2 * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
27 #include <sys/cdefs.h>
28 __FBSDID("$FreeBSD$");
33 #include "math_private.h"
36 * gcc doesn't implement complex multiplication or division correctly,
37 * so we need to handle infinities specially. We turn on this pragma to
38 * notify conforming c99 compilers that the fast-but-incorrect code that
39 * gcc generates is acceptable, since the special cases have already been
42 #pragma STDC CX_LIMITED_RANGE ON
45 csqrtf(float complex z)
47 float a = crealf(z), b = cimagf(z);
50 /* Handle special cases. */
52 return (cpackf(0, b));
54 return (cpackf(INFINITY, b));
56 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
57 return (cpackf(a, t)); /* return NaN + NaN i */
61 * csqrtf(inf + NaN i) = inf + NaN i
62 * csqrtf(inf + y i) = inf + 0 i
63 * csqrtf(-inf + NaN i) = NaN +- inf i
64 * csqrtf(-inf + y i) = 0 + inf i
67 return (cpackf(fabsf(b - b), copysignf(a, b)));
69 return (cpackf(a, copysignf(b - b, b)));
72 * The remaining special case (b is NaN) is handled just fine by
73 * the normal code path below.
77 * We compute t in double precision to avoid overflow and to
78 * provide correct rounding in nearly all cases.
79 * This is Algorithm 312, CACM vol 10, Oct 1967.
82 t = sqrt((a + hypot(a, b)) * 0.5);
83 return (cpackf(t, b / (2.0 * t)));
85 t = sqrt((-a + hypot(a, b)) * 0.5);
86 return (cpackf(fabsf(b) / (2.0 * t), copysignf(t, b)));