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 #include <sys/cdefs.h>
  17 __FBSDID("$FreeBSD$");
  18
  19 #include <float.h>
  20
  21 #include "math.h"
  22 #include "math_private.h"
  23
  24 static const float
  25 ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
  26 ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
  27 two25 =    3.355443200e+07,     /* 0x4c000000 */
  28 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
  29 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
  30 Lp3 = 2.8571429849e-01, /* 3E924925 */
  31 Lp4 = 2.2222198546e-01, /* 3E638E29 */
  32 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
  33 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
  34 Lp7 = 1.4798198640e-01; /* 3E178897 */
  35
  36 static const float zero = 0.0;
  37
  38 float
  39 log1pf(float x)
  40 {
  41         float hfsq,f,c,s,z,R,u;
  42         int32_t k,hx,hu,ax;
  43
  44         GET_FLOAT_WORD(hx,x);
  45         ax = hx&0x7fffffff;
  46
  47         k = 1;
  48         if (hx < 0x3ed413d0) {                  /* 1+x < sqrt(2)+  */
  49             if(ax>=0x3f800000) {                /* x <= -1.0 */
  50                 if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
  51                 else return (x-x)/(x-x);        /* log1p(x<-1)=NaN */
  52             }
  53             if(ax<0x38000000) {                 /* |x| < 2**-15 */
  54                 if(two25+x>zero                 /* raise inexact */
  55                     &&ax<0x33800000)            /* |x| < 2**-24 */
  56                     return x;
  57                 else
  58                     return x - x*x*(float)0.5;
  59             }
  60             if(hx>0||hx<=((int32_t)0xbe95f619)) {
  61                 k=0;f=x;hu=1;}          /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
  62         }
  63         if (hx >= 0x7f800000) return x+x;
  64         if(k!=0) {
  65             if(hx<0x5a000000) {
  66                 STRICT_ASSIGN(float,u,(float)1.0+x);
  67                 GET_FLOAT_WORD(hu,u);
  68                 k  = (hu>>23)-127;
  69                 /* correction term */
  70                 c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
  71                 c /= u;
  72             } else {
  73                 u  = x;
  74                 GET_FLOAT_WORD(hu,u);
  75                 k  = (hu>>23)-127;
  76                 c  = 0;
  77             }
  78             hu &= 0x007fffff;
  79             /*
  80              * The approximation to sqrt(2) used in thresholds is not
  81              * critical.  However, the ones used above must give less
  82              * strict bounds than the one here so that the k==0 case is
  83              * never reached from here, since here we have committed to
  84              * using the correction term but don't use it if k==0.
  85              */
  86             if(hu<0x3504f4) {                   /* u < sqrt(2) */
  87                 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
  88             } else {
  89                 k += 1;
  90                 SET_FLOAT_WORD(u,hu|0x3f000000);        /* normalize u/2 */
  91                 hu = (0x00800000-hu)>>2;
  92             }
  93             f = u-(float)1.0;
  94         }
  95         hfsq=(float)0.5*f*f;
  96         if(hu==0) {     /* |f| < 2**-20 */
  97             if(f==zero) {
  98                 if(k==0) {
  99                     return zero;
 100                 } else {
 101                     c += k*ln2_lo;
 102                     return k*ln2_hi+c;
 103                 }
 104             }
 105             R = hfsq*((float)1.0-(float)0.66666666666666666*f);
 106             if(k==0) return f-R; else
 107                      return k*ln2_hi-((R-(k*ln2_lo+c))-f);
 108         }
 109         s = f/((float)2.0+f);
 110         z = s*s;
 111         R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
 112         if(k==0) return f-(hfsq-s*(hfsq+R)); else
 113                  return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
 114 }