[444] | 1 | /* origin: FreeBSD /usr/src/lib/msun/src/s_cexpf.c */
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| 2 | /*-
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| 3 | * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
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| 4 | * All rights reserved.
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| 5 | *
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| 6 | * Redistribution and use in source and binary forms, with or without
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| 7 | * modification, are permitted provided that the following conditions
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| 8 | * are met:
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| 9 | * 1. Redistributions of source code must retain the above copyright
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| 10 | * notice, this list of conditions and the following disclaimer.
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| 11 | * 2. Redistributions in binary form must reproduce the above copyright
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| 12 | * notice, this list of conditions and the following disclaimer in the
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| 13 | * documentation and/or other materials provided with the distribution.
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| 14 | *
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| 15 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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| 16 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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| 17 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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| 18 | * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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| 19 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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| 20 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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| 21 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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| 22 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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| 23 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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| 24 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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| 25 | * SUCH DAMAGE.
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| 26 | */
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| 27 |
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| 28 | #include "libm.h"
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| 29 |
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| 30 | static const uint32_t
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| 31 | exp_ovfl = 0x42b17218, /* MAX_EXP * ln2 ~= 88.722839355 */
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| 32 | cexp_ovfl = 0x43400074; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
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| 33 |
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| 34 | float complex cexpf(float complex z)
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| 35 | {
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| 36 | float x, y, exp_x;
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| 37 | uint32_t hx, hy;
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| 38 |
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| 39 | x = crealf(z);
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| 40 | y = cimagf(z);
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| 41 |
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| 42 | GET_FLOAT_WORD(hy, y);
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| 43 | hy &= 0x7fffffff;
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| 44 |
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| 45 | /* cexp(x + I 0) = exp(x) + I 0 */
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| 46 | if (hy == 0)
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| 47 | return CMPLXF(expf(x), y);
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| 48 | GET_FLOAT_WORD(hx, x);
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| 49 | /* cexp(0 + I y) = cos(y) + I sin(y) */
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| 50 | if ((hx & 0x7fffffff) == 0)
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| 51 | return CMPLXF(cosf(y), sinf(y));
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| 52 |
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| 53 | if (hy >= 0x7f800000) {
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| 54 | if ((hx & 0x7fffffff) != 0x7f800000) {
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| 55 | /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
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| 56 | return CMPLXF(y - y, y - y);
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| 57 | } else if (hx & 0x80000000) {
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| 58 | /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
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| 59 | return CMPLXF(0.0, 0.0);
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| 60 | } else {
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| 61 | /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
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| 62 | return CMPLXF(x, y - y);
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| 63 | }
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| 64 | }
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| 65 |
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| 66 | if (hx >= exp_ovfl && hx <= cexp_ovfl) {
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| 67 | /*
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| 68 | * x is between 88.7 and 192, so we must scale to avoid
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| 69 | * overflow in expf(x).
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| 70 | */
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| 71 | return __ldexp_cexpf(z, 0);
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| 72 | } else {
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| 73 | /*
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| 74 | * Cases covered here:
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| 75 | * - x < exp_ovfl and exp(x) won't overflow (common case)
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| 76 | * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
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| 77 | * - x = +-Inf (generated by exp())
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| 78 | * - x = NaN (spurious inexact exception from y)
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| 79 | */
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| 80 | exp_x = expf(x);
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| 81 | return CMPLXF(exp_x * cosf(y), exp_x * sinf(y));
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| 82 | }
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| 83 | }
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