| /* origin: FreeBSD /usr/src/lib/msun/src/e_logf.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 <math.h> |
| #include <stdint.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 logf(float x) { |
| union { |
| float f; |
| uint32_t i; |
| } u = {x}; |
| float_t hfsq, f, s, z, R, w, t1, t2, dk; |
| uint32_t ix; |
| int k; |
| |
| ix = u.i; |
| k = 0; |
| if (ix < 0x00800000 || ix >> 31) { /* x < 2**-126 */ |
| if (ix << 1 == 0) |
| return -1 / (x * x); /* log(+-0)=-inf */ |
| if (ix >> 31) |
| return (x - x) / 0.0f; /* log(-#) = NaN */ |
| /* subnormal number, scale up x */ |
| k -= 25; |
| x *= 0x1p25f; |
| u.f = x; |
| ix = u.i; |
| } else if (ix >= 0x7f800000) { |
| return x; |
| } else if (ix == 0x3f800000) |
| return 0; |
| |
| /* reduce x into [sqrt(2)/2, sqrt(2)] */ |
| ix += 0x3f800000 - 0x3f3504f3; |
| k += (int)(ix >> 23) - 0x7f; |
| ix = (ix & 0x007fffff) + 0x3f3504f3; |
| u.i = ix; |
| x = u.f; |
| |
| f = x - 1.0f; |
| s = f / (2.0f + f); |
| z = s * s; |
| w = z * z; |
| t1 = w * (Lg2 + w * Lg4); |
| t2 = z * (Lg1 + w * Lg3); |
| R = t2 + t1; |
| hfsq = 0.5f * f * f; |
| dk = k; |
| return s * (hfsq + R) + dk * ln2_lo - hfsq + f + dk * ln2_hi; |
| } |
