1/*-
2 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 * SUCH DAMAGE.
25 */
26
27#include <sys/cdefs.h>
| 1/*-
2 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 * SUCH DAMAGE.
25 */
26
27#include <sys/cdefs.h>
|
28__FBSDID("$FreeBSD: head/lib/msun/src/s_cexpf.c 219359 2011-03-07 03:09:24Z das $");
| 28__FBSDID("$FreeBSD: head/lib/msun/src/s_cexpf.c 226413 2011-10-16 05:37:01Z das $");
|
29
30#include <complex.h>
31#include <math.h>
32
33#include "math_private.h"
34
35static const uint32_t
36exp_ovfl = 0x42b17218, /* MAX_EXP * ln2 ~= 88.722839355 */
37cexp_ovfl = 0x43400074, /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
38k = 235; /* constant for reduction */
39
40static const float
41kln2 = 162.88958740f; /* k * ln2 */
42
43float complex
44cexpf(float complex z)
45{
46 float x, y, exp_x;
47 uint32_t hx, hy;
48 int scale;
49
50 x = crealf(z);
51 y = cimagf(z);
52
53 GET_FLOAT_WORD(hy, y);
54 hy &= 0x7fffffff;
55
56 /* cexp(x + I 0) = exp(x) + I 0 */
57 if (hy == 0)
58 return (cpackf(expf(x), y));
59 GET_FLOAT_WORD(hx, x);
| 29
30#include <complex.h>
31#include <math.h>
32
33#include "math_private.h"
34
35static const uint32_t
36exp_ovfl = 0x42b17218, /* MAX_EXP * ln2 ~= 88.722839355 */
37cexp_ovfl = 0x43400074, /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */
38k = 235; /* constant for reduction */
39
40static const float
41kln2 = 162.88958740f; /* k * ln2 */
42
43float complex
44cexpf(float complex z)
45{
46 float x, y, exp_x;
47 uint32_t hx, hy;
48 int scale;
49
50 x = crealf(z);
51 y = cimagf(z);
52
53 GET_FLOAT_WORD(hy, y);
54 hy &= 0x7fffffff;
55
56 /* cexp(x + I 0) = exp(x) + I 0 */
57 if (hy == 0)
58 return (cpackf(expf(x), y));
59 GET_FLOAT_WORD(hx, x);
|
| 60 /* cexp(0 + I y) = cos(y) + I sin(y) */
61 if ((hx & 0x7fffffff) == 0)
62 return (cpackf(cosf(y), sinf(y)));
63
|
60 if (hy >= 0x7f800000) {
61 if ((hx & 0x7fffffff) != 0x7f800000) {
62 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
63 return (cpackf(y - y, y - y));
64 } else if (hx & 0x80000000) {
65 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
66 return (cpackf(0.0, 0.0));
67 } else {
68 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
69 return (cpackf(x, y - y));
70 }
71 }
72
73 if (hx >= exp_ovfl && hx <= cexp_ovfl) {
74 /*
75 * x is between 88.7 and 192, so we must scale to avoid
76 * overflow in expf(x). We use exp(x) = exp(x - kln2) * 2**k,
77 * carefully chosen to minimize |exp(kln2) - 2**k|. We also
78 * scale the exponent of exp(x) to MANT_DIG to avoid loss of
79 * accuracy due to underflow if sin(y) is tiny.
80 */
81 exp_x = expf(x - kln2);
82 GET_FLOAT_WORD(hx, exp_x);
83 SET_FLOAT_WORD(exp_x, (hx & 0x7fffff) | ((0x7f + 23) << 23));
84 scale = (hx >> 23) - (0x7f + 23) + k;
85 return (cpackf(scalbnf(cosf(y) * exp_x, scale),
86 scalbnf(sinf(y) * exp_x, scale)));
87 } else {
88 /*
89 * Cases covered here:
90 * - x < exp_ovfl and exp(x) won't overflow (common case)
91 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
92 * - x = +-Inf (generated by exp())
93 * - x = NaN (spurious inexact exception from y)
94 */
95 exp_x = expf(x);
96 return (cpackf(exp_x * cosf(y), exp_x * sinf(y)));
97 }
98}
| 64 if (hy >= 0x7f800000) {
65 if ((hx & 0x7fffffff) != 0x7f800000) {
66 /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
67 return (cpackf(y - y, y - y));
68 } else if (hx & 0x80000000) {
69 /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
70 return (cpackf(0.0, 0.0));
71 } else {
72 /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
73 return (cpackf(x, y - y));
74 }
75 }
76
77 if (hx >= exp_ovfl && hx <= cexp_ovfl) {
78 /*
79 * x is between 88.7 and 192, so we must scale to avoid
80 * overflow in expf(x). We use exp(x) = exp(x - kln2) * 2**k,
81 * carefully chosen to minimize |exp(kln2) - 2**k|. We also
82 * scale the exponent of exp(x) to MANT_DIG to avoid loss of
83 * accuracy due to underflow if sin(y) is tiny.
84 */
85 exp_x = expf(x - kln2);
86 GET_FLOAT_WORD(hx, exp_x);
87 SET_FLOAT_WORD(exp_x, (hx & 0x7fffff) | ((0x7f + 23) << 23));
88 scale = (hx >> 23) - (0x7f + 23) + k;
89 return (cpackf(scalbnf(cosf(y) * exp_x, scale),
90 scalbnf(sinf(y) * exp_x, scale)));
91 } else {
92 /*
93 * Cases covered here:
94 * - x < exp_ovfl and exp(x) won't overflow (common case)
95 * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0
96 * - x = +-Inf (generated by exp())
97 * - x = NaN (spurious inexact exception from y)
98 */
99 exp_x = expf(x);
100 return (cpackf(exp_x * cosf(y), exp_x * sinf(y)));
101 }
102}
|