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 __FBSDID("$FreeBSD$"); 31 32 #include <complex.h> 33 #include <math.h> 34 35 #include "math_private.h" 36 37 static const uint32_t 38 exp_ovfl = 0x42b17218, /* MAX_EXP * ln2 ~= 88.722839355 */ 39 cexp_ovfl = 0x43400074; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ 40 41 float complex 42 cexpf(float complex z) 43 { 44 float c, exp_x, s, x, y; 45 uint32_t hx, hy; 46 47 x = crealf(z); 48 y = cimagf(z); 49 50 GET_FLOAT_WORD(hy, y); 51 hy &= 0x7fffffff; 52 53 /* cexp(x + I 0) = exp(x) + I 0 */ 54 if (hy == 0) 55 return (CMPLXF(expf(x), y)); 56 GET_FLOAT_WORD(hx, x); 57 /* cexp(0 + I y) = cos(y) + I sin(y) */ 58 if ((hx & 0x7fffffff) == 0) { 59 sincosf(y, &s, &c); 60 return (CMPLXF(c, s)); 61 } 62 63 if (hy >= 0x7f800000) { 64 if ((hx & 0x7fffffff) != 0x7f800000) { 65 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ 66 return (CMPLXF(y - y, y - y)); 67 } else if (hx & 0x80000000) { 68 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ 69 return (CMPLXF(0.0, 0.0)); 70 } else { 71 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ 72 return (CMPLXF(x, y - y)); 73 } 74 } 75 76 if (hx >= exp_ovfl && hx <= cexp_ovfl) { 77 /* 78 * x is between 88.7 and 192, so we must scale to avoid 79 * overflow in expf(x). 80 */ 81 return (__ldexp_cexpf(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 = expf(x); 91 sincosf(y, &s, &c); 92 return (CMPLXF(exp_x * c, exp_x * s)); 93 } 94 } 95