nsz Git - musl/blob - src/math/log1pf.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */
   2 /*
   3  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   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 "libm.h"
  17
  18 static const float
  19 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
  20 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
  21 two25  = 3.355443200e+07,  /* 0x4c000000 */
  22 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
  23 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
  24 Lp3 = 2.8571429849e-01, /* 3E924925 */
  25 Lp4 = 2.2222198546e-01, /* 3E638E29 */
  26 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
  27 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
  28 Lp7 = 1.4798198640e-01; /* 3E178897 */
  29
  30 static const float zero = 0.0;
  31
  32 float log1pf(float x)
  33 {
  34         float hfsq,f,c,s,z,R,u;
  35         int32_t k,hx,hu,ax;
  36
  37         GET_FLOAT_WORD(hx, x);
  38         ax = hx & 0x7fffffff;
  39
  40         k = 1;
  41         if (hx < 0x3ed413d0) {  /* 1+x < sqrt(2)+  */
  42                 if (ax >= 0x3f800000) {  /* x <= -1.0 */
  43                         if (x == -1.0f)
  44                                 return -two25/zero; /* log1p(-1)=+inf */
  45                         return (x-x)/(x-x);         /* log1p(x<-1)=NaN */
  46                 }
  47                 if (ax < 0x38000000) {   /* |x| < 2**-15 */
  48                         /* raise inexact */
  49                         if (two25 + x > zero && ax < 0x33800000)  /* |x| < 2**-24 */
  50                                 return x;
  51                         return x - x*x*0.5f;
  52                 }
  53                 if (hx > 0 || hx <= (int32_t)0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
  54                         k = 0;
  55                         f = x;
  56                         hu = 1;
  57                 }
  58         }
  59         if (hx >= 0x7f800000)
  60                 return x+x;
  61         if (k != 0) {
  62                 if (hx < 0x5a000000) {
  63                         STRICT_ASSIGN(float, u, 1.0f + x);
  64                         GET_FLOAT_WORD(hu, u);
  65                         k = (hu>>23) - 127;
  66                         /* correction term */
  67                         c = k > 0 ? 1.0f-(u-x) : x-(u-1.0f);
  68                         c /= u;
  69                 } else {
  70                         u = x;
  71                         GET_FLOAT_WORD(hu,u);
  72                         k = (hu>>23) - 127;
  73                         c = 0;
  74                 }
  75                 hu &= 0x007fffff;
  76                 /*
  77                  * The approximation to sqrt(2) used in thresholds is not
  78                  * critical.  However, the ones used above must give less
  79                  * strict bounds than the one here so that the k==0 case is
  80                  * never reached from here, since here we have committed to
  81                  * using the correction term but don't use it if k==0.
  82                  */
  83                 if (hu < 0x3504f4) {  /* u < sqrt(2) */
  84                         SET_FLOAT_WORD(u, hu|0x3f800000);  /* normalize u */
  85                 } else {
  86                         k += 1;
  87                         SET_FLOAT_WORD(u, hu|0x3f000000);  /* normalize u/2 */
  88                         hu = (0x00800000-hu)>>2;
  89                 }
  90                 f = u - 1.0f;
  91         }
  92         hfsq = 0.5f * f * f;
  93         if (hu == 0) {  /* |f| < 2**-20 */
  94                 if (f == zero) {
  95                         if (k == 0)
  96                                 return zero;
  97                         c += k*ln2_lo;
  98                         return k*ln2_hi+c;
  99                 }
 100                 R = hfsq*(1.0f - 0.66666666666666666f * f);
 101                 if (k == 0)
 102                         return f - R;
 103                 return k*ln2_hi - ((R-(k*ln2_lo+c))-f);
 104         }
 105         s = f/(2.0f + f);
 106         z = s*s;
 107         R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
 108         if (k == 0)
 109                 return f - (hfsq-s*(hfsq+R));
 110         return k*ln2_hi - ((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
 111 }