src/math/log1pf.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.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 #include "libm.h"
  14
  15 static const float
  16 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
  17 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
  18 /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
  19 Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
  20 Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
  21 Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
  22 Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
  23
  24 float log1pf(float x)
  25 {
  26         union {float f; uint32_t i;} u = {x};
  27         float_t hfsq,f,c,s,z,R,w,t1,t2,dk;
  28         uint32_t ix,iu;
  29         int k;
  30
  31         ix = u.i;
  32         k = 1;
  33         if (ix < 0x3ed413d0 || ix>>31) {  /* 1+x < sqrt(2)+  */
  34                 if (ix >= 0xbf800000) {  /* x <= -1.0 */
  35                         if (x == -1)
  36                                 return x/0.0f; /* log1p(-1)=+inf */
  37                         return (x-x)/0.0f;     /* log1p(x<-1)=NaN */
  38                 }
  39                 if (ix<<1 < 0x33800000<<1) {   /* |x| < 2**-24 */
  40                         /* underflow if subnormal */
  41                         if ((ix&0x7f800000) == 0)
  42                                 FORCE_EVAL(x*x);
  43                         return x;
  44                 }
  45                 if (ix <= 0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
  46                         k = 0;
  47                         c = 0;
  48                         f = x;
  49                 }
  50         } else if (ix >= 0x7f800000)
  51                 return x;
  52         if (k) {
  53                 u.f = 1 + x;
  54                 iu = u.i;
  55                 iu += 0x3f800000 - 0x3f3504f3;
  56                 k = (int)(iu>>23) - 0x7f;
  57                 /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
  58                 if (k < 25) {
  59                         c = k >= 2 ? 1-(u.f-x) : x-(u.f-1);
  60                         c /= u.f;
  61                 } else
  62                         c = 0;
  63                 /* reduce u into [sqrt(2)/2, sqrt(2)] */
  64                 iu = (iu&0x007fffff) + 0x3f3504f3;
  65                 u.i = iu;
  66                 f = u.f - 1;
  67         }
  68         s = f/(2.0f + f);
  69         z = s*s;
  70         w = z*z;
  71         t1= w*(Lg2+w*Lg4);
  72         t2= z*(Lg1+w*Lg3);
  73         R = t2 + t1;
  74         hfsq = 0.5f*f*f;
  75         dk = k;
  76         return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi;
  77 }