1 /* $OpenBSD: s_csqrt.c,v 1.8 2016/09/12 19:47:02 guenther Exp $ */ 2 /* 3 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> 4 * 5 * Permission to use, copy, modify, and distribute this software for any 6 * purpose with or without fee is hereby granted, provided that the above 7 * copyright notice and this permission notice appear in all copies. 8 * 9 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 10 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 11 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 12 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 13 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 14 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 15 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 16 */ 17 18 /* csqrt() 19 * 20 * Complex square root 21 * 22 * 23 * 24 * SYNOPSIS: 25 * 26 * double complex csqrt(); 27 * double complex z, w; 28 * 29 * w = csqrt (z); 30 * 31 * 32 * 33 * DESCRIPTION: 34 * 35 * 36 * If z = x + iy, r = |z|, then 37 * 38 * 1/2 39 * Re w = [ (r + x)/2 ] , 40 * 41 * 1/2 42 * Im w = [ (r - x)/2 ] . 43 * 44 * Cancellation error in r-x or r+x is avoided by using the 45 * identity 2 Re w Im w = y. 46 * 47 * Note that -w is also a square root of z. The root chosen 48 * is always in the right half plane and Im w has the same sign as y. 49 * 50 * 51 * 52 * ACCURACY: 53 * 54 * Relative error: 55 * arithmetic domain # trials peak rms 56 * DEC -10,+10 25000 3.2e-17 9.6e-18 57 * IEEE -10,+10 1,000,000 2.9e-16 6.1e-17 58 * 59 */ 60 61 #include <complex.h> 62 #include <float.h> 63 #include <math.h> 64 65 double complex 66 csqrt(double complex z) 67 { 68 double complex w; 69 double x, y, r, t, scale; 70 71 x = creal (z); 72 y = cimag (z); 73 74 if (y == 0.0) { 75 if (x == 0.0) { 76 w = 0.0 + y * I; 77 } 78 else { 79 r = fabs (x); 80 r = sqrt (r); 81 if (x < 0.0) { 82 w = 0.0 + copysign(r, y) * I; 83 } 84 else { 85 w = r + y * I; 86 } 87 } 88 return (w); 89 } 90 if (x == 0.0) { 91 r = fabs (y); 92 r = sqrt (0.5*r); 93 if (y > 0) 94 w = r + r * I; 95 else 96 w = r - r * I; 97 return (w); 98 } 99 /* Rescale to avoid internal overflow or underflow. */ 100 if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) { 101 x *= 0.25; 102 y *= 0.25; 103 scale = 2.0; 104 } 105 else { 106 x *= 1.8014398509481984e16; /* 2^54 */ 107 y *= 1.8014398509481984e16; 108 scale = 7.450580596923828125e-9; /* 2^-27 */ 109 #if 0 110 x *= 4.0; 111 y *= 4.0; 112 scale = 0.5; 113 #endif 114 } 115 w = x + y * I; 116 r = cabs(w); 117 if (x > 0) { 118 t = sqrt(0.5 * r + 0.5 * x); 119 r = scale * fabs((0.5 * y) / t); 120 t *= scale; 121 } 122 else { 123 r = sqrt( 0.5 * r - 0.5 * x ); 124 t = scale * fabs( (0.5 * y) / r ); 125 r *= scale; 126 } 127 if (y < 0) 128 w = t - r * I; 129 else 130 w = t + r * I; 131 return (w); 132 } 133 DEF_STD(csqrt); 134 LDBL_MAYBE_CLONE(csqrt); 135