86 lines
2.3 KiB
C
86 lines
2.3 KiB
C
/*****************************************************************************/
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/*****************************************************************************/
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// log1pf from musl-0.9.15
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/*****************************************************************************/
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/*****************************************************************************/
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/* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */
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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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#pragma GCC diagnostic ignored "-Wfloat-equal"
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static const float
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ln2_hi = 6.9313812256e-01f, /* 0x3f317180 */
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ln2_lo = 9.0580006145e-06f, /* 0x3717f7d1 */
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/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
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Lg1 = 0xaaaaaa.0p-24f, /* 0.66666662693 */
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Lg2 = 0xccce13.0p-25f, /* 0.40000972152 */
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Lg3 = 0x91e9ee.0p-25f, /* 0.28498786688 */
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Lg4 = 0xf89e26.0p-26f; /* 0.24279078841 */
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float log1pf(float x)
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{
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union {float f; uint32_t i;} u = {x};
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float_t hfsq,f,c,s,z,R,w,t1,t2,dk;
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uint32_t ix,iu;
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int k;
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ix = u.i;
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k = 1;
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if (ix < 0x3ed413d0 || ix>>31) { /* 1+x < sqrt(2)+ */
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if (ix >= 0xbf800000) { /* x <= -1.0 */
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if (x == -1)
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return x/0.0f; /* log1p(-1)=+inf */
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return (x-x)/0.0f; /* log1p(x<-1)=NaN */
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}
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if (ix<<1 < 0x33800000<<1) { /* |x| < 2**-24 */
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/* underflow if subnormal */
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if ((ix&0x7f800000) == 0)
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FORCE_EVAL(x*x);
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return x;
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}
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if (ix <= 0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
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k = 0;
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c = 0;
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f = x;
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}
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} else if (ix >= 0x7f800000)
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return x;
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if (k) {
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u.f = 1 + x;
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iu = u.i;
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iu += 0x3f800000 - 0x3f3504f3;
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k = (int)(iu>>23) - 0x7f;
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/* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
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if (k < 25) {
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c = k >= 2 ? 1-(u.f-x) : x-(u.f-1);
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c /= u.f;
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} else
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c = 0;
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/* reduce u into [sqrt(2)/2, sqrt(2)] */
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iu = (iu&0x007fffff) + 0x3f3504f3;
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u.i = iu;
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f = u.f - 1;
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}
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s = f/(2.0f + f);
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z = s*s;
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w = z*z;
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t1= w*(Lg2+w*Lg4);
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t2= z*(Lg1+w*Lg3);
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R = t2 + t1;
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hfsq = 0.5f*f*f;
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dk = k;
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return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi;
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}
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