1 /* $NetBSD: csqrt.c,v 1.2 2016/12/31 15:33:03 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 if (y == 0.0) { 45 if (x == 0.0) { 46 w = 0.0 + y * I; 47 } else { 48 if (x < 0.0) { 49 r = sqrt(-x); 50 w = 0.0 + r * I; 51 } else { 52 r = sqrt(x); 53 w = r; 54 } 55 } 56 return w; 57 } 58 if (x == 0.0) { 59 if (y > 0) { 60 r = sqrt(0.5 * y); 61 w = r + r * I; 62 } else { 63 r = sqrt(-0.5 * y); 64 w = r - r * I; 65 } 66 return w; 67 } 68 /* Rescale to avoid internal overflow or underflow. */ 69 if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) { 70 x *= 0.25; 71 y *= 0.25; 72 scale = 2.0; 73 } else { 74 #if 1 75 x *= 1.8014398509481984e16; /* 2^54 */ 76 y *= 1.8014398509481984e16; 77 scale = 7.450580596923828125e-9; /* 2^-27 */ 78 #else 79 x *= 4.0; 80 y *= 4.0; 81 scale = 0.5; 82 #endif 83 } 84 w = x + y * I; 85 r = cabs(w); 86 if (x > 0) { 87 t = sqrt(0.5 * r + 0.5 * x); 88 r = scale * fabs((0.5 * y) / t ); 89 t *= scale; 90 } else { 91 r = sqrt(0.5 * r - 0.5 * x); 92 t = scale * fabs((0.5 * y) / r); 93 r *= scale; 94 } 95 if (y < 0) 96 w = t - r * I; 97 else 98 w = t + r * I; 99 return w; 100 } 101