/* 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 <float.h>

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

static const float
one     = 1.0,
halF[2] = {0.5,-0.5,},
o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
ln2HI[2]   ={ 6.9314575195e-01,         /* 0x3f317200 */
             -6.9314575195e-01,},       /* 0xbf317200 */
ln2LO[2]   ={ 1.4286067653e-06,         /* 0x35bfbe8e */
             -1.4286067653e-06,},       /* 0xb5bfbe8e */
invln2 =  1.4426950216e+00,             /* 0x3fb8aa3b */
/*
 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
 */
P1 =  1.6666625440e-1,          /*  0xaaaa8f.0p-26 */
P2 = -2.7667332906e-3;          /* -0xb55215.0p-32 */

static volatile float
huge    = 1.0e+30,
twom100 = 7.8886090522e-31;      /* 2**-100=0x0d800000 */

float
expf(float x)
{
        float y,hi=0.0,lo=0.0,c,t,twopk;
        int32_t k=0,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];
            }
            STRICT_ASSIGN(float, x, hi - lo);
        }
        else if(hx < 0x39000000)  {     /* when |x|<2**-14 */
            if(huge+x>one) return one+x;/* trigger inexact */
        }
        else k = 0;

    /* x is now in primary range */
        t  = x*x;
        if(k >= -125)
            SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+k))<<23);
        else
            SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+(k+100)))<<23);
        c  = x - t*(P1+t*P2);
        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) {
            if(k==128) return y*2.0F*0x1p127F;
            return y*twopk;
        } else {
            return y*twopk*twom100;
        }
}