| Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 1 | /*- |
| 2 | * Copyright (c) 2007-2008 David Schultz <das@FreeBSD.ORG> |
| 3 | * All rights reserved. |
| 4 | * |
| 5 | * Redistribution and use in source and binary forms, with or without |
| 6 | * modification, are permitted provided that the following conditions |
| 7 | * are met: |
| 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. |
| 13 | * |
| 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 |
| 24 | * SUCH DAMAGE. |
| 25 | */ |
| 26 | |
| 27 | #include <sys/cdefs.h> |
| 28 | __FBSDID("$FreeBSD$"); |
| 29 | |
| 30 | #include <complex.h> |
| 31 | #include <float.h> |
| 32 | #include <math.h> |
| 33 | |
| 34 | #include "math_private.h" |
| 35 | |
| 36 | /* |
| 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 |
| 41 | * handled. |
| 42 | */ |
| 43 | #pragma STDC CX_LIMITED_RANGE ON |
| 44 | |
| 45 | /* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */ |
| 46 | #define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L) |
| 47 | |
| 48 | long double complex |
| 49 | csqrtl(long double complex z) |
| 50 | { |
| 51 | long double complex result; |
| 52 | long double a, b; |
| 53 | long double t; |
| 54 | int scale; |
| 55 | |
| 56 | a = creall(z); |
| 57 | b = cimagl(z); |
| 58 | |
| 59 | /* Handle special cases. */ |
| 60 | if (z == 0) |
| 61 | return (cpackl(0, b)); |
| 62 | if (isinf(b)) |
| 63 | return (cpackl(INFINITY, b)); |
| 64 | if (isnan(a)) { |
| 65 | t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ |
| 66 | return (cpackl(a, t)); /* return NaN + NaN i */ |
| 67 | } |
| 68 | if (isinf(a)) { |
| 69 | /* |
| 70 | * csqrt(inf + NaN i) = inf + NaN i |
| 71 | * csqrt(inf + y i) = inf + 0 i |
| 72 | * csqrt(-inf + NaN i) = NaN +- inf i |
| 73 | * csqrt(-inf + y i) = 0 + inf i |
| 74 | */ |
| 75 | if (signbit(a)) |
| 76 | return (cpackl(fabsl(b - b), copysignl(a, b))); |
| 77 | else |
| 78 | return (cpackl(a, copysignl(b - b, b))); |
| 79 | } |
| 80 | /* |
| 81 | * The remaining special case (b is NaN) is handled just fine by |
| 82 | * the normal code path below. |
| 83 | */ |
| 84 | |
| 85 | /* Scale to avoid overflow. */ |
| 86 | if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) { |
| 87 | a *= 0.25; |
| 88 | b *= 0.25; |
| 89 | scale = 1; |
| 90 | } else { |
| 91 | scale = 0; |
| 92 | } |
| 93 | |
| 94 | /* Algorithm 312, CACM vol 10, Oct 1967. */ |
| 95 | if (a >= 0) { |
| 96 | t = sqrtl((a + hypotl(a, b)) * 0.5); |
| 97 | result = cpackl(t, b / (2 * t)); |
| 98 | } else { |
| 99 | t = sqrtl((-a + hypotl(a, b)) * 0.5); |
| 100 | result = cpackl(fabsl(b) / (2 * t), copysignl(t, b)); |
| 101 | } |
| 102 | |
| 103 | /* Rescale. */ |
| 104 | if (scale) |
| 105 | return (result * 2); |
| 106 | else |
| 107 | return (result); |
| 108 | } |