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/*-
* 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);
}
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