lib/libm/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 #include "math.h"
  17 #include "math_private.h"
  18
  19 static const float
  20 ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
  21 ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
  22 two25 =    3.355443200e+07,     /* 0x4c000000 */
  23 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
  24 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
  25 Lp3 = 2.8571429849e-01, /* 3E924925 */
  26 Lp4 = 2.2222198546e-01, /* 3E638E29 */
  27 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
  28 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
  29 Lp7 = 1.4798198640e-01; /* 3E178897 */
  30
  31 static const float zero = 0.0;
  32
  33 float
  34 log1pf(float x)
  35 {
  36         float hfsq,f,c,s,z,R,u;
  37         int32_t k,hx,hu,ax;
  38
  39         GET_FLOAT_WORD(hx,x);
  40         ax = hx&0x7fffffff;
  41
  42         k = 1;
  43         if (hx < 0x3ed413d7) {                  /* x < 0.41422  */
  44             if(ax>=0x3f800000) {                /* x <= -1.0 */
  45                 if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
  46                 else return (x-x)/(x-x);        /* log1p(x<-1)=NaN */
  47             }
  48             if(ax<0x31000000) {                 /* |x| < 2**-29 */
  49                 if(two25+x>zero                 /* raise inexact */
  50                     &&ax<0x24800000)            /* |x| < 2**-54 */
  51                     return x;
  52                 else
  53                     return x - x*x*(float)0.5;
  54             }
  55             if(hx>0||hx<=((int32_t)0xbe95f61f)) {
  56                 k=0;f=x;hu=1;}  /* -0.2929<x<0.41422 */
  57         }
  58         if (hx >= 0x7f800000) return x+x;
  59         if(k!=0) {
  60             if(hx<0x5a000000) {
  61                 u  = (float)1.0+x;
  62                 GET_FLOAT_WORD(hu,u);
  63                 k  = (hu>>23)-127;
  64                 /* correction term */
  65                 c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
  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             if(hu<0x3504f7) {
  75                 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
  76             } else {
  77                 k += 1;
  78                 SET_FLOAT_WORD(u,hu|0x3f000000);        /* normalize u/2 */
  79                 hu = (0x00800000-hu)>>2;
  80             }
  81             f = u-(float)1.0;
  82         }
  83         hfsq=(float)0.5*f*f;
  84         if(hu==0) {     /* |f| < 2**-20 */
  85             if(f==zero) if(k==0) return zero;
  86                         else {c += k*ln2_lo; return k*ln2_hi+c;}
  87             R = hfsq*((float)1.0-(float)0.66666666666666666*f);
  88             if(k==0) return f-R; else
  89                      return k*ln2_hi-((R-(k*ln2_lo+c))-f);
  90         }
  91         s = f/((float)2.0+f);
  92         z = s*s;
  93         R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
  94         if(k==0) return f-(hfsq-s*(hfsq+R)); else
  95                  return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
  96 }