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 } 109