lib/libm/src/e_expf.c

   1 /* e_expf.c -- float version of e_exp.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/e_expf.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 one     = 1.0,
  24 halF[2] = {0.5,-0.5,},
  25 o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
  26 u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
  27 ln2HI[2]   ={ 6.9314575195e-01,         /* 0x3f317200 */
  28              -6.9314575195e-01,},       /* 0xbf317200 */
  29 ln2LO[2]   ={ 1.4286067653e-06,         /* 0x35bfbe8e */
  30              -1.4286067653e-06,},       /* 0xb5bfbe8e */
  31 invln2 =  1.4426950216e+00,             /* 0x3fb8aa3b */
  32 /*
  33  * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
  34  * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
  35  */
  36 P1 =  1.6666625440e-1,          /*  0xaaaa8f.0p-26 */
  37 P2 = -2.7667332906e-3;          /* -0xb55215.0p-32 */
  38
  39 static volatile float
  40 huge    = 1.0e+30,
  41 twom100 = 7.8886090522e-31;      /* 2**-100=0x0d800000 */
  42
  43 float
  44 __ieee754_expf(float x)
  45 {
  46         float y,hi=0.0,lo=0.0,c,t,twopk;
  47         int32_t k=0,xsb;
  48         u_int32_t hx;
  49
  50         GET_FLOAT_WORD(hx,x);
  51         xsb = (hx>>31)&1;               /* sign bit of x */
  52         hx &= 0x7fffffff;               /* high word of |x| */
  53
  54     /* filter out non-finite argument */
  55         if(hx >= 0x42b17218) {                  /* if |x|>=88.721... */
  56             if(hx>0x7f800000)
  57                  return x+x;                    /* NaN */
  58             if(hx==0x7f800000)
  59                 return (xsb==0)? x:0.0;         /* exp(+-inf)={inf,0} */
  60             if(x > o_threshold) return huge*huge; /* overflow */
  61             if(x < u_threshold) return twom100*twom100; /* underflow */
  62         }
  63
  64     /* argument reduction */
  65         if(hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  66             if(hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  67                 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
  68             } else {
  69                 k  = invln2*x+halF[xsb];
  70                 t  = k;
  71                 hi = x - t*ln2HI[0];    /* t*ln2HI is exact here */
  72                 lo = t*ln2LO[0];
  73             }
  74             STRICT_ASSIGN(float, x, hi - lo);
  75         }
  76         else if(hx < 0x39000000)  {     /* when |x|<2**-14 */
  77             if(huge+x>one) return one+x;/* trigger inexact */
  78         }
  79         else k = 0;
  80
  81     /* x is now in primary range */
  82         t  = x*x;
  83         if(k >= -125)
  84             SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));
  85         else
  86             SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23));
  87         c  = x - t*(P1+t*P2);
  88         if(k==0)        return one-((x*c)/(c-(float)2.0)-x);
  89         else            y = one-((lo-(x*c)/((float)2.0-c))-hi);
  90         if(k >= -125) {
  91             if(k==128) return y*2.0F*0x1p127F;
  92             return y*twopk;
  93         } else {
  94             return y*twopk*twom100;
  95         }
  96 }