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/* origin: FreeBSD /usr/src/lib/msun/src/e_log2f.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 log2.c. */ #include <math.h> #include <stdint.h> static const float ivln2hi = 1.4428710938e+00, /* 0x3fb8b000 */ ivln2lo = -1.7605285393e-04, /* 0xb9389ad4 */ /* |(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 log2f(float x) { union {float f; uint32_t i;} u = {x}; float_t hfsq,f,s,z,R,w,t1,t2,hi,lo; 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; hi = f - hfsq; u.f = hi; u.i &= 0xfffff000; hi = u.f; lo = f - hi - hfsq + s*(hfsq+R); return (lo+hi)*ivln2lo + lo*ivln2hi + hi*ivln2hi + k; } |