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("$FreeBSD$");
35 #include "math_private.h"
38 * gcc doesn't implement complex multiplication or division correctly,
39 * so we need to handle infinities specially. We turn on this pragma to
40 * notify conforming c99 compilers that the fast-but-incorrect code that
41 * gcc generates is acceptable, since the special cases have already been
44 #pragma STDC CX_LIMITED_RANGE ON
47 csqrtf(float complex z)
49 float a = crealf(z), b = cimagf(z);
52 /* Handle special cases. */
54 return (CMPLXF(0, b));
56 return (CMPLXF(INFINITY, b));
58 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
59 return (CMPLXF(a, t)); /* return NaN + NaN i */
63 * csqrtf(inf + NaN i) = inf + NaN i
64 * csqrtf(inf + y i) = inf + 0 i
65 * csqrtf(-inf + NaN i) = NaN +- inf i
66 * csqrtf(-inf + y i) = 0 + inf i
69 return (CMPLXF(fabsf(b - b), copysignf(a, b)));
71 return (CMPLXF(a, copysignf(b - b, b)));
74 * The remaining special case (b is NaN) is handled just fine by
75 * the normal code path below.
79 * We compute t in double precision to avoid overflow and to
80 * provide correct rounding in nearly all cases.
81 * This is Algorithm 312, CACM vol 10, Oct 1967.
84 t = sqrt((a + hypot(a, b)) * 0.5);
85 return (CMPLXF(t, b / (2.0 * t)));
87 t = sqrt((-a + hypot(a, b)) * 0.5);
88 return (CMPLXF(fabsf(b) / (2.0 * t), copysignf(t, b)));