| /* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| #include "libm.h" |
| |
| static const float ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ |
| ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ |
| /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */ |
| Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */ |
| Lg2 = 0xccce13.0p-25, /* 0.40000972152 */ |
| Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */ |
| Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */ |
| |
| float log1pf(float x) { |
| union { |
| float f; |
| uint32_t i; |
| } u = {x}; |
| float_t hfsq, f, c, s, z, R, w, t1, t2, dk; |
| uint32_t ix, iu; |
| int k; |
| |
| ix = u.i; |
| k = 1; |
| if (ix < 0x3ed413d0 || ix >> 31) { /* 1+x < sqrt(2)+ */ |
| if (ix >= 0xbf800000) { /* x <= -1.0 */ |
| if (x == -1) |
| return x / 0.0f; /* log1p(-1)=+inf */ |
| return (x - x) / 0.0f; /* log1p(x<-1)=NaN */ |
| } |
| if (ix << 1 < 0x33800000 << 1) { /* |x| < 2**-24 */ |
| /* underflow if subnormal */ |
| if ((ix & 0x7f800000) == 0) |
| FORCE_EVAL(x * x); |
| return x; |
| } |
| if (ix <= 0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ |
| k = 0; |
| c = 0; |
| f = x; |
| } |
| } else if (ix >= 0x7f800000) |
| return x; |
| if (k) { |
| u.f = 1 + x; |
| iu = u.i; |
| iu += 0x3f800000 - 0x3f3504f3; |
| k = (int)(iu >> 23) - 0x7f; |
| /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */ |
| if (k < 25) { |
| c = k >= 2 ? 1 - (u.f - x) : x - (u.f - 1); |
| c /= u.f; |
| } else |
| c = 0; |
| /* reduce u into [sqrt(2)/2, sqrt(2)] */ |
| iu = (iu & 0x007fffff) + 0x3f3504f3; |
| u.i = iu; |
| f = u.f - 1; |
| } |
| s = f / (2.0f + f); |
| z = s * s; |
| w = z * z; |
| t1 = w * (Lg2 + w * Lg4); |
| t2 = z * (Lg1 + w * Lg3); |
| R = t2 + t1; |
| hfsq = 0.5f * f * f; |
| dk = k; |
| return s * (hfsq + R) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi; |
| } |
