1 /*-
2 * SPDX-License-Identifier: BSD-2-Clause
3 *
4 * Copyright (c) 2007-2008 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 /*
36 * Several thresholds require a 15-bit exponent and also the usual bias.
37 * s_logl.c and e_hypotl have less hard-coding but end up requiring the
38 * same for the exponent and more for the mantissa.
39 */
40 #if LDBL_MAX_EXP != 0x4000
41 #error "Unsupported long double format"
42 #endif
43
44 /*
45 * Overflow must be avoided for components >= LDBL_MAX / (1 + sqrt(2)).
46 * The precise threshold is nontrivial to determine and spell, so use a
47 * lower threshold of approximaely LDBL_MAX / 4, and don't use LDBL_MAX
48 * to spell this since LDBL_MAX is broken on i386 (it overflows in 53-bit
49 * precision).
50 */
51 #define THRESH 0x1p16382L
52
53 long double complex
csqrtl(long double complex z)54 csqrtl(long double complex z)
55 {
56 long double complex result;
57 long double a, b, rx, ry, scale, t;
58
59 a = creall(z);
60 b = cimagl(z);
61
62 /* Handle special cases. */
63 if (z == 0)
64 return (CMPLXL(0, b));
65 if (isinf(b))
66 return (CMPLXL(INFINITY, b));
67 if (isnan(a)) {
68 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
69 return (CMPLXL(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */
70 }
71 if (isinf(a)) {
72 /*
73 * csqrt(inf + NaN i) = inf + NaN i
74 * csqrt(inf + y i) = inf + 0 i
75 * csqrt(-inf + NaN i) = NaN +- inf i
76 * csqrt(-inf + y i) = 0 + inf i
77 */
78 if (signbit(a))
79 return (CMPLXL(fabsl(b - b), copysignl(a, b)));
80 else
81 return (CMPLXL(a, copysignl(b - b, b)));
82 }
83 if (isnan(b)) {
84 t = (a - a) / (a - a); /* raise invalid */
85 return (CMPLXL(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */
86 }
87
88 /* Scale to avoid overflow. */
89 if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
90 /*
91 * Don't scale a or b if this might give (spurious)
92 * underflow. Then the unscaled value is an equivalent
93 * infinitesmal (or 0).
94 */
95 if (fabsl(a) >= 0x1p-16380L)
96 a *= 0.25;
97 if (fabsl(b) >= 0x1p-16380L)
98 b *= 0.25;
99 scale = 2;
100 } else {
101 scale = 1;
102 }
103
104 /* Scale to reduce inaccuracies when both components are denormal. */
105 if (fabsl(a) < 0x1p-16382L && fabsl(b) < 0x1p-16382L) {
106 a *= 0x1p64;
107 b *= 0x1p64;
108 scale = 0x1p-32;
109 }
110
111 /* Algorithm 312, CACM vol 10, Oct 1967. */
112 if (a >= 0) {
113 t = sqrtl((a + hypotl(a, b)) * 0.5);
114 rx = scale * t;
115 ry = scale * b / (2 * t);
116 } else {
117 t = sqrtl((-a + hypotl(a, b)) * 0.5);
118 rx = scale * fabsl(b) / (2 * t);
119 ry = copysignl(scale * t, b);
120 }
121
122 return (CMPLXL(rx, ry));
123 }
124