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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 floor = require( '@stdlib/math/base/special/floor' );
// MAIN //
/**
* Factorizes a sequence length into a product of integers.
*
* ## Notes
*
* - Factorization results are stored in the input array as follows:
*
* ```text
* [ sequence_length | number_of_factors | integer_factors | unused_storage ]
* ```
*
* - The function mutates the input array.
*
* @private
* @param {NonNegativeInteger} N - length of the sequence
* @param {NonNegativeIntegerArray} initial - array of initial trial divisors
* @param {Collection} out - output array for storing factorization results
* @param {integer} stride - stride length for `out`
* @param {NonNegativeInteger} offset - starting index for `out`
* @returns {NonNegativeInteger} number of factors into which `N` was decomposed
*
* @example
* // Specify an initial list of potential divisors:
* var initial = [ 3, 4, 2, 5 ]; // as found in FFTPACK
*
* // Define a sequence length:
* var N = 630;
*
* // Initialize an array for storing factorization results:
* var factors = [ 0, 0, 0, 0, 0, 0, 0 ];
*
* // Factorize the sequence length into a product of integers:
* var numFactors = decompose( N, initial, factors, 1, 0 );
* // returns 5
*
* var f = factors.slice();
* // returns [ 630, 5, 2, 3, 3, 5, 7 ]
*
* @example
* // Specify an initial list of potential divisors:
* var initial = [ 3, 4, 2, 5 ]; // as found in FFTPACK
*
* // Define a sequence length:
* var N = 8;
*
* // Initialize an array for storing factorization results:
* var factors = [ 0, 0, 0, 0 ];
*
* // Factorize the sequence length into its a product of integers:
* var numFactors = decompose( N, initial, factors, 1, 0 );
* // returns 2
*
* var f = factors.slice();
* // returns [ 8, 2, 2, 4 ]
*/
function decompose( N, initial, out, stride, offset ) { // TODO: consider moving to a separate utility package
var divisor;
var ntrials;
var nl;
var nf;
var nq;
var nr;
var ib;
var i;
var j;
// Resolve the number of trial divisors:
ntrials = initial.length;
// Initialize a variable for storing a trial divisor:
divisor = 0;
// Initialize a variable for storing a sub-sequence length:
nl = N;
// Initialize a variable for keeping track of the number of factors into which `N` decomposes:
nf = 0;
j = 0;
do {
if ( j < ntrials ) {
divisor = initial[ j ];
} else {
divisor += 2;
}
j += 1;
while ( true ) {
// Compute the integer quotient:
nq = floor( nl / divisor );
// Compute the remainder:
nr = nl - ( divisor * nq );
// If the divisor did not evenly divide the current sub-sequence length, try a new divisor...
if ( nr !== 0 ) {
break;
}
// We found a new factor:
nf += 1;
// Update the sub-sequence length:
nl = nq;
// Store the factor in the output array:
out[ offset+((nf+1)*stride) ] = divisor;
// When the divisor is `2` and we've already found other factors, shift the other factors right to make room for the most recent `2` factor...
if ( divisor === 2 && nf !== 1 ) {
for ( i = 2; i <= nf; i++ ) {
ib = nf - i + 2;
out[ offset+((ib+1)*stride) ] = out[ offset+(ib*stride) ];
}
out[ offset+(2*stride) ] = 2;
}
// If we cannot further divide the sequence length into smaller sub-sequences, we're done...
if ( nl === 1 ) {
break;
}
}
} while ( nl !== 1 );
// Store the sequence length:
out[ offset ] = N;
// Store the number of factors:
out[ offset+stride ] = nf;
// Return the number of factors:
return nf;
}
// EXPORTS //
module.exports = decompose;
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