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  */
  15
  16 #include <sys/cdefs.h>
  17 #if defined(LIBM_SCCS) && !defined(lint)
  18 __RCSID("$NetBSD: e_expf.c,v 1.9 2002/05/26 22:01:49 wiz Exp $");
  19 #endif
  20
  21 #include "math.h"
  22 #include "math_private.h"
  23
  24 static const float huge = 1.0e+30;
  25
  26 static const float
  27 one     = 1.0,
  28 halF[2] = {0.5,-0.5,},
  29 twom100 = 7.8886090522e-31,      /* 2**-100=0x0d800000 */
  30 o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
  31 u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
  32 ln2HI[2]   ={ 6.9313812256e-01,         /* 0x3f317180 */
  33              -6.9313812256e-01,},       /* 0xbf317180 */
  34 ln2LO[2]   ={ 9.0580006145e-06,         /* 0x3717f7d1 */
  35              -9.0580006145e-06,},       /* 0xb717f7d1 */
  36 invln2 =  1.4426950216e+00,             /* 0x3fb8aa3b */
  37 P1   =  1.6666667163e-01, /* 0x3e2aaaab */
  38 P2   = -2.7777778450e-03, /* 0xbb360b61 */
  39 P3   =  6.6137559770e-05, /* 0x388ab355 */
  40 P4   = -1.6533901999e-06, /* 0xb5ddea0e */
  41 P5   =  4.1381369442e-08; /* 0x3331bb4c */
  42
  43 float
  44 __ieee754_expf(float x) /* default IEEE double exp */
  45 {
  46         float y,hi,lo,c,t;
  47         int32_t k,xsb;
  48         u_int32_t hx;
  49
  50         hi = lo = 0;
  51         k = 0;
  52         GET_FLOAT_WORD(hx,x);
  53         xsb = (hx>>31)&1;               /* sign bit of x */
  54         hx &= 0x7fffffff;               /* high word of |x| */
  55
  56     /* filter out non-finite argument */
  57         if(hx >= 0x42b17218) {                  /* if |x|>=88.721... */
  58             if(hx>0x7f800000)
  59                  return x+x;                    /* NaN */
  60             if(hx==0x7f800000)
  61                 return (xsb==0)? x:0.0;         /* exp(+-inf)={inf,0} */
  62             if(x > o_threshold) return huge*huge; /* overflow */
  63             if(x < u_threshold) return twom100*twom100; /* underflow */
  64         }
  65
  66     /* argument reduction */
  67         if(hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  68             if(hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  69                 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
  70             } else {
  71                 k  = invln2*x+halF[xsb];
  72                 t  = k;
  73                 hi = x - t*ln2HI[0];    /* t*ln2HI is exact here */
  74                 lo = t*ln2LO[0];
  75             }
  76             x  = hi - lo;
  77         }
  78         else if(hx < 0x31800000)  {     /* when |x|<2**-28 */
  79             if(huge+x>one) return one+x;/* trigger inexact */
  80         }
  81         else k = 0;
  82
  83     /* x is now in primary range */
  84         t  = x*x;
  85         c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
  86         if(k==0)        return one-((x*c)/(c-(float)2.0)-x);
  87         else            y = one-((lo-(x*c)/((float)2.0-c))-hi);
  88         if(k >= -125) {
  89             u_int32_t hy;
  90             GET_FLOAT_WORD(hy,y);
  91             SET_FLOAT_WORD(y,hy+(k<<23));       /* add k to y's exponent */
  92             return y;
  93         } else {
  94             u_int32_t hy;
  95             GET_FLOAT_WORD(hy,y);
  96             SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
  97             return y*twom100;
  98         }
  99 }