1*05a0b428SJohn Marino /* $OpenBSD: s_clogl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ 2*05a0b428SJohn Marino 3*05a0b428SJohn Marino /* 4*05a0b428SJohn Marino * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> 5*05a0b428SJohn Marino * 6*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this software for any 7*05a0b428SJohn Marino * purpose with or without fee is hereby granted, provided that the above 8*05a0b428SJohn Marino * copyright notice and this permission notice appear in all copies. 9*05a0b428SJohn Marino * 10*05a0b428SJohn Marino * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 11*05a0b428SJohn Marino * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 12*05a0b428SJohn Marino * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 13*05a0b428SJohn Marino * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 14*05a0b428SJohn Marino * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 15*05a0b428SJohn Marino * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 16*05a0b428SJohn Marino * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 17*05a0b428SJohn Marino */ 18*05a0b428SJohn Marino 19*05a0b428SJohn Marino /* clogl.c 20*05a0b428SJohn Marino * 21*05a0b428SJohn Marino * Complex natural logarithm 22*05a0b428SJohn Marino * 23*05a0b428SJohn Marino * 24*05a0b428SJohn Marino * 25*05a0b428SJohn Marino * SYNOPSIS: 26*05a0b428SJohn Marino * 27*05a0b428SJohn Marino * long double complex clogl(); 28*05a0b428SJohn Marino * long double complex z, w; 29*05a0b428SJohn Marino * 30*05a0b428SJohn Marino * w = clogl( z ); 31*05a0b428SJohn Marino * 32*05a0b428SJohn Marino * 33*05a0b428SJohn Marino * 34*05a0b428SJohn Marino * DESCRIPTION: 35*05a0b428SJohn Marino * 36*05a0b428SJohn Marino * Returns complex logarithm to the base e (2.718...) of 37*05a0b428SJohn Marino * the complex argument x. 38*05a0b428SJohn Marino * 39*05a0b428SJohn Marino * If z = x + iy, r = sqrt( x**2 + y**2 ), 40*05a0b428SJohn Marino * then 41*05a0b428SJohn Marino * w = log(r) + i arctan(y/x). 42*05a0b428SJohn Marino * 43*05a0b428SJohn Marino * The arctangent ranges from -PI to +PI. 44*05a0b428SJohn Marino * 45*05a0b428SJohn Marino * 46*05a0b428SJohn Marino * ACCURACY: 47*05a0b428SJohn Marino * 48*05a0b428SJohn Marino * Relative error: 49*05a0b428SJohn Marino * arithmetic domain # trials peak rms 50*05a0b428SJohn Marino * DEC -10,+10 7000 8.5e-17 1.9e-17 51*05a0b428SJohn Marino * IEEE -10,+10 30000 5.0e-15 1.1e-16 52*05a0b428SJohn Marino * 53*05a0b428SJohn Marino * Larger relative error can be observed for z near 1 +i0. 54*05a0b428SJohn Marino * In IEEE arithmetic the peak absolute error is 5.2e-16, rms 55*05a0b428SJohn Marino * absolute error 1.0e-16. 56*05a0b428SJohn Marino */ 57*05a0b428SJohn Marino 58*05a0b428SJohn Marino #include <complex.h> 59*05a0b428SJohn Marino #include <math.h> 60*05a0b428SJohn Marino 61*05a0b428SJohn Marino long double complex 62*05a0b428SJohn Marino clogl(long double complex z) 63*05a0b428SJohn Marino { 64*05a0b428SJohn Marino long double complex w; 65*05a0b428SJohn Marino long double p, rr; 66*05a0b428SJohn Marino 67*05a0b428SJohn Marino /*rr = sqrt(z->r * z->r + z->i * z->i);*/ 68*05a0b428SJohn Marino p = cabsl(z); 69*05a0b428SJohn Marino p = logl(p); 70*05a0b428SJohn Marino rr = atan2l(cimagl(z), creall(z)); 71*05a0b428SJohn Marino w = p + rr * I; 72*05a0b428SJohn Marino return (w); 73*05a0b428SJohn Marino } 74