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 /* cpowf 18 * 19 * Complex power function 20 * 21 * 22 * 23 * SYNOPSIS: 24 * 25 * float complex cpowf(); 26 * float complex a, z, w; 27 * 28 * w = cpowf (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 <math.h> 48 #include "math_private.h" 49 50 float complex 51 cpowf(float complex a, float complex z) 52 { 53 float complex w; 54 float x, y, r, theta, absa, arga; 55 56 x = crealf(z); 57 y = cimagf(z); 58 absa = cabsf (a); 59 if (absa == 0.0f) { 60 return (CMPLXF(0.0f, 0.0f)); 61 } 62 arga = cargf (a); 63 r = powf (absa, x); 64 theta = x * arga; 65 if (y != 0.0f) { 66 r = r * expf (-y * arga); 67 theta = theta + y * logf (absa); 68 } 69 w = CMPLXF(r * cosf (theta), r * sinf (theta)); 70 return (w); 71 } 72