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
53long double complex
54csqrtl(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