source: azure_iot_hub/trunk/musl-1.1.18/src/math/expf.c@ 389

/* origin: FreeBSD /usr/src/lib/msun/src/e_expf.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 "libm.h"

static const float
half[2] = {0.5,-0.5},
ln2hi   = 6.9314575195e-1f,  /* 0x3f317200 */
ln2lo   = 1.4286067653e-6f,  /* 0x35bfbe8e */
invln2  = 1.4426950216e+0f,  /* 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-1f, /*  0xaaaa8f.0p-26 */
P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */

float expf(float x)
{
        float_t hi, lo, c, xx, y;
        int k, sign;
        uint32_t hx;

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

        /* special cases */
        if (hx >= 0x42aeac50) {  /* if |x| >= -87.33655f or NaN */
                if (hx > 0x7f800000) /* NaN */
                        return x;
                if (hx >= 0x42b17218 && !sign) {  /* x >= 88.722839f */
                        /* overflow */
                        x *= 0x1p127f;
                        return x;
                }
                if (sign) {
                        /* underflow */
                        FORCE_EVAL(-0x1p-149f/x);
                        if (hx >= 0x42cff1b5)  /* x <= -103.972084f */
                                return 0;
                }
        }

        /* argument reduction */
        if (hx > 0x3eb17218) {  /* if |x| > 0.5 ln2 */
                if (hx > 0x3f851592)  /* if |x| > 1.5 ln2 */
                        k = invln2*x + half[sign];
                else
                        k = 1 - sign - sign;
                hi = x - k*ln2hi;  /* k*ln2hi is exact here */
                lo = k*ln2lo;
                x = hi - lo;
        } else if (hx > 0x39000000) {  /* |x| > 2**-14 */
                k = 0;
                hi = x;
                lo = 0;
        } else {
                /* raise inexact */
                FORCE_EVAL(0x1p127f + x);
                return 1 + x;
        }

        /* x is now in primary range */
        xx = x*x;
        c = x - xx*(P1+xx*P2);
        y = 1 + (x*c/(2-c) - lo + hi);
        if (k == 0)
                return y;
        return scalbnf(y, k);
}