1 /* $NetBSD: csqrt.c,v 1.4 2017/01/01 19:32:14 maya Exp $ */ 2 3 /*- 4 * Copyright (c) 2007 The NetBSD Foundation, Inc. 5 * All rights reserved. 6 * 7 * This code is derived from software written by Stephen L. Moshier. 8 * It is redistributed by the NetBSD Foundation by permission of the author. 9 * 10 * Redistribution and use in source and binary forms, with or without 11 * modification, are permitted provided that the following conditions 12 * are met: 13 * 1. Redistributions of source code must retain the above copyright 14 * notice, this list of conditions and the following disclaimer. 15 * 2. Redistributions in binary form must reproduce the above copyright 16 * notice, this list of conditions and the following disclaimer in the 17 * documentation and/or other materials provided with the distribution. 18 * 19 * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS 20 * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED 21 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 22 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS 23 * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 24 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 25 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 26 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 27 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 28 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 29 * POSSIBILITY OF SUCH DAMAGE. 30 */ 31 32 #include <complex.h> 33 #include <math.h> 34 35 double complex 36 csqrt(double complex z) 37 { 38 double complex w; 39 double x, y, r, t, scale; 40 41 x = creal (z); 42 y = cimag (z); 43 44 /* 45 * input is a real number and imaginary part isn't -0.0. 46 * negative zero is on the branch cut. 47 */ 48 if ((y == 0.0) && !signbit(y)) { 49 if (x == 0.0) { 50 w = 0.0 + y * I; 51 } else { 52 if (x < 0.0) { 53 r = sqrt(-x); 54 w = 0.0 + r * I; 55 } else { 56 r = sqrt(x); 57 w = r; 58 } 59 } 60 return w; 61 } 62 if (x == 0.0) { 63 if (y > 0) { 64 r = sqrt(0.5 * y); 65 w = r + r * I; 66 } else { 67 r = sqrt(-0.5 * y); 68 w = r - r * I; 69 } 70 return w; 71 } 72 /* Rescale to avoid internal overflow or underflow. */ 73 if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) { 74 x *= 0.25; 75 y *= 0.25; 76 scale = 2.0; 77 } else { 78 #if 1 79 x *= 1.8014398509481984e16; /* 2^54 */ 80 y *= 1.8014398509481984e16; 81 scale = 7.450580596923828125e-9; /* 2^-27 */ 82 #else 83 x *= 4.0; 84 y *= 4.0; 85 scale = 0.5; 86 #endif 87 } 88 w = x + y * I; 89 r = cabs(w); 90 if (x > 0) { 91 t = sqrt(0.5 * r + 0.5 * x); 92 r = scale * fabs((0.5 * y) / t ); 93 t *= scale; 94 } else { 95 r = sqrt(0.5 * r - 0.5 * x); 96 t = scale * fabs((0.5 * y) / r); 97 r *= scale; 98 } 99 if (y > 0) 100 w = t + r * I; 101 else 102 w = t - r * I; 103 return w; 104 } 105