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