1*05a0b428SJohn Marino /* $OpenBSD: s_clog.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */ 2*05a0b428SJohn Marino /* 3*05a0b428SJohn Marino * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> 4*05a0b428SJohn Marino * 5*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this software for any 6*05a0b428SJohn Marino * purpose with or without fee is hereby granted, provided that the above 7*05a0b428SJohn Marino * copyright notice and this permission notice appear in all copies. 8*05a0b428SJohn Marino * 9*05a0b428SJohn Marino * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 10*05a0b428SJohn Marino * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 11*05a0b428SJohn Marino * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 12*05a0b428SJohn Marino * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 13*05a0b428SJohn Marino * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 14*05a0b428SJohn Marino * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 15*05a0b428SJohn Marino * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 16*05a0b428SJohn Marino */ 17*05a0b428SJohn Marino 18*05a0b428SJohn Marino /* clog.c 19*05a0b428SJohn Marino * 20*05a0b428SJohn Marino * Complex natural logarithm 21*05a0b428SJohn Marino * 22*05a0b428SJohn Marino * 23*05a0b428SJohn Marino * 24*05a0b428SJohn Marino * SYNOPSIS: 25*05a0b428SJohn Marino * 26*05a0b428SJohn Marino * double complex clog(); 27*05a0b428SJohn Marino * double complex z, w; 28*05a0b428SJohn Marino * 29*05a0b428SJohn Marino * w = clog (z); 30*05a0b428SJohn Marino * 31*05a0b428SJohn Marino * 32*05a0b428SJohn Marino * 33*05a0b428SJohn Marino * DESCRIPTION: 34*05a0b428SJohn Marino * 35*05a0b428SJohn Marino * Returns complex logarithm to the base e (2.718...) of 36*05a0b428SJohn Marino * the complex argument x. 37*05a0b428SJohn Marino * 38*05a0b428SJohn Marino * If z = x + iy, r = sqrt( x**2 + y**2 ), 39*05a0b428SJohn Marino * then 40*05a0b428SJohn Marino * w = log(r) + i arctan(y/x). 41*05a0b428SJohn Marino * 42*05a0b428SJohn Marino * The arctangent ranges from -PI to +PI. 43*05a0b428SJohn Marino * 44*05a0b428SJohn Marino * 45*05a0b428SJohn Marino * ACCURACY: 46*05a0b428SJohn Marino * 47*05a0b428SJohn Marino * Relative error: 48*05a0b428SJohn Marino * arithmetic domain # trials peak rms 49*05a0b428SJohn Marino * DEC -10,+10 7000 8.5e-17 1.9e-17 50*05a0b428SJohn Marino * IEEE -10,+10 30000 5.0e-15 1.1e-16 51*05a0b428SJohn Marino * 52*05a0b428SJohn Marino * Larger relative error can be observed for z near 1 +i0. 53*05a0b428SJohn Marino * In IEEE arithmetic the peak absolute error is 5.2e-16, rms 54*05a0b428SJohn Marino * absolute error 1.0e-16. 55*05a0b428SJohn Marino */ 56*05a0b428SJohn Marino 57*05a0b428SJohn Marino #include <complex.h> 58*05a0b428SJohn Marino #include <float.h> 59*05a0b428SJohn Marino #include <math.h> 60*05a0b428SJohn Marino 61*05a0b428SJohn Marino double complex 62*05a0b428SJohn Marino clog(double complex z) 63*05a0b428SJohn Marino { 64*05a0b428SJohn Marino double complex w; 65*05a0b428SJohn Marino double p, rr; 66*05a0b428SJohn Marino 67*05a0b428SJohn Marino /*rr = sqrt( z->r * z->r + z->i * z->i );*/ 68*05a0b428SJohn Marino rr = cabs(z); 69*05a0b428SJohn Marino p = log(rr); 70*05a0b428SJohn Marino rr = atan2 (cimag (z), creal (z)); 71*05a0b428SJohn Marino w = p + rr * I; 72*05a0b428SJohn Marino return (w); 73*05a0b428SJohn Marino } 74*05a0b428SJohn Marino 75*05a0b428SJohn Marino #if LDBL_MANT_DIG == DBL_MANT_DIG 76*05a0b428SJohn Marino __strong_alias(clogl, clog); 77*05a0b428SJohn Marino #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 78