Restore math library

2022-04-14 15:49:55 +08:00 · 2022-04-14 15:49:55 +08:00 · ea670ff2d8
commit ea670ff2d8
parent 9e65a3c710
454 changed files with 20617 additions and 0 deletions
--- a/src/math/__cos.c
+++ b/src/math/__cos.c
@ -0,0 +1,71 @@
+/* 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));
+}
--- a/src/math/__cosdf.c
+++ b/src/math/__cosdf.c
@ -0,0 +1,35 @@
+/* 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;
+}
--- a/src/math/__cosl.c
+++ b/src/math/__cosl.c
@ -0,0 +1,96 @@
+/* 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
--- a/src/math/__expo2.c
+++ b/src/math/__expo2.c
@ -0,0 +1,17 @@
+#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;
+}
--- a/src/math/__expo2f.c
+++ b/src/math/__expo2f.c
@ -0,0 +1,17 @@
+#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;
+}
--- a/src/math/__fpclassify.c
+++ b/src/math/__fpclassify.c
@ -0,0 +1,11 @@
+#include <math.h>
+#include <stdint.h>
+
+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;
+}
--- a/src/math/__fpclassifyf.c
+++ b/src/math/__fpclassifyf.c
@ -0,0 +1,11 @@
+#include <math.h>
+#include <stdint.h>
+
+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;
+}
--- a/src/math/__fpclassifyl.c
+++ b/src/math/__fpclassifyl.c
@ -0,0 +1,42 @@
+#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
--- a/src/math/__invtrigl.c
+++ b/src/math/__invtrigl.c
@ -0,0 +1,63 @@
+#include <float.h>
+#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
--- a/src/math/__invtrigl.h
+++ b/src/math/__invtrigl.h
@ -0,0 +1,8 @@
+#include <features.h>
+
+/* 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);
--- a/src/math/__math_divzero.c
+++ b/src/math/__math_divzero.c
@ -0,0 +1,6 @@
+#include "libm.h"
+
+double __math_divzero(uint32_t sign)
+{
+	return fp_barrier(sign ? -1.0 : 1.0) / 0.0;
+}
--- a/src/math/__math_divzerof.c
+++ b/src/math/__math_divzerof.c
@ -0,0 +1,6 @@
+#include "libm.h"
+
+float __math_divzerof(uint32_t sign)
+{
+	return fp_barrierf(sign ? -1.0f : 1.0f) / 0.0f;
+}
--- a/src/math/__math_invalid.c
+++ b/src/math/__math_invalid.c
@ -0,0 +1,6 @@
+#include "libm.h"
+
+double __math_invalid(double x)
+{
+	return (x - x) / (x - x);
+}
--- a/src/math/__math_invalidf.c
+++ b/src/math/__math_invalidf.c
@ -0,0 +1,6 @@
+#include "libm.h"
+
+float __math_invalidf(float x)
+{
+	return (x - x) / (x - x);
+}
--- a/src/math/__math_invalidl.c
+++ b/src/math/__math_invalidl.c
@ -0,0 +1,9 @@
+#include <float.h>
+#include "libm.h"
+
+#if LDBL_MANT_DIG != DBL_MANT_DIG
+long double __math_invalidl(long double x)
+{
+	return (x - x) / (x - x);
+}
+#endif
--- a/src/math/__math_oflow.c
+++ b/src/math/__math_oflow.c
@ -0,0 +1,6 @@
+#include "libm.h"
+
+double __math_oflow(uint32_t sign)
+{
+	return __math_xflow(sign, 0x1p769);
+}
--- a/src/math/__math_oflowf.c
+++ b/src/math/__math_oflowf.c
@ -0,0 +1,6 @@
+#include "libm.h"
+
+float __math_oflowf(uint32_t sign)
+{
+	return __math_xflowf(sign, 0x1p97f);
+}
--- a/src/math/__math_uflow.c
+++ b/src/math/__math_uflow.c
@ -0,0 +1,6 @@
+#include "libm.h"
+
+double __math_uflow(uint32_t sign)
+{
+	return __math_xflow(sign, 0x1p-767);
+}
--- a/src/math/__math_uflowf.c
+++ b/src/math/__math_uflowf.c
@ -0,0 +1,6 @@
+#include "libm.h"
+
+float __math_uflowf(uint32_t sign)
+{
+	return __math_xflowf(sign, 0x1p-95f);
+}
--- a/src/math/__math_xflow.c
+++ b/src/math/__math_xflow.c
@ -0,0 +1,6 @@
+#include "libm.h"
+
+double __math_xflow(uint32_t sign, double y)
+{
+	return eval_as_double(fp_barrier(sign ? -y : y) * y);
+}
--- a/src/math/__math_xflowf.c
+++ b/src/math/__math_xflowf.c
@ -0,0 +1,6 @@
+#include "libm.h"
+
+float __math_xflowf(uint32_t sign, float y)
+{
+	return eval_as_float(fp_barrierf(sign ? -y : y) * y);
+}
--- a/src/math/__polevll.c
+++ b/src/math/__polevll.c
@ -0,0 +1,93 @@
+/* origin: OpenBSD /usr/src/lib/libm/src/polevll.c */
+/*
+ * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
+ *
+ * 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
--- a/src/math/__rem_pio2.c
+++ b/src/math/__rem_pio2.c
@ -0,0 +1,190 @@
+/* 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;
+}
--- a/src/math/__rem_pio2_large.c
+++ b/src/math/__rem_pio2_large.c
@ -0,0 +1,442 @@
+/* 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<jz; i++) {  /* compute 1-q */
+			j = iq[i];
+			if (carry == 0) {
+				if (j != 0) {
+					carry = 1;
+					iq[i] = 0x1000000 - j;
+				}
+			} else
+				iq[i] = 0xffffff - j;
+		}
+		if (q0 > 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;
+}
--- a/src/math/__rem_pio2f.c
+++ b/src/math/__rem_pio2f.c
@ -0,0 +1,86 @@
+/* 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;
+}
--- a/src/math/__rem_pio2l.c
+++ b/src/math/__rem_pio2l.c
@ -0,0 +1,155 @@
+/* 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
--- a/src/math/__signbit.c
+++ b/src/math/__signbit.c
@ -0,0 +1,13 @@
+#include "libm.h"
+
+// FIXME: macro in math.h
+int __signbit(double x)
+{
+	union {
+		double d;
+		uint64_t i;
+	} y = { x };
+	return y.i>>63;
+}
+
+
--- a/src/math/__signbitf.c
+++ b/src/math/__signbitf.c
@ -0,0 +1,11 @@
+#include "libm.h"
+
+// FIXME: macro in math.h
+int __signbitf(float x)
+{
+	union {
+		float f;
+		uint32_t i;
+	} y = { x };
+	return y.i>>31;
+}
--- a/src/math/__signbitl.c
+++ b/src/math/__signbitl.c
@ -0,0 +1,14 @@
+#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
--- a/src/math/__sin.c
+++ b/src/math/__sin.c
@ -0,0 +1,64 @@
+/* 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);
+}
--- a/src/math/__sindf.c
+++ b/src/math/__sindf.c
@ -0,0 +1,36 @@
+/* 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;
+}
--- a/src/math/__sinl.c
+++ b/src/math/__sinl.c
@ -0,0 +1,78 @@
+/* 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
--- a/src/math/__tan.c
+++ b/src/math/__tan.c
@ -0,0 +1,110 @@
+/* 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);
+}
--- a/src/math/__tandf.c
+++ b/src/math/__tandf.c
@ -0,0 +1,54 @@
+/* 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;
+}
--- a/src/math/__tanl.c
+++ b/src/math/__tanl.c
@ -0,0 +1,143 @@
+/* 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
--- a/src/math/aarch64/ceil.c
+++ b/src/math/aarch64/ceil.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+double ceil(double x)
+{
+	__asm__ ("frintp %d0, %d1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/ceilf.c
+++ b/src/math/aarch64/ceilf.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+float ceilf(float x)
+{
+	__asm__ ("frintp %s0, %s1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/fabs.c
+++ b/src/math/aarch64/fabs.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+double fabs(double x)
+{
+	__asm__ ("fabs %d0, %d1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/fabsf.c
+++ b/src/math/aarch64/fabsf.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+float fabsf(float x)
+{
+	__asm__ ("fabs %s0, %s1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/floor.c
+++ b/src/math/aarch64/floor.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+double floor(double x)
+{
+	__asm__ ("frintm %d0, %d1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/floorf.c
+++ b/src/math/aarch64/floorf.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+float floorf(float x)
+{
+	__asm__ ("frintm %s0, %s1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/fma.c
+++ b/src/math/aarch64/fma.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+double fma(double x, double y, double z)
+{
+	__asm__ ("fmadd %d0, %d1, %d2, %d3" : "=w"(x) : "w"(x), "w"(y), "w"(z));
+	return x;
+}
--- a/src/math/aarch64/fmaf.c
+++ b/src/math/aarch64/fmaf.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+float fmaf(float x, float y, float z)
+{
+	__asm__ ("fmadd %s0, %s1, %s2, %s3" : "=w"(x) : "w"(x), "w"(y), "w"(z));
+	return x;
+}
--- a/src/math/aarch64/fmax.c
+++ b/src/math/aarch64/fmax.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+double fmax(double x, double y)
+{
+	__asm__ ("fmaxnm %d0, %d1, %d2" : "=w"(x) : "w"(x), "w"(y));
+	return x;
+}
--- a/src/math/aarch64/fmaxf.c
+++ b/src/math/aarch64/fmaxf.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+float fmaxf(float x, float y)
+{
+	__asm__ ("fmaxnm %s0, %s1, %s2" : "=w"(x) : "w"(x), "w"(y));
+	return x;
+}
--- a/src/math/aarch64/fmin.c
+++ b/src/math/aarch64/fmin.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+double fmin(double x, double y)
+{
+	__asm__ ("fminnm %d0, %d1, %d2" : "=w"(x) : "w"(x), "w"(y));
+	return x;
+}
--- a/src/math/aarch64/fminf.c
+++ b/src/math/aarch64/fminf.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+float fminf(float x, float y)
+{
+	__asm__ ("fminnm %s0, %s1, %s2" : "=w"(x) : "w"(x), "w"(y));
+	return x;
+}
--- a/src/math/aarch64/llrint.c
+++ b/src/math/aarch64/llrint.c
@ -0,0 +1,10 @@
+#include <math.h>
+
+long long llrint(double x)
+{
+	long long n;
+	__asm__ (
+		"frintx %d1, %d1\n"
+		"fcvtzs %x0, %d1\n" : "=r"(n), "+w"(x));
+	return n;
+}
--- a/src/math/aarch64/llrintf.c
+++ b/src/math/aarch64/llrintf.c
@ -0,0 +1,10 @@
+#include <math.h>
+
+long long llrintf(float x)
+{
+	long long n;
+	__asm__ (
+		"frintx %s1, %s1\n"
+		"fcvtzs %x0, %s1\n" : "=r"(n), "+w"(x));
+	return n;
+}
--- a/src/math/aarch64/llround.c
+++ b/src/math/aarch64/llround.c
@ -0,0 +1,8 @@
+#include <math.h>
+
+long long llround(double x)
+{
+	long long n;
+	__asm__ ("fcvtas %x0, %d1" : "=r"(n) : "w"(x));
+	return n;
+}
--- a/src/math/aarch64/llroundf.c
+++ b/src/math/aarch64/llroundf.c
@ -0,0 +1,8 @@
+#include <math.h>
+
+long long llroundf(float x)
+{
+	long long n;
+	__asm__ ("fcvtas %x0, %s1" : "=r"(n) : "w"(x));
+	return n;
+}
--- a/src/math/aarch64/lrint.c
+++ b/src/math/aarch64/lrint.c
@ -0,0 +1,10 @@
+#include <math.h>
+
+long lrint(double x)
+{
+	long n;
+	__asm__ (
+		"frintx %d1, %d1\n"
+		"fcvtzs %x0, %d1\n" : "=r"(n), "+w"(x));
+	return n;
+}
--- a/src/math/aarch64/lrintf.c
+++ b/src/math/aarch64/lrintf.c
@ -0,0 +1,10 @@
+#include <math.h>
+
+long lrintf(float x)
+{
+	long n;
+	__asm__ (
+		"frintx %s1, %s1\n"
+		"fcvtzs %x0, %s1\n" : "=r"(n), "+w"(x));
+	return n;
+}
--- a/src/math/aarch64/lround.c
+++ b/src/math/aarch64/lround.c
@ -0,0 +1,8 @@
+#include <math.h>
+
+long lround(double x)
+{
+	long n;
+	__asm__ ("fcvtas %x0, %d1" : "=r"(n) : "w"(x));
+	return n;
+}
--- a/src/math/aarch64/lroundf.c
+++ b/src/math/aarch64/lroundf.c
@ -0,0 +1,8 @@
+#include <math.h>
+
+long lroundf(float x)
+{
+	long n;
+	__asm__ ("fcvtas %x0, %s1" : "=r"(n) : "w"(x));
+	return n;
+}
--- a/src/math/aarch64/nearbyint.c
+++ b/src/math/aarch64/nearbyint.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+double nearbyint(double x)
+{
+	__asm__ ("frinti %d0, %d1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/nearbyintf.c
+++ b/src/math/aarch64/nearbyintf.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+float nearbyintf(float x)
+{
+	__asm__ ("frinti %s0, %s1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/rint.c
+++ b/src/math/aarch64/rint.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+double rint(double x)
+{
+	__asm__ ("frintx %d0, %d1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/rintf.c
+++ b/src/math/aarch64/rintf.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+float rintf(float x)
+{
+	__asm__ ("frintx %s0, %s1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/round.c
+++ b/src/math/aarch64/round.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+double round(double x)
+{
+	__asm__ ("frinta %d0, %d1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/roundf.c
+++ b/src/math/aarch64/roundf.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+float roundf(float x)
+{
+	__asm__ ("frinta %s0, %s1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/sqrt.c
+++ b/src/math/aarch64/sqrt.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+double sqrt(double x)
+{
+	__asm__ ("fsqrt %d0, %d1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/sqrtf.c
+++ b/src/math/aarch64/sqrtf.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+float sqrtf(float x)
+{
+	__asm__ ("fsqrt %s0, %s1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/trunc.c
+++ b/src/math/aarch64/trunc.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+double trunc(double x)
+{
+	__asm__ ("frintz %d0, %d1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/aarch64/truncf.c
+++ b/src/math/aarch64/truncf.c
@ -0,0 +1,7 @@
+#include <math.h>
+
+float truncf(float x)
+{
+	__asm__ ("frintz %s0, %s1" : "=w"(x) : "w"(x));
+	return x;
+}
--- a/src/math/acos.c
+++ b/src/math/acos.c
@ -0,0 +1,101 @@
+/* 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);
+}
--- a/src/math/acosf.c
+++ b/src/math/acosf.c
@ -0,0 +1,71 @@
+/* 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);
+}
--- a/src/math/acosh.c
+++ b/src/math/acosh.c
@ -0,0 +1,24 @@
+#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;
+}
--- a/src/math/acoshf.c
+++ b/src/math/acoshf.c
@ -0,0 +1,26 @@
+#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;
+}
--- a/src/math/acoshl.c
+++ b/src/math/acoshl.c
@ -0,0 +1,29 @@
+#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
--- a/src/math/acosl.c
+++ b/src/math/acosl.c
@ -0,0 +1,67 @@
+/* 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 <das@FreeBSD.ORG>.
+ */
+
+#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
--- a/src/math/arm/fabs.c
+++ b/src/math/arm/fabs.c
@ -0,0 +1,15 @@
+#include <math.h>
+
+#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
--- a/src/math/arm/fabsf.c
+++ b/src/math/arm/fabsf.c
@ -0,0 +1,15 @@
+#include <math.h>
+
+#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
--- a/src/math/arm/fma.c
+++ b/src/math/arm/fma.c
@ -0,0 +1,15 @@
+#include <math.h>
+
+#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
--- a/src/math/arm/fmaf.c
+++ b/src/math/arm/fmaf.c
@ -0,0 +1,15 @@
+#include <math.h>
+
+#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
--- a/src/math/arm/sqrt.c
+++ b/src/math/arm/sqrt.c
@ -0,0 +1,15 @@
+#include <math.h>
+
+#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
--- a/src/math/arm/sqrtf.c
+++ b/src/math/arm/sqrtf.c
@ -0,0 +1,15 @@
+#include <math.h>
+
+#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
--- a/src/math/asin.c
+++ b/src/math/asin.c
@ -0,0 +1,107 @@
+/* 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;
+}
--- a/src/math/asinf.c
+++ b/src/math/asinf.c
@ -0,0 +1,61 @@
+/* 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;
+}
--- a/src/math/asinh.c
+++ b/src/math/asinh.c
@ -0,0 +1,28 @@
+#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;
+}
--- a/src/math/asinhf.c
+++ b/src/math/asinhf.c
@ -0,0 +1,28 @@
+#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;
+}
--- a/src/math/asinhl.c
+++ b/src/math/asinhl.c
@ -0,0 +1,41 @@
+#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
--- a/src/math/asinl.c
+++ b/src/math/asinl.c
@ -0,0 +1,71 @@
+/* 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 <das@FreeBSD.ORG>.
+ */
+
+#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
--- a/src/math/atan.c
+++ b/src/math/atan.c
@ -0,0 +1,116 @@
+/* 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;
+}
--- a/src/math/atan2.c
+++ b/src/math/atan2.c
@ -0,0 +1,107 @@
+/* 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(-,-) */
+	}
+}
--- a/src/math/atan2f.c
+++ b/src/math/atan2f.c
@ -0,0 +1,83 @@
+/* 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(-,-) */
+	}
+}
--- a/src/math/atan2l.c
+++ b/src/math/atan2l.c
@ -0,0 +1,85 @@
+/* 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 <das@FreeBSD.ORG>.
+ */
+
+#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
--- a/src/math/atanf.c
+++ b/src/math/atanf.c
@ -0,0 +1,94 @@
+/* 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;
+}
--- a/src/math/atanh.c
+++ b/src/math/atanh.c
@ -0,0 +1,29 @@
+#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;
+}
--- a/src/math/atanhf.c
+++ b/src/math/atanhf.c
@ -0,0 +1,28 @@
+#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;
+}
--- a/src/math/atanhl.c
+++ b/src/math/atanhl.c
@ -0,0 +1,35 @@
+#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
--- a/src/math/atanl.c
+++ b/src/math/atanl.c
@ -0,0 +1,184 @@
+/* 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 <das@FreeBSD.ORG>.
+ */
+
+#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
--- a/src/math/cbrt.c
+++ b/src/math/cbrt.c
@ -0,0 +1,103 @@
+/* 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 <math.h>
+#include <stdint.h>
+
+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;
+}
--- a/src/math/cbrtf.c
+++ b/src/math/cbrtf.c
@ -0,0 +1,66 @@
+/* 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 <math.h>
+#include <stdint.h>
+
+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;
+}
--- a/src/math/cbrtl.c
+++ b/src/math/cbrtl.c
@ -0,0 +1,124 @@
+/* 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
--- a/src/math/ceil.c
+++ b/src/math/ceil.c
@ -0,0 +1,31 @@
+#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;
+}
--- a/src/math/ceilf.c
+++ b/src/math/ceilf.c
@ -0,0 +1,27 @@
+#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;
+}
--- a/src/math/ceill.c
+++ b/src/math/ceill.c
@ -0,0 +1,34 @@
+#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
--- a/src/math/copysign.c
+++ b/src/math/copysign.c
@ -0,0 +1,8 @@
+#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;
+}
--- a/src/math/copysignf.c
+++ b/src/math/copysignf.c
@ -0,0 +1,10 @@
+#include <math.h>
+#include <stdint.h>
+
+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;
+}
--- a/Show More
+++ b/Show More