1 /* $OpenBSD: s_cpowl.c,v 1.2 2011/07/20 19:28:33 martynas Exp $ */ 2 3 /* 4 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> 5 * 6 * Permission to use, copy, modify, and distribute this software for any 7 * purpose with or without fee is hereby granted, provided that the above 8 * copyright notice and this permission notice appear in all copies. 9 * 10 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 11 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 12 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 13 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 14 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 15 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 16 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 17 */ 18 19 /* cpowl 20 * 21 * Complex power function 22 * 23 * 24 * 25 * SYNOPSIS: 26 * 27 * long double complex cpowl(); 28 * long double complex a, z, w; 29 * 30 * w = cpowl (a, z); 31 * 32 * 33 * 34 * DESCRIPTION: 35 * 36 * Raises complex A to the complex Zth power. 37 * Definition is per AMS55 # 4.2.8, 38 * analytically equivalent to cpow(a,z) = cexp(z clog(a)). 39 * 40 * ACCURACY: 41 * 42 * Relative error: 43 * arithmetic domain # trials peak rms 44 * IEEE -10,+10 30000 9.4e-15 1.5e-15 45 * 46 */ 47 48 #include <complex.h> 49 #include <openlibm.h> 50 #include "math_private.h" 51 52 DLLEXPORT long double complex 53 cpowl(long double complex a, long double complex z) 54 { 55 long double complex w; 56 long double x, y, r, theta, absa, arga; 57 58 x = creall(z); 59 y = cimagl(z); 60 absa = cabsl(a); 61 if (absa == 0.0L) { 62 return (0.0L + 0.0L * I); 63 } 64 arga = cargl(a); 65 r = powl(absa, x); 66 theta = x * arga; 67 if (y != 0.0L) { 68 r = r * expl(-y * arga); 69 theta = theta + y * logl(absa); 70 } 71 w = r * cosl(theta) + (r * sinl(theta)) * I; 72 return (w); 73 } 74