1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause 3 * 4 * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG> 5 * All rights reserved. 6 * 7 * Redistribution and use in source and binary forms, with or without 8 * modification, are permitted provided that the following conditions 9 * are met: 10 * 1. Redistributions of source code must retain the above copyright 11 * notice, this list of conditions and the following disclaimer. 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in the 14 * documentation and/or other materials provided with the distribution. 15 * 16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26 * SUCH DAMAGE. 27 */ 28 29 #include <complex.h> 30 #include <float.h> 31 #include <math.h> 32 33 #include "math_private.h" 34 35 /* For avoiding overflow for components >= DBL_MAX / (1 + sqrt(2)). */ 36 #define THRESH 0x1.a827999fcef32p+1022 37 38 double complex 39 csqrt(double complex z) 40 { 41 double complex result; 42 double a, b, rx, ry, scale, t; 43 44 a = creal(z); 45 b = cimag(z); 46 47 /* Handle special cases. */ 48 if (z == 0) 49 return (CMPLX(0, b)); 50 if (isinf(b)) 51 return (CMPLX(INFINITY, b)); 52 if (isnan(a)) { 53 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 54 return (CMPLX(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */ 55 } 56 if (isinf(a)) { 57 /* 58 * csqrt(inf + NaN i) = inf + NaN i 59 * csqrt(inf + y i) = inf + 0 i 60 * csqrt(-inf + NaN i) = NaN +- inf i 61 * csqrt(-inf + y i) = 0 + inf i 62 */ 63 if (signbit(a)) 64 return (CMPLX(fabs(b - b), copysign(a, b))); 65 else 66 return (CMPLX(a, copysign(b - b, b))); 67 } 68 if (isnan(b)) { 69 t = (a - a) / (a - a); /* raise invalid */ 70 return (CMPLX(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */ 71 } 72 73 /* Scale to avoid overflow. */ 74 if (fabs(a) >= THRESH || fabs(b) >= THRESH) { 75 /* 76 * Don't scale a or b if this might give (spurious) 77 * underflow. Then the unscaled value is an equivalent 78 * infinitesmal (or 0). 79 */ 80 if (fabs(a) >= 0x1p-1020) 81 a *= 0.25; 82 if (fabs(b) >= 0x1p-1020) 83 b *= 0.25; 84 scale = 2; 85 } else { 86 scale = 1; 87 } 88 89 /* Scale to reduce inaccuracies when both components are denormal. */ 90 if (fabs(a) < 0x1p-1022 && fabs(b) < 0x1p-1022) { 91 a *= 0x1p54; 92 b *= 0x1p54; 93 scale = 0x1p-27; 94 } 95 96 /* Algorithm 312, CACM vol 10, Oct 1967. */ 97 if (a >= 0) { 98 t = sqrt((a + hypot(a, b)) * 0.5); 99 rx = scale * t; 100 ry = scale * b / (2 * t); 101 } else { 102 t = sqrt((-a + hypot(a, b)) * 0.5); 103 rx = scale * fabs(b) / (2 * t); 104 ry = copysign(scale * t, b); 105 } 106 107 return (CMPLX(rx, ry)); 108 } 109 110 #if LDBL_MANT_DIG == 53 111 __weak_reference(csqrt, csqrtl); 112 #endif 113