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/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.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
one = 1.0,
huge = 1.0e+30,
tiny = 1.0e-30,
o_threshold = 8.8721679688e+01, /* 0x42b17180 */
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
/*
* Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
* |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
* Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
*/
Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
float expm1f(float x)
{
float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
int32_t k,xsb;
uint32_t hx;
GET_FLOAT_WORD(hx, x);
xsb = hx&0x80000000; /* sign bit of x */
hx &= 0x7fffffff; /* high word of |x| */
/* filter out huge and non-finite argument */
if (hx >= 0x4195b844) { /* if |x|>=27*ln2 */
if (hx >= 0x42b17218) { /* if |x|>=88.721... */
if (hx > 0x7f800000) /* NaN */
return x+x;
if (hx == 0x7f800000) /* exp(+-inf)={inf,-1} */
return xsb==0 ? x : -1.0;
if (x > o_threshold)
return huge*huge; /* overflow */
}
if (xsb != 0) { /* x < -27*ln2 */
/* raise inexact */
if (x+tiny < 0.0f)
return tiny-one; /* return -1 */
}
}
/* argument reduction */
if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
if (xsb == 0) {
hi = x - ln2_hi;
lo = ln2_lo;
k = 1;
} else {
hi = x + ln2_hi;
lo = -ln2_lo;
k = -1;
}
} else {
k = invln2*x + (xsb==0 ? 0.5f : -0.5f);
t = k;
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
lo = t*ln2_lo;
}
STRICT_ASSIGN(float, x, hi - lo);
c = (hi-x)-lo;
} else if (hx < 0x33000000) { /* when |x|<2**-25, return x */
t = huge+x; /* return x with inexact flags when x!=0 */
return x - (t-(huge+x));
} else
k = 0;
/* x is now in primary range */
hfx = 0.5f*x;
hxs = x*hfx;
r1 = one+hxs*(Q1+hxs*Q2);
t = 3.0f - r1*hfx;
e = hxs*((r1-t)/(6.0f - x*t));
if (k == 0) /* c is 0 */
return x - (x*e-hxs);
SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23)); /* 2^k */
e = x*(e-c) - c;
e -= hxs;
if (k == -1)
return 0.5f*(x-e) - 0.5f;
if (k == 1) {
if (x < -0.25f)
return -2.0f*(e-(x+0.5f));
return one + 2.0f*(x-e);
}
if (k <= -2 || k > 56) { /* suffice to return exp(x)-1 */
y = one - (e - x);
if (k == 128)
y = y*2.0f*0x1p127f;
else
y = y*twopk;
return y - one;
}
t = one;
if (k < 23) {
SET_FLOAT_WORD(t, 0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
y = t - (e - x);
y = y*twopk;
} else {
SET_FLOAT_WORD(t, (0x7f-k)<<23); /* 2^-k */
y = x - (e + t);
y += one;
y = y*twopk;
}
return y;
}
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