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 * src/s_cexp.c converted to long double complex by Steven G. Kargl 29 */ 30 31 #include <sys/cdefs.h> 32 __FBSDID("$FreeBSD$"); 33 34 #include <complex.h> 35 #include <float.h> 36 #ifdef __i386__ 37 #include <ieeefp.h> 38 #endif 39 40 #include "fpmath.h" 41 #include "math.h" 42 #include "math_private.h" 43 #include "k_expl.h" 44 45 long double complex 46 cexpl (long double complex z) 47 { 48 long double c, exp_x, s, x, y; 49 uint64_t lx, ly; 50 uint16_t hx, hy; 51 52 ENTERI(); 53 54 x = creall(z); 55 y = cimagl(z); 56 57 EXTRACT_LDBL80_WORDS(hy, ly, y); 58 hy &= 0x7fff; 59 60 /* cexp(x + I 0) = exp(x) + I 0 */ 61 if ((hy | ly) == 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) { 66 sincosl(y, &s, &c); 67 RETURNI(CMPLXL(c, s)); 68 } 69 70 if (hy >= 0x7fff) { 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)); 78 } else { 79 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ 80 RETURNI(CMPLXL(x, y - y)); 81 } 82 } 83 84 /* 85 * exp_ovfl = 11356.5234062941439497 86 * cexp_ovfl = 22755.3287906024445633 87 */ 88 if ((hx == 0x400c && lx > 0xb17217f7d1cf79acULL) || 89 (hx == 0x400d && lx < 0xb1c6a8573de9768cULL)) { 90 /* 91 * x is between exp_ovfl and cexp_ovfl, so we must scale to 92 * avoid overflow in exp(x). 93 */ 94 RETURNI(__ldexp_cexpl(z, 0)); 95 } else { 96 /* 97 * Cases covered here: 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) 102 */ 103 exp_x = expl(x); 104 sincosl(y, &s, &c); 105 RETURNI(CMPLXL(exp_x * c, exp_x * s)); 106 } 107 } 108