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 #include "math_config.h"
  18
  19 #ifdef __STDC__
  20 static const float
  21 #else
  22 static float
  23 #endif
  24 ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
  25 ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
  26 two25 =    3.355443200e+07,     /* 0x4c000000 */
  27 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
  28 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
  29 Lp3 = 2.8571429849e-01, /* 3E924925 */
  30 Lp4 = 2.2222198546e-01, /* 3E638E29 */
  31 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
  32 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
  33 Lp7 = 1.4798198640e-01; /* 3E178897 */
  34
  35 #ifdef __STDC__
  36 static const float zero = 0.0;
  37 #else
  38 static float zero = 0.0;
  39 #endif
  40
  41 #ifdef __STDC__
  42         float log1pf(float x)
  43 #else
  44         float log1pf(x)
  45         float x;
  46 #endif
  47 {
  48         float hfsq,f,c,s,z,R,u;
  49         __int32_t k,hx,hu,ax;
  50
  51         GET_FLOAT_WORD(hx,x);
  52         ax = hx&0x7fffffff;
  53
  54         k = 1;
  55         if (!FLT_UWORD_IS_FINITE(hx)) return x+x;
  56         if (hx < 0x3ed413d7) {                  /* x < 0.41422  */
  57             if(ax>=0x3f800000) {                /* x <= -1.0 */
  58                 if(x==(float)-1.0)
  59                     return __math_divzerof (1); /* log1p(-1)=-inf */
  60                 else
  61                     return __math_invalidf (x); /* log1p(x<-1)=NaN */
  62             }
  63             if(ax<0x31000000) {                 /* |x| < 2**-29 */
  64                 if(two25+x>zero                 /* raise inexact */
  65                     &&ax<0x24800000)            /* |x| < 2**-54 */
  66                     return x;
  67                 else
  68                     return x - x*x*(float)0.5;
  69             }
  70             if(hx>0||hx<=((__int32_t)0xbe95f61f)) {
  71                 k=0;f=x;hu=1;}  /* -0.2929<x<0.41422 */
  72         }
  73         if(k!=0) {
  74             if(hx<0x5a000000) {
  75                 u  = (float)1.0+x;
  76                 GET_FLOAT_WORD(hu,u);
  77                 k  = (hu>>23)-127;
  78                 /* correction term */
  79                 c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
  80                 c /= u;
  81             } else {
  82                 u  = x;
  83                 GET_FLOAT_WORD(hu,u);
  84                 k  = (hu>>23)-127;
  85                 c  = 0;
  86             }
  87             hu &= 0x007fffff;
  88             if(hu<0x3504f7) {
  89                 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
  90             } else {
  91                 k += 1;
  92                 SET_FLOAT_WORD(u,hu|0x3f000000);        /* normalize u/2 */
  93                 hu = (0x00800000-hu)>>2;
  94             }
  95             f = u-(float)1.0;
  96         }
  97         hfsq=(float)0.5*f*f;
  98         if(hu==0) {     /* |f| < 2**-20 */
  99            if(f==zero) { if(k==0) return zero;
 100                        else {c += k*ln2_lo; return k*ln2_hi+c;}}
 101             R = hfsq*((float)1.0-(float)0.66666666666666666*f);
 102             if(k==0) return f-R; else
 103                      return k*ln2_hi-((R-(k*ln2_lo+c))-f);
 104         }
 105         s = f/((float)2.0+f);
 106         z = s*s;
 107         R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
 108         if(k==0) return f-(hfsq-s*(hfsq+R)); else
 109                  return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
 110 }
 111
 112 #ifdef _DOUBLE_IS_32BITS
 113
 114 #ifdef __STDC__
 115         double log1p(double x)
 116 #else
 117         double log1p(x)
 118         double x;
 119 #endif
 120 {
 121         return (double) log1pf((float) x);
 122 }
 123
 124 #endif /* defined(_DOUBLE_IS_32BITS) */