/* 
 * Free FFT and convolution (JavaScript)
 * 
 * Copyright (c) 2014 Project Nayuki
 * http://www.nayuki.io/page/free-small-fft-in-multiple-languages
 *
 * (MIT License)
 * 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.
 *
 * Slightly restructured by Chris Cannam, cannam@all-day-breakfast.com
 *
 * Fix added by Jacques de Hooge, jdeh@geatec.com: 'this' added to inverse, indentation repaired
 */

// "use strict";

/* 
 * Construct an object for calculating the discrete Fourier transform (DFT) of size n, where n is a power of 2.
 */
function FFTNayuki(n) {
	
	this.n = n;
	this.levels = -1;
	
	for (var i = 0; i < 32; i++) {
		if (1 << i == n) {
			this.levels = i;  // Equal to log2(n)
		}
	}
	if (this.levels == -1) {
		throw "Length is not a power of 2";
	}

	this.cosTable = new Array(n / 2);
	this.sinTable = new Array(n / 2);
	for (var i = 0; i < n / 2; i++) {
		this.cosTable[i] = Math.cos(2 * Math.PI * i / n);
		this.sinTable[i] = Math.sin(2 * Math.PI * i / n);
	}

	/* 
	 * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
	 * The vector's length must be equal to the size n that was passed to the object constructor, and this must be a power of 2. Uses the Cooley-Tukey decimation-in-time radix-2 algorithm.
	 */
	this.forward = function(real, imag) {
	
		var n = this.n;
		
		// Bit-reversed addressing permutation
		for (var i = 0; i < n; i++) {
				var j = reverseBits(i, this.levels);
				if (j > i) {
			var temp = real[i];
			real[i] = real[j];
			real[j] = temp;
			temp = imag[i];
			imag[i] = imag[j];
			imag[j] = temp;
				}
		}
		
		// Cooley-Tukey decimation-in-time radix-2 FFT
		for (var size = 2; size <= n; size *= 2) {
			var halfsize = size / 2;
				var tablestep = n / size;
				for (var i = 0; i < n; i += size) {
					for (var j = i, k = 0; j < i + halfsize; j++, k += tablestep) {
						var tpre =	real[j+halfsize] * this.cosTable[k] +
						imag[j+halfsize] * this.sinTable[k];
						var tpim = -real[j+halfsize] * this.sinTable[k] +
						imag[j+halfsize] * this.cosTable[k];
						real[j + halfsize] = real[j] - tpre;
						imag[j + halfsize] = imag[j] - tpim;
						real[j] += tpre;
						imag[j] += tpim;
			}
				}
		}
		
		// Returns the integer whose value is the reverse of the lowest 'bits' bits of the integer 'x'.
		function reverseBits(x, bits) {
			var y = 0;
			for (var i = 0; i < bits; i++) {
			   y = (y << 1) | (x & 1);
			   x >>>= 1;
			}
			return y;
		}
	}

	/* 
	 * Computes the inverse discrete Fourier transform (IDFT) of the given complex vector, storing the result back into the vector.
	 * The vector's length must be equal to the size n that was passed to the object constructor, and this must be a power of 2. This is a wrapper function. This transform does not perform scaling, so the inverse is not a true inverse.
	 */
	this.inverse = function(real, imag) {
		this.forward(imag, real);	// Fix by JdeH: 'this' added
	}
}

