1/* origin: FreeBSD /usr/src/lib/msun/src/s_cexpf.c */ 2/*- 3 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> 4 * All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 25 * SUCH DAMAGE. 26 */ 27 28#include "libm.h" 29 30static const uint32_t 31exp_ovfl = 0x42b17218, /* MAX_EXP * ln2 ~= 88.722839355 */ 32cexp_ovfl = 0x43400074; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ 33 34float complex cexpf(float complex z) 35{ 36 float x, y, exp_x; 37 uint32_t hx, hy; 38 39 x = crealf(z); 40 y = cimagf(z); 41 42 GET_FLOAT_WORD(hy, y); 43 hy &= 0x7fffffff; 44 45 /* cexp(x + I 0) = exp(x) + I 0 */ 46 if (hy == 0) 47 return CMPLXF(expf(x), y); 48 GET_FLOAT_WORD(hx, x); 49 /* cexp(0 + I y) = cos(y) + I sin(y) */ 50 if ((hx & 0x7fffffff) == 0) 51 return CMPLXF(cosf(y), sinf(y)); 52 53 if (hy >= 0x7f800000) { 54 if ((hx & 0x7fffffff) != 0x7f800000) { 55 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ 56 return CMPLXF(y - y, y - y); 57 } else if (hx & 0x80000000) { 58 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ 59 return CMPLXF(0.0, 0.0); 60 } else { 61 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ 62 return CMPLXF(x, y - y); 63 } 64 } 65 66 if (hx >= exp_ovfl && hx <= cexp_ovfl) { 67 /* 68 * x is between 88.7 and 192, so we must scale to avoid 69 * overflow in expf(x). 70 */ 71 return __ldexp_cexpf(z, 0); 72 } else { 73 /* 74 * Cases covered here: 75 * - x < exp_ovfl and exp(x) won't overflow (common case) 76 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 77 * - x = +-Inf (generated by exp()) 78 * - x = NaN (spurious inexact exception from y) 79 */ 80 exp_x = expf(x); 81 return CMPLXF(exp_x * cosf(y), exp_x * sinf(y)); 82 } 83} 84