fft
Version:
A Fast Fourier Transform library for JS.
270 lines (204 loc) • 7.85 kB
JavaScript
<%= $:.unshift('.'); require "#{File.dirname(__FILE__)}/../src/complex.rb"; File.read "#{File.dirname(__FILE__)}/../LICENSE" %>
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++) {
<%= load('s0', 'output', 'outputOffset', 'i', 'outputStride') %>
<%= load('s1', 'output', 'outputOffset', 'i + m', 'outputStride') %>
<%= load('t1', 't', 0, 'i', 'fStride') %>
<%= cmul('v1', 's1', 't1') %>
<%= cadd('r0', 's0', 'v1') %>
<%= csub('r1', 's0', 'v1') %>
<%= store('r0', 'output', 'outputOffset', 'i', 'outputStride') %>
<%= store('r1', 'output', 'outputOffset', 'i + m', 'outputStride') %>
}
}
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 = <%= imag('t', 0, 'm', 'fStride') %>
for (var i = 0; i < m; i++) {
<%= load('s0', 'output', 'outputOffset', 'i', 'outputStride') %>
<%= load('s1', 'output', 'outputOffset', 'i + m1', 'outputStride') %>
<%= load('t1', 't', 0, 'i', 'fStride1') %>
<%= cmul('v1', 's1', 't1') %>
<%= load('s2', 'output', 'outputOffset', 'i + m2', 'outputStride') %>
<%= load('t2', 't', 0, 'i', 'fStride2') %>
<%= cmul('v2', 's2', 't2') %>
<%= cadd('i0', 'v1', 'v2') %>
<%= cadd('r0', 's0', 'i0') %>
<%= store('r0', 'output', 'outputOffset', 'i', 'outputStride') %>
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
<%= store('r1', 'output', 'outputOffset', 'i + m1', 'outputStride') %>
var r2_r = i1_r + i2_i
var r2_i = i1_i - i2_r
<%= store('r2', 'output', 'outputOffset', 'i + m2', 'outputStride') %>
}
}
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++) {
<%= load('s0', 'output', 'outputOffset', 'i', 'outputStride') %>
<%= load('s1', 'output', 'outputOffset', 'i + m1', 'outputStride') %>
<%= load('t1', 't', 0, 'i', 'fStride1') %>
<%= cmul('v1', 's1', 't1') %>
<%= load('s2', 'output', 'outputOffset', 'i + m2', 'outputStride') %>
<%= load('t2', 't', 0, 'i', 'fStride2') %>
<%= cmul('v2', 's2', 't2') %>
<%= load('s3', 'output', 'outputOffset', 'i + m3', 'outputStride') %>
<%= load('t3', 't', 0, 'i', 'fStride3') %>
<%= cmul('v3', 's3', 't3') %>
<%= cadd('i0', 's0', 'v2') %>
<%= csub('i1', 's0', 'v2') %>
<%= cadd('i2', 'v1', 'v3') %>
<%= csub('i3', 'v1', 'v3') %>
<%= cadd('r0', 'i0', 'i2') %>
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
}
<%= csub('r2', 'i0', 'i2') %>
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
}
<%= store('r0', 'output', 'outputOffset', 'i', 'outputStride') %>
<%= store('r1', 'output', 'outputOffset', 'i + m1', 'outputStride') %>
<%= store('r2', 'output', 'outputOffset', 'i + m2', 'outputStride') %>
<%= store('r3', 'output', 'outputOffset', 'i + m3', 'outputStride') %>
}
}
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) {
<%= load('x0', 'output', 'outputOffset', 'k', 'outputStride') %>
<%= store('x0', 'scratch', 'q1') %>
}
for (var q1 = 0, k = u; q1 < p; q1++, k += m) {
var tOffset = 0
<%= load('x0', 'scratch', 0) %>
<%= store('x0', 'output', 'outputOffset', 'k', 'outputStride') %>
for (var q = 1; q < p; q++) {
tOffset = (tOffset + fStride * k) % n
<%= load('s0', 'output', 'outputOffset', 'k', 'outputStride') %>
<%= load('s1', 'scratch', 'q') %>
<%= load('t1', 't', 'tOffset') %>
<%= cmul('v1', 's1', 't1') %>
<%= cadd('r0', 's0', 'v1') %>
<%= store('r0', 'output', 'outputOffset', 'k', 'outputStride') %>
}
}
}
}
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++) {
<%= load('x0', 'f', 'fOffset', 'i', 'fStride * inputStride') %>
<%= store('x0', 'output', 'outputOffset', 'i', 'outputStride') %>
}
} 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) {
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
}
<%= real('t', 'i') %> = Math.cos(phase)
<%= imag('t', 'i') %> = 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
<%= store('x0', 'this.state.scratch', '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++) {
<%= load('x0', 'this.state.scratch', 'i') %>
<%= store('x0', 'output', 'outputOffset', 'i', 'outputStride') %>
}
} else {
work(output, outputOffset, outputStride, input, inputOffset, 1, inputStride, this.state.factors.slice(), this.state)
}
}
}
namespace.complex = complex
}(FFT)