e_expf.c

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/* e_expf.c -- float version of e_exp.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

#include "math.h"
#include "math_private.h"

static const volatile float huge = 1.0e+30;

static const float
one = 1.0,
halF[2] = {0.5,-0.5,},
twom100 = 7.8886090522e-31,      /* 2**-100=0x0d800000 */
o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
ln2HI[2]   ={ 6.9313812256e-01,     /* 0x3f317180 */
         -6.9313812256e-01,},   /* 0xbf317180 */
ln2LO[2]   ={ 9.0580006145e-06,     /* 0x3717f7d1 */
         -9.0580006145e-06,},   /* 0xb717f7d1 */
invln2 =  1.4426950216e+00,         /* 0x3fb8aa3b */
P1   =  1.6666667163e-01, /* 0x3e2aaaab */
P2   = -2.7777778450e-03, /* 0xbb360b61 */
P3   =  6.6137559770e-05, /* 0x388ab355 */
P4   = -1.6533901999e-06, /* 0xb5ddea0e */
P5   =  4.1381369442e-08; /* 0x3331bb4c */

float
expf(float x)   /* default IEEE double exp */
{
    float y,hi,lo,c,t;
    int32_t k,xsb;
    u_int32_t hx;

    GET_FLOAT_WORD(hx,x);
    xsb = (hx>>31)&1;       /* sign bit of x */
    hx &= 0x7fffffff;       /* high word of |x| */

    /* filter out non-finite argument */
    if(hx >= 0x42b17218) {          /* if |x|>=88.721... */
        if(hx>0x7f800000)
         return x+x;            /* NaN */
            if(hx==0x7f800000)
        return (xsb==0)? x:0.0;     /* exp(+-inf)={inf,0} */
        if(x > o_threshold) return huge*huge; /* overflow */
        if(x < u_threshold) return twom100*twom100; /* underflow */
    }

    /* argument reduction */
    if(hx > 0x3eb17218) {       /* if  |x| > 0.5 ln2 */ 
        if(hx < 0x3F851592) {   /* and |x| < 1.5 ln2 */
        hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
        } else {
        k  = invln2*x+halF[xsb];
        t  = k;
        hi = x - t*ln2HI[0];    /* t*ln2HI is exact here */
        lo = t*ln2LO[0];
        }
        x  = hi - lo;
    } 
    else if(hx < 0x31800000)  { /* when |x|<2**-28 */
        if(huge+x>one) return one+x;/* trigger inexact */
    }
    else k = 0;

    /* x is now in primary range */
    t  = x*x;
    c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
    if(k==0)    return one-((x*c)/(c-(float)2.0)-x); 
    else        y = one-((lo-(x*c)/((float)2.0-c))-hi);
    if(k >= -125) {
        u_int32_t hy;
        GET_FLOAT_WORD(hy,y);
        SET_FLOAT_WORD(y,hy+(k<<23));   /* add k to y's exponent */
        return y;
    } else {
        u_int32_t hy;
        GET_FLOAT_WORD(hy,y);
        SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
        return y*twom100;
    }
}