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  * $FreeBSD: head/lib/msun/src/s_log1pf.c 251024 2013-05-27 08:50:10Z das $
  15  */
  16
  17 #include <float.h>
  18
  19 #include "math.h"
  20 #include "math_private.h"
  21
  22 static const float
  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 static const float zero = 0.0;
  35 static volatile float vzero = 0.0;
  36
  37 float
  38 log1pf(float x)
  39 {
  40         float hfsq,f,c,s,z,R,u;
  41         int32_t k,hx,hu,ax;
  42
  43         GET_FLOAT_WORD(hx,x);
  44         ax = hx&0x7fffffff;
  45
  46         k = 1;
  47         if (hx < 0x3ed413d0) {                  /* 1+x < sqrt(2)+  */
  48             if(ax>=0x3f800000) {                /* x <= -1.0 */
  49                 if(x==(float)-1.0) return -two25/vzero; /* log1p(-1)=+inf */
  50                 else return (x-x)/(x-x);        /* log1p(x<-1)=NaN */
  51             }
  52             if(ax<0x38000000) {                 /* |x| < 2**-15 */
  53                 if(two25+x>zero                 /* raise inexact */
  54                     &&ax<0x33800000)            /* |x| < 2**-24 */
  55                     return x;
  56                 else
  57                     return x - x*x*(float)0.5;
  58             }
  59             if(hx>0||hx<=((int32_t)0xbe95f619)) {
  60                 k=0;f=x;hu=1;}          /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
  61         }
  62         if (hx >= 0x7f800000) return x+x;
  63         if(k!=0) {
  64             if(hx<0x5a000000) {
  65                 STRICT_ASSIGN(float,u,(float)1.0+x);
  66                 GET_FLOAT_WORD(hu,u);
  67                 k  = (hu>>23)-127;
  68                 /* correction term */
  69                 c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
  70                 c /= u;
  71             } else {
  72                 u  = x;
  73                 GET_FLOAT_WORD(hu,u);
  74                 k  = (hu>>23)-127;
  75                 c  = 0;
  76             }
  77             hu &= 0x007fffff;
  78             /*
  79              * The approximation to sqrt(2) used in thresholds is not
  80              * critical.  However, the ones used above must give less
  81              * strict bounds than the one here so that the k==0 case is
  82              * never reached from here, since here we have committed to
  83              * using the correction term but don't use it if k==0.
  84              */
  85             if(hu<0x3504f4) {                   /* u < sqrt(2) */
  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) {
  97                 if(k==0) {
  98                     return zero;
  99                 } else {
 100                     c += k*ln2_lo;
 101                     return k*ln2_hi+c;
 102                 }
 103             }
 104             R = hfsq*((float)1.0-(float)0.66666666666666666*f);
 105             if(k==0) return f-R; else
 106                      return k*ln2_hi-((R-(k*ln2_lo+c))-f);
 107         }
 108         s = f/((float)2.0+f);
 109         z = s*s;
 110         R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
 111         if(k==0) return f-(hfsq-s*(hfsq+R)); else
 112                  return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
 113 }