1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause 3 * 4 * Copyright (c) 2019 Steven G. Kargl <kargl@FreeBSD.ORG> 5 * 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 * 16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26 * SUCH DAMAGE. 27 */ 28 29 #include <sys/cdefs.h> 30 __FBSDID("$FreeBSD$"); 31 32 #include <complex.h> 33 #include <float.h> 34 #include <math.h> 35 36 #include "fpmath.h" 37 #include "math_private.h" 38 #include "k_expl.h" 39 40 /* XXX cexpl() should be converted to use bits likeo src/s_cexp.c. */ 41 42 static const long double 43 cexp_ovfl = 2.27892930024498818830197576893019292e+04L, 44 exp_ovfl = 1.13565234062941439494919310779707649e+04L; 45 46 long double complex 47 cexpl(long double complex z) 48 { 49 long double c, exp_x, s, x, y; 50 51 x = creall(z); 52 y = cimagl(z); 53 54 /* cexp(x + I 0) = exp(x) + I 0 */ 55 if (y == 0) 56 return (CMPLXL(expl(x), y)); 57 /* cexp(0 + I y) = cos(y) + I sin(y) */ 58 if (x == 0) { 59 sincosl(y, &s, &c); 60 return (CMPLXL(c, s)); 61 } 62 63 if (!isfinite(y)) { 64 if (isfinite(x) || isnan(x)) { 65 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ 66 return (CMPLXL(y - y, y - y)); 67 } else if (isinf(x) && copysignl(1.L, x) < 0) { 68 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ 69 return (CMPLXL(0.0, 0.0)); 70 } else { 71 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ 72 return (CMPLXL(x, y - y)); 73 } 74 } 75 76 if (x > exp_ovfl && x < cexp_ovfl) { 77 /* 78 * x is between exp_ovfl and cexp_ovfl, so we must scale to 79 * avoid overflow in exp(x). 80 */ 81 return (__ldexp_cexpl(z, 0)); 82 } else { 83 /* 84 * Cases covered here: 85 * - x < exp_ovfl and exp(x) won't overflow (common case) 86 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 87 * - x = +-Inf (generated by exp()) 88 * - x = NaN (spurious inexact exception from y) 89 */ 90 exp_x = expl(x); 91 sincosl(y, &s, &c); 92 return (CMPLXL(exp_x * c, exp_x * s)); 93 } 94 } 95