1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause 3 * 4 * Copyright (c) 2011 David Schultz <das@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 "math_private.h" 35 36 static const uint32_t 37 exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */ 38 cexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ 39 40 double complex 41 cexp(double complex z) 42 { 43 double c, exp_x, s, x, y; 44 uint32_t hx, hy, lx, ly; 45 46 x = creal(z); 47 y = cimag(z); 48 49 EXTRACT_WORDS(hy, ly, y); 50 hy &= 0x7fffffff; 51 52 /* cexp(x + I 0) = exp(x) + I 0 */ 53 if ((hy | ly) == 0) 54 return (CMPLX(exp(x), y)); 55 EXTRACT_WORDS(hx, lx, x); 56 /* cexp(0 + I y) = cos(y) + I sin(y) */ 57 if (((hx & 0x7fffffff) | lx) == 0) { 58 sincos(y, &s, &c); 59 return (CMPLX(c, s)); 60 } 61 62 if (hy >= 0x7ff00000) { 63 if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) { 64 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ 65 return (CMPLX(y - y, y - y)); 66 } else if (hx & 0x80000000) { 67 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ 68 return (CMPLX(0.0, 0.0)); 69 } else { 70 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ 71 return (CMPLX(x, y - y)); 72 } 73 } 74 75 if (hx >= exp_ovfl && hx <= cexp_ovfl) { 76 /* 77 * x is between 709.7 and 1454.3, so we must scale to avoid 78 * overflow in exp(x). 79 */ 80 return (__ldexp_cexp(z, 0)); 81 } else { 82 /* 83 * Cases covered here: 84 * - x < exp_ovfl and exp(x) won't overflow (common case) 85 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 86 * - x = +-Inf (generated by exp()) 87 * - x = NaN (spurious inexact exception from y) 88 */ 89 exp_x = exp(x); 90 sincos(y, &s, &c); 91 return (CMPLX(exp_x * c, exp_x * s)); 92 } 93 } 94 95 #if (LDBL_MANT_DIG == 53) 96 __weak_reference(cexp, cexpl); 97 #endif 98