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/*-
* SPDX-License-Identifier: BSD-3-Clause
*
* Copyright (c) 1985, 1993
* The Regents of the University of California. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
/*
* See bsdsrc/b_exp.c for implementation details.
*
* bsdrc/b_exp.c converted to long double by Steven G. Kargl.
*/
#include "../ld/fpmath.h"
#include "../ld/math_private.h"
static const union IEEEl2bits
p0u = LD80C(0xaaaaaaaaaaaaaaab, -3, 1.66666666666666666671e-01L),
p1u = LD80C(0xb60b60b60b60b59a, -9, -2.77777777777777775377e-03L),
p2u = LD80C(0x8ab355e008a3cfce, -14, 6.61375661375629297465e-05L),
p3u = LD80C(0xddebbc994b0c1376, -20, -1.65343915327882529784e-06L),
p4u = LD80C(0xb354784cb4ef4c41, -25, 4.17535101591534118469e-08L),
p5u = LD80C(0x913e8a718382ce75, -30, -1.05679137034774806475e-09L),
p6u = LD80C(0xe8f0042aa134502e, -36, 2.64819349895429516863e-11L);
#define p1 (p0u.e)
#define p2 (p1u.e)
#define p3 (p2u.e)
#define p4 (p3u.e)
#define p5 (p4u.e)
#define p6 (p5u.e)
#define p7 (p6u.e)
/*
* lnhuge = (LDBL_MAX_EXP + 9) * log(2.)
* lntiny = (LDBL_MIN_EXP - 64 - 10) * log(2.)
* invln2 = 1 / log(2.)
*/
static const union IEEEl2bits
ln2hiu = LD80C(0xb17217f700000000, -1, 6.93147180369123816490e-01L),
ln2lou = LD80C(0xd1cf79abc9e3b398, -33, 1.90821492927058781614e-10L),
lnhugeu = LD80C(0xb18b0c0330a8fad9, 13, 1.13627617309191834574e+04L),
lntinyu = LD80C(0xb236f28a68bc3bd7, 13, -1.14057368561139000667e+04L),
invln2u = LD80C(0xb8aa3b295c17f0bc, 0, 1.44269504088896340739e+00L);
#define ln2hi (ln2hiu.e)
#define ln2lo (ln2lou.e)
#define lnhuge (lnhugeu.e)
#define lntiny (lntinyu.e)
#define invln2 (invln2u.e)
/* returns exp(r = x + c) for |c| < |x| with no overlap. */
static long double
__exp__D(long double x, long double c)
{
long double hi, lo, z;
int k;
if (x != x) /* x is NaN. */
return(x);
if (x <= lnhuge) {
if (x >= lntiny) {
/* argument reduction: x --> x - k*ln2 */
z = invln2 * x;
k = z + copysignl(0.5L, x);
/*
* Express (x + c) - k * ln2 as hi - lo.
* Let x = hi - lo rounded.
*/
hi = x - k * ln2hi; /* Exact. */
lo = k * ln2lo - c;
x = hi - lo;
/* Return 2^k*[1+x+x*c/(2+c)] */
z = x * x;
c = x - z * (p1 + z * (p2 + z * (p3 + z * (p4 +
z * (p5 + z * (p6 + z * p7))))));
c = (x * c) / (2 - c);
return (ldexpl(1 + (hi - (lo - c)), k));
} else {
/* exp(-INF) is 0. exp(-big) underflows to 0. */
return (isfinite(x) ? ldexpl(1., -5000) : 0);
}
} else
/* exp(INF) is INF, exp(+big#) overflows to INF */
return (isfinite(x) ? ldexpl(1., 5000) : x);
}
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