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 exp_ovfl = 0x42b17218, /* MAX_EXP * ln2 ~= 88.722839355 */ 31 cexp_ovfl = 0x43400074; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ 32 33float complex cexpf(float complex z) { 34 float x, y, exp_x; 35 uint32_t hx, hy; 36 37 x = crealf(z); 38 y = cimagf(z); 39 40 GET_FLOAT_WORD(hy, y); 41 hy &= 0x7fffffff; 42 43 /* cexp(x + I 0) = exp(x) + I 0 */ 44 if (hy == 0) 45 return CMPLXF(expf(x), y); 46 GET_FLOAT_WORD(hx, x); 47 /* cexp(0 + I y) = cos(y) + I sin(y) */ 48 if ((hx & 0x7fffffff) == 0) 49 return CMPLXF(cosf(y), sinf(y)); 50 51 if (hy >= 0x7f800000) { 52 if ((hx & 0x7fffffff) != 0x7f800000) { 53 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ 54 return CMPLXF(y - y, y - y); 55 } else if (hx & 0x80000000) { 56 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ 57 return CMPLXF(0.0, 0.0); 58 } else { 59 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ 60 return CMPLXF(x, y - y); 61 } 62 } 63 64 if (hx >= exp_ovfl && hx <= cexp_ovfl) { 65 /* 66 * x is between 88.7 and 192, so we must scale to avoid 67 * overflow in expf(x). 68 */ 69 return __ldexp_cexpf(z, 0); 70 } else { 71 /* 72 * Cases covered here: 73 * - x < exp_ovfl and exp(x) won't overflow (common case) 74 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 75 * - x = +-Inf (generated by exp()) 76 * - x = NaN (spurious inexact exception from y) 77 */ 78 exp_x = expf(x); 79 return CMPLXF(exp_x * cosf(y), exp_x * sinf(y)); 80 } 81} 82