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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 <sys/cdefs.h>
__FBSDID("$FreeBSD: head/lib/msun/src/e_expf.c 352710 2019-09-25 18:50:57Z dim $");
#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
__ieee754_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;
}
}
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