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 static volatile float vzero = 0.0;
  38
  39 float
  40 log1pf(float x)
  41 {
  42         float hfsq,f,c,s,z,R,u;
  43         int32_t k,hx,hu,ax;
  44
  45         GET_FLOAT_WORD(hx,x);
  46         ax = hx&0x7fffffff;
  47
  48         k = 1;
  49         if (hx < 0x3ed413d0) {                  /* 1+x < sqrt(2)+  */
  50             if(ax>=0x3f800000) {                /* x <= -1.0 */
  51                 if(x==(float)-1.0) return -two25/vzero; /* log1p(-1)=+inf */
  52                 else return (x-x)/(x-x);        /* log1p(x<-1)=NaN */
  53             }
  54             if(ax<0x38000000) {                 /* |x| < 2**-15 */
  55                 if(two25+x>zero                 /* raise inexact */
  56                     &&ax<0x33800000)            /* |x| < 2**-24 */
  57                     return x;
  58                 else
  59                     return x - x*x*(float)0.5;
  60             }
  61             if(hx>0||hx<=((int32_t)0xbe95f619)) {
  62                 k=0;f=x;hu=1;}          /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
  63         }
  64         if (hx >= 0x7f800000) return x+x;
  65         if(k!=0) {
  66             if(hx<0x5a000000) {
  67                 STRICT_ASSIGN(float,u,(float)1.0+x);
  68                 GET_FLOAT_WORD(hu,u);
  69                 k  = (hu>>23)-127;
  70                 /* correction term */
  71                 c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
  72                 c /= u;
  73             } else {
  74                 u  = x;
  75                 GET_FLOAT_WORD(hu,u);
  76                 k  = (hu>>23)-127;
  77                 c  = 0;
  78             }
  79             hu &= 0x007fffff;
  80             /*
  81              * The approximation to sqrt(2) used in thresholds is not
  82              * critical.  However, the ones used above must give less
  83              * strict bounds than the one here so that the k==0 case is
  84              * never reached from here, since here we have committed to
  85              * using the correction term but don't use it if k==0.
  86              */
  87             if(hu<0x3504f4) {                   /* u < sqrt(2) */
  88                 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
  89             } else {
  90                 k += 1;
  91                 SET_FLOAT_WORD(u,hu|0x3f000000);        /* normalize u/2 */
  92                 hu = (0x00800000-hu)>>2;
  93             }
  94             f = u-(float)1.0;
  95         }
  96         hfsq=(float)0.5*f*f;
  97         if(hu==0) {     /* |f| < 2**-20 */
  98             if(f==zero) {
  99                 if(k==0) {
 100                     return zero;
 101                 } else {
 102                     c += k*ln2_lo;
 103                     return k*ln2_hi+c;
 104                 }
 105             }
 106             R = hfsq*((float)1.0-(float)0.66666666666666666*f);
 107             if(k==0) return f-R; else
 108                      return k*ln2_hi-((R-(k*ln2_lo+c))-f);
 109         }
 110         s = f/((float)2.0+f);
 111         z = s*s;
 112         R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
 113         if(k==0) return f-(hfsq-s*(hfsq+R)); else
 114                  return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
 115 }