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 complex result; 51 double a, b; 52 double t; 53 int scale; 54 55 a = creal(z); 56 b = cimag(z); 57 58 /* Handle special cases. */ 59 if (z == 0) 60 return (cpack(0, b)); 61 if (isinf(b)) 62 return (cpack(INFINITY, b)); 63 if (isnan(a)) { 64 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 65 return (cpack(a, t)); /* return NaN + NaN i */ 66 } 67 if (isinf(a)) { 68 /* 69 * csqrt(inf + NaN i) = inf + NaN i 70 * csqrt(inf + y i) = inf + 0 i 71 * csqrt(-inf + NaN i) = NaN +- inf i 72 * csqrt(-inf + y i) = 0 + inf i 73 */ 74 if (signbit(a)) 75 return (cpack(fabs(b - b), copysign(a, b))); 76 else 77 return (cpack(a, copysign(b - b, b))); 78 } 79 /* 80 * The remaining special case (b is NaN) is handled just fine by 81 * the normal code path below. 82 */ 83 84 /* Scale to avoid overflow. */ 85 if (fabs(a) >= THRESH || fabs(b) >= THRESH) { 86 a *= 0.25; 87 b *= 0.25; 88 scale = 1; 89 } else { 90 scale = 0; 91 } 92 93 /* Algorithm 312, CACM vol 10, Oct 1967. */ 94 if (a >= 0) { 95 t = sqrt((a + hypot(a, b)) * 0.5); 96 result = cpack(t, b / (2 * t)); 97 } else { 98 t = sqrt((-a + hypot(a, b)) * 0.5); 99 result = cpack(fabs(b) / (2 * t), copysign(t, b)); 100 } 101 102 /* Rescale. */ 103 if (scale) 104 return (result * 2); 105 else 106 return (result); 107 } 108