src/math/expf.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/e_expf.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 half[2] = {0.5,-0.5},
  20 ln2hi   = 6.9314575195e-1f,  /* 0x3f317200 */
  21 ln2lo   = 1.4286067653e-6f,  /* 0x35bfbe8e */
  22 invln2  = 1.4426950216e+0f,  /* 0x3fb8aa3b */
  23 /*
  24  * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
  25  * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
  26  */
  27 P1 =  1.6666625440e-1f, /*  0xaaaa8f.0p-26 */
  28 P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
  29
  30 float expf(float x)
  31 {
  32         float hi, lo, c, xx;
  33         int k, sign;
  34         uint32_t hx;
  35
  36         GET_FLOAT_WORD(hx, x);
  37         sign = hx >> 31;   /* sign bit of x */
  38         hx &= 0x7fffffff;  /* high word of |x| */
  39
  40         /* special cases */
  41         if (hx >= 0x42b17218) {  /* if |x| >= 88.722839f or NaN */
  42                 if (hx > 0x7f800000)  /* NaN */
  43                         return x;
  44                 if (!sign) {
  45                         /* overflow if x!=inf */
  46                         STRICT_ASSIGN(float, x, x * 0x1p127f);
  47                         return x;
  48                 }
  49                 if (hx == 0x7f800000)  /* -inf */
  50                         return 0;
  51                 if (hx >= 0x42cff1b5) { /* x <= -103.972084f */
  52                         /* underflow */
  53                         STRICT_ASSIGN(float, x, 0x1p-100f*0x1p-100f);
  54                         return x;
  55                 }
  56         }
  57
  58         /* argument reduction */
  59         if (hx > 0x3eb17218) {  /* if |x| > 0.5 ln2 */
  60                 if (hx > 0x3f851592)  /* if |x| > 1.5 ln2 */
  61                         k = invln2*x + half[sign];
  62                 else
  63                         k = 1 - sign - sign;
  64                 hi = x - k*ln2hi;  /* k*ln2hi is exact here */
  65                 lo = k*ln2lo;
  66                 STRICT_ASSIGN(float, x, hi - lo);
  67         } else if (hx > 0x39000000) {  /* |x| > 2**-14 */
  68                 k = 0;
  69                 hi = x;
  70                 lo = 0;
  71         } else {
  72                 /* raise inexact */
  73                 FORCE_EVAL(0x1p127f + x);
  74                 return 1 + x;
  75         }
  76
  77         /* x is now in primary range */
  78         xx = x*x;
  79         c = x - xx*(P1+xx*P2);
  80         x = 1 + (x*c/(2-c) - lo + hi);
  81         if (k == 0)
  82                 return x;
  83         return scalbnf(x, k);
  84 }