112 lines
2.7 KiB
C
112 lines
2.7 KiB
C
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/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
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/*
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include "libm.h"
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static const float
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o_threshold = 8.8721679688e+01, /* 0x42b17180 */
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ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
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ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
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invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
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/*
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* Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
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* |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
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* Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
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*/
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Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
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Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
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float expm1f(float x)
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{
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float_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
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union {float f; uint32_t i;} u = {x};
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uint32_t hx = u.i & 0x7fffffff;
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int k, sign = u.i >> 31;
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/* filter out huge and non-finite argument */
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if (hx >= 0x4195b844) { /* if |x|>=27*ln2 */
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if (hx > 0x7f800000) /* NaN */
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return x;
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if (sign)
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return -1;
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if (x > o_threshold) {
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x *= 0x1p127f;
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return x;
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}
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}
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/* argument reduction */
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if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
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if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
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if (!sign) {
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hi = x - ln2_hi;
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lo = ln2_lo;
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k = 1;
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} else {
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hi = x + ln2_hi;
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lo = -ln2_lo;
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k = -1;
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}
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} else {
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k = invln2*x + (sign ? -0.5f : 0.5f);
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t = k;
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hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
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lo = t*ln2_lo;
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}
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x = hi-lo;
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c = (hi-x)-lo;
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} else if (hx < 0x33000000) { /* when |x|<2**-25, return x */
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if (hx < 0x00800000)
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FORCE_EVAL(x*x);
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return x;
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} else
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k = 0;
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/* x is now in primary range */
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hfx = 0.5f*x;
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hxs = x*hfx;
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r1 = 1.0f+hxs*(Q1+hxs*Q2);
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t = 3.0f - r1*hfx;
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e = hxs*((r1-t)/(6.0f - x*t));
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if (k == 0) /* c is 0 */
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return x - (x*e-hxs);
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e = x*(e-c) - c;
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e -= hxs;
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/* exp(x) ~ 2^k (x_reduced - e + 1) */
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if (k == -1)
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return 0.5f*(x-e) - 0.5f;
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if (k == 1) {
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if (x < -0.25f)
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return -2.0f*(e-(x+0.5f));
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return 1.0f + 2.0f*(x-e);
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}
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u.i = (0x7f+k)<<23; /* 2^k */
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twopk = u.f;
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if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */
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y = x - e + 1.0f;
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if (k == 128)
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y = y*2.0f*0x1p127f;
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else
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y = y*twopk;
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return y - 1.0f;
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}
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u.i = (0x7f-k)<<23; /* 2^-k */
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if (k < 23)
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y = (x-e+(1-u.f))*twopk;
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else
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y = (x-(e+u.f)+1)*twopk;
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return y;
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}
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