sysdeps/libm-ieee754/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  */
  15
  16 #if defined(LIBM_SCCS) && !defined(lint)
  17 static char rcsid[] = "$NetBSD: e_expf.c,v 1.6 1996/04/08 15:43:43 phil Exp $";
  18 #endif
  19
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 static const float huge = 1.0e+30;
  24
  25 #ifdef __STDC__
  26 static const float
  27 #else
  28 static float
  29 #endif
  30 one     = 1.0,
  31 halF[2] = {0.5,-0.5,},
  32 twom100 = 7.8886090522e-31,      /* 2**-100=0x0d800000 */
  33 o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
  34 u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
  35 ln2HI[2]   ={ 6.9313812256e-01,         /* 0x3f317180 */
  36              -6.9313812256e-01,},       /* 0xbf317180 */
  37 ln2LO[2]   ={ 9.0580006145e-06,         /* 0x3717f7d1 */
  38              -9.0580006145e-06,},       /* 0xb717f7d1 */
  39 invln2 =  1.4426950216e+00,             /* 0x3fb8aa3b */
  40 P1   =  1.6666667163e-01, /* 0x3e2aaaab */
  41 P2   = -2.7777778450e-03, /* 0xbb360b61 */
  42 P3   =  6.6137559770e-05, /* 0x388ab355 */
  43 P4   = -1.6533901999e-06, /* 0xb5ddea0e */
  44 P5   =  4.1381369442e-08; /* 0x3331bb4c */
  45
  46 #ifdef __STDC__
  47         float __ieee754_expf(float x)   /* default IEEE double exp */
  48 #else
  49         float __ieee754_expf(x) /* default IEEE double exp */
  50         float x;
  51 #endif
  52 {
  53         float y,hi,lo,c,t;
  54         int32_t k,xsb;
  55         u_int32_t hx;
  56
  57         GET_FLOAT_WORD(hx,x);
  58         xsb = (hx>>31)&1;               /* sign bit of x */
  59         hx &= 0x7fffffff;               /* high word of |x| */
  60
  61     /* filter out non-finite argument */
  62         if(hx >= 0x42b17218) {                  /* if |x|>=88.721... */
  63             if(hx>0x7f800000)
  64                  return x+x;                    /* NaN */
  65             if(hx==0x7f800000)
  66                 return (xsb==0)? x:0.0;         /* exp(+-inf)={inf,0} */
  67             if(x > o_threshold) return huge*huge; /* overflow */
  68             if(x < u_threshold) return twom100*twom100; /* underflow */
  69         }
  70
  71     /* argument reduction */
  72         if(hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  73             if(hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  74                 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
  75             } else {
  76                 k  = invln2*x+halF[xsb];
  77                 t  = k;
  78                 hi = x - t*ln2HI[0];    /* t*ln2HI is exact here */
  79                 lo = t*ln2LO[0];
  80             }
  81             x  = hi - lo;
  82         }
  83         else if(hx < 0x31800000)  {     /* when |x|<2**-28 */
  84             if(huge+x>one) return one+x;/* trigger inexact */
  85         }
  86         else k = 0;
  87
  88     /* x is now in primary range */
  89         t  = x*x;
  90         c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
  91         if(k==0)        return one-((x*c)/(c-(float)2.0)-x);
  92         else            y = one-((lo-(x*c)/((float)2.0-c))-hi);
  93         if(k >= -125) {
  94             u_int32_t hy;
  95             GET_FLOAT_WORD(hy,y);
  96             SET_FLOAT_WORD(y,hy+(k<<23));       /* add k to y's exponent */
  97             return y;
  98         } else {
  99             u_int32_t hy;
 100             GET_FLOAT_WORD(hy,y);
 101             SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
 102             return y*twom100;
 103         }
 104 }