1 /* $OpenBSD: s_cpow.c,v 1.6 2013/07/03 04:46:36 espie 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 /* cpow 19 * 20 * Complex power function 21 * 22 * 23 * 24 * SYNOPSIS: 25 * 26 * double complex cpow(); 27 * double complex a, z, w; 28 * 29 * w = cpow (a, z); 30 * 31 * 32 * 33 * DESCRIPTION: 34 * 35 * Raises complex A to the complex Zth power. 36 * Definition is per AMS55 # 4.2.8, 37 * analytically equivalent to cpow(a,z) = cexp(z clog(a)). 38 * 39 * ACCURACY: 40 * 41 * Relative error: 42 * arithmetic domain # trials peak rms 43 * IEEE -10,+10 30000 9.4e-15 1.5e-15 44 * 45 */ 46 47 #include <complex.h> 48 #include <float.h> 49 #include <math.h> 50 51 double complex 52 cpow(double complex a, double complex z) 53 { 54 double complex w; 55 double x, y, r, theta, absa, arga; 56 57 x = creal (z); 58 y = cimag (z); 59 absa = cabs (a); 60 if (absa == 0.0) { 61 return (0.0 + 0.0 * I); 62 } 63 arga = carg (a); 64 r = pow (absa, x); 65 theta = x * arga; 66 if (y != 0.0) { 67 r = r * exp (-y * arga); 68 theta = theta + y * log (absa); 69 } 70 w = r * cos (theta) + (r * sin (theta)) * I; 71 return (w); 72 } 73 74 #if LDBL_MANT_DIG == DBL_MANT_DIG 75 __strong_alias(cpowl, cpow); 76 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 77