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* @license Apache-2.0
*
* Copyright (c) 2025 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*
* ## Notice
*
* The original C code and copyright notice are from the [PFFFT library]{@link https://github.com/marton78/pffft/blob/master/fftpack.c}. The implementation follows the original, but has been modified for JavaScript.
*
* ```text
* Copyright (c) 2004 the University Corporation for Atmospheric
* Research ("UCAR"). All rights reserved. Developed by NCAR's
* Computational and Information Systems Laboratory, UCAR,
* www.cisl.ucar.edu.
*
* Redistribution and use of the Software in source and binary forms,
* with or without modification, is permitted provided that the
* following conditions are met:
*
* - Neither the names of NCAR's Computational and Information Systems
* Laboratory, the University Corporation for Atmospheric Research,
* nor the names of its sponsors or contributors may be used to
* endorse or promote products derived from this Software without
* specific prior written permission.
*
* - Redistributions of source code must retain the above copyright
* notices, this list of conditions, and the disclaimer below.
*
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions, and the disclaimer below in the
* documentation and/or other materials provided with the
* distribution.
*
* THIS 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 CONTRIBUTORS OR COPYRIGHT
* HOLDERS BE LIABLE FOR ANY CLAIM, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL 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 WITH THE
* SOFTWARE.
* ```
*/
'use strict';
// MODULES //
var sincos = require( '@stdlib/math/base/special/sincos' ).assign;
var TWO_PI = require( '@stdlib/constants/float64/two-pi' );
var floor = require( '@stdlib/math/base/special/floor' );
var decompose = require( './decompose.js' );
// VARIABLES //
// Define a list of initial trial factors for FFT factorization:
var TRIAL_FACTORS = [ 4, 2, 3, 5 ];
// MAIN //
/**
* Initializes the working arrays for applying a Fourier transform to a real-valued sequence.
*
* @private
* @param {NonNegativeInteger} N - length of the sequence
* @param {Collection} twiddles - array of twiddle factors
* @param {integer} strideT - stride length for `twiddles`
* @param {NonNegativeInteger} offsetT - starting index for `twiddles`
* @param {Collection} factors - array containing a radix factorization
* @param {integer} strideF - stride length for `factors`
* @param {NonNegativeInteger} offsetF - starting index for `factors`
* @returns {void}
*/
function rffti1( N, twiddles, strideT, offsetT, factors, strideF, offsetF ) {
var factor;
var argld;
var argh;
var fidx;
var nf;
var fi;
var l2;
var l1;
var ld;
var st;
var it;
var im;
var M;
var m;
var k;
var j;
// Decompose the sequence length into its radix factors:
nf = decompose( N, TRIAL_FACTORS, factors, strideF, offsetF );
// If the number of radix factors is `1`, the only twiddle factor we need is `W_N^0 = 1`, which the main transform kernels already hard-code, so nothing to pre-compute...
if ( nf-1 === 0 ) {
return;
}
// Compute the master angular step (i.e., the basic angle that generates all twiddles):
argh = TWO_PI / N;
// Define the location of the first sine term we want to compute:
im = 3;
// Initialize a running product of factors already processed:
l1 = 1;
// Compute the index of the first radix factor:
fidx = offsetF + ( 2*strideF );
// Compute the stride length for each cosine/sine pair:
st = 2 * strideT;
// Generate twiddle factors...
for ( k = 0; k < nf-1; k++ ) {
// Resolve the next radix factor:
factor = factors[ fidx ];
// Compute the length of the transform after including the current radix:
l2 = factor * l1;
// Compute the number of the "butterfly wings" (at this stage, the data is viewed as a `factor`-point transform of sub-vectors of length `l1`; `M` describes how many such vectors fit in the full array of length `N`):
M = floor( N / l2 );
// Initialize a running offset used to step the angle:
ld = 0;
// Iterate over each butterfly column within the current radix...
for ( j = 1; j < factor; j++ ) {
// Advance to the next column:
ld += l1;
// Compute the angle step for this column:
argld = ld * argh; // 2Ļ ā
j ā
li / N, which is the j-th column's base angle
// Initialize a counter which counts from `1` to `(M/2)-1` (i.e., all non-trivial harmonics):
fi = 1.0;
// Compute the index of the sine term:
it = offsetT + ( im*strideT );
// Iterate over each non-trivial harmonic in the column (note: we skip the `m=0` and `m=1` (i.e., the first cosine/sine pair, the first harmonic `W_N^0 = cos(0) + j sin(0) = 1 + jā
0` is trivial and hard-coded by transform kernels)...
for ( m = 2; m < M; m += 2 ) {
// Compute `(cos(fi*argld), sin(fi*argld))`:
sincos( fi*argld, twiddles, -strideT, it ); // note: `sincos` returns the sine and cosine, in that order, so we need to use a negative stride when assigning the values to `twiddles` to ensure that cosine comes before sine in the twiddles table
// Update for the next harmonic:
fi += 1.0;
// Resolve the index of the next sine term:
it += st;
}
// Advance `im` by the size of the current block, skipping the cosine/sine pairs we have just written:
im += M;
}
// Update the running product of factors already processed:
l1 = l2;
// Resolve the index of the next radix factor:
fidx += strideF;
}
}
// EXPORTS //
module.exports = rffti1;
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