2 * Copyright (c) 2007-2008 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("$FreeBSD$");
34 #include "math_private.h"
37 * gcc doesn't implement complex multiplication or division correctly,
38 * so we need to handle infinities specially. We turn on this pragma to
39 * notify conforming c99 compilers that the fast-but-incorrect code that
40 * gcc generates is acceptable, since the special cases have already been
43 #pragma STDC CX_LIMITED_RANGE ON
46 * We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)).
47 * Rather than determining the fully precise value at which we might
48 * overflow, just use a threshold of approximately LDBL_MAX / 4.
50 #if LDBL_MAX_EXP != 0x4000
51 #error "Unsupported long double format"
53 #define THRESH 0x1p16382L
57 csqrtl(long double complex z)
59 long double complex result;
67 /* Handle special cases. */
69 return (CMPLXL(0, b));
71 return (CMPLXL(INFINITY, b));
73 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
74 return (CMPLXL(a, t)); /* return NaN + NaN i */
78 * csqrt(inf + NaN i) = inf + NaN i
79 * csqrt(inf + y i) = inf + 0 i
80 * csqrt(-inf + NaN i) = NaN +- inf i
81 * csqrt(-inf + y i) = 0 + inf i
84 return (CMPLXL(fabsl(b - b), copysignl(a, b)));
86 return (CMPLXL(a, copysignl(b - b, b)));
89 * The remaining special case (b is NaN) is handled just fine by
90 * the normal code path below.
93 /* Scale to avoid overflow. */
94 if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
102 /* Algorithm 312, CACM vol 10, Oct 1967. */
104 t = sqrtl((a + hypotl(a, b)) * 0.5);
105 result = CMPLXL(t, b / (2 * t));
107 t = sqrtl((-a + hypotl(a, b)) * 0.5);
108 result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b));