/null @@ -1,48 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double tanhl(long double x) -{ - return tanh(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -long double tanhl(long double x) -{ - union ldshape u = {x}; - unsigned ex = u.i.se & 0x7fff; - unsigned sign = u.i.se & 0x8000; - uint32_t w; - long double t; - - /* x = |x| */ - u.i.se = ex; - x = u.f; - w = u.i.m >> 32; - - if (ex > 0x3ffe || (ex == 0x3ffe && w > 0x8c9f53d5)) { - /* |x| > log(3)/2 ~= 0.5493 or nan */ - if (ex >= 0x3fff+5) { - /* |x| >= 32 */ - t = 1 + 0/(x + 0x1p-120f); - } else { - t = expm1l(2*x); - t = 1 - 2/(t+2); - } - } else if (ex > 0x3ffd || (ex == 0x3ffd && w > 0x82c577d4)) { - /* |x| > log(5/3)/2 ~= 0.2554 */ - t = expm1l(2*x); - t = t/(t+2); - } else { - /* |x| is small */ - t = expm1l(-2*x); - t = -t/(t+2); - } - return sign ? -t : t; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double tanhl(long double x) -{ - return tanh(x); -} -#endif diff --git a/src/math/tanl.c b/src/math/tanl.c deleted file mode 100644 index 6af0671..0000000 --- a/src/math/tanl.c +++ /dev/null @@ -1,29 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double tanl(long double x) -{ - return tan(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 -long double tanl(long double x) -{ - union ldshape u = {x}; - long double y[2]; - unsigned n; - - u.i.se &= 0x7fff; - if (u.i.se == 0x7fff) - return x - x; - if (u.f < M_PI_4) { - if (u.i.se < 0x3fff - LDBL_MANT_DIG/2) { - /* raise inexact if x!=0 and underflow if subnormal */ - FORCE_EVAL(u.i.se == 0 ? x*0x1p-120f : x+0x1p120f); - return x; - } - return __tanl(x, 0, 0); - } - n = __rem_pio2l(x, y); - return __tanl(y[0], y[1], n&1); -} -#endif diff --git a/src/math/tgamma.c b/src/math/tgamma.c deleted file mode 100644 index 28f6e0f..0000000 --- a/src/math/tgamma.c +++ /dev/null @@ -1,222 +0,0 @@ -/* -"A Precision Approximation of the Gamma Function" - Cornelius Lanczos (1964) -"Lanczos Implementation of the Gamma Function" - Paul Godfrey (2001) -"An Analysis of the Lanczos Gamma Approximation" - Glendon Ralph Pugh (2004) - -approximation method: - - (x - 0.5) S(x) -Gamma(x) = (x + g - 0.5) * ---------------- - exp(x + g - 0.5) - -with - a1 a2 a3 aN -S(x) ~= [ a0 + ----- + ----- + ----- + ... + ----- ] - x + 1 x + 2 x + 3 x + N - -with a0, a1, a2, a3,.. aN constants which depend on g. - -for x < 0 the following reflection formula is used: - -Gamma(x)*Gamma(-x) = -pi/(x sin(pi x)) - -most ideas and constants are from boost and python -*/ -#include "libm.h" - -static const double pi = 3.141592653589793238462643383279502884; - -/* sin(pi x) with x > 0x1p-100, if sin(pi*x)==0 the sign is arbitrary */ -static double sinpi(double x) -{ - int n; - - /* argument reduction: x = |x| mod 2 */ - /* spurious inexact when x is odd int */ - x = x * 0.5; - x = 2 * (x - floor(x)); - - /* reduce x into [-.25,.25] */ - n = 4 * x; - n = (n+1)/2; - x -= n * 0.5; - - x *= pi; - switch (n) { - default: /* case 4 */ - case 0: - return __sin(x, 0, 0); - case 1: - return __cos(x, 0); - case 2: - return __sin(-x, 0, 0); - case 3: - return -__cos(x, 0); - } -} - -#define N 12 -//static const double g = 6.024680040776729583740234375; -static const double gmhalf = 5.524680040776729583740234375; -static const double Snum[N+1] = { - 23531376880.410759688572007674451636754734846804940, - 42919803642.649098768957899047001988850926355848959, - 35711959237.355668049440185451547166705960488635843, - 17921034426.037209699919755754458931112671403265390, - 6039542586.3520280050642916443072979210699388420708, - 1439720407.3117216736632230727949123939715485786772, - 248874557.86205415651146038641322942321632125127801, - 31426415.585400194380614231628318205362874684987640, - 2876370.6289353724412254090516208496135991145378768, - 186056.26539522349504029498971604569928220784236328, - 8071.6720023658162106380029022722506138218516325024, - 210.82427775157934587250973392071336271166969580291, - 2.5066282746310002701649081771338373386264310793408, -}; -static const double Sden[N+1] = { - 0, 39916800, 120543840, 150917976, 105258076, 45995730, 13339535, - 2637558, 357423, 32670, 1925, 66, 1, -}; -/* n! for small integer n */ -static const double fact[] = { - 1, 1, 2, 6, 24, 120, 720, 5040.0, 40320.0, 362880.0, 3628800.0, 39916800.0, - 479001600.0, 6227020800.0, 87178291200.0, 1307674368000.0, 20922789888000.0, - 355687428096000.0, 6402373705728000.0, 121645100408832000.0, - 2432902008176640000.0, 51090942171709440000.0, 1124000727777607680000.0, -}; - -/* S(x) rational function for positive x */ -static double S(double x) -{ - double_t num = 0, den = 0; - int i; - - /* to avoid overflow handle large x differently */ - if (x < 8) - for (i = N; i >= 0; i--) { - num = num * x + Snum[i]; - den = den * x + Sden[i]; - } - else - for (i = 0; i <= N; i++) { - num = num / x + Snum[i]; - den = den / x + Sden[i]; - } - return num/den; -} - -double tgamma(double x) -{ - union {double f; uint64_t i;} u = {x}; - double absx, y; - double_t dy, z, r; - uint32_t ix = u.i>>32 & 0x7fffffff; - int sign = u.i>>63; - - /* special cases */ - if (ix >= 0x7ff00000) - /* tgamma(nan)=nan, tgamma(inf)=inf, tgamma(-inf)=nan with invalid */ - return x + INFINITY; - if (ix < (0x3ff-54)<<20) - /* |x| < 2^-54: tgamma(x) ~ 1/x, +-0 raises div-by-zero */ - return 1/x; - - /* integer arguments */ - /* raise inexact when non-integer */ - if (x == floor(x)) { - if (sign) - return 0/0.0; - if (x <= sizeof fact/sizeof *fact) - return fact[(int)x - 1]; - } - - /* x >= 172: tgamma(x)=inf with overflow */ - /* x =< -184: tgamma(x)=+-0 with underflow */ - if (ix >= 0x40670000) { /* |x| >= 184 */ - if (sign) { - FORCE_EVAL((float)(0x1p-126/x)); - if (floor(x) * 0.5 == floor(x * 0.5)) - return 0; - return -0.0; - } - x *= 0x1p1023; - return x; - } - - absx = sign ? -x : x; - - /* handle the error of x + g - 0.5 */ - y = absx + gmhalf; - if (absx > gmhalf) { - dy = y - absx; - dy -= gmhalf; - } else { - dy = y - gmhalf; - dy -= absx; - } - - z = absx - 0.5; - r = S(absx) * exp(-y); - if (x < 0) { - /* reflection formula for negative x */ - /* sinpi(absx) is not 0, integers are already handled */ - r = -pi / (sinpi(absx) * absx * r); - dy = -dy; - z = -z; - } - r += dy * (gmhalf+0.5) * r / y; - z = pow(y, 0.5*z); - y = r * z * z; - return y; -} - -#if 0 -double __lgamma_r(double x, int *sign) -{ - double r, absx; - - *sign = 1; - - /* special cases */ - if (!isfinite(x)) - /* lgamma(nan)=nan, lgamma(+-inf)=inf */ - return x*x; - - /* integer arguments */ - if (x == floor(x) && x <= 2) { - /* n <= 0: lgamma(n)=inf with divbyzero */ - /* n == 1,2: lgamma(n)=0 */ - if (x <= 0) - return 1/0.0; - return 0; - } - - absx = fabs(x); - - /* lgamma(x) ~ -log(|x|) for tiny |x| */ - if (absx < 0x1p-54) { - *sign = 1 - 2*!!signbit(x); - return -log(absx); - } - - /* use tgamma for smaller |x| */ - if (absx < 128) { - x = tgamma(x); - *sign = 1 - 2*!!signbit(x); - return log(fabs(x)); - } - - /* second term (log(S)-g) could be more precise here.. */ - /* or with stirling: (|x|-0.5)*(log(|x|)-1) + poly(1/|x|) */ - r = (absx-0.5)*(log(absx+gmhalf)-1) + (log(S(absx)) - (gmhalf+0.5)); - if (x < 0) { - /* reflection formula for negative x */ - x = sinpi(absx); - *sign = 2*!!signbit(x) - 1; - r = log(pi/(fabs(x)*absx)) - r; - } - return r; -} - -weak_alias(__lgamma_r, lgamma_r); -#endif diff --git a/src/math/tgammaf.c b/src/math/tgammaf.c deleted file mode 100644 index b4ca51c..0000000 --- a/src/math/tgammaf.c +++ /dev/null @@ -1,6 +0,0 @@ -#include - -float tgammaf(float x) -{ - return tgamma(x); -} diff --git a/src/math/tgammal.c b/src/math/tgammal.c deleted file mode 100644 index 5336c5b..0000000 --- a/src/math/tgammal.c +++ /dev/null @@ -1,281 +0,0 @@ -/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_tgammal.c */ -/* - * Copyright (c) 2008 Stephen L. Moshier - * - * Permission to use, copy, modify, and distribute this software for any - * purpose with or without fee is hereby granted, provided that the above - * copyright notice and this permission notice appear in all copies. - * - * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES - * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF - * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR - * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES - * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN - * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF - * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. - */ -/* - * Gamma function - * - * - * SYNOPSIS: - * - * long double x, y, tgammal(); - * - * y = tgammal( x ); - * - * - * DESCRIPTION: - * - * Returns gamma function of the argument. The result is - * correctly signed. - * - * Arguments |x| <= 13 are reduced by recurrence and the function - * approximated by a rational function of degree 7/8 in the - * interval (2,3). Large arguments are handled by Stirling's - * formula. Large negative arguments are made positive using - * a reflection formula. - * - * - * ACCURACY: - * - * Relative error: - * arithmetic domain # trials peak rms - * IEEE -40,+40 10000 3.6e-19 7.9e-20 - * IEEE -1755,+1755 10000 4.8e-18 6.5e-19 - * - * Accuracy for large arguments is dominated by error in powl(). - * - */ - -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double tgammal(long double x) -{ - return tgamma(x); -} -#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 -/* -tgamma(x+2) = tgamma(x+2) P(x)/Q(x) -0 <= x <= 1 -Relative error -n=7, d=8 -Peak error = 1.83e-20 -Relative error spread = 8.4e-23 -*/ -static const long double P[8] = { - 4.212760487471622013093E-5L, - 4.542931960608009155600E-4L, - 4.092666828394035500949E-3L, - 2.385363243461108252554E-2L, - 1.113062816019361559013E-1L, - 3.629515436640239168939E-1L, - 8.378004301573126728826E-1L, - 1.000000000000000000009E0L, -}; -static const long double Q[9] = { --1.397148517476170440917E-5L, - 2.346584059160635244282E-4L, --1.237799246653152231188E-3L, --7.955933682494738320586E-4L, - 2.773706565840072979165E-2L, --4.633887671244534213831E-2L, --2.243510905670329164562E-1L, - 4.150160950588455434583E-1L, - 9.999999999999999999908E-1L, -}; - -/* -static const long double P[] = { --3.01525602666895735709e0L, --3.25157411956062339893e1L, --2.92929976820724030353e2L, --1.70730828800510297666e3L, --7.96667499622741999770e3L, --2.59780216007146401957e4L, --5.99650230220855581642e4L, --7.15743521530849602425e4L -}; -static const long double Q[] = { - 1.00000000000000000000e0L, --1.67955233807178858919e1L, - 8.85946791747759881659e1L, - 5.69440799097468430177e1L, --1.98526250512761318471e3L, - 3.31667508019495079814e3L, - 1.60577839621734713377e4L, --2.97045081369399940529e4L, --7.15743521530849602412e4L -}; -*/ -#define MAXGAML 1755.455L -/*static const long double LOGPI = 1.14472988584940017414L;*/ - -/* Stirling's formula for the gamma function -tgamma(x) = sqrt(2 pi) x^(x-.5) exp(-x) (1 + 1/x P(1/x)) -z(x) = x -13 <= x <= 1024 -Relative error -n=8, d=0 -Peak error = 9.44e-21 -Relative error spread = 8.8e-4 -*/ -static const long double STIR[9] = { - 7.147391378143610789273E-4L, --2.363848809501759061727E-5L, --5.950237554056330156018E-4L, - 6.989332260623193171870E-5L, - 7.840334842744753003862E-4L, --2.294719747873185405699E-4L, --2.681327161876304418288E-3L, - 3.472222222230075327854E-3L, - 8.333333333333331800504E-2L, -}; - -#define MAXSTIR 1024.0L -static const long double SQTPI = 2.50662827463100050242E0L; - -/* 1/tgamma(x) = z P(z) - * z(x) = 1/x - * 0 < x < 0.03125 - * Peak relative error 4.2e-23 - */ -static const long double S[9] = { --1.193945051381510095614E-3L, - 7.220599478036909672331E-3L, --9.622023360406271645744E-3L, --4.219773360705915470089E-2L, - 1.665386113720805206758E-1L, --4.200263503403344054473E-2L, --6.558780715202540684668E-1L, - 5.772156649015328608253E-1L, - 1.000000000000000000000E0L, -}; - -/* 1/tgamma(-x) = z P(z) - * z(x) = 1/x - * 0 < x < 0.03125 - * Peak relative error 5.16e-23 - * Relative error spread = 2.5e-24 - */ -static const long double SN[9] = { - 1.133374167243894382010E-3L, - 7.220837261893170325704E-3L, - 9.621911155035976733706E-3L, --4.219773343731191721664E-2L, --1.665386113944413519335E-1L, --4.200263503402112910504E-2L, - 6.558780715202536547116E-1L, - 5.772156649015328608727E-1L, --1.000000000000000000000E0L, -}; - -static const long double PIL = 3.1415926535897932384626L; - -/* Gamma function computed by Stirling's formula. - */ -static long double stirf(long double x) -{ - long double y, w, v; - - w = 1.0/x; - /* For large x, use rational coefficients from the analytical expansion. */ - if (x > 1024.0) - w = (((((6.97281375836585777429E-5L * w - + 7.84039221720066627474E-4L) * w - - 2.29472093621399176955E-4L) * w - - 2.68132716049382716049E-3L) * w - + 3.47222222222222222222E-3L) * w - + 8.33333333333333333333E-2L) * w - + 1.0; - else - w = 1.0 + w * __polevll(w, STIR, 8); - y = expl(x); - if (x > MAXSTIR) { /* Avoid overflow in pow() */ - v = powl(x, 0.5L * x - 0.25L); - y = v * (v / y); - } else { - y = powl(x, x - 0.5L) / y; - } - y = SQTPI * y * w; - return y; -} - -long double tgammal(long double x) -{ - long double p, q, z; - - if (!isfinite(x)) - return x + INFINITY; - - q = fabsl(x); - if (q > 13.0) { - if (x < 0.0) { - p = floorl(q); - z = q - p; - if (z == 0) - return 0 / z; - if (q > MAXGAML) { - z = 0; - } else { - if (z > 0.5) { - p += 1.0; - z = q - p; - } - z = q * sinl(PIL * z); - z = fabsl(z) * stirf(q); - z = PIL/z; - } - if (0.5 * p == floorl(q * 0.5)) - z = -z; - } else if (x > MAXGAML) { - z = x * 0x1p16383L; - } else { - z = stirf(x); - } - return z; - } - - z = 1.0; - while (x >= 3.0) { - x -= 1.0; - z *= x; - } - while (x < -0.03125L) { - z /= x; - x += 1.0; - } - if (x <= 0.03125L) - goto small; - while (x < 2.0) { - z /= x; - x += 1.0; - } - if (x == 2.0) - return z; - - x -= 2.0; - p = __polevll(x, P, 7); - q = __polevll(x, Q, 8); - z = z * p / q; - return z; - -small: - /* z==1 if x was originally +-0 */ - if (x == 0 && z != 1) - return x / x; - if (x < 0.0) { - x = -x; - q = z / (x * __polevll(x, SN, 8)); - } else - q = z / (x * __polevll(x, S, 8)); - return q; -} -#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 -// TODO: broken implementation to make things compile -long double tgammal(long double x) -{ - return tgamma(x); -} -#endif diff --git a/src/math/trunc.c b/src/math/trunc.c deleted file mode 100644 index d13711b..0000000 --- a/src/math/trunc.c +++ /dev/null @@ -1,19 +0,0 @@ -#include "libm.h" - -double trunc(double x) -{ - union {double f; uint64_t i;} u = {x}; - int e = (int)(u.i >> 52 & 0x7ff) - 0x3ff + 12; - uint64_t m; - - if (e >= 52 + 12) - return x; - if (e < 12) - e = 1; - m = -1ULL >> e; - if ((u.i & m) == 0) - return x; - FORCE_EVAL(x + 0x1p120f); - u.i &= ~m; - return u.f; -} diff --git a/src/math/truncf.c b/src/math/truncf.c deleted file mode 100644 index 1a7d03c..0000000 --- a/src/math/truncf.c +++ /dev/null @@ -1,19 +0,0 @@ -#include "libm.h" - -float truncf(float x) -{ - union {float f; uint32_t i;} u = {x}; - int e = (int)(u.i >> 23 & 0xff) - 0x7f + 9; - uint32_t m; - - if (e >= 23 + 9) - return x; - if (e < 9) - e = 1; - m = -1U >> e; - if ((u.i & m) == 0) - return x; - FORCE_EVAL(x + 0x1p120f); - u.i &= ~m; - return u.f; -} diff --git a/src/math/truncl.c b/src/math/truncl.c deleted file mode 100644 index f07b193..0000000 --- a/src/math/truncl.c +++ /dev/null @@ -1,34 +0,0 @@ -#include "libm.h" - -#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 -long double truncl(long double x) -{ - return trunc(x); -} -#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384 - -static const long double toint = 1/LDBL_EPSILON; - -long double truncl(long double x) -{ - union ldshape u = {x}; - int e = u.i.se & 0x7fff; - int s = u.i.se >> 15; - long double y; - - if (e >= 0x3fff+LDBL_MANT_DIG-1) - return x; - if (e <= 0x3fff-1) { - FORCE_EVAL(x + 0x1p120f); - return x*0; - } - /* y = int(|x|) - |x|, where int(|x|) is an integer neighbor of |x| */ - if (s) - x = -x; - y = x + toint - toint - x; - if (y > 0) - y -= 1; - x += y; - return s ? -x : x; -} -#endif diff --git a/src/math/x32/__invtrigl.s b/src/math/x32/__invtrigl.s deleted file mode 100644 index e69de29..0000000 diff --git a/src/math/x32/acosl.s b/src/math/x32/acosl.s deleted file mode 100644 index 1abca12..0000000 --- a/src/math/x32/acosl.s +++ /dev/null @@ -1,16 +0,0 @@ -# see ../i386/acos.s - -.global acosl -.type acosl,@function -acosl: - fldt 8(%esp) -1: fld %st(0) - fld1 - fsub %st(0),%st(1) - fadd %st(2) - fmulp - fsqrt - fabs - fxch %st(1) - fpatan - ret diff --git a/src/math/x32/asinl.s b/src/math/x32/asinl.s deleted file mode 100644 index 7fe9f12..0000000 --- a/src/math/x32/asinl.s +++ /dev/null @@ -1,12 +0,0 @@ -.global asinl -.type asinl,@function -asinl: - fldt 8(%esp) -1: fld %st(0) - fld1 - fsub %st(0),%st(1) - fadd %st(2) - fmulp - fsqrt - fpatan - ret diff --git a/src/math/x32/atan2l.s b/src/math/x32/atan2l.s deleted file mode 100644 index 1ead078..0000000 --- a/src/math/x32/atan2l.s +++ /dev/null @@ -1,7 +0,0 @@ -.global atan2l -.type atan2l,@function -atan2l: - fldt 8(%esp) - fldt 24(%esp) - fpatan - ret diff --git a/src/math/x32/atanl.s b/src/math/x32/atanl.s deleted file mode 100644 index f475fe0..0000000 --- a/src/math/x32/atanl.s +++ /dev/null @@ -1,7 +0,0 @@ -.global atanl -.type atanl,@function -atanl: - fldt 8(%esp) - fld1 - fpatan - ret diff --git a/src/math/x32/ceill.s b/src/math/x32/ceill.s deleted file mode 100644 index f5cfa3b..0000000 --- a/src/math/x32/ceill.s +++ /dev/null @@ -1 +0,0 @@ -# see floorl.s diff --git a/src/math/x32/exp2l.s b/src/math/x32/exp2l.s deleted file mode 100644 index e9edb96..0000000 --- a/src/math/x32/exp2l.s +++ /dev/null @@ -1,83 +0,0 @@ -.global expm1l -.type expm1l,@function -expm1l: - fldt 8(%esp) - fldl2e - fmulp - movl $0xc2820000,-4(%esp) - flds -4(%esp) - fucomip %st(1),%st - fld1 - jb 1f - # x*log2e <= -65, return -1 without underflow - fstp %st(1) - fchs - ret -1: fld %st(1) - fabs - fucomip %st(1),%st - fstp %st(0) - ja 1f - f2xm1 - ret -1: push %rax - call 1f - pop %rax - fld1 - fsubrp - ret - -.global exp2l -.type exp2l,@function -exp2l: - fldt 8(%esp) -1: fld %st(0) - sub $16,%esp - fstpt (%esp) - mov 8(%esp),%ax - and $0x7fff,%ax - cmp $0x3fff+13,%ax - jb 4f # |x| < 8192 - cmp $0x3fff+15,%ax - jae 3f # |x| >= 32768 - fsts (%esp) - cmpl $0xc67ff800,(%esp) - jb 2f # x > -16382 - movl $0x5f000000,(%esp) - flds (%esp) # 0x1p63 - fld %st(1) - fsub %st(1) - faddp - fucomip %st(1),%st - je 2f # x - 0x1p63 + 0x1p63 == x - movl $1,(%esp) - flds (%esp) # 0x1p-149 - fdiv %st(1) - fstps (%esp) # raise underflow -2: fld1 - fld %st(1) - frndint - fxch %st(2) - fsub %st(2) # st(0)=x-rint(x), st(1)=1, st(2)=rint(x) - f2xm1 - faddp # 2^(x-rint(x)) -1: fscale - fstp %st(1) - add $16,%esp - ret -3: xor %eax,%eax -4: cmp $0x3fff-64,%ax - fld1 - jb 1b # |x| < 0x1p-64 - fstpt (%esp) - fistl 8(%esp) - fildl 8(%esp) - fsubrp %st(1) - addl $0x3fff,8(%esp) - f2xm1 - fld1 - faddp # 2^(x-rint(x)) - fldt (%esp) # 2^rint(x) - fmulp - add $16,%esp - ret diff --git a/src/math/x32/expl.s b/src/math/x32/expl.s deleted file mode 100644 index 369f7bd..0000000 --- a/src/math/x32/expl.s +++ /dev/null @@ -1,101 +0,0 @@ -# exp(x) = 2^hi + 2^hi (2^lo - 1) -# where hi+lo = log2e*x with 128bit precision -# exact log2e*x calculation depends on nearest rounding mode -# using the exact multiplication method of Dekker and Veltkamp - -.global expl -.type expl,@function -expl: - fldt 8(%esp) - - # interesting case: 0x1p-32 <= |x| < 16384 - # check if (exponent|0x8000) is in [0xbfff-32, 0xbfff+13] - mov 16(%esp), %ax - or $0x8000, %ax - sub $0xbfdf, %ax - cmp $45, %ax - jbe 2f - test %ax, %ax - fld1 - js 1f - # if |x|>=0x1p14 or nan return 2^trunc(x) - fscale - fstp %st(1) - ret - # if |x|<0x1p-32 return 1+x -1: faddp - ret - - # should be 0x1.71547652b82fe178p0L == 0x3fff b8aa3b29 5c17f0bc - # it will be wrong on non-nearest rounding mode -2: fldl2e - sub $48, %esp - # hi = log2e_hi*x - # 2^hi = exp2l(hi) - fmul %st(1),%st - fld %st(0) - fstpt (%esp) - fstpt 16(%esp) - fstpt 32(%esp) - call exp2l@PLT - # if 2^hi == inf return 2^hi - fld %st(0) - fstpt (%esp) - cmpw $0x7fff, 8(%esp) - je 1f - fldt 32(%esp) - fldt 16(%esp) - # fpu stack: 2^hi x hi - # exact mult: x*log2e - fld %st(1) - # c = 0x1p32+1 - movq $0x41f0000000100000,%rax - pushq %rax - fldl (%esp) - # xh = x - c*x + c*x - # xl = x - xh - fmulp - fld %st(2) - fsub %st(1), %st - faddp - fld %st(2) - fsub %st(1), %st - # yh = log2e_hi - c*log2e_hi + c*log2e_hi - movq $0x3ff7154765200000,%rax - pushq %rax - fldl (%esp) - # fpu stack: 2^hi x hi xh xl yh - # lo = hi - xh*yh + xl*yh - fld %st(2) - fmul %st(1), %st - fsubp %st, %st(4) - fmul %st(1), %st - faddp %st, %st(3) - # yl = log2e_hi - yh - movq $0x3de705fc2f000000,%rax - pushq %rax - fldl (%esp) - # fpu stack: 2^hi x lo xh xl yl - # lo += xh*yl + xl*yl - fmul %st, %st(2) - fmulp %st, %st(1) - fxch %st(2) - faddp - faddp - # log2e_lo - movq $0xbfbe,%rax - pushq %rax - movq $0x82f0025f2dc582ee,%rax - pushq %rax - fldt (%esp) - add $40,%esp - # fpu stack: 2^hi x lo log2e_lo - # lo += log2e_lo*x - # return 2^hi + 2^hi (2^lo - 1) - fmulp %st, %st(2) - faddp - f2xm1 - fmul %st(1), %st - faddp -1: add $48, %esp - ret diff --git a/src/math/x32/expm1l.s b/src/math/x32/expm1l.s deleted file mode 100644 index e773f08..0000000 --- a/src/math/x32/expm1l.s +++ /dev/null @@ -1 +0,0 @@ -# see exp2l.s diff --git a/src/math/x32/fabs.s b/src/math/x32/fabs.s deleted file mode 100644 index 5715005..0000000 --- a/src/math/x32/fabs.s +++ /dev/null @@ -1,9 +0,0 @@ -.global fabs -.type fabs,@function -fabs: - xor %eax,%eax - dec %rax - shr %rax - movq %rax,%xmm1 - andpd %xmm1,%xmm0 - ret diff --git a/src/math/x32/fabsf.s b/src/math/x32/fabsf.s deleted file mode 100644 index 501a1f1..0000000 --- a/src/math/x32/fabsf.s +++ /dev/null @@ -1,7 +0,0 @@ -.global fabsf -.type fabsf,@function -fabsf: - mov $0x7fffffff,%eax - movq %rax,%xmm1 - andps %xmm1,%xmm0 - ret diff --git a/src/math/x32/fabsl.s b/src/math/x32/fabsl.s deleted file mode 100644 index 4f215df..0000000 --- a/src/math/x32/fabsl.s +++ /dev/null @@ -1,6 +0,0 @@ -.global fabsl -.type fabsl,@function -fabsl: - fldt 8(%esp) - fabs - ret diff --git a/src/math/x32/floorl.s b/src/math/x32/floorl.s deleted file mode 100644 index 78dcb6d..0000000 --- a/src/math/x32/floorl.s +++ /dev/null @@ -1,27 +0,0 @@ -.global floorl -.type floorl,@function -floorl: - fldt 8(%esp) -1: mov $0x7,%al -1: fstcw 8(%esp) - mov 9(%esp),%ah - mov %al,9(%esp) - fldcw 8(%esp) - frndint - mov %ah,9(%esp) - fldcw 8(%esp) - ret - -.global ceill -.type ceill,@function -ceill: - fldt 8(%esp) - mov $0xb,%al - jmp 1b - -.global truncl -.type truncl,@function -truncl: - fldt 8(%esp) - mov $0xf,%al - jmp 1b diff --git a/src/math/x32/fma.c b/src/math/x32/fma.c deleted file mode 100644 index 4dd53f2..0000000 --- a/src/math/x32/fma.c +++ /dev/null @@ -1,23 +0,0 @@ -#include - -#if __FMA__ - -double fma(double x, double y, double z) -{ - __asm__ ("vfmadd132sd %1, %2, %0" : "+x" (x) : "x" (y), "x" (z)); - return x; -} - -#elif __FMA4__ - -double fma(double x, double y, double z) -{ - __asm__ ("vfmaddsd %3, %2, %1, %0" : "=x" (x) : "x" (x), "x" (y), "x" (z)); - return x; -} - -#else - -#include "../fma.c" - -#endif diff --git a/src/math/x32/fmaf.c b/src/math/x32/fmaf.c deleted file mode 100644 index 30b971f..0000000 --- a/src/math/x32/fmaf.c +++ /dev/null @@ -1,23 +0,0 @@ -#include - -#if __FMA__ - -float fmaf(float x, float y, float z) -{ - __asm__ ("vfmadd132ss %1, %2, %0" : "+x" (x) : "x" (y), "x" (z)); - return x; -} - -#elif __FMA4__ - -float fmaf(float x, float y, float z) -{ - __asm__ ("vfmaddss %3, %2, %1, %0" : "=x" (x) : "x" (x), "x" (y), "x" (z)); - return x; -} - -#else - -#include "../fmaf.c" - -#endif diff --git a/src/math/x32/fmodl.s b/src/math/x32/fmodl.s deleted file mode 100644 index c3f790c..0000000 --- a/src/math/x32/fmodl.s +++ /dev/null @@ -1,11 +0,0 @@ -.global fmodl -.type fmodl,@function -fmodl: - fldt 24(%esp) - fldt 8(%esp) -1: fprem - fnstsw %ax - testb $4,%ah - jnz 1b - fstp %st(1) - ret diff --git a/src/math/x32/llrint.s b/src/math/x32/llrint.s deleted file mode 100644 index bf47649..0000000 --- a/src/math/x32/llrint.s +++ /dev/null @@ -1,5 +0,0 @@ -.global llrint -.type llrint,@function -llrint: - cvtsd2si %xmm0,%rax - ret diff --git a/src/math/x32/llrintf.s b/src/math/x32/llrintf.s deleted file mode 100644 index d7204ac..0000000 --- a/src/math/x32/llrintf.s +++ /dev/null @@ -1,5 +0,0 @@ -.global llrintf -.type llrintf,@function -llrintf: - cvtss2si %xmm0,%rax - ret diff --git a/src/math/x32/llrintl.s b/src/math/x32/llrintl.s deleted file mode 100644 index 0938607..0000000 --- a/src/math/x32/llrintl.s +++ /dev/null @@ -1,7 +0,0 @@ -.global llrintl -.type llrintl,@function -llrintl: - fldt 8(%esp) - fistpll 8(%esp) - mov 8(%esp),%rax - ret diff --git a/src/math/x32/log10l.s b/src/math/x32/log10l.s deleted file mode 100644 index ef5bea3..0000000 --- a/src/math/x32/log10l.s +++ /dev/null @@ -1,7 +0,0 @@ -.global log10l -.type log10l,@function -log10l: - fldlg2 - fldt 8(%esp) - fyl2x - ret diff --git a/src/math/x32/log1pl.s b/src/math/x32/log1pl.s deleted file mode 100644 index 2e64fd4..0000000 --- a/src/math/x32/log1pl.s +++ /dev/null @@ -1,15 +0,0 @@ -.global log1pl -.type log1pl,@function -log1pl: - mov 14(%esp),%eax - fldln2 - and $0x7fffffff,%eax - fldt 8(%esp) - cmp $0x3ffd9400,%eax - ja 1f - fyl2xp1 - ret -1: fld1 - faddp - fyl2x - ret diff --git a/src/math/x32/log2l.s b/src/math/x32/log2l.s deleted file mode 100644 index bf88e8e..0000000 --- a/src/math/x32/log2l.s +++ /dev/null @@ -1,7 +0,0 @@ -.global log2l -.type log2l,@function -log2l: - fld1 - fldt 8(%esp) - fyl2x - ret diff --git a/src/math/x32/logl.s b/src/math/x32/logl.s deleted file mode 100644 index eff6450..0000000 --- a/src/math/x32/logl.s +++ /dev/null @@ -1,7 +0,0 @@ -.global logl -.type logl,@function -logl: - fldln2 - fldt 8(%esp) - fyl2x - ret diff --git a/src/math/x32/lrint.s b/src/math/x32/lrint.s deleted file mode 100644 index 15fc245..0000000 --- a/src/math/x32/lrint.s +++ /dev/null @@ -1,5 +0,0 @@ -.global lrint -.type lrint,@function -lrint: - cvtsd2si %xmm0,%rax - ret diff --git a/src/math/x32/lrintf.s b/src/math/x32/lrintf.s deleted file mode 100644 index 488423d..0000000 --- a/src/math/x32/lrintf.s +++ /dev/null @@ -1,5 +0,0 @@ -.global lrintf -.type lrintf,@function -lrintf: - cvtss2si %xmm0,%rax - ret diff --git a/src/math/x32/lrintl.s b/src/math/x32/lrintl.s deleted file mode 100644 index d4355c3..0000000 --- a/src/math/x32/lrintl.s +++ /dev/null @@ -1,7 +0,0 @@ -.global lrintl -.type lrintl,@function -lrintl: - fldt 8(%esp) - fistpl 8(%esp) - movl 8(%esp),%eax - ret diff --git a/src/math/x32/remainderl.s b/src/math/x32/remainderl.s deleted file mode 100644 index 376ba0e..0000000 --- a/src/math/x32/remainderl.s +++ /dev/null @@ -1,11 +0,0 @@ -.global remainderl -.type remainderl,@function -remainderl: - fldt 24(%esp) - fldt 8(%esp) -1: fprem1 - fnstsw %ax - testb $4,%ah - jnz 1b - fstp %st(1) - ret diff --git a/src/math/x32/rintl.s b/src/math/x32/rintl.s deleted file mode 100644 index be1d2fa..0000000 --- a/src/math/x32/rintl.s +++ /dev/null @@ -1,6 +0,0 @@ -.global rintl -.type rintl,@function -rintl: - fldt 8(%esp) - frndint - ret diff --git a/src/math/x32/sqrt.s b/src/math/x32/sqrt.s deleted file mode 100644 index d3c609f..0000000 --- a/src/math/x32/sqrt.s +++ /dev/null @@ -1,4 +0,0 @@ -.global sqrt -.type sqrt,@function -sqrt: sqrtsd %xmm0, %xmm0 - ret diff --git a/src/math/x32/sqrtf.s b/src/math/x32/sqrtf.s deleted file mode 100644 index eec48c6..0000000 --- a/src/math/x32/sqrtf.s +++ /dev/null @@ -1,4 +0,0 @@ -.global sqrtf -.type sqrtf,@function -sqrtf: sqrtss %xmm0, %xmm0 - ret diff --git a/src/math/x32/sqrtl.s b/src/math/x32/sqrtl.s deleted file mode 100644 index 8d70856..0000000 --- a/src/math/x32/sqrtl.s +++ /dev/null @@ -1,5 +0,0 @@ -.global sqrtl -.type sqrtl,@function -sqrtl: fldt 8(%esp) - fsqrt - ret diff --git a/src/math/x32/truncl.s b/src/math/x32/truncl.s deleted file mode 100644 index f5cfa3b..0000000 --- a/src/math/x32/truncl.s +++ /dev/null @@ -1 +0,0 @@ -# see floorl.s diff --git a/src/math/x86_64/__invtrigl.s b/src/math/x86_64/__invtrigl.s deleted file mode 100644 index e69de29..0000000 diff --git a/src/math/x86_64/acosl.s b/src/math/x86_64/acosl.s deleted file mode 100644 index 88e01b4..0000000 --- a/src/math/x86_64/acosl.s +++ /dev/null @@ -1,16 +0,0 @@ -# see ../i386/acos.s - -.global acosl -.type acosl,@function -acosl: - fldt 8(%rsp) -1: fld %st(0) - fld1 - fsub %st(0),%st(1) - fadd %st(2) - fmulp - fsqrt - fabs - fxch %st(1) - fpatan - ret diff --git a/src/math/x86_64/asinl.s b/src/math/x86_64/asinl.s deleted file mode 100644 index ed212d9..0000000 --- a/src/math/x86_64/asinl.s +++ /dev/null @@ -1,12 +0,0 @@ -.global asinl -.type asinl,@function -asinl: - fldt 8(%rsp) -1: fld %st(0) - fld1 - fsub %st(0),%st(1) - fadd %st(2) - fmulp - fsqrt - fpatan - ret diff --git a/src/math/x86_64/atan2l.s b/src/math/x86_64/atan2l.s deleted file mode 100644 index e5f0a3d..0000000 --- a/src/math/x86_64/atan2l.s +++ /dev/null @@ -1,7 +0,0 @@ -.global atan2l -.type atan2l,@function -atan2l: - fldt 8(%rsp) - fldt 24(%rsp) - fpatan - ret diff --git a/src/math/x86_64/atanl.s b/src/math/x86_64/atanl.s deleted file mode 100644 index df76de5..0000000 --- a/src/math/x86_64/atanl.s +++ /dev/null @@ -1,7 +0,0 @@ -.global atanl -.type atanl,@function -atanl: - fldt 8(%rsp) - fld1 - fpatan - ret diff --git a/src/math/x86_64/ceill.s b/src/math/x86_64/ceill.s deleted file mode 100644 index f5cfa3b..0000000 --- a/src/math/x86_64/ceill.s +++ /dev/null @@ -1 +0,0 @@ -# see floorl.s diff --git a/src/math/x86_64/exp2l.s b/src/math/x86_64/exp2l.s deleted file mode 100644 index effab2b..0000000 --- a/src/math/x86_64/exp2l.s +++ /dev/null @@ -1,83 +0,0 @@ -.global expm1l -.type expm1l,@function -expm1l: - fldt 8(%rsp) - fldl2e - fmulp - movl $0xc2820000,-4(%rsp) - flds -4(%rsp) - fucomip %st(1),%st - fld1 - jb 1f - # x*log2e <= -65, return -1 without underflow - fstp %st(1) - fchs - ret -1: fld %st(1) - fabs - fucomip %st(1),%st - fstp %st(0) - ja 1f - f2xm1 - ret -1: push %rax - call 1f - pop %rax - fld1 - fsubrp - ret - -.global exp2l -.type exp2l,@function -exp2l: - fldt 8(%rsp) -1: fld %st(0) - sub $16,%rsp - fstpt (%rsp) - mov 8(%rsp),%ax - and $0x7fff,%ax - cmp $0x3fff+13,%ax - jb 4f # |x| < 8192 - cmp $0x3fff+15,%ax - jae 3f # |x| >= 32768 - fsts (%rsp) - cmpl $0xc67ff800,(%rsp) - jb 2f # x > -16382 - movl $0x5f000000,(%rsp) - flds (%rsp) # 0x1p63 - fld %st(1) - fsub %st(1) - faddp - fucomip %st(1),%st - je 2f # x - 0x1p63 + 0x1p63 == x - movl $1,(%rsp) - flds (%rsp) # 0x1p-149 - fdiv %st(1) - fstps (%rsp) # raise underflow -2: fld1 - fld %st(1) - frndint - fxch %st(2) - fsub %st(2) # st(0)=x-rint(x), st(1)=1, st(2)=rint(x) - f2xm1 - faddp # 2^(x-rint(x)) -1: fscale - fstp %st(1) - add $16,%rsp - ret -3: xor %eax,%eax -4: cmp $0x3fff-64,%ax - fld1 - jb 1b # |x| < 0x1p-64 - fstpt (%rsp) - fistl 8(%rsp) - fildl 8(%rsp) - fsubrp %st(1) - addl $0x3fff,8(%rsp) - f2xm1 - fld1 - faddp # 2^(x-rint(x)) - fldt (%rsp) # 2^rint(x) - fmulp - add $16,%rsp - ret diff --git a/src/math/x86_64/expl.s b/src/math/x86_64/expl.s deleted file mode 100644 index 3add810..0000000 --- a/src/math/x86_64/expl.s +++ /dev/null @@ -1,101 +0,0 @@ -# exp(x) = 2^hi + 2^hi (2^lo - 1) -# where hi+lo = log2e*x with 128bit precision -# exact log2e*x calculation depends on nearest rounding mode -# using the exact multiplication method of Dekker and Veltkamp - -.global expl -.type expl,@function -expl: - fldt 8(%rsp) - - # interesting case: 0x1p-32 <= |x| < 16384 - # check if (exponent|0x8000) is in [0xbfff-32, 0xbfff+13] - mov 16(%rsp), %ax - or $0x8000, %ax - sub $0xbfdf, %ax - cmp $45, %ax - jbe 2f - test %ax, %ax - fld1 - js 1f - # if |x|>=0x1p14 or nan return 2^trunc(x) - fscale - fstp %st(1) - ret - # if |x|<0x1p-32 return 1+x -1: faddp - ret - - # should be 0x1.71547652b82fe178p0L == 0x3fff b8aa3b29 5c17f0bc - # it will be wrong on non-nearest rounding mode -2: fldl2e - subq $48, %rsp - # hi = log2e_hi*x - # 2^hi = exp2l(hi) - fmul %st(1),%st - fld %st(0) - fstpt (%rsp) - fstpt 16(%rsp) - fstpt 32(%rsp) - call exp2l - # if 2^hi == inf return 2^hi - fld %st(0) - fstpt (%rsp) - cmpw $0x7fff, 8(%rsp) - je 1f - fldt 32(%rsp) - fldt 16(%rsp) - # fpu stack: 2^hi x hi - # exact mult: x*log2e - fld %st(1) - # c = 0x1p32+1 - movq $0x41f0000000100000,%rax - pushq %rax - fldl (%rsp) - # xh = x - c*x + c*x - # xl = x - xh - fmulp - fld %st(2) - fsub %st(1), %st - faddp - fld %st(2) - fsub %st(1), %st - # yh = log2e_hi - c*log2e_hi + c*log2e_hi - movq $0x3ff7154765200000,%rax - pushq %rax - fldl (%rsp) - # fpu stack: 2^hi x hi xh xl yh - # lo = hi - xh*yh + xl*yh - fld %st(2) - fmul %st(1), %st - fsubp %st, %st(4) - fmul %st(1), %st - faddp %st, %st(3) - # yl = log2e_hi - yh - movq $0x3de705fc2f000000,%rax - pushq %rax - fldl (%rsp) - # fpu stack: 2^hi x lo xh xl yl - # lo += xh*yl + xl*yl - fmul %st, %st(2) - fmulp %st, %st(1) - fxch %st(2) - faddp - faddp - # log2e_lo - movq $0xbfbe,%rax - pushq %rax - movq $0x82f0025f2dc582ee,%rax - pushq %rax - fldt (%rsp) - addq $40,%rsp - # fpu stack: 2^hi x lo log2e_lo - # lo += log2e_lo*x - # return 2^hi + 2^hi (2^lo - 1) - fmulp %st, %st(2) - faddp - f2xm1 - fmul %st(1), %st - faddp -1: addq $48, %rsp - ret diff --git a/src/math/x86_64/expm1l.s b/src/math/x86_64/expm1l.s deleted file mode 100644 index e773f08..0000000 --- a/src/math/x86_64/expm1l.s +++ /dev/null @@ -1 +0,0 @@ -# see exp2l.s diff --git a/src/math/x86_64/fabs.c b/src/math/x86_64/fabs.c deleted file mode 100644 index 1656247..0000000 --- a/src/math/x86_64/fabs.c +++ /dev/null @@ -1,10 +0,0 @@ -#include - -double fabs(double x) -{ - double t; - __asm__ ("pcmpeqd %0, %0" : "=x"(t)); // t = ~0 - __asm__ ("psrlq $1, %0" : "+x"(t)); // t >>= 1 - __asm__ ("andps %1, %0" : "+x"(x) : "x"(t)); // x &= t - return x; -} diff --git a/src/math/x86_64/fabsf.c b/src/math/x86_64/fabsf.c deleted file mode 100644 index 36ea748..0000000 --- a/src/math/x86_64/fabsf.c +++ /dev/null @@ -1,10 +0,0 @@ -#include - -float fabsf(float x) -{ - float t; - __asm__ ("pcmpeqd %0, %0" : "=x"(t)); // t = ~0 - __asm__ ("psrld $1, %0" : "+x"(t)); // t >>= 1 - __asm__ ("andps %1, %0" : "+x"(x) : "x"(t)); // x &= t - return x; -} diff --git a/src/math/x86_64/fabsl.c b/src/math/x86_64/fabsl.c deleted file mode 100644 index cc1c9ed..0000000 --- a/src/math/x86_64/fabsl.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -long double fabsl(long double x) -{ - __asm__ ("fabs" : "+t"(x)); - return x; -} diff --git a/src/math/x86_64/floorl.s b/src/math/x86_64/floorl.s deleted file mode 100644 index 80da466..0000000 --- a/src/math/x86_64/floorl.s +++ /dev/null @@ -1,27 +0,0 @@ -.global floorl -.type floorl,@function -floorl: - fldt 8(%rsp) -1: mov $0x7,%al -1: fstcw 8(%rsp) - mov 9(%rsp),%ah - mov %al,9(%rsp) - fldcw 8(%rsp) - frndint - mov %ah,9(%rsp) - fldcw 8(%rsp) - ret - -.global ceill -.type ceill,@function -ceill: - fldt 8(%rsp) - mov $0xb,%al - jmp 1b - -.global truncl -.type truncl,@function -truncl: - fldt 8(%rsp) - mov $0xf,%al - jmp 1b diff --git a/src/math/x86_64/fma.c b/src/math/x86_64/fma.c deleted file mode 100644 index 4dd53f2..0000000 --- a/src/math/x86_64/fma.c +++ /dev/null @@ -1,23 +0,0 @@ -#include - -#if __FMA__ - -double fma(double x, double y, double z) -{ - __asm__ ("vfmadd132sd %1, %2, %0" : "+x" (x) : "x" (y), "x" (z)); - return x; -} - -#elif __FMA4__ - -double fma(double x, double y, double z) -{ - __asm__ ("vfmaddsd %3, %2, %1, %0" : "=x" (x) : "x" (x), "x" (y), "x" (z)); - return x; -} - -#else - -#include "../fma.c" - -#endif diff --git a/src/math/x86_64/fmaf.c b/src/math/x86_64/fmaf.c deleted file mode 100644 index 30b971f..0000000 --- a/src/math/x86_64/fmaf.c +++ /dev/null @@ -1,23 +0,0 @@ -#include - -#if __FMA__ - -float fmaf(float x, float y, float z) -{ - __asm__ ("vfmadd132ss %1, %2, %0" : "+x" (x) : "x" (y), "x" (z)); - return x; -} - -#elif __FMA4__ - -float fmaf(float x, float y, float z) -{ - __asm__ ("vfmaddss %3, %2, %1, %0" : "=x" (x) : "x" (x), "x" (y), "x" (z)); - return x; -} - -#else - -#include "../fmaf.c" - -#endif diff --git a/src/math/x86_64/fmodl.c b/src/math/x86_64/fmodl.c deleted file mode 100644 index 3daeab0..0000000 --- a/src/math/x86_64/fmodl.c +++ /dev/null @@ -1,9 +0,0 @@ -#include - -long double fmodl(long double x, long double y) -{ - unsigned short fpsr; - do __asm__ ("fprem; fnstsw %%ax" : "+t"(x), "=a"(fpsr) : "u"(y)); - while (fpsr & 0x400); - return x; -} diff --git a/src/math/x86_64/llrint.c b/src/math/x86_64/llrint.c deleted file mode 100644 index dd38a72..0000000 --- a/src/math/x86_64/llrint.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long long llrint(double x) -{ - long long r; - __asm__ ("cvtsd2si %1, %0" : "=r"(r) : "x"(x)); - return r; -} diff --git a/src/math/x86_64/llrintf.c b/src/math/x86_64/llrintf.c deleted file mode 100644 index fc8625e..0000000 --- a/src/math/x86_64/llrintf.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long long llrintf(float x) -{ - long long r; - __asm__ ("cvtss2si %1, %0" : "=r"(r) : "x"(x)); - return r; -} diff --git a/src/math/x86_64/llrintl.c b/src/math/x86_64/llrintl.c deleted file mode 100644 index c439ef2..0000000 --- a/src/math/x86_64/llrintl.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long long llrintl(long double x) -{ - long long r; - __asm__ ("fistpll %0" : "=m"(r) : "t"(x) : "st"); - return r; -} diff --git a/src/math/x86_64/log10l.s b/src/math/x86_64/log10l.s deleted file mode 100644 index 48ea4af..0000000 --- a/src/math/x86_64/log10l.s +++ /dev/null @@ -1,7 +0,0 @@ -.global log10l -.type log10l,@function -log10l: - fldlg2 - fldt 8(%rsp) - fyl2x - ret diff --git a/src/math/x86_64/log1pl.s b/src/math/x86_64/log1pl.s deleted file mode 100644 index 955c9db..0000000 --- a/src/math/x86_64/log1pl.s +++ /dev/null @@ -1,15 +0,0 @@ -.global log1pl -.type log1pl,@function -log1pl: - mov 14(%rsp),%eax - fldln2 - and $0x7fffffff,%eax - fldt 8(%rsp) - cmp $0x3ffd9400,%eax - ja 1f - fyl2xp1 - ret -1: fld1 - faddp - fyl2x - ret diff --git a/src/math/x86_64/log2l.s b/src/math/x86_64/log2l.s deleted file mode 100644 index ba08b9f..0000000 --- a/src/math/x86_64/log2l.s +++ /dev/null @@ -1,7 +0,0 @@ -.global log2l -.type log2l,@function -log2l: - fld1 - fldt 8(%rsp) - fyl2x - ret diff --git a/src/math/x86_64/logl.s b/src/math/x86_64/logl.s deleted file mode 100644 index 20dd1f8..0000000 --- a/src/math/x86_64/logl.s +++ /dev/null @@ -1,7 +0,0 @@ -.global logl -.type logl,@function -logl: - fldln2 - fldt 8(%rsp) - fyl2x - ret diff --git a/src/math/x86_64/lrint.c b/src/math/x86_64/lrint.c deleted file mode 100644 index a742fec..0000000 --- a/src/math/x86_64/lrint.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long lrint(double x) -{ - long r; - __asm__ ("cvtsd2si %1, %0" : "=r"(r) : "x"(x)); - return r; -} diff --git a/src/math/x86_64/lrintf.c b/src/math/x86_64/lrintf.c deleted file mode 100644 index 2ba5639..0000000 --- a/src/math/x86_64/lrintf.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long lrintf(float x) -{ - long r; - __asm__ ("cvtss2si %1, %0" : "=r"(r) : "x"(x)); - return r; -} diff --git a/src/math/x86_64/lrintl.c b/src/math/x86_64/lrintl.c deleted file mode 100644 index 068e2e4..0000000 --- a/src/math/x86_64/lrintl.c +++ /dev/null @@ -1,8 +0,0 @@ -#include - -long lrintl(long double x) -{ - long r; - __asm__ ("fistpll %0" : "=m"(r) : "t"(x) : "st"); - return r; -} diff --git a/src/math/x86_64/remainderl.c b/src/math/x86_64/remainderl.c deleted file mode 100644 index 8cf7507..0000000 --- a/src/math/x86_64/remainderl.c +++ /dev/null @@ -1,9 +0,0 @@ -#include - -long double remainderl(long double x, long double y) -{ - unsigned short fpsr; - do __asm__ ("fprem1; fnstsw %%ax" : "+t"(x), "=a"(fpsr) : "u"(y)); - while (fpsr & 0x400); - return x; -} diff --git a/src/math/x86_64/remquol.c b/src/math/x86_64/remquol.c deleted file mode 100644 index 60eef08..0000000 --- a/src/math/x86_64/remquol.c +++ /dev/null @@ -1,32 +0,0 @@ -#include - -long double remquol(long double x, long double y, int *quo) -{ - signed char *cx = (void *)&x, *cy = (void *)&y; - /* By ensuring that addresses of x and y cannot be discarded, - * this empty asm guides GCC into representing extraction of - * their sign bits as memory loads rather than making x and y - * not-address-taken internally and using bitfield operations, - * which in the end wouldn't work out, as extraction from FPU - * registers needs to go through memory anyway. This way GCC - * should manage to use incoming stack slots without spills. */ - __asm__ ("" :: "X"(cx), "X"(cy)); - - long double t = x; - unsigned fpsr; - do __asm__ ("fprem1; fnstsw %%ax" : "+t"(t), "=a"(fpsr) : "u"(y)); - while (fpsr & 0x400); - /* C0, C1, C3 flags in x87 status word carry low bits of quotient: - * 15 14 13 12 11 10 9 8 - * . C3 . . . C2 C1 C0 - * . b1 . . . 0 b0 b2 */ - unsigned char i = fpsr >> 8; - i = i>>4 | i<<4; - /* i[5:2] is now {b0 b2 ? b1}. Retrieve {0 b2 b1 b0} via - * in-register table lookup. */ - unsigned qbits = 0x7575313164642020 >> (i & 60); - qbits &= 7; - - *quo = (cx[9]^cy[9]) < 0 ? -qbits : qbits; - return t; -} diff --git a/src/math/x86_64/rintl.c b/src/math/x86_64/rintl.c deleted file mode 100644 index e1a9207..0000000 --- a/src/math/x86_64/rintl.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -long double rintl(long double x) -{ - __asm__ ("frndint" : "+t"(x)); - return x; -} diff --git a/src/math/x86_64/sqrt.c b/src/math/x86_64/sqrt.c deleted file mode 100644 index 657e09e..0000000 --- a/src/math/x86_64/sqrt.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -double sqrt(double x) -{ - __asm__ ("sqrtsd %1, %0" : "=x"(x) : "x"(x)); - return x; -} diff --git a/src/math/x86_64/sqrtf.c b/src/math/x86_64/sqrtf.c deleted file mode 100644 index 720baec..0000000 --- a/src/math/x86_64/sqrtf.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -float sqrtf(float x) -{ - __asm__ ("sqrtss %1, %0" : "=x"(x) : "x"(x)); - return x; -} diff --git a/src/math/x86_64/sqrtl.c b/src/math/x86_64/sqrtl.c deleted file mode 100644 index 864cfcc..0000000 --- a/src/math/x86_64/sqrtl.c +++ /dev/null @@ -1,7 +0,0 @@ -#include - -long double sqrtl(long double x) -{ - __asm__ ("fsqrt" : "+t"(x)); - return x; -} diff --git a/src/math/x86_64/truncl.s b/src/math/x86_64/truncl.s deleted file mode 100644 index f5cfa3b..0000000 --- a/src/math/x86_64/truncl.s +++ /dev/null @@ -1 +0,0 @@ -# see floorl.s