/* 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,},
huge = 1.0e+30,
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 const volatile float 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;
uint32_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) /* NaN */
return x+x;
if (hx == 0x7f800000) /* exp(+-inf)={inf,0} */
return xsb==0 ? x : 0.0;
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) { /* |x|<2**-14 */
/* raise inexact */
if (huge+x > 1.0f)
return 1.0f + x;
} else
k = 0;
/* x is now in primary range */
t = x*x;
if (k >= -125)
SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23));
else
SET_FLOAT_WORD(twopk, 0x3f800000+((k+100)<<23));
c = x - t*(P1+t*P2);
if (k == 0)
return 1.0f - ((x*c)/(c - 2.0f) - x);
y = 1.0f - ((lo - (x*c)/(2.0f - c)) - hi);
if (k < -125)
return y*twopk*twom100;
if (k == 128)
return y*2.0f*0x1p127f;
return y*twopk;
}
