2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
4 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
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
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14 * documentation and/or other materials provided with the distribution.
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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28 * src/s_cexp.c converted to long double complex by Steven G. Kargl
31 #include <sys/cdefs.h>
32 __FBSDID("$FreeBSD$");
42 #include "math_private.h"
46 cexpl (long double complex z)
48 long double c, exp_x, s, x, y;
57 EXTRACT_LDBL80_WORDS(hy, ly, y);
60 /* cexp(x + I 0) = exp(x) + I 0 */
62 RETURNI(CMPLXL(expl(x), y));
63 EXTRACT_LDBL80_WORDS(hx, lx, x);
64 /* cexp(0 + I y) = cos(y) + I sin(y) */
65 if (((hx & 0x7fff) | lx) == 0) {
67 RETURNI(CMPLXL(c, s));
71 if ((hx & 0x7fff) < 0x7fff || ((hx & 0x7fff) == 0x7fff &&
72 (lx & 0x7fffffffffffffffULL) != 0)) {
73 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
74 RETURNI(CMPLXL(y - y, y - y));
75 } else if (hx & 0x8000) {
76 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
77 RETURNI(CMPLXL(0.0, 0.0));
79 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
80 RETURNI(CMPLXL(x, y - y));
85 * exp_ovfl = 11356.5234062941439497
86 * cexp_ovfl = 22755.3287906024445633
88 if ((hx == 0x400c && lx > 0xb17217f7d1cf79acULL) ||
89 (hx == 0x400d && lx < 0xb1c6a8573de9768cULL)) {
91 * x is between exp_ovfl and cexp_ovfl, so we must scale to
92 * avoid overflow in exp(x).
94 RETURNI(__ldexp_cexpl(z, 0));
98 * - x < exp_ovfl and exp(x) won't overflow (common case)
99 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
100 * - x = +-Inf (generated by exp())
101 * - x = NaN (spurious inexact exception from y)
105 RETURNI(CMPLXL(exp_x * c, exp_x * s));