2 * SPDX-License-Identifier: BSD-2-Clause
4 * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
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.
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
29 #include <sys/cdefs.h>
34 #include "math_private.h"
36 /* For avoiding overflow for components >= DBL_MAX / (1 + sqrt(2)). */
37 #define THRESH 0x1.a827999fcef32p+1022
40 csqrt(double complex z)
42 double complex result;
43 double a, b, rx, ry, scale, t;
48 /* Handle special cases. */
52 return (CMPLX(INFINITY, b));
54 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
55 return (CMPLX(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */
59 * csqrt(inf + NaN i) = inf + NaN i
60 * csqrt(inf + y i) = inf + 0 i
61 * csqrt(-inf + NaN i) = NaN +- inf i
62 * csqrt(-inf + y i) = 0 + inf i
65 return (CMPLX(fabs(b - b), copysign(a, b)));
67 return (CMPLX(a, copysign(b - b, b)));
70 t = (a - a) / (a - a); /* raise invalid */
71 return (CMPLX(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */
74 /* Scale to avoid overflow. */
75 if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
77 * Don't scale a or b if this might give (spurious)
78 * underflow. Then the unscaled value is an equivalent
79 * infinitesmal (or 0).
81 if (fabs(a) >= 0x1p-1020)
83 if (fabs(b) >= 0x1p-1020)
90 /* Scale to reduce inaccuracies when both components are denormal. */
91 if (fabs(a) < 0x1p-1022 && fabs(b) < 0x1p-1022) {
97 /* Algorithm 312, CACM vol 10, Oct 1967. */
99 t = sqrt((a + hypot(a, b)) * 0.5);
101 ry = scale * b / (2 * t);
103 t = sqrt((-a + hypot(a, b)) * 0.5);
104 rx = scale * fabs(b) / (2 * t);
105 ry = copysign(scale * t, b);
108 return (CMPLX(rx, ry));
111 #if LDBL_MANT_DIG == 53
112 __weak_reference(csqrt, csqrtl);