1 /*- 2 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> 3 * 4 * Permission to use, copy, modify, and distribute this software for any 5 * purpose with or without fee is hereby granted, provided that the above 6 * copyright notice and this permission notice appear in all copies. 7 * 8 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 9 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 10 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 11 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 12 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 13 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 14 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 15 */ 16 17 /* cpow 18 * 19 * Complex power function 20 * 21 * 22 * 23 * SYNOPSIS: 24 * 25 * double complex cpow(); 26 * double complex a, z, w; 27 * 28 * w = cpow (a, z); 29 * 30 * 31 * 32 * DESCRIPTION: 33 * 34 * Raises complex A to the complex Zth power. 35 * Definition is per AMS55 # 4.2.8, 36 * analytically equivalent to cpow(a,z) = cexp(z clog(a)). 37 * 38 * ACCURACY: 39 * 40 * Relative error: 41 * arithmetic domain # trials peak rms 42 * IEEE -10,+10 30000 9.4e-15 1.5e-15 43 * 44 */ 45 46 #include <complex.h> 47 #include <float.h> 48 #include <math.h> 49 #include "math_private.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 (CMPLX(0.0, 0.0)); 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 = CMPLX(r * cos (theta), r * sin (theta)); 71 return (w); 72 } 73