1 /* $OpenBSD: s_clog.c,v 1.2 2011/07/08 19:25:31 martynas 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 /* LINTLIBRARY */ 19 20 /* clog.c 21 * 22 * Complex natural logarithm 23 * 24 * 25 * 26 * SYNOPSIS: 27 * 28 * double complex clog(); 29 * double complex z, w; 30 * 31 * w = clog (z); 32 * 33 * 34 * 35 * DESCRIPTION: 36 * 37 * Returns complex logarithm to the base e (2.718...) of 38 * the complex argument x. 39 * 40 * If z = x + iy, r = sqrt( x**2 + y**2 ), 41 * then 42 * w = log(r) + i arctan(y/x). 43 * 44 * The arctangent ranges from -PI to +PI. 45 * 46 * 47 * ACCURACY: 48 * 49 * Relative error: 50 * arithmetic domain # trials peak rms 51 * DEC -10,+10 7000 8.5e-17 1.9e-17 52 * IEEE -10,+10 30000 5.0e-15 1.1e-16 53 * 54 * Larger relative error can be observed for z near 1 +i0. 55 * In IEEE arithmetic the peak absolute error is 5.2e-16, rms 56 * absolute error 1.0e-16. 57 */ 58 59 #include <sys/cdefs.h> 60 #include <complex.h> 61 #include <float.h> 62 #include <math.h> 63 64 double complex 65 clog(double complex z) 66 { 67 double complex w; 68 double p, rr; 69 70 /*rr = sqrt( z->r * z->r + z->i * z->i );*/ 71 rr = cabs(z); 72 p = log(rr); 73 rr = atan2 (cimag (z), creal (z)); 74 w = p + rr * I; 75 return (w); 76 } 77 78 #if LDBL_MANT_DIG == 53 79 #ifdef lint 80 /* PROTOLIB1 */ 81 long double complex clogl(long double complex); 82 #else /* lint */ 83 __weak_alias(clogl, clog); 84 #endif /* lint */ 85 #endif /* LDBL_MANT_DIG == 53 */ 86