1 /*-
2 * SPDX-License-Identifier: BSD-2-Clause
3 *
4 * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
19 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
26 * SUCH DAMAGE.
27 */
28
29 #include <complex.h>
30 #include <float.h>
31 #include <math.h>
32
33 #include "math_private.h"
34
35 /* For avoiding overflow for components >= DBL_MAX / (1 + sqrt(2)). */
36 #define THRESH 0x1.a827999fcef32p+1022
37
38 double complex
csqrt(double complex z)39 csqrt(double complex z)
40 {
41 double complex result;
42 double a, b, rx, ry, scale, t;
43
44 a = creal(z);
45 b = cimag(z);
46
47 /* Handle special cases. */
48 if (z == 0)
49 return (CMPLX(0, b));
50 if (isinf(b))
51 return (CMPLX(INFINITY, b));
52 if (isnan(a)) {
53 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
54 return (CMPLX(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */
55 }
56 if (isinf(a)) {
57 /*
58 * csqrt(inf + NaN i) = inf + NaN i
59 * csqrt(inf + y i) = inf + 0 i
60 * csqrt(-inf + NaN i) = NaN +- inf i
61 * csqrt(-inf + y i) = 0 + inf i
62 */
63 if (signbit(a))
64 return (CMPLX(fabs(b - b), copysign(a, b)));
65 else
66 return (CMPLX(a, copysign(b - b, b)));
67 }
68 if (isnan(b)) {
69 t = (a - a) / (a - a); /* raise invalid */
70 return (CMPLX(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */
71 }
72
73 /* Scale to avoid overflow. */
74 if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
75 /*
76 * Don't scale a or b if this might give (spurious)
77 * underflow. Then the unscaled value is an equivalent
78 * infinitesmal (or 0).
79 */
80 if (fabs(a) >= 0x1p-1020)
81 a *= 0.25;
82 if (fabs(b) >= 0x1p-1020)
83 b *= 0.25;
84 scale = 2;
85 } else {
86 scale = 1;
87 }
88
89 /* Scale to reduce inaccuracies when both components are denormal. */
90 if (fabs(a) < 0x1p-1022 && fabs(b) < 0x1p-1022) {
91 a *= 0x1p54;
92 b *= 0x1p54;
93 scale = 0x1p-27;
94 }
95
96 /* Algorithm 312, CACM vol 10, Oct 1967. */
97 if (a >= 0) {
98 t = sqrt((a + hypot(a, b)) * 0.5);
99 rx = scale * t;
100 ry = scale * b / (2 * t);
101 } else {
102 t = sqrt((-a + hypot(a, b)) * 0.5);
103 rx = scale * fabs(b) / (2 * t);
104 ry = copysign(scale * t, b);
105 }
106
107 return (CMPLX(rx, ry));
108 }
109
110 #if LDBL_MANT_DIG == 53
111 __weak_reference(csqrt, csqrtl);
112 #endif
113