/* 
 * Fast discrete cosine transform algorithms (Java)
 * 
 * Copyright (c) 2017 Project Nayuki. (MIT License)
 * https://www.nayuki.io/page/fast-discrete-cosine-transform-algorithms
 * 
 * Permission is hereby granted, free of charge, to any person obtaining a copy of
 * this software and associated documentation files (the "Software"), to deal in
 * the Software without restriction, including without limitation the rights to
 * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
 * the Software, and to permit persons to whom the Software is furnished to do so,
 * subject to the following conditions:
 * - The above copyright notice and this permission notice shall be included in
 *   all copies or substantial portions of the Software.
 * - The Software is provided "as is", without warranty of any kind, express or
 *   implied, including but not limited to the warranties of merchantability,
 *   fitness for a particular purpose and noninfringement. In no event shall the
 *   authors or copyright holders be liable for any claim, damages or other
 *   liability, whether in an action of contract, tort or otherwise, arising from,
 *   out of or in connection with the Software or the use or other dealings in the
 *   Software.
 */


public final class FastDct8 {
	
	/**
	 * Computes the scaled DCT type II on the specified length-8 array in place.
	 * <p>The inverse of this function is {@link #inverseTransform}, except for rounding errors.</p>
	 * @param vector the vector of numbers to transform
	 * @throws NullPointerException if the array is {@code null}
	 */
	public static void transform(double[] vector) {
		// Algorithm by Arai, Agui, Nakajima, 1988. For details, see:
		// https://web.stanford.edu/class/ee398a/handouts/lectures/07-TransformCoding.pdf#page=30
		final double v0, v1, v2, v3, v4, v5, v6, v7, v8, v9,
			v10, v11, v12, v13, v14, v15, v16, v17, v18, v19,
			v20, v21, v22, v23, v24, v25, v26, v27, v28;
		
		v0 = vector[0] + vector[7];
		v1 = vector[1] + vector[6];
		v2 = vector[2] + vector[5];
		v3 = vector[3] + vector[4];
		v4 = vector[3] - vector[4];
		v5 = vector[2] - vector[5];
		v6 = vector[1] - vector[6];
		v7 = vector[0] - vector[7];
		
		v8 = v0 + v3;
		v9 = v1 + v2;
		v10 = v1 - v2;
		v11 = v0 - v3;
		v12 = -v4 - v5;
		v13 = (v5 + v6) * A[3];
		v14 = v6 + v7;
		
		v15 = v8 + v9;
		v16 = v8 - v9;
		v17 = (v10 + v11) * A[1];
		v18 = (v12 + v14) * A[5];
		
		v19 = -v12 * A[2] - v18;
		v20 = v14 * A[4] - v18;
		
		v21 = v17 + v11;
		v22 = v11 - v17;
		v23 = v13 + v7;
		v24 = v7 - v13;
		
		v25 = v19 + v24;
		v26 = v23 + v20;
		v27 = v23 - v20;
		v28 = v24 - v19;
		
		vector[0] = S[0] * v15;
		vector[1] = S[1] * v26;
		vector[2] = S[2] * v21;
		vector[3] = S[3] * v28;
		vector[4] = S[4] * v16;
		vector[5] = S[5] * v25;
		vector[6] = S[6] * v22;
		vector[7] = S[7] * v27;
	}
	
	
	/**
	 * Computes the scaled DCT type III on the specified length-8 array in place.
	 * <p>The inverse of this function is {@link #transform}, except for rounding errors.</p>
	 * @param vector the vector of numbers to transform
	 * @throws NullPointerException if the array is {@code null}
	 */
	public static void inverseTransform(double[] vector) {
		// A straightforward inverse of the forward algorithm
		final double v0, v1, v2, v3, v4, v5, v6, v7, v8, v9,
			v10, v11, v12, v13, v14, v15, v16, v17, v18, v19,
			v20, v21, v22, v23, v24, v25, v26, v27, v28;
		
		v15 = vector[0] / S[0];
		v26 = vector[1] / S[1];
		v21 = vector[2] / S[2];
		v28 = vector[3] / S[3];
		v16 = vector[4] / S[4];
		v25 = vector[5] / S[5];
		v22 = vector[6] / S[6];
		v27 = vector[7] / S[7];
		
		v19 = (v25 - v28) / 2;
		v20 = (v26 - v27) / 2;
		v23 = (v26 + v27) / 2;
		v24 = (v25 + v28) / 2;
		
		v7  = (v23 + v24) / 2;
		v11 = (v21 + v22) / 2;
		v13 = (v23 - v24) / 2;
		v17 = (v21 - v22) / 2;
		
		v8 = (v15 + v16) / 2;
		v9 = (v15 - v16) / 2;
		
		v18 = (v19 - v20) * A[5];  // Different from original
		v12 = (v19 * A[4] - v18) / (A[2] * A[5] - A[2] * A[4] - A[4] * A[5]);
		v14 = (v18 - v20 * A[2]) / (A[2] * A[5] - A[2] * A[4] - A[4] * A[5]);
		
		v6 = v14 - v7;
		v5 = v13 / A[3] - v6;
		v4 = -v5 - v12;
		v10 = v17 / A[1] - v11;
		
		v0 = (v8 + v11) / 2;
		v1 = (v9 + v10) / 2;
		v2 = (v9 - v10) / 2;
		v3 = (v8 - v11) / 2;
		
		vector[0] = (v0 + v7) / 2;
		vector[1] = (v1 + v6) / 2;
		vector[2] = (v2 + v5) / 2;
		vector[3] = (v3 + v4) / 2;
		vector[4] = (v3 - v4) / 2;
		vector[5] = (v2 - v5) / 2;
		vector[6] = (v1 - v6) / 2;
		vector[7] = (v0 - v7) / 2;
	}
	
	
	/*---- Tables of constants ----*/
	
	private static double[] S = new double[8];
	private static double[] A = new double[6];
	
	static {
		double[] C = new double[8];
		for (int i = 0; i < C.length; i++) {
			C[i] = Math.cos(Math.PI / 16 * i);
			S[i] = 1 / (4 * C[i]);
		}
		S[0] = 1 / (2 * Math.sqrt(2));
		// A[0] is unused
		A[1] = C[4];
		A[2] = C[2] - C[6];
		A[3] = C[4];
		A[4] = C[6] + C[2];
		A[5] = C[6];
	}
	
}