/*
 * Zorbage: an algebraic data hierarchy for use in numeric processing.
 *
 * Copyright (C) 2016-2018 Barry DeZonia
 * 
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 * 
 * 1. Redistributions of source code must retain the above copyright notice,
 *    this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright notice,
 *    this list of conditions and the following disclaimer in the documentation
 *    and/or other materials provided with the distribution.
 * 
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 */
package nom.bdezonia.zorbage.algorithm;

import nom.bdezonia.zorbage.groups.G;
import nom.bdezonia.zorbage.type.data.float64.complex.ComplexFloat64Member;

/**
 * 
 * @author Barry DeZonia
 *
 */
public class ComplexRootOfUnity {

	// do not instantiate
	
	private ComplexRootOfUnity() {}
	
	// TODO: for values of m very large this math will break down

	/**
	 * Compute the principal root of unity given the order m.
	 * @param m Order of principal root.
	 * @param principalRoot Output value.
	 */
	public static
		void compute(long m, ComplexFloat64Member principalRoot)
	{
		ComplexFloat64Member e = G.CDBL.construct();
		ComplexFloat64Member power = G.CDBL.construct();
		ComplexFloat64Member two = G.CDBL.construct();
		ComplexFloat64Member I = G.CDBL.construct();
		ComplexFloat64Member M = G.CDBL.construct();
		two.setR(2);
		I.setI(1);
		M.setR(m);
		G.CDBL.E(e);
		G.CDBL.PI(power);
		G.CDBL.multiply(power, two, power);
		G.CDBL.multiply(power, I, power);
		G.CDBL.divide(power, M, power);
		G.CDBL.pow(e, power, principalRoot);
	}
}

@@ -1740,16 +1740,18 @@
 ues of m
+/n
  very la
@@ -1802,21 +1802,9 @@
 ute 
-the principal
+a
  roo
@@ -1831,16 +1831,31 @@
  order m
+ and suborder n
 .%0A%09 * @p
@@ -1874,22 +1874,87 @@
  of 
-principal root
+the root. The m'th root of unity.%0A%09 * @param n Suborder of the root. 0 %3C= n %3C m
 .%0A%09 
@@ -1962,26 +1962,17 @@
  @param 
-principalR
+r
 oot Outp
@@ -2023,16 +2023,24 @@
 (long m,
+ long n,
  Complex
@@ -2057,25 +2057,127 @@
 ber 
-principalRoot)%0A%09%7B
+root)%0A%09%7B%0A%09%09if (n %3C 0 %7C%7C n %3E= m)%0A%09%09%09throw new IllegalArgumentException(%22n outside bounds of %5B0,m-1%5D: n = %22+n+%22 m = %22+m);
 %0A%09%09C
@@ -2414,16 +2414,63 @@
 ruct();%0A
+%09%09ComplexFloat64Member N = G.CDBL.construct();%0A
 %09%09two.se
@@ -2502,16 +2502,29 @@
 etR(m);%0A
+%09%09N.setR(n);%0A
 %09%09G.CDBL
@@ -2650,32 +2650,68 @@
 wer, M, power);%0A
+%09%09G.CDBL.multiply(power, N, power);%0A
 %09%09G.CDBL.pow(e, 
@@ -2721,18 +2721,9 @@
 er, 
-principalR
+r
 oot)

Generalize complex roots of unity calculations