1/*-
2 * SPDX-License-Identifier: BSD-3-Clause
3 *
4 * Copyright (c) 1985, 1993
5 *	The Regents of the University of California.  All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 *    notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 *    notice, this list of conditions and the following disclaimer in the
14 *    documentation and/or other materials provided with the distribution.
15 * 3. Neither the name of the University nor the names of its contributors
16 *    may be used to endorse or promote products derived from this software
17 *    without specific prior written permission.
18 *
19 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
20 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
21 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
22 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
23 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
24 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
25 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
26 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
27 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
28 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
29 * SUCH DAMAGE.
30 */
31
32/*
33 * See bsdsrc/b_exp.c for implementation details.
34 *
35 * bsdrc/b_exp.c converted to long double by Steven G. Kargl.
36 */
37
38#include "math_private.h"
39
40static const union ieee_ext_u
41    p0u = LD80C(0xaaaaaaaaaaaaaaab,    -3,  1.66666666666666666671e-01L),
42    p1u = LD80C(0xb60b60b60b60b59a,    -9, -2.77777777777777775377e-03L),
43    p2u = LD80C(0x8ab355e008a3cfce,   -14,  6.61375661375629297465e-05L),
44    p3u = LD80C(0xddebbc994b0c1376,   -20, -1.65343915327882529784e-06L),
45    p4u = LD80C(0xb354784cb4ef4c41,   -25,  4.17535101591534118469e-08L),
46    p5u = LD80C(0x913e8a718382ce75,   -30, -1.05679137034774806475e-09L),
47    p6u = LD80C(0xe8f0042aa134502e,   -36,  2.64819349895429516863e-11L);
48#define	p1	(p0u.extu_ld)
49#define	p2	(p1u.extu_ld)
50#define	p3	(p2u.extu_ld)
51#define	p4	(p3u.extu_ld)
52#define	p5	(p4u.extu_ld)
53#define	p6	(p5u.extu_ld)
54#define	p7	(p6u.extu_ld)
55
56/*
57 * lnhuge = (LDBL_MAX_EXP + 9) * log(2.)
58 * lntiny = (LDBL_MIN_EXP - 64 - 10) * log(2.)
59 * invln2 = 1 / log(2.)
60 */
61static const union ieee_ext_u
62ln2hiu  = LD80C(0xb17217f700000000,  -1,  6.93147180369123816490e-01L),
63ln2lou  = LD80C(0xd1cf79abc9e3b398, -33,  1.90821492927058781614e-10L),
64lnhugeu = LD80C(0xb18b0c0330a8fad9,  13,  1.13627617309191834574e+04L),
65lntinyu = LD80C(0xb236f28a68bc3bd7,  13, -1.14057368561139000667e+04L),
66invln2u = LD80C(0xb8aa3b295c17f0bc,   0,  1.44269504088896340739e+00L);
67#define	ln2hi	(ln2hiu.extu_ld)
68#define ln2lo	(ln2lou.extu_ld)
69#define lnhuge	(lnhugeu.extu_ld)
70#define	lntiny	(lntinyu.extu_ld)
71#define	invln2	(invln2u.extu_ld)
72
73/* returns exp(r = x + c) for |c| < |x| with no overlap.  */
74
75static long double
76__exp__D(long double x, long double c)
77{
78	long double hi, lo, z;
79	int k;
80
81	if (x != x)	/* x is NaN. */
82		return(x);
83
84	if (x <= lnhuge) {
85		if (x >= lntiny) {
86			/* argument reduction: x --> x - k*ln2 */
87			z = invln2 * x;
88			k = z + copysignl(0.5L, x);
89
90		    	/*
91			 * Express (x + c) - k * ln2 as hi - lo.
92			 * Let x = hi - lo rounded.
93			 */
94			hi = x - k * ln2hi;	/* Exact. */
95			lo = k * ln2lo - c;
96			x = hi - lo;
97
98			/* Return 2^k*[1+x+x*c/(2+c)]  */
99			z = x * x;
100			c = x - z * (p1 + z * (p2 + z * (p3 + z * (p4 +
101			    z * (p5 + z * (p6 + z * p7))))));
102			c = (x * c) / (2 - c);
103
104			return (ldexpl(1 + (hi - (lo - c)), k));
105		} else {
106			/* exp(-INF) is 0. exp(-big) underflows to 0.  */
107			return (isfinite(x) ? ldexpl(1., -5000) : 0);
108		}
109	} else
110		/* exp(INF) is INF, exp(+big#) overflows to INF */
111		return (isfinite(x) ? ldexpl(1., 5000) : x);
112}
113