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 /* cpowl 18 * 19 * Complex power function 20 * 21 * 22 * 23 * SYNOPSIS: 24 * 25 * long double complex cpowl(); 26 * long double complex a, z, w; 27 * 28 * w = cpowl (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 <sys/cdefs.h> 47 __FBSDID("$FreeBSD$"); 48 49 #include <complex.h> 50 #include <math.h> 51 #include "math_private.h" 52 53 long double complex 54 cpowl(long double complex a, long double complex z) 55 { 56 long double complex w; 57 long double x, y, r, theta, absa, arga; 58 59 x = creall(z); 60 y = cimagl(z); 61 absa = cabsl(a); 62 if (absa == 0.0L) { 63 return (CMPLXL(0.0L, 0.0L)); 64 } 65 arga = cargl(a); 66 r = powl(absa, x); 67 theta = x * arga; 68 if (y != 0.0L) { 69 r = r * expl(-y * arga); 70 theta = theta + y * logl(absa); 71 } 72 w = CMPLXL(r * cosl(theta), r * sinl(theta)); 73 return (w); 74 } 75