1 /* $OpenBSD: s_cpowf.c,v 1.2 2010/07/18 18:42:26 guenther 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 /* cpowf 19 * 20 * Complex power function 21 * 22 * 23 * 24 * SYNOPSIS: 25 * 26 * float complex cpowf(); 27 * float complex a, z, w; 28 * 29 * w = cpowf (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 <openlibm.h> 48 #include <openlibm_complex.h> 49 50 #include "math_private.h" 51 52 DLLEXPORT float complex 53 cpowf(float complex a, float complex z) 54 { 55 float complex w; 56 float x, y, r, theta, absa, arga; 57 58 x = crealf(z); 59 y = cimagf(z); 60 absa = cabsf (a); 61 if (absa == 0.0f) { 62 return (0.0f + 0.0f * I); 63 } 64 arga = cargf (a); 65 r = powf (absa, x); 66 theta = x * arga; 67 if (y != 0.0f) { 68 r = r * expf (-y * arga); 69 theta = theta + y * logf (absa); 70 } 71 w = r * cosf (theta) + (r * sinf (theta)) * I; 72 return (w); 73 } 74