annotate fft/fft.js/lib/complex.js @ 40:223f770b5341 kissfft-double tip

Try a double-precision kissfft

/* Copyright (c) 2012, Jens Nockert <[e-mail]>, Jussi Kalliokoski <[e-mail]>
 * All rights reserved.
 * 
 * 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 OWNER 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.
 */

if (!FFT) {
	var FFT = {}
}

void function (namespace) {
	"use strict"
	
	function butterfly2(output, outputOffset, outputStride, fStride, state, m) {
		var t = state.twiddle
		
		for (var i = 0; i < m; i++) {
			var s0_r = output[2 * ((outputOffset) + (outputStride) * (i))], s0_i = output[2 * ((outputOffset) + (outputStride) * (i)) + 1]
			var s1_r = output[2 * ((outputOffset) + (outputStride) * (i + m))], s1_i = output[2 * ((outputOffset) + (outputStride) * (i + m)) + 1]
			
			var t1_r = t[2 * ((0) + (fStride) * (i))], t1_i = t[2 * ((0) + (fStride) * (i)) + 1]
			
			var v1_r = s1_r * t1_r - s1_i * t1_i, v1_i = s1_r * t1_i + s1_i * t1_r
			
			var r0_r = s0_r + v1_r, r0_i = s0_i + v1_i
			var r1_r = s0_r - v1_r, r1_i = s0_i - v1_i
			
			output[2 * ((outputOffset) + (outputStride) * (i))] = r0_r, output[2 * ((outputOffset) + (outputStride) * (i)) + 1] = r0_i
			output[2 * ((outputOffset) + (outputStride) * (i + m))] = r1_r, output[2 * ((outputOffset) + (outputStride) * (i + m)) + 1] = r1_i
		}
	}
	
	function butterfly3(output, outputOffset, outputStride, fStride, state, m) {
		var t = state.twiddle
		var m1 = m, m2 = 2 * m
		var fStride1 = fStride, fStride2 = 2 * fStride
		
		var e = t[2 * ((0) + (fStride) * (m)) + 1]
		
		for (var i = 0; i < m; i++) {
			var s0_r = output[2 * ((outputOffset) + (outputStride) * (i))], s0_i = output[2 * ((outputOffset) + (outputStride) * (i)) + 1]
			
			var s1_r = output[2 * ((outputOffset) + (outputStride) * (i + m1))], s1_i = output[2 * ((outputOffset) + (outputStride) * (i + m1)) + 1]
			var t1_r = t[2 * ((0) + (fStride1) * (i))], t1_i = t[2 * ((0) + (fStride1) * (i)) + 1]
			var v1_r = s1_r * t1_r - s1_i * t1_i, v1_i = s1_r * t1_i + s1_i * t1_r
			
			var s2_r = output[2 * ((outputOffset) + (outputStride) * (i + m2))], s2_i = output[2 * ((outputOffset) + (outputStride) * (i + m2)) + 1]
			var t2_r = t[2 * ((0) + (fStride2) * (i))], t2_i = t[2 * ((0) + (fStride2) * (i)) + 1]
			var v2_r = s2_r * t2_r - s2_i * t2_i, v2_i = s2_r * t2_i + s2_i * t2_r
			
			var i0_r = v1_r + v2_r, i0_i = v1_i + v2_i
			
			var r0_r = s0_r + i0_r, r0_i = s0_i + i0_i
			output[2 * ((outputOffset) + (outputStride) * (i))] = r0_r, output[2 * ((outputOffset) + (outputStride) * (i)) + 1] = r0_i
			
			var i1_r = s0_r - i0_r * 0.5
			var i1_i = s0_i - i0_i * 0.5
			
			var i2_r = (v1_r - v2_r) * e
			var i2_i = (v1_i - v2_i) * e
			
			var r1_r = i1_r - i2_i
			var r1_i = i1_i + i2_r
			output[2 * ((outputOffset) + (outputStride) * (i + m1))] = r1_r, output[2 * ((outputOffset) + (outputStride) * (i + m1)) + 1] = r1_i
			
			var r2_r = i1_r + i2_i
			var r2_i = i1_i - i2_r
			output[2 * ((outputOffset) + (outputStride) * (i + m2))] = r2_r, output[2 * ((outputOffset) + (outputStride) * (i + m2)) + 1] = r2_i
		}
	}
	
	function butterfly4(output, outputOffset, outputStride, fStride, state, m) {
		var t = state.twiddle
		var m1 = m, m2 = 2 * m, m3 = 3 * m
		var fStride1 = fStride, fStride2 = 2 * fStride, fStride3 = 3 * fStride
		
		for (var i = 0; i < m; i++) {
			var s0_r = output[2 * ((outputOffset) + (outputStride) * (i))], s0_i = output[2 * ((outputOffset) + (outputStride) * (i)) + 1]
			
			var s1_r = output[2 * ((outputOffset) + (outputStride) * (i + m1))], s1_i = output[2 * ((outputOffset) + (outputStride) * (i + m1)) + 1]
			var t1_r = t[2 * ((0) + (fStride1) * (i))], t1_i = t[2 * ((0) + (fStride1) * (i)) + 1]
			var v1_r = s1_r * t1_r - s1_i * t1_i, v1_i = s1_r * t1_i + s1_i * t1_r
			
			var s2_r = output[2 * ((outputOffset) + (outputStride) * (i + m2))], s2_i = output[2 * ((outputOffset) + (outputStride) * (i + m2)) + 1]
			var t2_r = t[2 * ((0) + (fStride2) * (i))], t2_i = t[2 * ((0) + (fStride2) * (i)) + 1]
			var v2_r = s2_r * t2_r - s2_i * t2_i, v2_i = s2_r * t2_i + s2_i * t2_r
			
			var s3_r = output[2 * ((outputOffset) + (outputStride) * (i + m3))], s3_i = output[2 * ((outputOffset) + (outputStride) * (i + m3)) + 1]
			var t3_r = t[2 * ((0) + (fStride3) * (i))], t3_i = t[2 * ((0) + (fStride3) * (i)) + 1]
			var v3_r = s3_r * t3_r - s3_i * t3_i, v3_i = s3_r * t3_i + s3_i * t3_r
			
			var i0_r = s0_r + v2_r, i0_i = s0_i + v2_i
			var i1_r = s0_r - v2_r, i1_i = s0_i - v2_i
			var i2_r = v1_r + v3_r, i2_i = v1_i + v3_i
			var i3_r = v1_r - v3_r, i3_i = v1_i - v3_i
			
			var r0_r = i0_r + i2_r, r0_i = i0_i + i2_i
			
			if (state.inverse) {
				var r1_r = i1_r - i3_i
				var r1_i = i1_i + i3_r
			} else {
				var r1_r = i1_r + i3_i
				var r1_i = i1_i - i3_r
			}
			
			var r2_r = i0_r - i2_r, r2_i = i0_i - i2_i
			
			if (state.inverse) {
				var r3_r = i1_r + i3_i
				var r3_i = i1_i - i3_r
			} else {
				var r3_r = i1_r - i3_i
				var r3_i = i1_i + i3_r
			}
			
			output[2 * ((outputOffset) + (outputStride) * (i))] = r0_r, output[2 * ((outputOffset) + (outputStride) * (i)) + 1] = r0_i
			output[2 * ((outputOffset) + (outputStride) * (i + m1))] = r1_r, output[2 * ((outputOffset) + (outputStride) * (i + m1)) + 1] = r1_i
			output[2 * ((outputOffset) + (outputStride) * (i + m2))] = r2_r, output[2 * ((outputOffset) + (outputStride) * (i + m2)) + 1] = r2_i
			output[2 * ((outputOffset) + (outputStride) * (i + m3))] = r3_r, output[2 * ((outputOffset) + (outputStride) * (i + m3)) + 1] = r3_i
		}
	}
	
	function butterfly(output, outputOffset, outputStride, fStride, state, m, p) {
		var t = state.twiddle, n = state.n, scratch = new Float64Array(2 * p)
		
		for (var u = 0; u < m; u++) {
			for (var q1 = 0, k = u; q1 < p; q1++, k += m) {
				var x0_r = output[2 * ((outputOffset) + (outputStride) * (k))], x0_i = output[2 * ((outputOffset) + (outputStride) * (k)) + 1]
				scratch[2 * (q1)] = x0_r, scratch[2 * (q1) + 1] = x0_i
			}
			
			for (var q1 = 0, k = u; q1 < p; q1++, k += m) {
				var tOffset = 0
				
				var x0_r = scratch[2 * (0)], x0_i = scratch[2 * (0) + 1]
				output[2 * ((outputOffset) + (outputStride) * (k))] = x0_r, output[2 * ((outputOffset) + (outputStride) * (k)) + 1] = x0_i
				
				for (var q = 1; q < p; q++) {
					tOffset = (tOffset + fStride * k) % n
					
					var s0_r = output[2 * ((outputOffset) + (outputStride) * (k))], s0_i = output[2 * ((outputOffset) + (outputStride) * (k)) + 1]
					
					var s1_r = scratch[2 * (q)], s1_i = scratch[2 * (q) + 1]
					var t1_r = t[2 * (tOffset)], t1_i = t[2 * (tOffset) + 1]
					var v1_r = s1_r * t1_r - s1_i * t1_i, v1_i = s1_r * t1_i + s1_i * t1_r
					
					var r0_r = s0_r + v1_r, r0_i = s0_i + v1_i
					output[2 * ((outputOffset) + (outputStride) * (k))] = r0_r, output[2 * ((outputOffset) + (outputStride) * (k)) + 1] = r0_i
				}
			}
		}
	}
	
	function work(output, outputOffset, outputStride, f, fOffset, fStride, inputStride, factors, state) {
		var p = factors.shift()
		var m = factors.shift()
		
		if (m == 1) {
			for (var i = 0; i < p * m; i++) {
				var x0_r = f[2 * ((fOffset) + (fStride * inputStride) * (i))], x0_i = f[2 * ((fOffset) + (fStride * inputStride) * (i)) + 1]
				output[2 * ((outputOffset) + (outputStride) * (i))] = x0_r, output[2 * ((outputOffset) + (outputStride) * (i)) + 1] = x0_i
			}
		} else {
			for (var i = 0; i < p; i++) {
				work(output, outputOffset + outputStride * i * m, outputStride, f, fOffset + i * fStride * inputStride, fStride * p, inputStride, factors.slice(), state)
			}
		}
		
		switch (p) {
			case 2: butterfly2(output, outputOffset, outputStride, fStride, state, m); break
			case 3: butterfly3(output, outputOffset, outputStride, fStride, state, m); break
			case 4: butterfly4(output, outputOffset, outputStride, fStride, state, m); break
			default: butterfly(output, outputOffset, outputStride, fStride, state, m, p); break
		}
	}
	
	var complex = function (n, inverse) {
		if (arguments.length < 2) {
			throw new RangeError("You didn't pass enough arguments, passed `" + arguments.length + "'")
		}
		
		var n = ~~n, inverse = !!inverse
		
		if (n < 1) {
			throw new RangeError("n is outside range, should be positive integer, was `" + n + "'")
		}
		
		var state = {
			n: n,
			inverse: inverse,
			
			factors: [],
			twiddle: new Float64Array(2 * n),
			scratch: new Float64Array(2 * n)
		}
		
		var t = state.twiddle, theta = 2 * Math.PI / n
		
		for (var i = 0; i < n; i++) {
			if (inverse) {
				var phase =  theta * i
			} else {
				var phase = -theta * i
			}
			
			t[2 * (i)] = Math.cos(phase)
			t[2 * (i) + 1] = Math.sin(phase)
		}
		
		var p = 4, v = Math.floor(Math.sqrt(n))
		
		while (n > 1) {
			while (n % p) {
				switch (p) {
					case 4: p = 2; break
					case 2: p = 3; break
					default: p += 2; break
				}
				
				if (p > v) {
					p = n
				}
			}
			
			n /= p
			
			state.factors.push(p)
			state.factors.push(n)
		}
		
		this.state = state
	}
	
	complex.prototype.simple = function (output, input, t) {
		this.process(output, 0, 1, input, 0, 1, t)
	}
	
	complex.prototype.process = function(output, outputOffset, outputStride, input, inputOffset, inputStride, t) {
		var outputStride = ~~outputStride, inputStride = ~~inputStride
		
		var type = t == 'real' ? t : 'complex'
		
		if (outputStride < 1) {
			throw new RangeError("outputStride is outside range, should be positive integer, was `" + outputStride + "'")
		}
		
		if (inputStride < 1) {
			throw new RangeError("inputStride is outside range, should be positive integer, was `" + inputStride + "'")
		}
		
		if (type == 'real') {
			for (var i = 0; i < this.state.n; i++) {
				var x0_r = input[inputOffset + inputStride * i]
				var x0_i = 0.0
				
				this.state.scratch[2 * (i)] = x0_r, this.state.scratch[2 * (i) + 1] = x0_i
			}
			
			work(output, outputOffset, outputStride, this.state.scratch, 0, 1, 1, this.state.factors.slice(), this.state)
		} else {
			if (input == output) {
				work(this.state.scratch, 0, 1, input, inputOffset, 1, inputStride, this.state.factors.slice(), this.state)
				
				for (var i = 0; i < this.state.n; i++) {
					var x0_r = this.state.scratch[2 * (i)], x0_i = this.state.scratch[2 * (i) + 1]
					
					output[2 * ((outputOffset) + (outputStride) * (i))] = x0_r, output[2 * ((outputOffset) + (outputStride) * (i)) + 1] = x0_i
				}
			} else {
				work(output, outputOffset, outputStride, input, inputOffset, 1, inputStride, this.state.factors.slice(), this.state)
			}
		}
	}
	
	namespace.complex = complex
}(FFT)