newlib/libm/common/sf_log1p.c

   1 /* sf_log1p.c -- float version of s_log1p.c.
   2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   3  */
   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 "fdlibm.h"
  17
  18 #ifdef __STDC__
  19 static const float
  20 #else
  21 static float
  22 #endif
  23 ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
  24 ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
  25 two25 =    3.355443200e+07,     /* 0x4c000000 */
  26 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
  27 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
  28 Lp3 = 2.8571429849e-01, /* 3E924925 */
  29 Lp4 = 2.2222198546e-01, /* 3E638E29 */
  30 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
  31 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
  32 Lp7 = 1.4798198640e-01; /* 3E178897 */
  33
  34 #ifdef __STDC__
  35 static const float zero = 0.0;
  36 #else
  37 static float zero = 0.0;
  38 #endif
  39
  40 #ifdef __STDC__
  41         float log1pf(float x)
  42 #else
  43         float log1pf(x)
  44         float x;
  45 #endif
  46 {
  47         float hfsq,f,c,s,z,R,u;
  48         __int32_t k,hx,hu,ax;
  49
  50         GET_FLOAT_WORD(hx,x);
  51         ax = hx&0x7fffffff;
  52
  53         k = 1;
  54         if (!FLT_UWORD_IS_FINITE(hx)) return x+x;
  55         if (hx < 0x3ed413d7) {                  /* x < 0.41422  */
  56             if(ax>=0x3f800000) {                /* x <= -1.0 */
  57                 if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
  58                 else return (x-x)/(x-x);        /* log1p(x<-1)=NaN */
  59             }
  60             if(ax<0x31000000) {                 /* |x| < 2**-29 */
  61                 if(two25+x>zero                 /* raise inexact */
  62                     &&ax<0x24800000)            /* |x| < 2**-54 */
  63                     return x;
  64                 else
  65                     return x - x*x*(float)0.5;
  66             }
  67             if(hx>0||hx<=((__int32_t)0xbe95f61f)) {
  68                 k=0;f=x;hu=1;}  /* -0.2929<x<0.41422 */
  69         }
  70         if(k!=0) {
  71             if(hx<0x5a000000) {
  72                 u  = (float)1.0+x;
  73                 GET_FLOAT_WORD(hu,u);
  74                 k  = (hu>>23)-127;
  75                 /* correction term */
  76                 c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
  77                 c /= u;
  78             } else {
  79                 u  = x;
  80                 GET_FLOAT_WORD(hu,u);
  81                 k  = (hu>>23)-127;
  82                 c  = 0;
  83             }
  84             hu &= 0x007fffff;
  85             if(hu<0x3504f7) {
  86                 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
  87             } else {
  88                 k += 1;
  89                 SET_FLOAT_WORD(u,hu|0x3f000000);        /* normalize u/2 */
  90                 hu = (0x00800000-hu)>>2;
  91             }
  92             f = u-(float)1.0;
  93         }
  94         hfsq=(float)0.5*f*f;
  95         if(hu==0) {     /* |f| < 2**-20 */
  96            if(f==zero) { if(k==0) return zero;
  97                        else {c += k*ln2_lo; return k*ln2_hi+c;}}
  98             R = hfsq*((float)1.0-(float)0.66666666666666666*f);
  99             if(k==0) return f-R; else
 100                      return k*ln2_hi-((R-(k*ln2_lo+c))-f);
 101         }
 102         s = f/((float)2.0+f);
 103         z = s*s;
 104         R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
 105         if(k==0) return f-(hfsq-s*(hfsq+R)); else
 106                  return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
 107 }
 108
 109 #ifdef _DOUBLE_IS_32BITS
 110
 111 #ifdef __STDC__
 112         double log1p(double x)
 113 #else
 114         double log1p(x)
 115         double x;
 116 #endif
 117 {
 118         return (double) log1pf((float) x);
 119 }
 120
 121 #endif /* defined(_DOUBLE_IS_32BITS) */