| /* origin: FreeBSD /usr/src/lib/msun/src/s_cexp.c */ | |
| /*- | |
| * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> | |
| * All rights reserved. | |
| * | |
| * Redistribution and use in source and binary forms, with or without | |
| * modification, are permitted provided that the following conditions | |
| * are met: | |
| * 1. Redistributions of source code must retain the above copyright | |
| * notice, this list of conditions and the following disclaimer. | |
| * 2. Redistributions in binary form must reproduce the above copyright | |
| * notice, this list of conditions and the following disclaimer in the | |
| * documentation and/or other materials provided with the distribution. | |
| * | |
| * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND | |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE | |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL | |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS | |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT | |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY | |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF | |
| * SUCH DAMAGE. | |
| */ | |
| static const uint32_t | |
| exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */ | |
| cexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ | |
| double complex cexp(double complex z) | |
| { | |
| double x, y, exp_x; | |
| uint32_t hx, hy, lx, ly; | |
| x = creal(z); | |
| y = cimag(z); | |
| EXTRACT_WORDS(hy, ly, y); | |
| hy &= 0x7fffffff; | |
| /* cexp(x + I 0) = exp(x) + I 0 */ | |
| if ((hy | ly) == 0) | |
| return CMPLX(exp(x), y); | |
| EXTRACT_WORDS(hx, lx, x); | |
| /* cexp(0 + I y) = cos(y) + I sin(y) */ | |
| if (((hx & 0x7fffffff) | lx) == 0) | |
| return CMPLX(cos(y), sin(y)); | |
| if (hy >= 0x7ff00000) { | |
| if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) { | |
| /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ | |
| return CMPLX(y - y, y - y); | |
| } else if (hx & 0x80000000) { | |
| /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ | |
| return CMPLX(0.0, 0.0); | |
| } else { | |
| /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ | |
| return CMPLX(x, y - y); | |
| } | |
| } | |
| if (hx >= exp_ovfl && hx <= cexp_ovfl) { | |
| /* | |
| * x is between 709.7 and 1454.3, so we must scale to avoid | |
| * overflow in exp(x). | |
| */ | |
| return __ldexp_cexp(z, 0); | |
| } else { | |
| /* | |
| * Cases covered here: | |
| * - x < exp_ovfl and exp(x) won't overflow (common case) | |
| * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 | |
| * - x = +-Inf (generated by exp()) | |
| * - x = NaN (spurious inexact exception from y) | |
| */ | |
| exp_x = exp(x); | |
| return CMPLX(exp_x * cos(y), exp_x * sin(y)); | |
| } | |
| } | |