src/math/log10f.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/e_log10f.c */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12 /*
  13  * See comments in log10.c.
  14  */
  15
  16 #include <math.h>
  17 #include <stdint.h>
  18
  19 static const float
  20 ivln10hi  =  4.3432617188e-01, /* 0x3ede6000 */
  21 ivln10lo  = -3.1689971365e-05, /* 0xb804ead9 */
  22 log10_2hi =  3.0102920532e-01, /* 0x3e9a2080 */
  23 log10_2lo =  7.9034151668e-07, /* 0x355427db */
  24 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
  25 Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
  26 Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
  27 Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
  28 Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
  29
  30 float log10f(float x)
  31 {
  32         union {float f; uint32_t i;} u = {x};
  33         float_t hfsq,f,s,z,R,w,t1,t2,dk,hi,lo;
  34         uint32_t ix;
  35         int k;
  36
  37         ix = u.i;
  38         k = 0;
  39         if (ix < 0x00800000 || ix>>31) {  /* x < 2**-126  */
  40                 if (ix<<1 == 0)
  41                         return -1/(x*x);  /* log(+-0)=-inf */
  42                 if (ix>>31)
  43                         return (x-x)/0.0f; /* log(-#) = NaN */
  44                 /* subnormal number, scale up x */
  45                 k -= 25;
  46                 x *= 0x1p25f;
  47                 u.f = x;
  48                 ix = u.i;
  49         } else if (ix >= 0x7f800000) {
  50                 return x;
  51         } else if (ix == 0x3f800000)
  52                 return 0;
  53
  54         /* reduce x into [sqrt(2)/2, sqrt(2)] */
  55         ix += 0x3f800000 - 0x3f3504f3;
  56         k += (int)(ix>>23) - 0x7f;
  57         ix = (ix&0x007fffff) + 0x3f3504f3;
  58         u.i = ix;
  59         x = u.f;
  60
  61         f = x - 1.0f;
  62         s = f/(2.0f + f);
  63         z = s*s;
  64         w = z*z;
  65         t1= w*(Lg2+w*Lg4);
  66         t2= z*(Lg1+w*Lg3);
  67         R = t2 + t1;
  68         hfsq = 0.5f*f*f;
  69
  70         hi = f - hfsq;
  71         u.f = hi;
  72         u.i &= 0xfffff000;
  73         hi = u.f;
  74         lo = f - hi - hfsq + s*(hfsq+R);
  75         dk = k;
  76         return dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi + hi*ivln10hi + dk*log10_2hi;
  77 }