| /*- |
| * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> |
| * |
| * Permission to use, copy, modify, and distribute this software for any |
| * purpose with or without fee is hereby granted, provided that the above |
| * copyright notice and this permission notice appear in all copies. |
| * |
| * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
| * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
| * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR |
| * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
| * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN |
| * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF |
| * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. |
| */ |
| |
| /* cpowl |
| * |
| * Complex power function |
| * |
| * |
| * |
| * SYNOPSIS: |
| * |
| * long double complex cpowl(); |
| * long double complex a, z, w; |
| * |
| * w = cpowl (a, z); |
| * |
| * |
| * |
| * DESCRIPTION: |
| * |
| * Raises complex A to the complex Zth power. |
| * Definition is per AMS55 # 4.2.8, |
| * analytically equivalent to cpow(a,z) = cexp(z clog(a)). |
| * |
| * ACCURACY: |
| * |
| * Relative error: |
| * arithmetic domain # trials peak rms |
| * IEEE -10,+10 30000 9.4e-15 1.5e-15 |
| * |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| #include <complex.h> |
| #include <math.h> |
| #include "math_private.h" |
| |
| long double complex |
| cpowl(long double complex a, long double complex z) |
| { |
| long double complex w; |
| long double x, y, r, theta, absa, arga; |
| |
| x = creall(z); |
| y = cimagl(z); |
| absa = cabsl(a); |
| if (absa == 0.0L) { |
| return (CMPLXL(0.0L, 0.0L)); |
| } |
| arga = cargl(a); |
| r = powl(absa, x); |
| theta = x * arga; |
| if (y != 0.0L) { |
| r = r * expl(-y * arga); |
| theta = theta + y * logl(absa); |
| } |
| w = CMPLXL(r * cosl(theta), r * sinl(theta)); |
| return (w); |
| } |