1 /*-
2 * Copyright (c) 2007-2008 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 #define _GNU_SOURCE
28 #include <sys/cdefs.h>
29 #include <complex.h>
30 #include <float.h>
31 #include <math.h>
32 #include <stdbool.h>
33
34 /*
35 * gcc doesn't implement complex multiplication or division correctly,
36 * so we need to handle infinities specially. We turn on this pragma to
37 * notify conforming c99 compilers that the fast-but-incorrect code that
38 * gcc generates is acceptable, since the special cases have already been
39 * handled.
40 */
41 // #pragma STDC CX_LIMITED_RANGE ON
42
43 /* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */
44 #define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L)
45
46 #define cpackl(r, i) ((r) + (i) * (long double complex) I)
47
48 long double complex
csqrtl(long double complex z)49 csqrtl(long double complex z)
50 {
51 long double complex result;
52 long double a, b;
53 long double t;
54 bool scale;
55
56 a = creall(z);
57 b = cimagl(z);
58
59 /* Handle special cases. */
60 if (z == 0.0L)
61 return (cpackl((long double) 0.0L, b));
62 if (isinf(b))
63 return (cpackl((long double) INFINITY, b));
64 if (isnan(a)) {
65 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
66 return (cpackl(a, t)); /* return NaN + NaN i */
67 }
68 if (isinf(a)) {
69 /*
70 * csqrt(inf + NaN i) = inf + NaN i
71 * csqrt(inf + y i) = inf + 0 i
72 * csqrt(-inf + NaN i) = NaN +- inf i
73 * csqrt(-inf + y i) = 0 + inf i
74 */
75 if (signbit(a))
76 return (cpackl(fabsl(b - b), copysignl(a, b)));
77 else
78 return (cpackl(a, copysignl(b - b, b)));
79 }
80 /*
81 * The remaining special case (b is NaN) is handled just fine by
82 * the normal code path below.
83 */
84
85 /* Scale to avoid overflow. */
86 if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
87 a *= 0.25L;
88 b *= 0.25L;
89 scale = true;
90 } else {
91 scale = false;
92 }
93
94 /* Algorithm 312, CACM vol 10, Oct 1967. */
95 if (a >= 0L) {
96 t = sqrtl((a + hypotl(a, b)) * 0.5L);
97 result = cpackl(t, b / (2.0L * t));
98 } else {
99 t = sqrtl((-a + hypotl(a, b)) * 0.5L);
100 result = cpackl(fabsl(b) / (2.0L * t), copysignl(t, b));
101 }
102
103 /* Rescale. */
104 if (scale)
105 return (result * 2.0L);
106 else
107 return (result);
108 }
109
