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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.
* ```
*/
/* eslint-disable max-len, max-statements */
'use strict';
// MODULES //
var sincos = require( '@stdlib/math/base/special/sincos' );
var TWO_PI = require( '@stdlib/constants/float64/two-pi' );
var chRef = require( './ch_ref.js' );
var ccRef = require( './cc_ref.js' );
var c1Ref = require( './c1_ref.js' );
var c2Ref = require( './c2_ref.js' );
var ch2Ref = require( './ch2_ref.js' );
// MAIN //
/**
* Performs the backward FFT for real-valued sequences.
*
* @private
* @param {integer} ido - number of real values for each transform
* @param {integer} ip - radix of the transform
* @param {integer} l1 - length of the input sequences
* @param {integer} idl1 - stride for the transform
* @param {Float64Array} cc - input array containing sequences to be transformed
* @param {number} ccOffset - offset for the input array
* @param {Float64Array} c1 - first work array
* @param {number} c1Offset - offset for the first work array
* @param {Float64Array} c2 - second work array
* @param {number} c2Offset - offset for the second work array
* @param {Float64Array} ch - output array containing transformed sequences
* @param {number} chOffset - offset for the output array
* @param {Float64Array} ch2 - work array for transformed sequences
* @param {number} ch2Offset - offset for the work array
* @param {Float64Array} wa - array of twiddle factors
* @param {number} waOffset - offset for the twiddle factors array
* @returns {void}
*/
function radbg( ido, ip, l1, idl1, cc, ccOffset, c1, c1Offset, c2, c2Offset, ch, chOffset, ch2, ch2Offset, wa, waOffset ) { // eslint-disable-line max-params
var ar1h;
var ar2h;
var idp2;
var ipp2;
var idij;
var ipph;
var dc2;
var ai1;
var ai2;
var ar1;
var ar2;
var ds2;
var nbd;
var dcp;
var arg;
var dsp;
var j2;
var ic;
var jc;
var lc;
var ik;
var is;
var sc;
var i;
var j;
var k;
var l;
// Parameter adjustments...
chOffset -= 1 + ( ido * ( 1 + l1 ) );
c1Offset -= 1 + ( ido * ( 1 + l1 ) );
ccOffset -= 1 + ( ido * ( 1 + ip ) );
ch2Offset -= 1 + idl1;
c2Offset -= 1 + idl1;
waOffset -= 1;
// Function body:
arg = TWO_PI / ip;
sc = sincos( arg );
dcp = sc[ 1 ];
dsp = sc[ 0 ];
idp2 = ido + 2;
nbd = ( ido - 1 ) / 2;
ipp2 = ip + 2;
ipph = ( ip + 1 ) / 2;
if ( ido >= l1 ) {
for ( k = 1; k <= l1; k++ ) {
for ( i = 1; i <= ido; i++ ) {
ch[ chRef( i, k, 1, l1, ido ) + chOffset ] = cc[ ccRef( i, 1, k, ip, ido ) + ccOffset ];
}
}
} else {
for ( i = 1; i <= ido; i++ ) {
for ( k = 1; k <= l1; k++ ) {
ch[ chRef( i, k, 1, l1, ido ) + chOffset ] = cc[ ccRef( i, 1, k, ip, ido ) + ccOffset ];
}
}
}
for ( j = 2; j <= ipph; j++ ) {
jc = ipp2 - j;
j2 = j + j;
for ( k = 1; k <= l1; k++ ) {
ch[ chRef( 1, k, j, l1, ido ) + chOffset ] = cc[ ccRef( ido, j2 - 2, k, ip, ido ) + ccOffset ] + cc[ ccRef( ido, j2 - 2, k, ip, ido ) + ccOffset ];
ch[ chRef( 1, k, jc, l1, ido ) + chOffset ] = cc[ ccRef( 1, j2 - 1, k, ip, ido ) + ccOffset ] + cc[ ccRef( 1, j2 - 1, k, ip, ido ) + ccOffset ];
}
}
if ( ido !== 1 ) {
if ( nbd >= l1 ) {
for ( j = 2; j <= ipph; j++ ) {
jc = ipp2 - j;
for ( k = 1; k <= l1; k++ ) {
for ( i = 3; i <= ido; i += 2 ) {
ic = idp2 - i;
ch[ chRef( i - 1, k, j, l1, ido ) + chOffset ] = cc[ ccRef( i - 1, ( j << 1 ) - 1, k, ip, ido ) + ccOffset ] + cc[ ccRef( ic - 1, ( j << 1 ) - 2, k, ip, ido ) + ccOffset ];
ch[ chRef( i - 1, k, jc, l1, ido ) + chOffset ] = cc[ ccRef( i - 1, ( j << 1 ) - 1, k, ip, ido ) + ccOffset ] - cc[ ccRef( ic - 1, ( j << 1 ) - 2, k, ip, ido ) + ccOffset ];
ch[ chRef( i, k, j, l1, ido ) + chOffset ] = cc[ ccRef( i, ( j << 1 ) - 1, k, ip, ido ) + ccOffset ] - cc[ ccRef( ic, ( j << 1 ) - 2, k, ip, ido ) + ccOffset ];
ch[ chRef( i, k, jc, l1, ido ) + chOffset ] = cc[ ccRef( i, ( j << 1 ) - 1, k, ip, ido ) + ccOffset ] + cc[ ccRef( ic, ( j << 1 ) - 2, k, ip, ido ) + ccOffset ];
}
}
}
} else {
for ( j = 2; j <= ipph; j++ ) {
jc = ipp2 - j;
for ( i = 3; i <= ido; i += 2 ) {
ic = idp2 - i;
for ( k = 1; k <= l1; k++ ) {
ch[ chRef( i - 1, k, j, l1, ido ) + chOffset ] = cc[ ccRef( i - 1, ( j << 1 ) - 1, k, ip, ido ) + ccOffset ] + cc[ ccRef( ic - 1, ( j << 1 ) - 2, k, ip, ido ) + ccOffset ];
ch[ chRef( i - 1, k, jc, l1, ido ) + chOffset ] = cc[ ccRef( i - 1, ( j << 1 ) - 1, k, ip, ido ) + ccOffset ] - cc[ ccRef( ic - 1, ( j << 1 ) - 2, k, ip, ido ) + ccOffset ];
ch[ chRef( i, k, j, l1, ido ) + chOffset ] = cc[ ccRef( i, ( j << 1 ) - 1, k, ip, ido ) + ccOffset ] - cc[ ccRef( ic, ( j << 1 ) - 2, k, ip, ido ) + ccOffset ];
ch[ chRef( i, k, jc, l1, ido ) + chOffset ] = cc[ ccRef( i, ( j << 1 ) - 1, k, ip, ido ) + ccOffset ] + cc[ ccRef( ic, ( j << 1 ) - 2, k, ip, ido ) + ccOffset ];
}
}
}
}
}
ar1 = 1.0;
ai1 = 0.0;
for ( l = 2; l <= ipph; l++ ) {
lc = ipp2 - l;
ar1h = ( dcp * ar1 ) - ( dsp * ai1 );
ai1 = ( dcp * ai1 ) + ( dsp * ar1 );
ar1 = ar1h;
for ( ik = 1; ik <= idl1; ik++ ) {
c2[ c2Ref( ik, l, idl1 ) + c2Offset ] = ch2[ ch2Ref( ik, 1, idl1 ) + ch2Offset ] + ( ar1 * ch2[ ch2Ref( ik, 2, idl1 ) + ch2Offset ] );
c2[ c2Ref( ik, lc, idl1 ) + c2Offset ] = ai1 * ch2[ ch2Ref( ik, ip, idl1 ) + ch2Offset ];
}
dc2 = ar1;
ds2 = ai1;
ar2 = ar1;
ai2 = ai1;
for ( j = 3; j <= ipph; j++ ) {
jc = ipp2 - j;
ar2h = ( dc2 * ar2 ) - ( ds2 * ai2 );
ai2 = ( dc2 * ai2 ) + ( ds2 * ar2 );
ar2 = ar2h;
for ( ik = 1; ik <= idl1; ik++ ) {
c2[ c2Ref( ik, l, idl1 ) + c2Offset ] += ( ar2 * ch2[ ch2Ref( ik, j, idl1 ) + ch2Offset ] );
c2[ c2Ref( ik, lc, idl1 ) + c2Offset ] += ( ai2 * ch2[ ch2Ref( ik, jc, idl1 ) + ch2Offset ] );
}
}
}
for ( j = 2; j <= ipph; j++ ) {
for ( ik = 1; ik <= idl1; ik++ ) {
ch2[ ch2Ref( ik, 1, idl1 ) + ch2Offset ] += ch2[ ch2Ref( ik, j, idl1 ) + ch2Offset ];
}
}
for ( j = 2; j <= ipph; j++ ) {
jc = ipp2 - j;
for ( k = 1; k <= l1; k++ ) {
ch[ chRef( 1, k, j, l1, ido ) + chOffset ] = c1[ c1Ref( 1, k, j, l1, ido ) + c1Offset ] - c1[ c1Ref( 1, k, jc, l1, ido ) + c1Offset ];
ch[ chRef( 1, k, jc, l1, ido ) + chOffset ] = c1[ c1Ref( 1, k, j, l1, ido ) + c1Offset ] + c1[ c1Ref( 1, k, jc, l1, ido ) + c1Offset ];
}
}
if ( ido !== 1 ) {
if ( nbd >= l1 ) {
for ( j = 2; j <= ipph; j++ ) {
jc = ipp2 - j;
for ( k = 1; k <= l1; k++ ) {
for ( i = 3; i <= ido; i += 2 ) {
ch[ chRef( i - 1, k, j, l1, ido ) + chOffset ] = c1[ c1Ref( i - 1, k, j, l1, ido ) + c1Offset ] - c1[ c1Ref( i, k, jc, l1, ido ) + c1Offset ];
ch[ chRef( i - 1, k, jc, l1, ido ) + chOffset ] = c1[ c1Ref( i - 1, k, j, l1, ido ) + c1Offset ] + c1[ c1Ref( i, k, jc, l1, ido ) + c1Offset ];
ch[ chRef( i, k, j, l1, ido ) + chOffset ] = c1[ c1Ref( i, k, j, l1, ido ) + c1Offset ] + c1[ c1Ref( i - 1, k, jc, l1, ido ) + c1Offset ];
ch[ chRef( i, k, jc, l1, ido ) + chOffset ] = c1[ c1Ref( i, k, j, l1, ido ) + c1Offset ] - c1[ c1Ref( i - 1, k, jc, l1, ido ) + c1Offset ];
}
}
}
} else {
for ( j = 2; j <= ipph; j++ ) {
jc = ipp2 - j;
for ( i = 3; i <= ido; i += 2 ) {
for ( k = 1; k <= l1; k++ ) {
ch[ chRef( i - 1, k, j, l1, ido ) + chOffset ] = c1[ c1Ref( i - 1, k, j, l1, ido ) + c1Offset ] - c1[ c1Ref( i, k, jc, l1, ido ) + c1Offset ];
ch[ chRef( i - 1, k, jc, l1, ido ) + chOffset ] = c1[ c1Ref( i - 1, k, j, l1, ido ) + c1Offset ] + c1[ c1Ref( i, k, jc, l1, ido ) + c1Offset ];
ch[ chRef( i, k, j, l1, ido ) + chOffset ] = c1[ c1Ref( i, k, j, l1, ido ) + c1Offset ] + c1[ c1Ref( i - 1, k, jc, l1, ido ) + c1Offset ];
ch[ chRef( i, k, jc, l1, ido ) + chOffset ] = c1[ c1Ref( i, k, j, l1, ido ) + c1Offset ] - c1[ c1Ref( i - 1, k, jc, l1, ido ) + c1Offset ];
}
}
}
}
}
if ( ido === 1 ) {
return;
}
for ( ik = 1; ik <= idl1; ik++ ) {
c2[ c2Ref( ik, 1, idl1 ) + c2Offset ] = ch2[ ch2Ref( ik, 1, idl1 ) + ch2Offset ];
}
for ( j = 2; j <= ip; j++ ) {
for ( k = 1; k <= l1; k++ ) {
c1[ c1Ref( 1, k, j, l1, ido ) + c1Offset ] = ch[ chRef( 1, k, j, l1, ido ) + chOffset ];
}
}
if ( nbd <= l1 ) {
is = -ido;
for ( j = 2; j <= ip; j++ ) {
is += ido;
idij = is;
for ( i = 3; i <= ido; i += 2 ) {
idij += 2;
for ( k = 1; k <= l1; k++ ) {
c1[ c1Ref( i - 1, k, j, l1, ido ) + c1Offset ] = ( wa[ idij - 1 + waOffset ] * ch[ chRef( i - 1, k, j, l1, ido ) + chOffset ] ) - ( wa[ idij + waOffset ] * ch[ chRef( i, k, j, l1, ido ) + chOffset ] );
c1[ c1Ref( i, k, j, l1, ido ) + c1Offset ] = ( wa[ idij - 1 + waOffset ] * ch[ chRef( i, k, j, l1, ido ) + chOffset ] ) + ( wa[ idij + waOffset ] * ch[ chRef( i - 1, k, j, l1, ido ) + chOffset ] );
}
}
}
} else {
is = -ido;
for ( j = 2; j <= ip; j++ ) {
is += ido;
for ( k = 1; k <= l1; k++ ) {
idij = is;
for ( i = 3; i <= ido; i += 2 ) {
idij += 2;
c1[ c1Ref( i - 1, k, j, l1, ido ) + c1Offset ] = ( wa[ idij - 1 + waOffset ] * ch[ chRef( i - 1, k, j, l1, ido ) + chOffset ] ) - ( wa[ idij + waOffset ] * ch[ chRef( i, k, j, l1, ido ) + chOffset ] );
c1[ c1Ref( i, k, j, l1, ido ) + c1Offset ] = ( wa[ idij - 1 + waOffset ] * ch[ chRef( i, k, j, l1, ido ) + chOffset ] ) + ( wa[ idij + waOffset ] * ch[ chRef( i - 1, k, j, l1, ido ) + chOffset ] );
}
}
}
}
}
// EXPORTS //
module.exports = radbg;
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