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1 /* origin: FreeBSD /usr/src/lib/msun/src/s_cexpf.c */ | 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_cexpf.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 = 0x42b17218, /* MAX_EXP * ln2 ~= 88.722839355 */ |
31 exp_ovfl = 0x42b17218, /* MAX_EXP * ln2 ~= 88.722839355 */ | 31 cexp_ovfl = 0x43400074; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ |
32 cexp_ovfl = 0x43400074; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ | |
33 | 32 |
34 float complex cexpf(float complex z) | 33 float complex cexpf(float complex z) { |
35 { | 34 float x, y, exp_x; |
36 » float x, y, exp_x; | 35 uint32_t hx, hy; |
37 » uint32_t hx, hy; | |
38 | 36 |
39 » x = crealf(z); | 37 x = crealf(z); |
40 » y = cimagf(z); | 38 y = cimagf(z); |
41 | 39 |
42 » GET_FLOAT_WORD(hy, y); | 40 GET_FLOAT_WORD(hy, y); |
43 » hy &= 0x7fffffff; | 41 hy &= 0x7fffffff; |
44 | 42 |
45 » /* cexp(x + I 0) = exp(x) + I 0 */ | 43 /* cexp(x + I 0) = exp(x) + I 0 */ |
46 » if (hy == 0) | 44 if (hy == 0) |
47 » » return CMPLXF(expf(x), y); | 45 return CMPLXF(expf(x), y); |
48 » GET_FLOAT_WORD(hx, x); | 46 GET_FLOAT_WORD(hx, x); |
49 » /* cexp(0 + I y) = cos(y) + I sin(y) */ | 47 /* cexp(0 + I y) = cos(y) + I sin(y) */ |
50 » if ((hx & 0x7fffffff) == 0) | 48 if ((hx & 0x7fffffff) == 0) |
51 » » return CMPLXF(cosf(y), sinf(y)); | 49 return CMPLXF(cosf(y), sinf(y)); |
52 | 50 |
53 » if (hy >= 0x7f800000) { | 51 if (hy >= 0x7f800000) { |
54 » » if ((hx & 0x7fffffff) != 0x7f800000) { | 52 if ((hx & 0x7fffffff) != 0x7f800000) { |
55 » » » /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ | 53 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ |
56 » » » return CMPLXF(y - y, y - y); | 54 return CMPLXF(y - y, y - y); |
57 » » } else if (hx & 0x80000000) { | 55 } else if (hx & 0x80000000) { |
58 » » » /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ | 56 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ |
59 » » » return CMPLXF(0.0, 0.0); | 57 return CMPLXF(0.0, 0.0); |
60 » » } else { | 58 } else { |
61 » » » /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ | 59 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ |
62 » » » return CMPLXF(x, y - y); | 60 return CMPLXF(x, y - y); |
63 » » } | 61 } |
64 » } | 62 } |
65 | 63 |
66 » if (hx >= exp_ovfl && hx <= cexp_ovfl) { | 64 if (hx >= exp_ovfl && hx <= cexp_ovfl) { |
67 » » /* | 65 /* |
68 » » * x is between 88.7 and 192, so we must scale to avoid | 66 * x is between 88.7 and 192, so we must scale to avoid |
69 » » * overflow in expf(x). | 67 * overflow in expf(x). |
70 » » */ | 68 */ |
71 » » return __ldexp_cexpf(z, 0); | 69 return __ldexp_cexpf(z, 0); |
72 » } else { | 70 } else { |
73 » » /* | 71 /* |
74 » » * Cases covered here: | 72 * Cases covered here: |
75 » » * - x < exp_ovfl and exp(x) won't overflow (common case) | 73 * - x < exp_ovfl and exp(x) won't overflow (common case) |
76 » » * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 | 74 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 |
77 » » * - x = +-Inf (generated by exp()) | 75 * - x = +-Inf (generated by exp()) |
78 » » * - x = NaN (spurious inexact exception from y) | 76 * - x = NaN (spurious inexact exception from y) |
79 » » */ | 77 */ |
80 » » exp_x = expf(x); | 78 exp_x = expf(x); |
81 » » return CMPLXF(exp_x * cosf(y), exp_x * sinf(y)); | 79 return CMPLXF(exp_x * cosf(y), exp_x * sinf(y)); |
82 » } | 80 } |
83 } | 81 } |
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