/*===========================================================================*\
 * Fast Fourier Transform (Cooley-Tukey Method)
 *
 * (c) Vail Systems. Joshua Jung and Ben Bryan. 2015
 *
 * This code is not designed to be highly optimized but as an educational
 * tool to understand the Fast Fourier Transform.
\*===========================================================================*/

//------------------------------------------------
// Note: Some of this code is not optimized and is
// primarily designed as an educational and testing
// tool.
// To get high performace would require transforming
// the recursive calls into a loop and then loop
// unrolling. All of this is best accomplished
// in C or assembly.
//-------------------------------------------------

//-------------------------------------------------
// The following code assumes a complex number is
// an array: [real, imaginary]
//-------------------------------------------------
var complex = require("./complex"),
  fftUtil = require("./fftutil");

//-------------------------------------------------
// Calculate FFT for vector where vector.length
// is assumed to be a power of 2.
//-------------------------------------------------
export function fft(vector) {
	var X = [],
	  N = vector.length;

	// Base case is X = x + 0i since our input is assumed to be real only.
	if (N == 1) {
	  if (Array.isArray(vector[0]))
		//If input vector contains complex numbers
		return [[vector[0][0], vector[0][1]]];
	  else return [[vector[0], 0]];
	}

	// Recurse: all even samples
	var X_evens = fft(vector.filter(even)),
	  // Recurse: all odd samples
	  X_odds = fft(vector.filter(odd));
	// console.log(`vector.length:${vector.length}, evens:${X_evens.length}, odds:${X_odds.length}`);

	// Now, perform N/2 operations!
	for (var k = 0; k < N / 2; k++) {
	  // t is a complex number!
	  var t = X_evens[k];
	  // console.log(`k:${k}, N:${N}, t:${t}, X_odds[k]: ${X_odds[k]}`);
	  var e = complex.multiply(fftUtil.exponent(k, N), X_odds[k]);

	  X[k] = complex.add(t, e);
	  X[k + N / 2] = complex.subtract(t, e);
	}

	function even(__, ix) {
	  return ix % 2 == 0;
	}

	function odd(__, ix) {
	  return ix % 2 == 1;
	}

	return X;
}