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 #include <complex.h> 31 #include <float.h> 32 #include <math.h> 33 34 #include "fpmath.h" 35 #include "math_private.h" 36 #include "k_expl.h" 37 38 /* XXX cexpl() should be converted to use bits likeo src/s_cexp.c. */ 39 40 static const long double 41 cexp_ovfl = 2.27892930024498818830197576893019292e+04L, 42 exp_ovfl = 1.13565234062941439494919310779707649e+04L; 43 44 long double complex 45 cexpl(long double complex z) 46 { 47 long double c, exp_x, s, x, y; 48 49 x = creall(z); 50 y = cimagl(z); 51 52 /* cexp(x + I 0) = exp(x) + I 0 */ 53 if (y == 0) 54 return (CMPLXL(expl(x), y)); 55 /* cexp(0 + I y) = cos(y) + I sin(y) */ 56 if (x == 0) { 57 sincosl(y, &s, &c); 58 return (CMPLXL(c, s)); 59 } 60 61 if (!isfinite(y)) { 62 if (isfinite(x) || isnan(x)) { 63 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ 64 return (CMPLXL(y - y, y - y)); 65 } else if (isinf(x) && copysignl(1.L, x) < 0) { 66 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ 67 return (CMPLXL(0.0, 0.0)); 68 } else { 69 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ 70 return (CMPLXL(x, y - y)); 71 } 72 } 73 74 if (x > exp_ovfl && x < cexp_ovfl) { 75 /* 76 * x is between exp_ovfl and cexp_ovfl, so we must scale to 77 * avoid overflow in exp(x). 78 */ 79 return (__ldexp_cexpl(z, 0)); 80 } else { 81 /* 82 * Cases covered here: 83 * - x < exp_ovfl and exp(x) won't overflow (common case) 84 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 85 * - x = +-Inf (generated by exp()) 86 * - x = NaN (spurious inexact exception from y) 87 */ 88 exp_x = expl(x); 89 sincosl(y, &s, &c); 90 return (CMPLXL(exp_x * c, exp_x * s)); 91 } 92 } 93