1 /* $OpenBSD: s_csqrtl.c,v 1.4 2016/09/12 19:47:02 guenther Exp $ */ 2 3 /* 4 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> 5 * 6 * Permission to use, copy, modify, and distribute this software for any 7 * purpose with or without fee is hereby granted, provided that the above 8 * copyright notice and this permission notice appear in all copies. 9 * 10 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 11 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 12 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 13 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 14 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 15 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 16 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 17 */ 18 19 /* csqrtl() 20 * 21 * Complex square root 22 * 23 * 24 * 25 * SYNOPSIS: 26 * 27 * long double complex csqrtl(); 28 * long double complex z, w; 29 * 30 * w = csqrtl( z ); 31 * 32 * 33 * 34 * DESCRIPTION: 35 * 36 * 37 * If z = x + iy, r = |z|, then 38 * 39 * 1/2 40 * Re w = [ (r + x)/2 ] , 41 * 42 * 1/2 43 * Im w = [ (r - x)/2 ] . 44 * 45 * Cancellation error in r-x or r+x is avoided by using the 46 * identity 2 Re w Im w = y. 47 * 48 * Note that -w is also a square root of z. The root chosen 49 * is always in the right half plane and Im w has the same sign as y. 50 * 51 * 52 * 53 * ACCURACY: 54 * 55 * Relative error: 56 * arithmetic domain # trials peak rms 57 * IEEE -10,+10 500000 1.1e-19 3.0e-20 58 * 59 */ 60 61 #include <complex.h> 62 #include <math.h> 63 64 long double complex 65 csqrtl(long double complex z) 66 { 67 long double complex w; 68 long double x, y, r, t, scale; 69 70 x = creall(z); 71 y = cimagl(z); 72 73 if (y == 0.0L) { 74 if (x < 0.0L) { 75 w = 0.0L + copysign(sqrtl(-x), y) * I; 76 return (w); 77 } 78 else { 79 w = sqrtl(x) + 0.0L * I; 80 return (w); 81 } 82 } 83 84 if (x == 0.0L) { 85 r = fabsl(y); 86 r = sqrtl(0.5L * r); 87 if (y > 0.0L) 88 w = r + r * I; 89 else 90 w = r - r * I; 91 return (w); 92 } 93 94 /* Rescale to avoid internal overflow or underflow. */ 95 if ((fabsl(x) > 4.0L) || (fabsl(y) > 4.0L)) { 96 x *= 0.25L; 97 y *= 0.25L; 98 scale = 2.0L; 99 } 100 else { 101 #if 1 102 x *= 7.3786976294838206464e19; /* 2^66 */ 103 y *= 7.3786976294838206464e19; 104 scale = 1.16415321826934814453125e-10; /* 2^-33 */ 105 #else 106 x *= 4.0L; 107 y *= 4.0L; 108 scale = 0.5L; 109 #endif 110 } 111 w = x + y * I; 112 r = cabsl(w); 113 if (x > 0) { 114 t = sqrtl(0.5L * r + 0.5L * x); 115 r = scale * fabsl((0.5L * y) / t); 116 t *= scale; 117 } 118 else { 119 r = sqrtl(0.5L * r - 0.5L * x); 120 t = scale * fabsl((0.5L * y) / r); 121 r *= scale; 122 } 123 if (y < 0) 124 w = t - r * I; 125 else 126 w = t + r * I; 127 return (w); 128 } 129 DEF_STD(csqrtl); 130