1 /* $OpenBSD: s_clog.c,v 1.7 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 /* clog.c 19 * 20 * Complex natural logarithm 21 * 22 * 23 * 24 * SYNOPSIS: 25 * 26 * double complex clog(); 27 * double complex z, w; 28 * 29 * w = clog (z); 30 * 31 * 32 * 33 * DESCRIPTION: 34 * 35 * Returns complex logarithm to the base e (2.718...) of 36 * the complex argument x. 37 * 38 * If z = x + iy, r = sqrt( x**2 + y**2 ), 39 * then 40 * w = log(r) + i arctan(y/x). 41 * 42 * The arctangent ranges from -PI to +PI. 43 * 44 * 45 * ACCURACY: 46 * 47 * Relative error: 48 * arithmetic domain # trials peak rms 49 * DEC -10,+10 7000 8.5e-17 1.9e-17 50 * IEEE -10,+10 30000 5.0e-15 1.1e-16 51 * 52 * Larger relative error can be observed for z near 1 +i0. 53 * In IEEE arithmetic the peak absolute error is 5.2e-16, rms 54 * absolute error 1.0e-16. 55 */ 56 57 #include <complex.h> 58 #include <float.h> 59 #include <math.h> 60 61 double complex 62 clog(double complex z) 63 { 64 double complex w; 65 double p, rr; 66 67 /*rr = sqrt( z->r * z->r + z->i * z->i );*/ 68 rr = cabs(z); 69 p = log(rr); 70 rr = atan2 (cimag (z), creal (z)); 71 w = p + rr * I; 72 return (w); 73 } 74 DEF_STD(clog); 75 LDBL_MAYBE_CLONE(clog); 76