| /* 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. |
| */ |
| |
| #include "complex_impl.h" |
| |
| 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)); |
| } |
| } |