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 #include <sys/cdefs.h>
28 #if 0
29 __FBSDID("$FreeBSD: head/lib/msun/src/s_csqrtl.c 181402 2008-08-08 00:15:16Z das $");
30 #else
31 __RCSID("$NetBSD: csqrtl.c,v 1.2 2014/10/11 00:43:51 christos Exp $");
32 #endif
33
34 #include "../src/namespace.h"
35 #include <complex.h>
36 #include <float.h>
37 #include <math.h>
38 #include <stdbool.h>
39
40 /*
41 * gcc doesn't implement complex multiplication or division correctly,
42 * so we need to handle infinities specially. We turn on this pragma to
43 * notify conforming c99 compilers that the fast-but-incorrect code that
44 * gcc generates is acceptable, since the special cases have already been
45 * handled.
46 */
47 // #pragma STDC CX_LIMITED_RANGE ON
48
49 /* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */
50 #define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L)
51
52 #define cpackl(r, i) ((r) + (i) * I)
53
54 long double complex
csqrtl(long double complex z)55 csqrtl(long double complex z)
56 {
57 long double complex result;
58 long double a, b;
59 long double t;
60 bool scale;
61
62 a = creall(z);
63 b = cimagl(z);
64
65 /* Handle special cases. */
66 if (z == 0.0L)
67 return (cpackl(0.0L, b));
68 if (isinf(b))
69 return (cpackl(INFINITY, b));
70 if (isnan(a)) {
71 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
72 return (cpackl(a, t)); /* return NaN + NaN i */
73 }
74 if (isinf(a)) {
75 /*
76 * csqrt(inf + NaN i) = inf + NaN i
77 * csqrt(inf + y i) = inf + 0 i
78 * csqrt(-inf + NaN i) = NaN +- inf i
79 * csqrt(-inf + y i) = 0 + inf i
80 */
81 if (signbit(a))
82 return (cpackl(fabsl(b - b), copysignl(a, b)));
83 else
84 return (cpackl(a, copysignl(b - b, b)));
85 }
86 /*
87 * The remaining special case (b is NaN) is handled just fine by
88 * the normal code path below.
89 */
90
91 /* Scale to avoid overflow. */
92 if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
93 a *= 0.25L;
94 b *= 0.25L;
95 scale = true;
96 } else {
97 scale = false;
98 }
99
100 /* Algorithm 312, CACM vol 10, Oct 1967. */
101 if (a >= 0L) {
102 t = sqrtl((a + hypotl(a, b)) * 0.5L);
103 result = cpackl(t, b / (2.0L * t));
104 } else {
105 t = sqrtl((-a + hypotl(a, b)) * 0.5L);
106 result = cpackl(fabsl(b) / (2.0L * t), copysignl(t, b));
107 }
108
109 /* Rescale. */
110 if (scale)
111 return (result * 2.0L);
112 else
113 return (result);
114 }
115