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/* 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 hi, lo, c, xx;
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 >= 0x42b17218) { /* if |x| >= 88.722839f or NaN */
if (hx > 0x7f800000) /* NaN */
return x;
if (!sign) {
/* overflow if x!=inf */
STRICT_ASSIGN(float, x, x * 0x1p127f);
return x;
}
if (hx == 0x7f800000) /* -inf */
return 0;
if (hx >= 0x42cff1b5) { /* x <= -103.972084f */
/* underflow */
STRICT_ASSIGN(float, x, 0x1p-100f*0x1p-100f);
return x;
}
}
/* 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;
STRICT_ASSIGN(float, 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);
x = 1 + (x*c/(2-c) - lo + hi);
if (k == 0)
return x;
return scalbnf(x, k);
}
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