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 __FBSDID("$FreeBSD$");
29
30 #include <complex.h>
31 #include <float.h>
32 #include <math.h>
33
34 #include "math_private.h"
35
36 /*
37 * gcc doesn't implement complex multiplication or division correctly,
38 * so we need to handle infinities specially. We turn on this pragma to
39 * notify conforming c99 compilers that the fast-but-incorrect code that
40 * gcc generates is acceptable, since the special cases have already been
41 * handled.
42 */
43 #pragma STDC CX_LIMITED_RANGE ON
44
45 /*
46 * We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)).
47 * Rather than determining the fully precise value at which we might
48 * overflow, just use a threshold of approximately LDBL_MAX / 4.
49 */
50 #if LDBL_MAX_EXP != 0x4000
51 #error "Unsupported long double format"
52 #else
53 #define THRESH 0x1p16382L
54 #endif
55
56 long double complex
csqrtl(long double complex z)57 csqrtl(long double complex z)
58 {
59 long double complex result;
60 long double a, b;
61 long double t;
62 int scale;
63
64 a = creall(z);
65 b = cimagl(z);
66
67 /* Handle special cases. */
68 if (z == 0)
69 return (CMPLXL(0, b));
70 if (isinf(b))
71 return (CMPLXL(INFINITY, b));
72 if (isnan(a)) {
73 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
74 return (CMPLXL(a, t)); /* return NaN + NaN i */
75 }
76 if (isinf(a)) {
77 /*
78 * csqrt(inf + NaN i) = inf + NaN i
79 * csqrt(inf + y i) = inf + 0 i
80 * csqrt(-inf + NaN i) = NaN +- inf i
81 * csqrt(-inf + y i) = 0 + inf i
82 */
83 if (signbit(a))
84 return (CMPLXL(fabsl(b - b), copysignl(a, b)));
85 else
86 return (CMPLXL(a, copysignl(b - b, b)));
87 }
88 /*
89 * The remaining special case (b is NaN) is handled just fine by
90 * the normal code path below.
91 */
92
93 /* Scale to avoid overflow. */
94 if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
95 a *= 0.25;
96 b *= 0.25;
97 scale = 1;
98 } else {
99 scale = 0;
100 }
101
102 /* Algorithm 312, CACM vol 10, Oct 1967. */
103 if (a >= 0) {
104 t = sqrtl((a + hypotl(a, b)) * 0.5);
105 result = CMPLXL(t, b / (2 * t));
106 } else {
107 t = sqrtl((-a + hypotl(a, b)) * 0.5);
108 result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b));
109 }
110
111 /* Rescale. */
112 if (scale)
113 return (result * 2);
114 else
115 return (result);
116 }
117