1 /*-
2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
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 <sys/cdefs.h>
30 __FBSDID("$FreeBSD: head/lib/msun/src/s_csqrt.c 336488 2018-07-19 15:04:10Z bde $");
31
32 #include <complex.h>
33 #include <float.h>
34 #include <math.h>
35
36 #include "math_private.h"
37
38 /* For avoiding overflow for components >= DBL_MAX / (1 + sqrt(2)). */
39 #define THRESH 0x1.a827999fcef32p+1022
40
41 double complex
csqrt(double complex z)42 csqrt(double complex z)
43 {
44 double complex result;
45 double a, b, rx, ry, scale, t;
46
47 a = creal(z);
48 b = cimag(z);
49
50 /* Handle special cases. */
51 if (z == 0)
52 return (CMPLX(0, b));
53 if (isinf(b))
54 return (CMPLX(INFINITY, b));
55 if (isnan(a)) {
56 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
57 return (CMPLX(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */
58 }
59 if (isinf(a)) {
60 /*
61 * csqrt(inf + NaN i) = inf + NaN i
62 * csqrt(inf + y i) = inf + 0 i
63 * csqrt(-inf + NaN i) = NaN +- inf i
64 * csqrt(-inf + y i) = 0 + inf i
65 */
66 if (signbit(a))
67 return (CMPLX(fabs(b - b), copysign(a, b)));
68 else
69 return (CMPLX(a, copysign(b - b, b)));
70 }
71 if (isnan(b)) {
72 t = (a - a) / (a - a); /* raise invalid */
73 return (CMPLX(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */
74 }
75
76 /* Scale to avoid overflow. */
77 if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
78 /*
79 * Don't scale a or b if this might give (spurious)
80 * underflow. Then the unscaled value is an equivalent
81 * infinitesmal (or 0).
82 */
83 if (fabs(a) >= 0x1p-1020)
84 a *= 0.25;
85 if (fabs(b) >= 0x1p-1020)
86 b *= 0.25;
87 scale = 2;
88 } else {
89 scale = 1;
90 }
91
92 /* Scale to reduce inaccuracies when both components are denormal. */
93 if (fabs(a) < 0x1p-1022 && fabs(b) < 0x1p-1022) {
94 a *= 0x1p54;
95 b *= 0x1p54;
96 scale = 0x1p-27;
97 }
98
99 /* Algorithm 312, CACM vol 10, Oct 1967. */
100 if (a >= 0) {
101 t = sqrt((a + hypot(a, b)) * 0.5);
102 rx = scale * t;
103 ry = scale * b / (2 * t);
104 } else {
105 t = sqrt((-a + hypot(a, b)) * 0.5);
106 rx = scale * fabs(b) / (2 * t);
107 ry = copysign(scale * t, b);
108 }
109
110 return (CMPLX(rx, ry));
111 }
112
113 #if LDBL_MANT_DIG == 53
114 __weak_reference(csqrt, csqrtl);
115 #endif
116