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  * $FreeBSD: src/lib/msun/src/s_log1pf.c,v 1.5 1999/08/28 00:06:52 peter Exp $
   5  * $DragonFly: src/lib/msun/src/Attic/s_log1pf.c,v 1.2 2003/06/17 04:26:53 dillon Exp $
   6  */
   7
   8 /*
   9  * ====================================================
  10  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  11  *
  12  * Developed at SunPro, a Sun Microsystems, Inc. business.
  13  * Permission to use, copy, modify, and distribute this
  14  * software is freely granted, provided that this notice
  15  * is preserved.
  16  * ====================================================
  17  */
  18
  19 #include "math.h"
  20 #include "math_private.h"
  21
  22 #ifdef __STDC__
  23 static const float
  24 #else
  25 static float
  26 #endif
  27 ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
  28 ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
  29 two25 =    3.355443200e+07,     /* 0x4c000000 */
  30 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
  31 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
  32 Lp3 = 2.8571429849e-01, /* 3E924925 */
  33 Lp4 = 2.2222198546e-01, /* 3E638E29 */
  34 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
  35 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
  36 Lp7 = 1.4798198640e-01; /* 3E178897 */
  37
  38 #ifdef __STDC__
  39 static const float zero = 0.0;
  40 #else
  41 static float zero = 0.0;
  42 #endif
  43
  44 #ifdef __STDC__
  45         float log1pf(float x)
  46 #else
  47         float log1pf(x)
  48         float x;
  49 #endif
  50 {
  51         float hfsq,f,c,s,z,R,u;
  52         int32_t k,hx,hu,ax;
  53
  54         GET_FLOAT_WORD(hx,x);
  55         ax = hx&0x7fffffff;
  56
  57         k = 1;
  58         if (hx < 0x3ed413d7) {                  /* x < 0.41422  */
  59             if(ax>=0x3f800000) {                /* x <= -1.0 */
  60                 if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
  61                 else return (x-x)/(x-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 (hx >= 0x7f800000) return x+x;
  74         if(k!=0) {
  75             if(hx<0x5a000000) {
  76                 u  = (float)1.0+x;
  77                 GET_FLOAT_WORD(hu,u);
  78                 k  = (hu>>23)-127;
  79                 /* correction term */
  80                 c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
  81                 c /= u;
  82             } else {
  83                 u  = x;
  84                 GET_FLOAT_WORD(hu,u);
  85                 k  = (hu>>23)-127;
  86                 c  = 0;
  87             }
  88             hu &= 0x007fffff;
  89             if(hu<0x3504f7) {
  90                 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
  91             } else {
  92                 k += 1;
  93                 SET_FLOAT_WORD(u,hu|0x3f000000);        /* normalize u/2 */
  94                 hu = (0x00800000-hu)>>2;
  95             }
  96             f = u-(float)1.0;
  97         }
  98         hfsq=(float)0.5*f*f;
  99         if(hu==0) {     /* |f| < 2**-20 */
 100             if(f==zero) if(k==0) return zero;
 101                         else {c += k*ln2_lo; return k*ln2_hi+c;}
 102             R = hfsq*((float)1.0-(float)0.66666666666666666*f);
 103             if(k==0) return f-R; else
 104                      return k*ln2_hi-((R-(k*ln2_lo+c))-f);
 105         }
 106         s = f/((float)2.0+f);
 107         z = s*s;
 108         R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
 109         if(k==0) return f-(hfsq-s*(hfsq+R)); else
 110                  return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
 111 }