1 /*- 2 * Copyright (c) 2007 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 <math.h> 32 33 #include "math_private.h" 34 35 /* 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 40 * handled. 41 */ 42 #pragma STDC CX_LIMITED_RANGE on 43 44 /* We risk spurious overflow for components >= DBL_MAX/(1+sqrt(2)) */ 45 #define THRESH 0x1.a827999fcef32p+1022 46 47 double complex 48 csqrt(double complex z) 49 { 50 double a = creal(z), b = cimag(z); 51 double t; 52 double complex result; 53 int scale; 54 55 /* Handle special cases. */ 56 if (z == 0) 57 return (cpack(0, b)); 58 if (isinf(b)) 59 return (cpack(INFINITY, b)); 60 if (isnan(a)) { 61 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 62 return (cpack(t, t)); /* return NaN + NaN i */ 63 } 64 if (isinf(a)) { 65 /* 66 * csqrt(inf + nan i) = inf + nan i 67 * csqrt(inf + y i) = inf + 0 i 68 * csqrt(-inf + nan i) = nan +- inf i 69 * csqrt(-inf + y i) = 0 + inf i 70 */ 71 if (signbit(a)) 72 return (cpack(fabs(b - b), copysign(a, b))); 73 else 74 return (cpack(a, copysign(b - b, b))); 75 } 76 /* 77 * The remaining special case (b is NaN) is handled just fine by 78 * the normal code path below. 79 */ 80 81 /* Scale to avoid overflow. */ 82 if (a >= THRESH || b >= THRESH) { 83 a *= 0.25; 84 b *= 0.25; 85 scale = 1; 86 } else { 87 scale = 0; 88 } 89 90 /* Algorithm 312, CACM vol 10, Oct 1967 */ 91 if (a >= 0) { 92 t = sqrt((a + hypot(a, b)) * 0.5); 93 result = cpack(t, b / (2 * t)); 94 } else { 95 t = sqrt((-a + hypot(a, b)) * 0.5); 96 result = cpack(fabs(b) / (2 * t), copysign(t, b)); 97 } 98 99 /* Rescale */ 100 if (scale) 101 return (result * 2); 102 else 103 return (result); 104 } 105