2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
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>
30 __FBSDID("$FreeBSD$");
36 #include "math_private.h"
39 * gcc doesn't implement complex multiplication or division correctly,
40 * so we need to handle infinities specially. We turn on this pragma to
41 * notify conforming c99 compilers that the fast-but-incorrect code that
42 * gcc generates is acceptable, since the special cases have already been
45 #pragma STDC CX_LIMITED_RANGE ON
47 /* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */
48 #define THRESH 0x1.a827999fcef32p+1022
51 csqrt(double complex z)
53 double complex result;
61 /* Handle special cases. */
65 return (CMPLX(INFINITY, b));
67 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
68 return (CMPLX(a, t)); /* return NaN + NaN i */
72 * csqrt(inf + NaN i) = inf + NaN i
73 * csqrt(inf + y i) = inf + 0 i
74 * csqrt(-inf + NaN i) = NaN +- inf i
75 * csqrt(-inf + y i) = 0 + inf i
78 return (CMPLX(fabs(b - b), copysign(a, b)));
80 return (CMPLX(a, copysign(b - b, b)));
83 * The remaining special case (b is NaN) is handled just fine by
84 * the normal code path below.
87 /* Scale to avoid overflow. */
88 if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
96 /* Algorithm 312, CACM vol 10, Oct 1967. */
98 t = sqrt((a + hypot(a, b)) * 0.5);
99 result = CMPLX(t, b / (2 * t));
101 t = sqrt((-a + hypot(a, b)) * 0.5);
102 result = CMPLX(fabs(b) / (2 * t), copysign(t, b));
112 #if LDBL_MANT_DIG == 53
113 __weak_reference(csqrt, csqrtl);