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1 /* origin: FreeBSD /usr/src/lib/msun/src/s_cexp.c */ | 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_cexp.c */ |
2 /*- | 2 /*- |
3 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> | 3 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> |
4 * All rights reserved. | 4 * All rights reserved. |
5 * | 5 * |
6 * Redistribution and use in source and binary forms, with or without | 6 * Redistribution and use in source and binary forms, with or without |
7 * modification, are permitted provided that the following conditions | 7 * modification, are permitted provided that the following conditions |
8 * are met: | 8 * are met: |
9 * 1. Redistributions of source code must retain the above copyright | 9 * 1. Redistributions of source code must retain the above copyright |
10 * notice, this list of conditions and the following disclaimer. | 10 * notice, this list of conditions and the following disclaimer. |
11 * 2. Redistributions in binary form must reproduce the above copyright | 11 * 2. Redistributions in binary form must reproduce the above copyright |
12 * notice, this list of conditions and the following disclaimer in the | 12 * notice, this list of conditions and the following disclaimer in the |
13 * documentation and/or other materials provided with the distribution. | 13 * documentation and/or other materials provided with the distribution. |
14 * | 14 * |
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND | 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 | 16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | 17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE | 18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL | 19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS | 20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | 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 | 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 | 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 | 24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
25 * SUCH DAMAGE. | 25 * SUCH DAMAGE. |
26 */ | 26 */ |
27 | 27 |
28 #include "libm.h" | 28 #include "libm.h" |
29 | 29 |
30 static const uint32_t | 30 static const uint32_t exp_ovfl = |
31 exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */ | 31 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */ |
32 cexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ | 32 cexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ |
33 | 33 |
34 double complex cexp(double complex z) | 34 double complex cexp(double complex z) { |
35 { | 35 double x, y, exp_x; |
36 » double x, y, exp_x; | 36 uint32_t hx, hy, lx, ly; |
37 » uint32_t hx, hy, lx, ly; | |
38 | 37 |
39 » x = creal(z); | 38 x = creal(z); |
40 » y = cimag(z); | 39 y = cimag(z); |
41 | 40 |
42 » EXTRACT_WORDS(hy, ly, y); | 41 EXTRACT_WORDS(hy, ly, y); |
43 » hy &= 0x7fffffff; | 42 hy &= 0x7fffffff; |
44 | 43 |
45 » /* cexp(x + I 0) = exp(x) + I 0 */ | 44 /* cexp(x + I 0) = exp(x) + I 0 */ |
46 » if ((hy | ly) == 0) | 45 if ((hy | ly) == 0) |
47 » » return CMPLX(exp(x), y); | 46 return CMPLX(exp(x), y); |
48 » EXTRACT_WORDS(hx, lx, x); | 47 EXTRACT_WORDS(hx, lx, x); |
49 » /* cexp(0 + I y) = cos(y) + I sin(y) */ | 48 /* cexp(0 + I y) = cos(y) + I sin(y) */ |
50 » if (((hx & 0x7fffffff) | lx) == 0) | 49 if (((hx & 0x7fffffff) | lx) == 0) |
51 » » return CMPLX(cos(y), sin(y)); | 50 return CMPLX(cos(y), sin(y)); |
52 | 51 |
53 » if (hy >= 0x7ff00000) { | 52 if (hy >= 0x7ff00000) { |
54 » » if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) { | 53 if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) { |
55 » » » /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ | 54 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ |
56 » » » return CMPLX(y - y, y - y); | 55 return CMPLX(y - y, y - y); |
57 » » } else if (hx & 0x80000000) { | 56 } else if (hx & 0x80000000) { |
58 » » » /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ | 57 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ |
59 » » » return CMPLX(0.0, 0.0); | 58 return CMPLX(0.0, 0.0); |
60 » » } else { | 59 } else { |
61 » » » /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ | 60 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ |
62 » » » return CMPLX(x, y - y); | 61 return CMPLX(x, y - y); |
63 » » } | 62 } |
64 » } | 63 } |
65 | 64 |
66 » if (hx >= exp_ovfl && hx <= cexp_ovfl) { | 65 if (hx >= exp_ovfl && hx <= cexp_ovfl) { |
67 » » /* | 66 /* |
68 » » * x is between 709.7 and 1454.3, so we must scale to avoid | 67 * x is between 709.7 and 1454.3, so we must scale to avoid |
69 » » * overflow in exp(x). | 68 * overflow in exp(x). |
70 » » */ | 69 */ |
71 » » return __ldexp_cexp(z, 0); | 70 return __ldexp_cexp(z, 0); |
72 » } else { | 71 } else { |
73 » » /* | 72 /* |
74 » » * Cases covered here: | 73 * Cases covered here: |
75 » » * - x < exp_ovfl and exp(x) won't overflow (common case) | 74 * - x < exp_ovfl and exp(x) won't overflow (common case) |
76 » » * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 | 75 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 |
77 » » * - x = +-Inf (generated by exp()) | 76 * - x = +-Inf (generated by exp()) |
78 » » * - x = NaN (spurious inexact exception from y) | 77 * - x = NaN (spurious inexact exception from y) |
79 » » */ | 78 */ |
80 » » exp_x = exp(x); | 79 exp_x = exp(x); |
81 » » return CMPLX(exp_x * cos(y), exp_x * sin(y)); | 80 return CMPLX(exp_x * cos(y), exp_x * sin(y)); |
82 » } | 81 } |
83 } | 82 } |
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