lib/msun/src/s_log1pf.c

   1 /* s_log1pf.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 #ifndef lint
  17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_log1pf.c,v 1.5 1999/08/28 00:06:52 peter Exp $";
  18 #endif
  19
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 #ifdef __STDC__
  24 static const float
  25 #else
  26 static float
  27 #endif
  28 ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
  29 ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
  30 two25 =    3.355443200e+07,     /* 0x4c000000 */
  31 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
  32 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
  33 Lp3 = 2.8571429849e-01, /* 3E924925 */
  34 Lp4 = 2.2222198546e-01, /* 3E638E29 */
  35 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
  36 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
  37 Lp7 = 1.4798198640e-01; /* 3E178897 */
  38
  39 #ifdef __STDC__
  40 static const float zero = 0.0;
  41 #else
  42 static float zero = 0.0;
  43 #endif
  44
  45 #ifdef __STDC__
  46         float log1pf(float x)
  47 #else
  48         float log1pf(x)
  49         float x;
  50 #endif
  51 {
  52         float hfsq,f,c,s,z,R,u;
  53         int32_t k,hx,hu,ax;
  54
  55         GET_FLOAT_WORD(hx,x);
  56         ax = hx&0x7fffffff;
  57
  58         k = 1;
  59         if (hx < 0x3ed413d7) {                  /* x < 0.41422  */
  60             if(ax>=0x3f800000) {                /* x <= -1.0 */
  61                 if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
  62                 else return (x-x)/(x-x);        /* log1p(x<-1)=NaN */
  63             }
  64             if(ax<0x31000000) {                 /* |x| < 2**-29 */
  65                 if(two25+x>zero                 /* raise inexact */
  66                     &&ax<0x24800000)            /* |x| < 2**-54 */
  67                     return x;
  68                 else
  69                     return x - x*x*(float)0.5;
  70             }
  71             if(hx>0||hx<=((int32_t)0xbe95f61f)) {
  72                 k=0;f=x;hu=1;}  /* -0.2929<x<0.41422 */
  73         }
  74         if (hx >= 0x7f800000) return x+x;
  75         if(k!=0) {
  76             if(hx<0x5a000000) {
  77                 u  = (float)1.0+x;
  78                 GET_FLOAT_WORD(hu,u);
  79                 k  = (hu>>23)-127;
  80                 /* correction term */
  81                 c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
  82                 c /= u;
  83             } else {
  84                 u  = x;
  85                 GET_FLOAT_WORD(hu,u);
  86                 k  = (hu>>23)-127;
  87                 c  = 0;
  88             }
  89             hu &= 0x007fffff;
  90             if(hu<0x3504f7) {
  91                 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
  92             } else {
  93                 k += 1;
  94                 SET_FLOAT_WORD(u,hu|0x3f000000);        /* normalize u/2 */
  95                 hu = (0x00800000-hu)>>2;
  96             }
  97             f = u-(float)1.0;
  98         }
  99         hfsq=(float)0.5*f*f;
 100         if(hu==0) {     /* |f| < 2**-20 */
 101             if(f==zero) if(k==0) return zero;
 102                         else {c += k*ln2_lo; return k*ln2_hi+c;}
 103             R = hfsq*((float)1.0-(float)0.66666666666666666*f);
 104             if(k==0) return f-R; else
 105                      return k*ln2_hi-((R-(k*ln2_lo+c))-f);
 106         }
 107         s = f/((float)2.0+f);
 108         z = s*s;
 109         R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
 110         if(k==0) return f-(hfsq-s*(hfsq+R)); else
 111                  return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
 112 }