src/math/log1pf.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */
   2 /*
   3  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   4  */
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 #include "libm.h"
  17
  18 static const float
  19 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
  20 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
  21 two25  = 3.355443200e+07,  /* 0x4c000000 */
  22 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
  23 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
  24 Lp3 = 2.8571429849e-01, /* 3E924925 */
  25 Lp4 = 2.2222198546e-01, /* 3E638E29 */
  26 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
  27 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
  28 Lp7 = 1.4798198640e-01; /* 3E178897 */
  29
  30 float log1pf(float x)
  31 {
  32         float hfsq,f,c,s,z,R,u;
  33         int32_t k,hx,hu,ax;
  34
  35         GET_FLOAT_WORD(hx, x);
  36         ax = hx & 0x7fffffff;
  37
  38         k = 1;
  39         if (hx < 0x3ed413d0) {  /* 1+x < sqrt(2)+  */
  40                 if (ax >= 0x3f800000) {  /* x <= -1.0 */
  41                         if (x == -1.0f)
  42                                 return -two25/0.0f; /* log1p(-1)=+inf */
  43                         return (x-x)/(x-x);         /* log1p(x<-1)=NaN */
  44                 }
  45                 if (ax < 0x38000000) {   /* |x| < 2**-15 */
  46                         /* raise inexact */
  47                         if (two25 + x > 0.0f && ax < 0x33800000)  /* |x| < 2**-24 */
  48                                 return x;
  49                         return x - x*x*0.5f;
  50                 }
  51                 if (hx > 0 || hx <= (int32_t)0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
  52                         k = 0;
  53                         f = x;
  54                         hu = 1;
  55                 }
  56         }
  57         if (hx >= 0x7f800000)
  58                 return x+x;
  59         if (k != 0) {
  60                 if (hx < 0x5a000000) {
  61                         STRICT_ASSIGN(float, u, 1.0f + x);
  62                         GET_FLOAT_WORD(hu, u);
  63                         k = (hu>>23) - 127;
  64                         /* correction term */
  65                         c = k > 0 ? 1.0f-(u-x) : x-(u-1.0f);
  66                         c /= u;
  67                 } else {
  68                         u = x;
  69                         GET_FLOAT_WORD(hu,u);
  70                         k = (hu>>23) - 127;
  71                         c = 0;
  72                 }
  73                 hu &= 0x007fffff;
  74                 /*
  75                  * The approximation to sqrt(2) used in thresholds is not
  76                  * critical.  However, the ones used above must give less
  77                  * strict bounds than the one here so that the k==0 case is
  78                  * never reached from here, since here we have committed to
  79                  * using the correction term but don't use it if k==0.
  80                  */
  81                 if (hu < 0x3504f4) {  /* u < sqrt(2) */
  82                         SET_FLOAT_WORD(u, hu|0x3f800000);  /* normalize u */
  83                 } else {
  84                         k += 1;
  85                         SET_FLOAT_WORD(u, hu|0x3f000000);  /* normalize u/2 */
  86                         hu = (0x00800000-hu)>>2;
  87                 }
  88                 f = u - 1.0f;
  89         }
  90         hfsq = 0.5f * f * f;
  91         if (hu == 0) {  /* |f| < 2**-20 */
  92                 if (f == 0.0f) {
  93                         if (k == 0)
  94                                 return 0.0f;
  95                         c += k*ln2_lo;
  96                         return k*ln2_hi+c;
  97                 }
  98                 R = hfsq*(1.0f - 0.66666666666666666f * f);
  99                 if (k == 0)
 100                         return f - R;
 101                 return k*ln2_hi - ((R-(k*ln2_lo+c))-f);
 102         }
 103         s = f/(2.0f + f);
 104         z = s*s;
 105         R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
 106         if (k == 0)
 107                 return f - (hfsq-s*(hfsq+R));
 108         return k*ln2_hi - ((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
 109 }