From d2a3c99894e200a6d8ed96d6430f7d6b0a9e552e Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Fri, 8 May 2026 21:27:49 +0530 Subject: [PATCH 01/19] feat: copy older implementation, add radf3 --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rfftf/lib/index.js | 49 +++ .../fft/base/fftpack/rfftf/lib/main.js | 124 ++++++ .../fft/base/fftpack/rfftf/lib/radf2.js | 366 ++++++++++++++++ .../fft/base/fftpack/rfftf/lib/radf3.js | 397 ++++++++++++++++++ 4 files changed, 936 insertions(+) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/index.js create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/index.js new file mode 100644 index 000000000000..d4e7f52daa0a --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/index.js @@ -0,0 +1,49 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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. +*/ + +'use strict'; + +/** +* Compute the forward real-valued fast Fourier transform (FFT). +* +* @module @stdlib/fft/base/fftpack/rfftf +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); +* var rfftf = require( '@stdlib/fft/base/fftpack/rfftf' ); +* +* var N = 4; +* +* var workspace = new Float64Array( ( 2*N ) + 34 ); +* rffti( N, workspace, 1, 0 ); +* +* var r = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] ); +* +* rfftf( N, r, 1, 0, workspace, 1, 0 ); +* // r => [ 10.0, -2.0, 2.0, -2.0 ] +*/ + +// MODULES // + +var main = require( './main.js' ); + + +// EXPORTS // + +module.exports = main; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js new file mode 100644 index 000000000000..0e54338933a1 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js @@ -0,0 +1,124 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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 isNonNegativeInteger = require( '@stdlib/assert/is-nonnegative-integer' ); +var isFloat64Array = require( '@stdlib/assert/is-float64array' ); +var isInteger = require( '@stdlib/assert/is-integer' ); +var rfftf1 = require( './rfftf1.js' ); + + +// MAIN // + +/** +* Computes the forward real-valued fast Fourier transform (FFT). +* +* @param {NonNegativeInteger} N - length of the sequence to transform +* @param {Float64Array} r - input array containing the sequence to transform +* @param {integer} strideR - stride length for `r` +* @param {NonNegativeInteger} offsetR - starting index for `r` +* @param {Float64Array} workspace - workspace array containing pre-computed values +* @param {integer} strideW - stride length for `workspace` +* @param {NonNegativeInteger} offsetW - starting index for `workspace` +* @returns {void} +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); +* +* var N = 4; +* +* var workspace = new Float64Array( ( 2*N ) + 34 ); +* rffti( N, workspace, 1, 0 ); +* +* var r = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] ); +* +* rfftf( N, r, 1, 0, workspace, 1, 0 ); +* // r => [ 10.0, -2.0, 2.0, -2.0 ] +*/ +function rfftf( N, r, strideR, offsetR, workspace, strideW, offsetW ) { + var offsetT; + var offsetF; + + if ( !isNonNegativeInteger( N ) || !isFloat64Array( r ) || + !isInteger( strideR ) || !isNonNegativeInteger( offsetR ) || + !isFloat64Array( workspace ) || !isInteger( strideW ) || + !isNonNegativeInteger( offsetW ) || + workspace.length < offsetW + ( ( ( 2*N ) + 34 ) * strideW ) ) { + return; + } + + // When a sub-sequence is a single data point, the FFT is the identity, so no transformation necessary... + if ( N === 1 ) { + return; + } + + // Resolve the starting indices for storing twiddle factors and factorization results: + offsetT = offsetW + (N * strideW); // index offset for twiddle factors + offsetF = offsetT + (N * strideW); // index offset for factors describing the sub-transforms + + rfftf1( N, r, offsetR, workspace, offsetW, workspace, offsetT, workspace, offsetF ); // eslint-disable-line max-len +} + + +// EXPORTS // + +module.exports = rfftf; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js new file mode 100644 index 000000000000..0d0af15bbf79 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js @@ -0,0 +1,366 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/0b4ee12c4ba45a4a8e567550c16d96d1679f50ce/src/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 */ + +'use strict'; + +// FUNCTIONS // + +/** +* Resolves an index into the input array. +* +* ## Notes +* +* In a forward real FFT, the previous stage writes its results as two "rows" per sub-sequence. +* +* Thus, when reading from an input array stored in linear memory, we can reinterpret the array as a three-dimensional logical view containing `L` independent sub-sequences having two "rows" (`even + odd` and `even - odd`, respectively) and where each "row" is arranged as `M*L` contiguous elements corresponding to interleaved real and imaginary components. +* +* Accordingly, the following is a logical view of an input array (zero-based indexing) which contains `L = 3` transforms and in which each sub-sequence has length `M = 4`: +* +* ```text +* │ k = 0 k = 1 k = 2 +* │ ──────────────────────────────────────────────────────────────────────────→ k +* j = 0 (even+odd) │ cc(0,0,0) ... cc(3,0,0) cc(0,1,0) ... cc(3,1,0) cc(0,2,0) ... cc(3,2,0) +* │ +* j = 1 (even-odd) │ cc(0,0,1) ... cc(3,0,1) cc(0,1,1) ... cc(3,1,1) cc(0,2,1) ... cc(3,2,1) +* └───────────────────────────────────────────────────────────────────────────→ i +* ↑ ↑ ↑ ↑ ↑ ↑ +* i = 0 M-1 0 M-1 0 M-1 +* ``` +* +* In the above, +* +* - `i` is the fastest varying index, which walks within one short sub-sequence corresponding to either the `even + odd` or `even - odd` row. +* - `j` selects between the `even + odd` and `even - odd` row. +* - `k` specifies the index of one of the `L` independent transforms we are processing. +* +* In linear memory, the three-dimensional logical view is arranged as follows: +* +* ```text +* | cc(0,0,0)...cc(3,0,0) ... cc(0,2,0)...cc(3,2,0) | cc(0,0,1)...cc(3,0,1) ... cc(0,2,1)...cc(3,2,1) | +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* 0 M-1 LM LM-1 (L+1)M (L+1)M-1 (2L-1)M 2LM-1 +* ``` +* +* @private +* @param {NonNegativeInteger} i - index of an element within a sub-sequence +* @param {NonNegativeInteger} k - index of the sub-sequence being transformed +* @param {NonNegativeInteger} j - input row +* @param {NonNegativeInteger} L - number of sub-sequences +* @param {NonNegativeInteger} M - sub-sequence length +* @param {integer} stride - stride length of the input array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the output array +* @returns {NonNegativeInteger} computed index +* +* @example +* var stride = 1; +* var offset = 0; +* +* var M = 4; // sub-sequence length +* var L = 3; // number of sub-sequences +* +* var idx = iptr( 0, 0, 0, L, M, stride, offset ); +* // returns 0 +* +* idx = iptr( 1, 0, 0, L, M, stride, offset ); +* // returns 1 +* +* idx = iptr( M-1, 0, 0, L, M, stride, offset ); +* // returns 3 +* +* idx = iptr( 0, 1, 0, L, M, stride, offset ); +* // returns 4 +* +* // ... +* +* idx = iptr( M-1, L-1, 1, L, M, stride, offset ); +* // returns 23 +*/ +function iptr( i, k, j, L, M, stride, offset ) { + var n = i + ( ( k+(j*L) ) * M ); + return ( n*stride ) + offset; +} + +/** +* Resolves an index into the output array. +* +* ## Notes +* +* When writing to an output array stored in linear memory, we can reinterpret the array as a three-dimensional logical view containing `L` independent sub-sequences having two "columns" corresponding to the even and odd half-spectrum of a folded complex vector (with real and imaginary parts of each half-spectrum interleaved along each sub-sequence) and where each "column" has `M` elements. +* +* Accordingly, the following is a logical view of an output array (zero-based indexing) which contains `L = 3` transforms and in which each "column" sub-sequence has length `M = 4`: +* +* ```text +* j = 0 ("even" column) j = 1 ("odd" column) +* k = 0 ─┬───────────────────────────────────────┬───────────────────────────────────────┐ +* │ out(0,0,0) out(1,0,0) ... out(3,0,0) │ out(0,1,0) out(1,1,0) ... out(3,1,0) │ +* └───────────────────────────────────────┴───────────────────────────────────────┤ +* k = 1 ─┬───────────────────────────────────────┬───────────────────────────────────────┤ +* │ out(0,0,1) out(1,0,1) ... out(3,0,1) │ out(0,1,1) out(1,1,1) ... out(3,1,1) │ +* └───────────────────────────────────────┴───────────────────────────────────────┤ +* k = 2 ─┬───────────────────────────────────────┬───────────────────────────────────────┤ +* │ out(0,0,2) out(1,0,2) ... out(3,0,2) │ out(0,1,2) out(1,1,2) ... out(3,1,2) │ +* └───────────────────────────────────────┴───────────────────────────────────────┘ +* ↑ ↑ ↑ ↑ ↑ ↑ +* i = 0 1 M-1 0 1 M-1 +* ``` +* +* In the above, +* +* - `i` is the fastest varying index, which walks within one short "column" sub-sequence. +* - `j` selects between the even (0) and odd (1) column. +* - `k` specifies the index of one of the `L` independent transforms we are processing. +* +* In linear memory, the three-dimensional logical view is arranged as follows: +* +* ```text +* | out(0,0,0)...out(3,0,0) | out(0,1,0)...out(3,1,0) | out(0,0,1)...out(3,0,1) | ... | out(0,1,2)...out(3,1,2) | +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* 0 M-1 M 2M-1 2M 3M-1 (2L-1)M 2LM-1 +* ``` +* +* As may be observed, when resolving an index in the output array, the `j` and `k` dimensions are swapped relative index resolution in the input array. This stems from `radf2` being only one stage in a multi-stage driver which alternates between using `cc` and `out` as workspace buffers. After each stage, the next stage reads what the previous stage wrote. +* +* Each stage expects a transpose, and, in order to avoid explicit transposition between the stages, we swap the last two logical dimensions while still maintaining cache locality within the inner loop logical dimension, as indexed by `i`. +* +* @private +* @param {NonNegativeInteger} i - index of an element within a sub-sequence +* @param {NonNegativeInteger} j - index specifying which of the two complex halves we are in (either `0` or `1`) +* @param {NonNegativeInteger} k - index of the sub-sequence being transformed +* @param {NonNegativeInteger} M - sub-sequence length +* @param {integer} stride - stride length of the output array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the output array +* @returns {NonNegativeInteger} computed index +* +* @example +* var stride = 1; +* var offset = 0; +* +* var M = 4; // sub-sequence length +* var L = 3; // number of sub-sequences +* +* var idx = optr( 0, 0, 0, M, stride, offset ); +* // returns 0 +* +* idx = optr( 1, 0, 0, M, stride, offset ); +* // returns 1 +* +* idx = optr( M-1, 0, 0, M, stride, offset ); +* // returns 3 +* +* idx = optr( 0, 1, 0, M, stride, offset ); +* // returns 4 +* +* // ... +* +* idx = optr( M-1, 1, L-1, M, stride, offset ); +* // returns 23 +*/ +function optr( i, j, k, M, stride, offset ) { + var n = i + ( ( j+(k*2) ) * M ); + return ( n*stride ) + offset; +} + + +// MAIN // + +/** +* Performs one radix-2 stage within a forward Fourier transform for a real-valued sequence. +* +* @private +* @param {NonNegativeInteger} M - number of elements in each sub-sequence to be transformed +* @param {NonNegativeInteger} L - number of sub-sequences to be transformed +* @param {Float64Array} cc - input array containing the sub-sequences to be transformed +* @param {integer} sc - stride length for `cc` +* @param {NonNegativeInteger} oc - index offset for `cc` +* @param {Float64Array} out - output array containing transformed sub-sequences +* @param {integer} so - stride length for `out` +* @param {NonNegativeInteger} oo - index offset for `out` +* @param {Float64Array} twiddles - array containing twiddle factors +* @param {integer} st - stride length for `twiddles` +* @param {NonNegativeInteger} ot - index offset for `twiddles` +* @returns {void} +*/ +function radf2( M, L, cc, sc, oc, out, so, oo, twiddles, st, ot ) { // eslint-disable-line max-params + var tr2; + var ti2; + var ip1; + var ip2; + var it1; + var it2; + var io; + var im; + var i; + var k; + + /* + * First, perform the core butterfly for each sub-sequence being transformed. + * + * In the following loop, we handle harmonic `n = 0` for every transform. As described for `iptr`, the input array is interpreted as a three-dimensional array, containing two "rows" per sub-sequence. + * + * row0 = even + odd (j = 0) + * row1 = even - odd (j = 1) + * + * For a radix-2 forward FFT of a real-valued signal `x` and `n = 0`, + * + * x[0] = row0 + row1 = 2⋅even + * x[M] = row0 - row1 = 2⋅odd + * + * Because `W_2^0 = 1`, no twiddle multiplication is necessary. + */ + for ( k = 0; k < L; k++ ) { + ip1 = iptr( 0, k, 0, L, M, sc, oc ); // real part row 0 + ip2 = iptr( 0, k, 1, L, M, sc, oc ); // real part row 1 + + io = optr( 0, 0, k, M, so, oo ); + out[ io ] = cc[ ip1 ] + cc[ ip2 ]; // even + odd + + io = optr( M-1, 1, k, M, so, oo ); + out[ io ] = cc[ ip1 ] - cc[ ip2 ]; // even - odd + } + // When the number of elements in a sub-sequence is less than `2`, there is nothing more to do, as the above butterfly produced the full result... + if ( M < 2 ) { + return; + } + /* + * Next, apply the general case where we need to loop through the non-trivial harmonics. + * + * For each harmonic `n = 1, ..., M/2-1`, we need to + * + * - recover even/odd spectra from the two input rows. + * - multiply the odd part by the twiddle factor `W_n = cos(θ) - j sin(θ)`. + * - form the following + * + * x[2n] = E_n + W_n⋅O_n => column 0 + * x[2n+1] = E_n - W_n⋅O_n => column 1 + * + * The mirror index `im = M - i` selects the conjugate-symmetric partner, thus allowing the routine to read each symmetry pair only once. + */ + if ( M >= 3 ) { + // Loop over each sub-sequence to be transformed... + for ( k = 0; k < L; k++ ) { + // Loop over the elements in each sub-sequence... + for ( i = 2; i < M; i += 2 ) { + im = M - i; // "mirror" index + + // Resolve twiddle factor indices: + it1 = ( (i-2)*st ) + ot; // cos(θ) + it2 = ( (i-1)*st ) + ot; // sin(θ) + + // Load the `even-odd` row... + ip1 = iptr( i-1, k, 1, L, M, sc, oc ); // c = Re(row1) + ip2 = iptr( i, k, 1, L, M, sc, oc ); // d = Im(row1) + + // eslint-disable-next-line stdlib/capitalized-comments, stdlib/empty-line-before-comment + // tmp = W_n ⋅ (c + j⋅d) + tr2 = ( twiddles[ it1 ] * cc[ ip1 ] ) + ( twiddles[ it2 ] * cc[ ip2 ] ); // Re(tmp) + ti2 = ( twiddles[ it1 ] * cc[ ip2 ] ) - ( twiddles[ it2 ] * cc[ ip1 ] ); // Im(tmp) + + // Load the `even+odd` row... + ip1 = iptr( i, k, 0, L, M, sc, oc ); // b = Im(row0) + io = optr( i, 0, k, M, so, oo ); // Im(x[2n]) + out[ io ] = cc[ ip1 ] + ti2; + + io = optr( im, 1, k, M, so, oo ); // Im(x[2n+1]) + out[ io ] = ti2 - cc[ ip1 ]; + + ip1 = iptr( i-1, k, 0, L, M, sc, oc ); // a = Re(row0) + io = optr( i-1, 0, k, M, so, oo ); // Re(x[2n]) + out[ io ] = cc[ ip1 ] + tr2; + + io = optr( im-1, 1, k, M, so, oo ); // Re(x[2n+1]) + out[ io ] = cc[ ip1 ] - tr2; + } + } + // When `M` is odd, there is no Nyquist pair to process, so we do not need to perform any further transformations... + if ( M%2 === 1 ) { + return; + } + } + /* + * Lastly, handle the Nyquist frequency where `i = M-1` (i.e., the last element of each sub-sequence). + * + * When `M` is even, the Nyquist index is `i = M/2`. In this stage, we've stored that element at the end of each sub-sequence (i.e., `i = M-1` in the packed layout). + * + * At this point, the cosine term is -1 and the sine term is 0, so the twiddle multiplication collapses to simple addition/subtraction. + * + * In this case, + * + * W_n⋅O_n = ±Re(O_n) + * + * where + * + * row0 = Re(E_n) + * row1 = -Re(O_n) + */ + for ( k = 0; k < L; k++ ) { + ip1 = iptr( M-1, k, 1, L, M, sc, oc ); // -Re(O_n) + io = optr( 0, 1, k, M, so, oo ); + out[ io ] = -cc[ ip1 ]; // -(-Re(O_n)) = Re(O_n) + + ip1 = iptr( M-1, k, 0, L, M, sc, oc ); // Re(E_n) + io = optr( M-1, 0, k, M, so, oo ); + out[ io ] = cc[ ip1 ]; + } +} + + +// EXPORTS // + +module.exports = radf2; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js new file mode 100644 index 000000000000..2fced4b2c683 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js @@ -0,0 +1,397 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/0b4ee12c4ba45a4a8e567550c16d96d1679f50ce/src/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 */ + +'use strict'; + +// VARIABLES // + +var TAUR = -0.5; // cos( 2π/3 ) +var TAUI = 0.866025403784439; // sin( 2π/3 ) + + +// FUNCTIONS // + +/** +* Resolves an index into the input array. +* +* ## Notes +* +* In a forward real FFT, the previous stage writes its results as three "rows" per sub-sequence. +* +* Thus, when reading from an input array stored in linear memory, we can reinterpret the array as a three-dimensional logical view containing `L` independent sub-sequences having three "rows" (components 0, 1, and 2) and where each "row" is arranged as `M*L` contiguous elements corresponding to interleaved real and imaginary components. +* +* Accordingly, the following is a logical view of an input array (zero-based indexing) which contains `L = 3` transforms and in which each sub-sequence has length `M = 4`: +* +* ```text +* │ k = 0 k = 1 k = 2 +* │ ──────────────────────────────────────────────────────────────────────────→ k +* j = 0 │ cc(0,0,0) ... cc(3,0,0) cc(0,1,0) ... cc(3,1,0) cc(0,2,0) ... cc(3,2,0) +* │ +* j = 1 │ cc(0,0,1) ... cc(3,0,1) cc(0,1,1) ... cc(3,1,1) cc(0,2,1) ... cc(3,2,1) +* │ +* j = 2 │ cc(0,0,2) ... cc(3,0,2) cc(0,1,2) ... cc(3,1,2) cc(0,2,2) ... cc(3,2,2) +* └───────────────────────────────────────────────────────────────────────────→ i +* ↑ ↑ ↑ ↑ ↑ ↑ +* i = 0 M-1 0 M-1 0 M-1 +* ``` +* +* In the above, +* +* - `i` is the fastest varying index, which walks within one short sub-sequence corresponding to one of the three component rows. +* - `j` selects between the three component rows (0, 1, or 2). +* - `k` specifies the index of one of the `L` independent transforms we are processing. +* +* In linear memory, the three-dimensional logical view is arranged as follows: +* +* ```text +* | cc(0,0,0)...cc(3,0,0) ... cc(0,2,0)...cc(3,2,0) | cc(0,0,1)...cc(3,0,1) ... cc(0,2,1)...cc(3,2,1) | cc(0,0,2)...cc(3,0,2) ... cc(0,2,2)...cc(3,2,2) | +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* 0 M-1 LM LM-1 (L+1)M (L+1)M-1 (2L-1)M 2LM-1 2LM (2L+1)M-1 (3L-1)M 3LM-1 +* ``` +* +* @private +* @param {NonNegativeInteger} i - index of an element within a sub-sequence +* @param {NonNegativeInteger} k - index of the sub-sequence being transformed +* @param {NonNegativeInteger} j - input row +* @param {NonNegativeInteger} L - number of sub-sequences +* @param {NonNegativeInteger} M - sub-sequence length +* @param {integer} stride - stride length of the input array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the output array +* @returns {NonNegativeInteger} computed index +* +* @example +* var stride = 1; +* var offset = 0; +* +* var M = 4; // sub-sequence length +* var L = 3; // number of sub-sequences +* +* var idx = iptr( 0, 0, 0, L, M, stride, offset ); +* // returns 0 +* +* idx = iptr( 1, 0, 0, L, M, stride, offset ); +* // returns 1 +* +* idx = iptr( M-1, 0, 0, L, M, stride, offset ); +* // returns 3 +* +* idx = iptr( 0, 1, 0, L, M, stride, offset ); +* // returns 4 +* +* // ... +* +* idx = iptr( M-1, L-1, 1, L, M, stride, offset ); +* // returns 23 +*/ +function iptr( i, k, j, L, M, stride, offset ) { + var n = i + ( ( k+(j*L) ) * M ); + return ( n*stride ) + offset; +} + +/** +* Resolves an index into the output array. +* +* ## Notes +* +* When writing to an output array stored in linear memory, we can reinterpret the array as a three-dimensional logical view containing `L` independent sub-sequences having three "columns" corresponding to the three components of a radix-3 stage (with real and imaginary parts of each component interleaved along each sub-sequence) and where each "column" has `M` elements. +* +* Accordingly, the following is a logical view of an output array (zero-based indexing) which contains `L = 3` transforms and in which each "column" sub-sequence has length `M = 4`: +* +* ```text +* j = 0 (component 0) j = 1 (component 1) j = 2 (component 2) +* k = 0 ─┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┐ +* │ out(0,0,0) out(1,0,0) ... out(3,0,0) │ out(0,1,0) out(1,1,0) ... out(3,1,0) │ out(0,2,0) out(1,2,0) ... out(3,2,0) │ +* └───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┤ +* k = 1 ─┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┤ +* │ out(0,0,1) out(1,0,1) ... out(3,0,1) │ out(0,1,1) out(1,1,1) ... out(3,1,1) │ out(0,2,1) out(1,2,1) ... out(3,2,1) │ +* └───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┤ +* k = 2 ─┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┤ +* │ out(0,0,2) out(1,0,2) ... out(3,0,2) │ out(0,1,2) out(1,1,2) ... out(3,1,2) │ out(0,2,2) out(1,2,2) ... out(3,2,2) │ +* └───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┘ +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* i = 0 1 M-1 0 1 M-1 0 1 M-1 +* ``` +* +* In the above, +* +* - `i` is the fastest varying index, which walks within one short "column" sub-sequence. +* - `j` selects between one of the three components (0, 1, or 2). +* - `k` specifies the index of one of the `L` independent transforms we are processing. +* +* In linear memory, the three-dimensional logical view is arranged as follows: +* +* ```text +* | out(0,0,0)...out(3,0,0) | out(0,1,0)...out(3,1,0) | out(0,2,0)...out(3,2,0) | out(0,0,1)...out(3,0,1) | ... | out(0,2,2)...out(3,2,2) | +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* 0 M-1 M 2M-1 2M 3M-1 3M 4M-1 (3L-1)M 3LM-1 +* ``` +* +* As may be observed, when resolving an index in the output array, the `j` and `k` dimensions are swapped relative index resolution in the input array. This stems from `radf3` being only one stage in a multi-stage driver which alternates between using `cc` and `out` as workspace buffers. After each stage, the next stage reads what the previous stage wrote. +* +* Each stage expects a transpose, and, in order to avoid explicit transposition between the stages, we swap the last two logical dimensions while still maintaining cache locality within the inner loop logical dimension, as indexed by `i`. +* +* @private +* @param {NonNegativeInteger} i - index of an element within a sub-sequence +* @param {NonNegativeInteger} j - index specifying which of the three complex components we are in (0, 1, or 2) +* @param {NonNegativeInteger} k - index of the sub-sequence being transformed +* @param {NonNegativeInteger} M - sub-sequence length +* @param {integer} stride - stride length of the output array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the output array +* @returns {NonNegativeInteger} computed index +* +* @example +* var stride = 1; +* var offset = 0; +* +* var M = 4; // sub-sequence length +* var L = 3; // number of sub-sequences +* +* var idx = optr( 0, 0, 0, M, stride, offset ); +* // returns 0 +* +* idx = optr( 1, 0, 0, M, stride, offset ); +* // returns 1 +* +* idx = optr( M-1, 0, 0, M, stride, offset ); +* // returns 3 +* +* idx = optr( 0, 1, 0, M, stride, offset ); +* // returns 4 +* +* // ... +* +* idx = optr( M-1, 2, L-1, M, stride, offset ); +* // returns 35 +*/ +function optr( i, j, k, M, stride, offset ) { + var n = i + ( ( j+(k*3) ) * M ); + return ( n*stride ) + offset; +} + + +// MAIN // + +/** +* Performs one radix-3 stage within a forward Fourier transform for a real-valued sequence. +* +* @private +* @param {NonNegativeInteger} M - number of elements in each sub-sequence to be transformed +* @param {NonNegativeInteger} L - number of sub-sequences to be transformed +* @param {Float64Array} cc - input array containing the sub-sequences to be transformed +* @param {integer} sc - stride length for `cc` +* @param {NonNegativeInteger} oc - index offset for `cc` +* @param {Float64Array} out - output array containing transformed sub-sequences +* @param {integer} so - stride length for `out` +* @param {NonNegativeInteger} oo - index offset for `out` +* @param {Float64Array} twiddles1 - first array containing twiddle factors +* @param {integer} st1 - stride length for `twiddles1` +* @param {NonNegativeInteger} ot1 - index offset for `twiddles1` +* @param {Float64Array} twiddles2 - second array containing twiddle factors +* @param {integer} st2 - stride length for `twiddles2` +* @param {NonNegativeInteger} ot2 - index offset for `twiddles2` +* @returns {void} +*/ +function radf3( M, L, cc, sc, oc, out, so, oo, twiddles1, st1, ot1, twiddles2, st2, ot2 ) { // eslint-disable-line max-params + var it11; + var it12; + var it21; + var it22; + var tr2; + var ti2; + var tr3; + var ti3; + var cr2; + var ci2; + var dr2; + var di2; + var dr3; + var di3; + var ip1; + var ip2; + var ip3; + var io; + var im; + var i; + var k; + + /* + * First, perform the core butterfly for each sub-sequence being transformed. + * + * In the following loop, we handle harmonic `n = 0` for every transform. As described for `iptr`, the input array is interpreted as a three-dimensional array, containing three "rows" per sub-sequence. + * + * row0 = input component 0 (j = 0) + * row1 = input component 1 (j = 1) + * row2 = input component 2 (j = 2) + * + * For a radix-3 forward FFT of a real-valued signal `x` and `n = 0`, + * + * x[0] = row0 + row1 + row2 + * x[2M] = taui * ( row2-row1 ) + * x[M] = row0 + ( taur * ( row1+row2 ) ) + * + * where `taur = cos(2π/3)` and `taui = sin(2π/3)`. + * + * Because `W_3^0 = 1`, no twiddle multiplication is necessary beyond these constant factors (`taur` and `taui`). + */ + for ( k = 0; k < L; k++ ) { + ip1 = iptr( 0, k, 0, L, M, sc, oc ); // real part row 0 + ip2 = iptr( 0, k, 1, L, M, sc, oc ); // real part row 1 + ip3 = iptr( 0, k, 2, L, M, sc, oc ); // real part row 2 + + cr2 = cc[ ip2 ] + cc[ ip3 ]; + + io = optr( 0, 0, k, M, so, oo ); + out[ io ] = cc[ ip1 ] + cr2; // row0 + row1 + row2 + + io = optr( 0, 2, k, M, so, oo ); + out[ io ] = TAUI * ( cc[ ip3 ] - cc[ ip2 ] ); // taui * ( row2-row1 ) + + io = optr( M-1, 1, k, M, so, oo ); + out[ io ] = cc[ ip1 ] + ( TAUR * cr2 ); // row0 + ( taur * ( row1+row2 ) ) + } + // When the number of elements in a sub-sequence is less than `2`, there is nothing more to do, as the above butterfly produced the full result... + if ( M < 2 ) { + return; + } + /* + * Next, apply the general case where we need to loop through the non-trivial harmonics. + * + * For each harmonic `n = 1, ..., M/2-1`, we need to + * + * - recover three spectra from the three input rows. + * - apply radix-3 twiddle factors to rows 1 and 2, then combine with row 0 to form three output columns. + * - form the following + * + * x[3n] = X₀ + (W₁⋅X₁ + W₂⋅X₂) => column 0 + * x[3n+1] = X₀ + taur⋅(W₁⋅X₁ + W₂⋅X₂) + taui⋅i⋅(W₁⋅X₁ - W₂⋅X₂) => column 2 + * x[3n+2] = X₀ + taur⋅(W₁⋅X₁ + W₂⋅X₂) - taui⋅i⋅(W₁⋅X₁ - W₂⋅X₂) => column 1 + * + * The mirror index `im = M - i` selects the conjugate-symmetric partner, thus allowing the routine to read each symmetry pair only once. + */ + // Loop over each sub-sequence to be transformed... + for ( k = 0; k < L; k++ ) { + // Loop over the elements in each sub-sequence... + for ( i = 2; i < M; i += 2 ) { + im = M - i; // "mirror" index + + // Resolve twiddle factor indices for component 1: + it11 = ( (i-2)*st1 ) + ot1; // cos(θ) for component 1 + it12 = ( (i-1)*st1 ) + ot1; // sin(θ) for component 1 + + // Resolve twiddle factor indices for component 2: + it21 = ( (i-2)*st2 ) + ot2; // cos(θ) for component 2 + it22 = ( (i-1)*st2 ) + ot2; // sin(θ) for component 2 + + // Load component 1 data... + ip1 = iptr( i-1, k, 1, L, M, sc, oc ); // real part component 1 + ip2 = iptr( i, k, 1, L, M, sc, oc ); // imag part component 1 + + // Apply twiddle factor for component 1 + dr2 = ( twiddles1[ it11 ] * cc[ ip1 ] ) + ( twiddles1[ it12 ] * cc[ ip2 ] ); + di2 = ( twiddles1[ it11 ] * cc[ ip2 ] ) - ( twiddles1[ it12 ] * cc[ ip1 ] ); + + // Load component 2 data... + ip1 = iptr( i-1, k, 2, L, M, sc, oc ); // real part component 2 + ip2 = iptr( i, k, 2, L, M, sc, oc ); // imag part component 2 + + // Apply twiddle factor for component 2 + dr3 = ( twiddles2[ it21 ] * cc[ ip1 ] ) + ( twiddles2[ it22 ] * cc[ ip2 ] ); + di3 = ( twiddles2[ it21 ] * cc[ ip2 ] ) - ( twiddles2[ it22 ] * cc[ ip1 ] ); + + // Combine the twiddled components + cr2 = dr2 + dr3; // sum of real parts + ci2 = di2 + di3; // sum of imag parts + + // Load component 0 data... + ip1 = iptr( i-1, k, 0, L, M, sc, oc ); // real part component 0 + io = optr( i-1, 0, k, M, so, oo ); + out[ io ] = cc[ ip1 ] + cr2; + + ip2 = iptr( i, k, 0, L, M, sc, oc ); // imag part component 0 + io = optr( i, 0, k, M, so, oo ); + out[ io ] = cc[ ip2 ] + ci2; + + // Intermediate results for components 1 and 2 + tr2 = cc[ ip1 ] + ( TAUR * cr2 ); + ti2 = cc[ ip2 ] + ( TAUR * ci2 ); + tr3 = TAUI * ( di2 - di3 ); + ti3 = TAUI * ( dr3 - dr2 ); + + // Output component 1 + io = optr( i-1, 2, k, M, so, oo ); + out[ io ] = tr2 + tr3; + + io = optr( im-1, 1, k, M, so, oo ); + out[ io ] = tr2 - tr3; + + // Output component 2 + io = optr( i, 2, k, M, so, oo ); + out[ io ] = ti2 + ti3; + + io = optr( im, 1, k, M, so, oo ); + out[ io ] = ti3 - ti2; + } + } +} + + +// EXPORTS // + +module.exports = radf3; From dd7b9bcd3d95f62bf94112e07d0bc1739521ef9f Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Mon, 11 May 2026 00:53:35 +0530 Subject: [PATCH 02/19] feat: add radf4 --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rfftf/lib/radf2.js | 14 +- .../fft/base/fftpack/rfftf/lib/radf3.js | 11 +- .../fft/base/fftpack/rfftf/lib/radf4.js | 492 ++++++++++++++++++ 3 files changed, 505 insertions(+), 12 deletions(-) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf4.js diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js index 0d0af15bbf79..4b41a74e2ae3 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js @@ -304,7 +304,7 @@ function radf2( M, L, cc, sc, oc, out, so, oo, twiddles, st, ot ) { // eslint-di it2 = ( (i-1)*st ) + ot; // sin(θ) // Load the `even-odd` row... - ip1 = iptr( i-1, k, 1, L, M, sc, oc ); // c = Re(row1) + ip1 = iptr( i-1, k, 1, L, M, sc, oc ); // c = Re(row1) ip2 = iptr( i, k, 1, L, M, sc, oc ); // d = Im(row1) // eslint-disable-next-line stdlib/capitalized-comments, stdlib/empty-line-before-comment @@ -314,17 +314,17 @@ function radf2( M, L, cc, sc, oc, out, so, oo, twiddles, st, ot ) { // eslint-di // Load the `even+odd` row... ip1 = iptr( i, k, 0, L, M, sc, oc ); // b = Im(row0) - io = optr( i, 0, k, M, so, oo ); // Im(x[2n]) + io = optr( i, 0, k, M, so, oo ); // Im(x[2n]) out[ io ] = cc[ ip1 ] + ti2; - io = optr( im, 1, k, M, so, oo ); // Im(x[2n+1]) + io = optr( im, 1, k, M, so, oo ); // Im(x[2n+1]) out[ io ] = ti2 - cc[ ip1 ]; - ip1 = iptr( i-1, k, 0, L, M, sc, oc ); // a = Re(row0) - io = optr( i-1, 0, k, M, so, oo ); // Re(x[2n]) + ip1 = iptr( i-1, k, 0, L, M, sc, oc ); // a = Re(row0) + io = optr( i-1, 0, k, M, so, oo ); // Re(x[2n]) out[ io ] = cc[ ip1 ] + tr2; - io = optr( im-1, 1, k, M, so, oo ); // Re(x[2n+1]) + io = optr( im-1, 1, k, M, so, oo ); // Re(x[2n+1]) out[ io ] = cc[ ip1 ] - tr2; } } @@ -352,7 +352,7 @@ function radf2( M, L, cc, sc, oc, out, so, oo, twiddles, st, ot ) { // eslint-di for ( k = 0; k < L; k++ ) { ip1 = iptr( M-1, k, 1, L, M, sc, oc ); // -Re(O_n) io = optr( 0, 1, k, M, so, oo ); - out[ io ] = -cc[ ip1 ]; // -(-Re(O_n)) = Re(O_n) + out[ io ] = -cc[ ip1 ]; // -(-Re(O_n)) = Re(O_n) ip1 = iptr( M-1, k, 0, L, M, sc, oc ); // Re(E_n) io = optr( M-1, 0, k, M, so, oo ); diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js index 2fced4b2c683..3aae60305bf8 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js @@ -282,12 +282,13 @@ function radf3( M, L, cc, sc, oc, out, so, oo, twiddles1, st1, ot1, twiddles2, s * * For a radix-3 forward FFT of a real-valued signal `x` and `n = 0`, * + * taur = cos(2π/3) + * taui = sin(2π/3) + * * x[0] = row0 + row1 + row2 * x[2M] = taui * ( row2-row1 ) * x[M] = row0 + ( taur * ( row1+row2 ) ) * - * where `taur = cos(2π/3)` and `taui = sin(2π/3)`. - * * Because `W_3^0 = 1`, no twiddle multiplication is necessary beyond these constant factors (`taur` and `taui`). */ for ( k = 0; k < L; k++ ) { @@ -341,7 +342,7 @@ function radf3( M, L, cc, sc, oc, out, so, oo, twiddles1, st1, ot1, twiddles2, s // Load component 1 data... ip1 = iptr( i-1, k, 1, L, M, sc, oc ); // real part component 1 - ip2 = iptr( i, k, 1, L, M, sc, oc ); // imag part component 1 + ip2 = iptr( i, k, 1, L, M, sc, oc ); // imag part component 1 // Apply twiddle factor for component 1 dr2 = ( twiddles1[ it11 ] * cc[ ip1 ] ) + ( twiddles1[ it12 ] * cc[ ip2 ] ); @@ -349,7 +350,7 @@ function radf3( M, L, cc, sc, oc, out, so, oo, twiddles1, st1, ot1, twiddles2, s // Load component 2 data... ip1 = iptr( i-1, k, 2, L, M, sc, oc ); // real part component 2 - ip2 = iptr( i, k, 2, L, M, sc, oc ); // imag part component 2 + ip2 = iptr( i, k, 2, L, M, sc, oc ); // imag part component 2 // Apply twiddle factor for component 2 dr3 = ( twiddles2[ it21 ] * cc[ ip1 ] ) + ( twiddles2[ it22 ] * cc[ ip2 ] ); @@ -364,7 +365,7 @@ function radf3( M, L, cc, sc, oc, out, so, oo, twiddles1, st1, ot1, twiddles2, s io = optr( i-1, 0, k, M, so, oo ); out[ io ] = cc[ ip1 ] + cr2; - ip2 = iptr( i, k, 0, L, M, sc, oc ); // imag part component 0 + ip2 = iptr( i, k, 0, L, M, sc, oc ); // imag part component 0 io = optr( i, 0, k, M, so, oo ); out[ io ] = cc[ ip2 ] + ci2; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf4.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf4.js new file mode 100644 index 000000000000..c3e52effe63f --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf4.js @@ -0,0 +1,492 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/0b4ee12c4ba45a4a8e567550c16d96d1679f50ce/src/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 SQRT_HALF = require( '@stdlib/constants/float64/sqrt-half' ); + + +// FUNCTIONS // + +/** +* Resolves an index into the input array. +* +* ## Notes +* +* In a forward real FFT, the previous stage writes its results as four "rows" per sub-sequence. +* +* Thus, when reading from an input array stored in linear memory, we can reinterpret the array as a three-dimensional logical view containing `L` independent sub-sequences having four "rows" (components 0, 1, 2, and 3) and where each "row" is arranged as `M*L` contiguous elements corresponding to interleaved real and imaginary components. +* +* Accordingly, the following is a logical view of an input array (zero-based indexing) which contains `L = 3` transforms and in which each sub-sequence has length `M = 4`: +* +* ```text +* │ k = 0 k = 1 k = 2 +* │ ──────────────────────────────────────────────────────────────────────────→ k +* j = 0 │ cc(0,0,0) ... cc(3,0,0) cc(0,1,0) ... cc(3,1,0) cc(0,2,0) ... cc(3,2,0) +* │ +* j = 1 │ cc(0,0,1) ... cc(3,0,1) cc(0,1,1) ... cc(3,1,1) cc(0,2,1) ... cc(3,2,1) +* │ +* j = 2 │ cc(0,0,2) ... cc(3,0,2) cc(0,1,2) ... cc(3,1,2) cc(0,2,2) ... cc(3,2,2) +* │ +* j = 3 │ cc(0,0,3) ... cc(3,0,3) cc(0,1,3) ... cc(3,1,3) cc(0,2,3) ... cc(3,2,3) +* └───────────────────────────────────────────────────────────────────────────→ i +* ↑ ↑ ↑ ↑ ↑ ↑ +* i = 0 M-1 0 M-1 0 M-1 +* ``` +* +* In the above, +* +* - `i` is the fastest varying index, which walks within one short sub-sequence corresponding to one of the four component rows. +* - `j` selects between the four component rows (0, 1, 2, or 3). +* - `k` specifies the index of one of the `L` independent transforms we are processing. +* +* In linear memory, the three-dimensional logical view is arranged as follows: +* +* ```text +* | cc(0,0,0)...cc(3,0,0) ... cc(0,2,0)...cc(3,2,0) | cc(0,0,1)...cc(3,0,1) ... cc(0,2,1)...cc(3,2,1) | ... | cc(0,0,3)...cc(3,0,3) ... cc(0,2,3)...cc(3,2,3) | +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* 0 M-1 LM LM-1 (L+1)M (L+1)M-1 (2L-1)M 2LM-1 3LM (3L+1)M-1 (4L-1)M 4LM-1 +* ``` +* +* @private +* @param {NonNegativeInteger} i - index of an element within a sub-sequence +* @param {NonNegativeInteger} k - index of the sub-sequence being transformed +* @param {NonNegativeInteger} j - input row +* @param {NonNegativeInteger} L - number of sub-sequences +* @param {NonNegativeInteger} M - sub-sequence length +* @param {integer} stride - stride length of the input array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the output array +* @returns {NonNegativeInteger} computed index +* +* @example +* var stride = 1; +* var offset = 0; +* +* var M = 4; // sub-sequence length +* var L = 3; // number of sub-sequences +* +* var idx = iptr( 0, 0, 0, L, M, stride, offset ); +* // returns 0 +* +* idx = iptr( 1, 0, 0, L, M, stride, offset ); +* // returns 1 +* +* idx = iptr( M-1, 0, 0, L, M, stride, offset ); +* // returns 3 +* +* idx = iptr( 0, 1, 0, L, M, stride, offset ); +* // returns 4 +* +* // ... +* +* idx = iptr( M-1, L-1, 1, L, M, stride, offset ); +* // returns 23 +*/ +function iptr( i, k, j, L, M, stride, offset ) { + var n = i + ( ( k+(j*L) ) * M ); + return ( n*stride ) + offset; +} + +/** +* Resolves an index into the output array. +* +* ## Notes +* +* When writing to an output array stored in linear memory, we can reinterpret the array as a three-dimensional logical view containing `L` independent sub-sequences having four "columns" corresponding to the four components of a radix-4 stage (with real and imaginary parts of each component interleaved along each sub-sequence) and where each "column" has `M` elements. +* +* Accordingly, the following is a logical view of an output array (zero-based indexing) which contains `L = 3` transforms and in which each "column" sub-sequence has length `M = 4`: +* +* ```text +* j = 0 (component 0) j = 1 (component 1) j = 2 (component 2) j = 3 (component 3) +* k = 0 ─┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┐ +* │ out(0,0,0) out(1,0,0) ... out(3,0,0) │ out(0,1,0) out(1,1,0) ... out(3,1,0) │ out(0,2,0) out(1,2,0) ... out(3,2,0) │ out(0,3,0) out(1,3,0) ... out(3,3,0) │ +* └───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┤ +* k = 1 ─┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┤ +* │ out(0,0,1) out(1,0,1) ... out(3,0,1) │ out(0,1,1) out(1,1,1) ... out(3,1,1) │ out(0,2,1) out(1,2,1) ... out(3,2,1) │ out(0,3,1) out(1,3,1) ... out(3,3,1) │ +* └───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┤ +* k = 2 ─┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┤ +* │ out(0,0,2) out(1,0,2) ... out(3,0,2) │ out(0,1,2) out(1,1,2) ... out(3,1,2) │ out(0,2,2) out(1,2,2) ... out(3,2,2) │ out(0,3,2) out(1,3,2) ... out(3,3,2) │ +* └───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┘ +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* i = 0 1 M-1 0 1 M-1 0 1 M-1 0 1 M-1 +* ``` +* +* In the above, +* +* - `i` is the fastest varying index, which walks within one short "column" sub-sequence. +* - `j` selects which of the four components (0, 1, 2, or 3). +* - `k` specifies the index of one of the `L` independent transforms we are processing. +* +* In linear memory, the three-dimensional logical view is arranged as follows: +* +* ```text +* | out(0,0,0)...out(3,0,0) | out(0,1,0)...out(3,1,0) | out(0,2,0)...out(3,2,0) | out(0,3,0)...out(3,3,0) | out(0,0,1)...out(3,0,1) | ... | out(0,3,2)...out(3,3,2) | +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* 0 M-1 M 2M-1 2M 3M-1 3M 4M-1 4M 5M-1 (4L-1)M 4LM-1 +* ``` +* +* As may be observed, when resolving an index in the output array, the `j` and `k` dimensions are swapped relative index resolution in the input array. This stems from `radf4` being only one stage in a multi-stage driver which alternates between using `cc` and `out` as workspace buffers. After each stage, the next stage reads what the previous stage wrote. +* +* Each stage expects a transpose, and, in order to avoid explicit transposition between the stages, we swap the last two logical dimensions while still maintaining cache locality within the inner loop logical dimension, as indexed by `i`. +* +* @private +* @param {NonNegativeInteger} i - index of an element within a sub-sequence +* @param {NonNegativeInteger} j - index specifying which of the four complex components we are in (0, 1, 2, or 3) +* @param {NonNegativeInteger} k - index of the sub-sequence being transformed +* @param {NonNegativeInteger} M - sub-sequence length +* @param {integer} stride - stride length of the output array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the output array +* @returns {NonNegativeInteger} computed index +* +* @example +* var stride = 1; +* var offset = 0; +* +* var M = 4; // sub-sequence length +* var L = 3; // number of sub-sequences +* +* var idx = optr( 0, 0, 0, M, stride, offset ); +* // returns 0 +* +* idx = optr( 1, 0, 0, M, stride, offset ); +* // returns 1 +* +* idx = optr( M-1, 0, 0, M, stride, offset ); +* // returns 3 +* +* idx = optr( 0, 1, 0, M, stride, offset ); +* // returns 4 +* +* // ... +* +* idx = optr( M-1, 3, L-1, M, stride, offset ); +* // returns 47 +*/ +function optr( i, j, k, M, stride, offset ) { + var n = i + ( ( j+(k*4) ) * M ); + return ( n*stride ) + offset; +} + + +// MAIN // + +/** +* Performs one radix-4 stage within a forward Fourier transform for a real-valued sequence. +* +* @private +* @param {NonNegativeInteger} M - number of elements in each sub-sequence to be transformed +* @param {NonNegativeInteger} L - number of sub-sequences to be transformed +* @param {Float64Array} cc - input array containing the sub-sequences to be transformed +* @param {integer} sc - stride length for `cc` +* @param {NonNegativeInteger} oc - index offset for `cc` +* @param {Float64Array} out - output array containing transformed sub-sequences +* @param {integer} so - stride length for `out` +* @param {NonNegativeInteger} oo - index offset for `out` +* @param {Float64Array} twiddles1 - first array containing twiddle factors +* @param {integer} st1 - stride length for `twiddles1` +* @param {NonNegativeInteger} ot1 - index offset for `twiddles1` +* @param {Float64Array} twiddles2 - second array containing twiddle factors +* @param {integer} st2 - stride length for `twiddles2` +* @param {NonNegativeInteger} ot2 - index offset for `twiddles2` +* @param {Float64Array} twiddles3 - third array containing twiddle factors +* @param {integer} st3 - stride length for `twiddles3` +* @param {NonNegativeInteger} ot3 - index offset for `twiddles3` +* @returns {void} +*/ +function radf4( M, L, cc, sc, oc, out, so, oo, twiddles1, st1, ot1, twiddles2, st2, ot2, twiddles3, st3, ot3 ) { // eslint-disable-line max-params + var it11; + var it12; + var it21; + var it22; + var it31; + var it32; + var tr1; + var tr2; + var tr3; + var tr4; + var ti1; + var ti2; + var ti3; + var ti4; + var cr2; + var cr3; + var cr4; + var ci2; + var ci3; + var ci4; + var ip1; + var ip2; + var ip3; + var ip4; + var io; + var im; + var i; + var k; + + /* + * First, perform the core butterfly for each sub-sequence being transformed. + * + * In the following loop, we handle harmonic `n = 0` for every transform. As described for `iptr`, the input array is interpreted as a three-dimensional array, containing four "rows" per sub-sequence. + * + * row0 = input component 0 (j = 0) + * row1 = input component 1 (j = 1) + * row2 = input component 2 (j = 2) + * row3 = input component 3 (j = 3) + * + * For a radix-4 forward FFT of a real-valued signal `x` and `n = 0`, + * + * tr1 = row1 + row3 + * tr2 = row0 + row2 + * + * x[0] = tr1 + tr2 + * x[2M-1] = row0 - row2 + * x[2M] = row3 - row1 + * x[4M-1] = tr2 - tr1 + * + * Because `W_4^0 = 1`, no twiddle multiplication is necessary. + */ + for ( k = 0; k < L; k++ ) { + ip1 = iptr( 0, k, 0, L, M, sc, oc ); // real part row 0 + ip2 = iptr( 0, k, 1, L, M, sc, oc ); // real part row 1 + ip3 = iptr( 0, k, 2, L, M, sc, oc ); // real part row 2 + ip4 = iptr( 0, k, 3, L, M, sc, oc ); // real part row 3 + + tr1 = cc[ ip2 ] + cc[ ip4 ]; // row1 + row3 + tr2 = cc[ ip1 ] + cc[ ip3 ]; // row0 + row2 + + io = optr( 0, 0, k, M, so, oo ); + out[ io ] = tr1 + tr2; + + io = optr( M-1, 3, k, M, so, oo ); + out[ io ] = tr2 - tr1; + + io = optr( M-1, 1, k, M, so, oo ); + out[ io ] = cc[ ip1 ] - cc[ ip3 ]; + + io = optr( 0, 2, k, M, so, oo ); + out[ io ] = cc[ ip4 ] - cc[ ip2 ]; + } + // When the number of elements in a sub-sequence is equal to `1`, there is nothing more to do, as the above butterfly produced the full result... + if ( M < 2 ) { + return; + } + /* + * Next, apply the general case where we need to loop through the non-trivial harmonics. + * + * For each harmonic `n = 1, ..., M/2-1`, we need to + * + * - recover four spectra from the four input rows. + * - apply radix-4 twiddle factors to rows 1, 2, and 3, then combine with row 0 to form four output columns. + * - form the following + * + * x[4n] = X₀ + W₂·X₂ + (W₁·X₁ + W₃·X₃) => column 0 + * x[4n+1] = X₀ + W₂·X₂ - (W₁·X₁ + W₃·X₃) => column 3 + * x[4n+2] = X₀ - W₂·X₂ + i·(W₁·X₁ - W₃·X₃) => column 2 + * x[4n+3] = X₀ - W₂·X₂ - i·(W₁·X₁ - W₃·X₃) => column 1 + * + * The mirror index `im = M - i` selects the conjugate-symmetric partner, thus allowing the routine to read each symmetry pair only once. + */ + if ( M >= 3 ) { + // Loop over each sub-sequence to be transformed... + for ( k = 0; k < L; k++ ) { + // Loop over the elements in each sub-sequence... + for ( i = 2; i < M; i += 2 ) { + im = M - i; // "mirror" index + + // Resolve twiddle factor indices for component 1: + it11 = ( (i-2)*st1 ) + ot1; // cos(θ) for component 1 + it12 = ( (i-1)*st1 ) + ot1; // sin(θ) for component 1 + + // Resolve twiddle factor indices for component 2: + it21 = ( (i-2)*st2 ) + ot2; // cos(θ) for component 2 + it22 = ( (i-1)*st2 ) + ot2; // sin(θ) for component 2 + + // Resolve twiddle factor indices for component 3: + it31 = ( (i-2)*st3 ) + ot3; // cos(θ) for component 3 + it32 = ( (i-1)*st3 ) + ot3; // sin(θ) for component 3 + + // Load component 1 data and apply twiddle... + ip1 = iptr( i-1, k, 1, L, M, sc, oc ); // real part component 1 + ip2 = iptr( i, k, 1, L, M, sc, oc ); // imag part component 1 + + // Apply the twiddle factors for component 1: + cr2 = ( twiddles1[ it11 ] * cc[ ip1 ] ) + ( twiddles1[ it12 ] * cc[ ip2 ] ); + ci2 = ( twiddles1[ it11 ] * cc[ ip2 ] ) - ( twiddles1[ it12 ] * cc[ ip1 ] ); + + // Load component 2 data and apply twiddle... + ip1 = iptr( i-1, k, 2, L, M, sc, oc ); // real part component 2 + ip2 = iptr( i, k, 2, L, M, sc, oc ); // imag part component 2 + + // Apply the twiddle factors for component 2: + cr3 = ( twiddles2[ it21 ] * cc[ ip1 ] ) + ( twiddles2[ it22 ] * cc[ ip2 ] ); + ci3 = ( twiddles2[ it21 ] * cc[ ip2 ] ) - ( twiddles2[ it22 ] * cc[ ip1 ] ); + + // Load component 3 data and apply twiddle... + ip1 = iptr( i-1, k, 3, L, M, sc, oc ); // real part component 3 + ip2 = iptr( i, k, 3, L, M, sc, oc ); // imag part component 3 + + // Apply the twiddle factors for component 3: + cr4 = ( twiddles3[ it31 ] * cc[ ip1 ] ) + ( twiddles3[ it32 ] * cc[ ip2 ] ); + ci4 = ( twiddles3[ it31 ] * cc[ ip2 ] ) - ( twiddles3[ it32 ] * cc[ ip1 ] ); + + // Radix-4 butterfly intermediate computations: + tr1 = cr2 + cr4; + tr4 = cr4 - cr2; + ti1 = ci2 + ci4; + ti4 = ci2 - ci4; + + // Load component 0 data and compute intermediates... + ip1 = iptr( i-1, k, 0, L, M, sc, oc ); // real part component 0 + tr2 = cc[ ip1 ] + cr3; + tr3 = cc[ ip1 ] - cr3; + + ip2 = iptr( i, k, 0, L, M, sc, oc ); // imag part component 0 + ti2 = cc[ ip2 ] + ci3; + ti3 = cc[ ip2 ] - ci3; + + // Output column 0 (real part) + io = optr( i-1, 0, k, M, so, oo ); + out[ io ] = tr1 + tr2; + + // Output column 3 (real part) + io = optr( im-1, 3, k, M, so, oo ); + out[ io ] = tr2 - tr1; + + // Output column 0 (imag part) + io = optr( i, 0, k, M, so, oo ); + out[ io ] = ti1 + ti2; + + // Output column 3 (imag part) + io = optr( im, 3, k, M, so, oo ); + out[ io ] = ti1 - ti2; + + // Output column 2 (real part) + io = optr( i-1, 2, k, M, so, oo ); + out[ io ] = ti4 + tr3; + + // Output column 1 (real part) + io = optr( im-1, 1, k, M, so, oo ); + out[ io ] = tr3 - ti4; + + // Output column 2 (imag part) + io = optr( i, 2, k, M, so, oo ); + out[ io ] = tr4 + ti3; + + // Output column 1 (imag part) + io = optr( im, 1, k, M, so, oo ); + out[ io ] = tr4 - ti3; + } + } + + // When `M` is odd, there is no Nyquist pair to process, so we do not need to perform any further transformations... + if ( M%2 === 1 ) { + return; + } + } + + /* + * Lastly, handle the Nyquist frequency where `i = M-1` (i.e., the last element of each sub-sequence). + * + * When `M` is even, the Nyquist index is `i = M/2`. In this stage, we've stored that element at the end of each sub-sequence (i.e., `i = M-1` in the packed layout). + * + * At this point, only real components exist for rows 1 and 3 (imaginary parts are zero due to symmetry), and the twiddle multiplication simplifies to involve √(1/2) factors. + * + * In this case, + * + * ti1 = -√(1/2) ⋅ (row1 + row3) + * tr1 = √(1/2) ⋅ (row1 - row3) + * + * where + * + * row0 = Re(X₀) + * row1 = Re(X₁) (imaginary part is zero) + * row2 = Re(X₂) + * row3 = Re(X₃) (imaginary part is zero) + */ + for ( k = 0; k < L; k++ ) { + ip1 = iptr( M-1, k, 1, L, M, sc, oc ); // Re(X₁) + ip2 = iptr( M-1, k, 3, L, M, sc, oc ); // Re(X₃) + + ti1 = -SQRT_HALF * ( cc[ ip1 ] + cc[ ip2 ] ); + tr1 = SQRT_HALF * ( cc[ ip1 ] - cc[ ip2 ] ); + + ip3 = iptr( M-1, k, 0, L, M, sc, oc ); // Re(X₀) + ip4 = iptr( M-1, k, 2, L, M, sc, oc ); // Re(X₂) + + io = optr( M-1, 0, k, M, so, oo ); + out[ io ] = cc[ ip3 ] + tr1; + + io = optr( M-1, 2, k, M, so, oo ); + out[ io ] = cc[ ip3 ] - tr1; + + io = optr( 0, 1, k, M, so, oo ); + out[ io ] = ti1 - cc[ ip4 ]; + + io = optr( 0, 3, k, M, so, oo ); + out[ io ] = cc[ ip4 ] + ti1; + } +} + + +// EXPORTS // + +module.exports = radf4; From b1762929a192685d9db7ad41ffc328ecea7a1357 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Tue, 12 May 2026 00:45:19 +0530 Subject: [PATCH 03/19] feat: add radf5 --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rfftf/lib/radf2.js | 2 +- .../fft/base/fftpack/rfftf/lib/radf3.js | 2 +- .../fft/base/fftpack/rfftf/lib/radf4.js | 2 +- .../fft/base/fftpack/rfftf/lib/radf5.js | 517 ++++++++++++++++++ 4 files changed, 520 insertions(+), 3 deletions(-) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf5.js diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js index 4b41a74e2ae3..d7ac34b18d32 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js @@ -105,7 +105,7 @@ * @param {NonNegativeInteger} L - number of sub-sequences * @param {NonNegativeInteger} M - sub-sequence length * @param {integer} stride - stride length of the input array -* @param {NonNegativeInteger} offset - index specifying the first indexed element in the output array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the input array * @returns {NonNegativeInteger} computed index * * @example diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js index 3aae60305bf8..54783ad72d3b 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js @@ -113,7 +113,7 @@ var TAUI = 0.866025403784439; // sin( 2π/3 ) * @param {NonNegativeInteger} L - number of sub-sequences * @param {NonNegativeInteger} M - sub-sequence length * @param {integer} stride - stride length of the input array -* @param {NonNegativeInteger} offset - index specifying the first indexed element in the output array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the input array * @returns {NonNegativeInteger} computed index * * @example diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf4.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf4.js index c3e52effe63f..d657a5cf8005 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf4.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf4.js @@ -114,7 +114,7 @@ var SQRT_HALF = require( '@stdlib/constants/float64/sqrt-half' ); * @param {NonNegativeInteger} L - number of sub-sequences * @param {NonNegativeInteger} M - sub-sequence length * @param {integer} stride - stride length of the input array -* @param {NonNegativeInteger} offset - index specifying the first indexed element in the output array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the input array * @returns {NonNegativeInteger} computed index * * @example diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf5.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf5.js new file mode 100644 index 000000000000..6ad5dea1f911 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf5.js @@ -0,0 +1,517 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/0b4ee12c4ba45a4a8e567550c16d96d1679f50ce/src/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 cospi = require( '@stdlib/math/base/special/cospi' ); +var sinpi = require( '@stdlib/math/base/special/sinpi' ); + + +// VARIABLES // + +// cos( 2π/5 ) = 0.30901699437494734 +var TR11 = cospi( 2.0 / 5.0 ); + +// sin( 2π/5 ) = 0.9510565162951536 +var TI11 = sinpi( 2.0 / 5.0 ); + +// cos( 4π/5 ) = -0.8090169943749475 +var TR12 = cospi( 4.0 / 5.0 ); + +// sin( 4π/5 ) = 0.587785252292473 +var TI12 = sinpi( 4.0 / 5.0 ); + + +// FUNCTIONS // + +/** +* Resolves an index into the input array. +* +* ## Notes +* +* In a forward real FFT, the previous stage writes its results as five "rows" per sub-sequence. +* +* Thus, when reading from an input array stored in linear memory, we can reinterpret the array as a three-dimensional logical view containing `L` independent sub-sequences having five "rows" (components 0, 1, 2, 3, and 4) and where each "row" is arranged as `M*L` contiguous elements corresponding to interleaved real and imaginary components. +* +* Accordingly, the following is a logical view of an input array (zero-based indexing) which contains `L = 3` transforms and in which each sub-sequence has length `M = 4`: +* +* ```text +* │ k = 0 k = 1 k = 2 +* │ ──────────────────────────────────────────────────────────────────────────→ k +* j = 0 │ cc(0,0,0) ... cc(3,0,0) cc(0,1,0) ... cc(3,1,0) cc(0,2,0) ... cc(3,2,0) +* │ +* j = 1 │ cc(0,0,1) ... cc(3,0,1) cc(0,1,1) ... cc(3,1,1) cc(0,2,1) ... cc(3,2,1) +* │ +* j = 2 │ cc(0,0,2) ... cc(3,0,2) cc(0,1,2) ... cc(3,1,2) cc(0,2,2) ... cc(3,2,2) +* │ +* j = 3 │ cc(0,0,3) ... cc(3,0,3) cc(0,1,3) ... cc(3,1,3) cc(0,2,3) ... cc(3,2,3) +* │ +* j = 4 │ cc(0,0,4) ... cc(3,0,4) cc(0,1,4) ... cc(3,1,4) cc(0,2,4) ... cc(3,2,4) +* └───────────────────────────────────────────────────────────────────────────→ i +* ↑ ↑ ↑ ↑ ↑ ↑ +* i = 0 M-1 0 M-1 0 M-1 +* ``` +* +* In the above, +* +* - `i` is the fastest varying index, which walks within one short sub-sequence corresponding to one of the five component rows. +* - `j` selects between the five component rows (0, 1, 2, 3, or 4). +* - `k` specifies the index of one of the `L` independent transforms we are processing. +* +* In linear memory, the three-dimensional logical view is arranged as follows: +* +* ```text +* | cc(0,0,0)...cc(3,0,0) ... cc(0,2,0)...cc(3,2,0) | cc(0,0,1)...cc(3,0,1) ... cc(0,2,1)...cc(3,2,1) | ... | cc(0,0,4)...cc(3,0,4) ... cc(0,2,4)...cc(3,2,4) | +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* 0 M-1 LM LM-1 (L+1)M (L+1)M-1 (2L-1)M 2LM-1 4LM (4L+1)M-1 (5L-1)M 5LM-1 +* ``` +* +* @private +* @param {NonNegativeInteger} i - index of an element within a sub-sequence +* @param {NonNegativeInteger} k - index of the sub-sequence being transformed +* @param {NonNegativeInteger} j - input row +* @param {NonNegativeInteger} L - number of sub-sequences +* @param {NonNegativeInteger} M - sub-sequence length +* @param {integer} stride - stride length of the input array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the input array +* @returns {NonNegativeInteger} computed index +* +* @example +* var stride = 1; +* var offset = 0; +* +* var M = 4; // sub-sequence length +* var L = 3; // number of sub-sequences +* +* var idx = iptr( 0, 0, 0, L, M, stride, offset ); +* // returns 0 +* +* idx = iptr( 1, 0, 0, L, M, stride, offset ); +* // returns 1 +* +* idx = iptr( M-1, 0, 0, L, M, stride, offset ); +* // returns 3 +* +* idx = iptr( 0, 1, 0, L, M, stride, offset ); +* // returns 4 +* +* // ... +* +* idx = iptr( M-1, L-1, 1, L, M, stride, offset ); +* // returns 23 +*/ +function iptr( i, k, j, L, M, stride, offset ) { + var n = i + ( ( k+(j*L) ) * M ); + return ( n*stride ) + offset; +} + +/** +* Resolves an index into the output array. +* +* ## Notes +* +* When writing to an output array stored in linear memory, we can reinterpret the array as a three-dimensional logical view containing `L` independent sub-sequences having five "columns" corresponding to the five components of a radix-5 stage (with real and imaginary parts of each component interleaved along each sub-sequence) and where each "column" has `M` elements. +* +* Accordingly, the following is a logical view of an output array (zero-based indexing) which contains `L = 3` transforms and in which each "column" sub-sequence has length `M = 4`: +* +* ```text +* j = 0 (component 0) j = 1 (component 1) j = 2 (component 2) j = 3 (component 3) j = 4 (component 4) +* k = 0 ─┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┐ +* │ out(0,0,0) out(1,0,0) ... out(3,0,0) │ out(0,1,0) out(1,1,0) ... out(3,1,0) │ out(0,2,0) out(1,2,0) ... out(3,2,0) │ out(0,3,0) out(1,3,0) ... out(3,3,0) │ out(0,4,0) out(1,4,0) ... out(3,4,0) │ +* └───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┤ +* k = 1 ─┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┤ +* │ out(0,0,1) out(1,0,1) ... out(3,0,1) │ out(0,1,1) out(1,1,1) ... out(3,1,1) │ out(0,2,1) out(1,2,1) ... out(3,2,1) │ out(0,3,1) out(1,3,1) ... out(3,3,1) │ out(0,4,1) out(1,4,1) ... out(3,4,1) │ +* └───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┤ +* k = 2 ─┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┤ +* │ out(0,0,2) out(1,0,2) ... out(3,0,2) │ out(0,1,2) out(1,1,2) ... out(3,1,2) │ out(0,2,2) out(1,2,2) ... out(3,2,2) │ out(0,3,2) out(1,3,2) ... out(3,3,2) │ out(0,4,2) out(1,4,2) ... out(3,4,2) │ +* └───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┘ +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* i = 0 1 M-1 0 1 M-1 0 1 M-1 0 1 M-1 0 1 M-1 +* ``` +* +* In the above, +* +* - `i` is the fastest varying index, which walks within one short "column" sub-sequence. +* - `j` selects which of the five components (0, 1, 2, 3, or 4). +* - `k` specifies the index of one of the `L` independent transforms we are processing. +* +* In linear memory, the three-dimensional logical view is arranged as follows: +* +* ```text +* | out(0,0,0)...out(3,0,0) | out(0,1,0)...out(3,1,0) | out(0,2,0)...out(3,2,0) | out(0,3,0)...out(3,3,0) | out(0,4,0)...out(3,4,0) | out(0,0,1)...out(3,0,1) | ... | out(0,4,2)...out(3,4,2) | +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* 0 M-1 M 2M-1 2M 3M-1 3M 4M-1 4M 5M-1 5M 6M-1 (5L-1)M 5LM-1 +* ``` +* +* As may be observed, when resolving an index in the output array, the `j` and `k` dimensions are swapped relative index resolution in the input array. This stems from `radf5` being only one stage in a multi-stage driver which alternates between using `cc` and `out` as workspace buffers. After each stage, the next stage reads what the previous stage wrote. +* +* Each stage expects a transpose, and, in order to avoid explicit transposition between the stages, we swap the last two logical dimensions while still maintaining cache locality within the inner loop logical dimension, as indexed by `i`. +* +* @private +* @param {NonNegativeInteger} i - index of an element within a sub-sequence +* @param {NonNegativeInteger} j - index specifying which of the five complex components we are in (0, 1, 2, 3, or 4) +* @param {NonNegativeInteger} k - index of the sub-sequence being transformed +* @param {NonNegativeInteger} M - sub-sequence length +* @param {integer} stride - stride length of the output array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the output array +* @returns {NonNegativeInteger} computed index +* +* @example +* var stride = 1; +* var offset = 0; +* +* var M = 4; // sub-sequence length +* var L = 3; // number of sub-sequences +* +* var idx = optr( 0, 0, 0, M, stride, offset ); +* // returns 0 +* +* idx = optr( 1, 0, 0, M, stride, offset ); +* // returns 1 +* +* idx = optr( M-1, 0, 0, M, stride, offset ); +* // returns 3 +* +* idx = optr( 0, 1, 0, M, stride, offset ); +* // returns 4 +* +* // ... +* +* idx = optr( M-1, 4, L-1, M, stride, offset ); +* // returns 59 +*/ +function optr( i, j, k, M, stride, offset ) { + var n = i + ( ( j+(k*5) ) * M ); + return ( n*stride ) + offset; +} + + +// MAIN // + +/** +* Performs one radix-5 stage within a forward Fourier transform for a real-valued sequence. +* +* @private +* @param {NonNegativeInteger} M - number of elements in each sub-sequence to be transformed +* @param {NonNegativeInteger} L - number of sub-sequences to be transformed +* @param {Float64Array} cc - input array containing the sub-sequences to be transformed +* @param {integer} sc - stride length for `cc` +* @param {NonNegativeInteger} oc - index offset for `cc` +* @param {Float64Array} out - output array containing transformed sub-sequences +* @param {integer} so - stride length for `out` +* @param {NonNegativeInteger} oo - index offset for `out` +* @param {Float64Array} twiddles1 - first array containing twiddle factors +* @param {integer} st1 - stride length for `twiddles1` +* @param {NonNegativeInteger} ot1 - index offset for `twiddles1` +* @param {Float64Array} twiddles2 - second array containing twiddle factors +* @param {integer} st2 - stride length for `twiddles2` +* @param {NonNegativeInteger} ot2 - index offset for `twiddles2` +* @param {Float64Array} twiddles3 - third array containing twiddle factors +* @param {integer} st3 - stride length for `twiddles3` +* @param {NonNegativeInteger} ot3 - index offset for `twiddles3` +* @param {Float64Array} twiddles4 - fourth array containing twiddle factors +* @param {integer} st4 - stride length for `twiddles4` +* @param {NonNegativeInteger} ot4 - index offset for `twiddles4` +* @returns {void} +*/ +function radf5( M, L, cc, sc, oc, out, so, oo, twiddles1, st1, ot1, twiddles2, st2, ot2, twiddles3, st3, ot3, twiddles4, st4, ot4 ) { // eslint-disable-line max-params + var it11; + var it12; + var it21; + var it22; + var it31; + var it32; + var it41; + var it42; + var ci2; + var ci3; + var ci4; + var ci5; + var cr2; + var cr3; + var cr4; + var cr5; + var dr2; + var dr3; + var dr4; + var dr5; + var di2; + var di3; + var di4; + var di5; + var ti2; + var ti3; + var ti4; + var ti5; + var tr2; + var tr3; + var tr4; + var tr5; + var ip1; + var ip2; + var ip3; + var ip4; + var ip5; + var io; + var im; + var i; + var k; + + /* + * First, perform the core butterfly for each sub-sequence being transformed. + * + * In the following loop, we handle harmonic `n = 0` for every transform. As described for `iptr`, the input array is interpreted as a three-dimensional array, containing five "rows" per sub-sequence. + * + * row0 = input component 0 (j = 0) + * row1 = input component 1 (j = 1) + * row2 = input component 2 (j = 2) + * row3 = input component 3 (j = 3) + * row4 = input component 4 (j = 4) + * + * For a radix-5 forward FFT of a real-valued signal `x` and `n = 0`, + * + * cr2 = row4 + row1 + * ci5 = row4 - row1 + * cr3 = row3 + row2 + * ci4 = row3 - row2 + * + * x[0] = row0 + cr2 + cr3 + * x[M] = row0 + ( TR11*cr2 ) + ( TR12*cr3 ) + * x[2M] = ( TI11*ci5 ) + ( TI12*ci4 ) + * x[3M] = row0 + ( TR12*cr2 ) + ( TR11*cr3 ) + * x[4M] = ( TI12*ci5 ) - ( TI11*ci4 ) + * + * Because `W_5^0 = 1`, no frequency-dependent twiddle multiplication is necessary beyond these constant factors. + */ + for ( k = 0; k < L; k++ ) { + ip1 = iptr( 0, k, 0, L, M, sc, oc ); // row 0 + ip2 = iptr( 0, k, 1, L, M, sc, oc ); // row 1 + ip3 = iptr( 0, k, 2, L, M, sc, oc ); // row 2 + ip4 = iptr( 0, k, 3, L, M, sc, oc ); // row 3 + ip5 = iptr( 0, k, 4, L, M, sc, oc ); // row 4 + + cr2 = cc[ ip5 ] + cc[ ip2 ]; // row4 + row1 + ci5 = cc[ ip5 ] - cc[ ip2 ]; // row4 - row1 + cr3 = cc[ ip4 ] + cc[ ip3 ]; // row3 + row2 + ci4 = cc[ ip4 ] - cc[ ip3 ]; // row3 - row2 + + io = optr( 0, 0, k, M, so, oo ); + out[ io ] = cc[ ip1 ] + cr2 + cr3; + + io = optr( M-1, 1, k, M, so, oo ); + out[ io ] = cc[ ip1 ] + ( TR11 * cr2 ) + ( TR12 * cr3 ); + + io = optr( 0, 2, k, M, so, oo ); + out[ io ] = ( TI11 * ci5 ) + ( TI12 * ci4 ); + + io = optr( M-1, 3, k, M, so, oo ); + out[ io ] = cc[ ip1 ] + ( TR12 * cr2 ) + ( TR11 * cr3 ); + + io = optr( 0, 4, k, M, so, oo ); + out[ io ] = ( TI12 * ci5 ) - ( TI11 * ci4 ); + } + // When the number of elements in a sub-sequence is less than `2`, there is nothing more to do, as the above butterfly produced the full result... + if ( M < 2 ) { + return; + } + /* + * Next, apply the general case where we need to loop through the non-trivial harmonics. + * + * For each harmonic `n = 1, ..., M/2-1`, we need to + * + * - recover five spectra from the five input rows. + * - apply radix-5 twiddle factors to rows 1, 2, 3, and 4, then combine with row 0 to form five output columns. + * - form the following + * + * x[5n] = X₀ + (W₁⋅X₁ + W₄⋅X₄) + (W₂⋅X₂ + W₃⋅X₃) => column 0 + * x[5n+1] = X₀ + TR11⋅(W₁⋅X₁ + W₄⋅X₄) + TR12⋅(W₂⋅X₂ + W₃⋅X₃) - i⋅(TI11⋅(W₁⋅X₁ - W₄⋅X₄) + TI12⋅(W₂⋅X₂ - W₃⋅X₃)) => column 1 + * x[5n+2] = X₀ + TR11⋅(W₁⋅X₁ + W₄⋅X₄) + TR12⋅(W₂⋅X₂ + W₃⋅X₃) + i⋅(TI11⋅(W₁⋅X₁ - W₄⋅X₄) + TI12⋅(W₂⋅X₂ - W₃⋅X₃)) => column 2 + * x[5n+3] = X₀ + TR12⋅(W₁⋅X₁ + W₄⋅X₄) + TR11⋅(W₂⋅X₂ + W₃⋅X₃) - i⋅(TI12⋅(W₁⋅X₁ - W₄⋅X₄) - TI11⋅(W₂⋅X₂ - W₃⋅X₃)) => column 3 + * x[5n+4] = X₀ + TR12⋅(W₁⋅X₁ + W₄⋅X₄) + TR11⋅(W₂⋅X₂ + W₃⋅X₃) + i⋅(TI12⋅(W₁⋅X₁ - W₄⋅X₄) - TI11⋅(W₂⋅X₂ - W₃⋅X₃)) => column 4 + * + * The mirror index `im = M - i` selects the conjugate-symmetric partner, thus allowing the routine to read each symmetry pair only once. + */ + // Loop over each sub-sequence to be transformed... + for ( k = 0; k < L; k++ ) { + // Loop over the elements in each sub-sequence... + for ( i = 2; i < M; i += 2 ) { + im = M - i; // "mirror" index + + // Resolve twiddle factor indices for component 1: + it11 = ( (i-2)*st1 ) + ot1; // cos(θ) for component 1 + it12 = ( (i-1)*st1 ) + ot1; // sin(θ) for component 1 + + // Resolve twiddle factor indices for component 2: + it21 = ( (i-2)*st2 ) + ot2; // cos(θ) for component 2 + it22 = ( (i-1)*st2 ) + ot2; // sin(θ) for component 2 + + // Resolve twiddle factor indices for component 3: + it31 = ( (i-2)*st3 ) + ot3; // cos(θ) for component 3 + it32 = ( (i-1)*st3 ) + ot3; // sin(θ) for component 3 + + // Resolve twiddle factor indices for component 4: + it41 = ( (i-2)*st4 ) + ot4; // cos(θ) for component 4 + it42 = ( (i-1)*st4 ) + ot4; // sin(θ) for component 4 + + // Load component 1 data and apply twiddle... + ip1 = iptr( i-1, k, 1, L, M, sc, oc ); // real part component 1 + ip2 = iptr( i, k, 1, L, M, sc, oc ); // imag part component 1 + + // Apply the twiddle factors for component 1: + dr2 = ( twiddles1[ it11 ] * cc[ ip1 ] ) + ( twiddles1[ it12 ] * cc[ ip2 ] ); // Re(dr2) + di2 = ( twiddles1[ it11 ] * cc[ ip2 ] ) - ( twiddles1[ it12 ] * cc[ ip1 ] ); // Im(di2) + + // Load component 2 data and apply twiddle... + ip1 = iptr( i-1, k, 2, L, M, sc, oc ); // real part component 2 + ip2 = iptr( i, k, 2, L, M, sc, oc ); // imag part component 2 + + // Apply the twiddle factors for component 2: + dr3 = ( twiddles2[ it21 ] * cc[ ip1 ] ) + ( twiddles2[ it22 ] * cc[ ip2 ] ); // Re(dr3) + di3 = ( twiddles2[ it21 ] * cc[ ip2 ] ) - ( twiddles2[ it22 ] * cc[ ip1 ] ); // Im(di3) + + // Load component 3 data and apply twiddle... + ip1 = iptr( i-1, k, 3, L, M, sc, oc ); // real part component 3 + ip2 = iptr( i, k, 3, L, M, sc, oc ); // imag part component 3 + + // Apply the twiddle factors for component 3: + dr4 = ( twiddles3[ it31 ] * cc[ ip1 ] ) + ( twiddles3[ it32 ] * cc[ ip2 ] ); // Re(dr4) + di4 = ( twiddles3[ it31 ] * cc[ ip2 ] ) - ( twiddles3[ it32 ] * cc[ ip1 ] ); // Im(di4) + + // Load component 4 data and apply twiddle... + ip1 = iptr( i-1, k, 4, L, M, sc, oc ); // real part component 4 + ip2 = iptr( i, k, 4, L, M, sc, oc ); // imag part component 4 + + // Apply the twiddle factors for component 4: + dr5 = ( twiddles4[ it41 ] * cc[ ip1 ] ) + ( twiddles4[ it42 ] * cc[ ip2 ] ); // Re(dr5) + di5 = ( twiddles4[ it41 ] * cc[ ip2 ] ) - ( twiddles4[ it42 ] * cc[ ip1 ] ); // Im(di5) + + // Radix-5 butterfly intermediate computations (symmetric/antisymmetric combinations): + cr2 = dr2 + dr5; + ci5 = dr5 - dr2; + cr5 = di2 - di5; + ci2 = di5 + di2; + cr3 = dr3 + dr4; + ci4 = dr4 - dr3; + cr4 = di3 - di4; + ci3 = di3 + di4; + + // Output column 0 (real part) + ip1 = iptr( i-1, k, 0, L, M, sc, oc ); + io = optr( i-1, 0, k, M, so, oo ); + out[ io ] = cc[ ip1 ] + cr2 + cr3; + + // Output column 0 (imag part) + ip2 = iptr( i, k, 0, L, M, sc, oc ); + io = optr( i, 0, k, M, so, oo ); + out[ io ] = cc[ ip2 ] + ci2 + ci3; + + // Load component 0 data and compute intermediates... + tr2 = cc[ ip1 ] + ( TR11 * cr2 ) + ( TR12 * cr3 ); + ti2 = cc[ ip2 ] + ( TR11 * ci2 ) + ( TR12 * ci3 ); + tr3 = cc[ ip1 ] + ( TR12 * cr2 ) + ( TR11 * cr3 ); + ti3 = cc[ ip2 ] + ( TR12 * ci2 ) + ( TR11 * ci3 ); + + // Additional intermediates: + tr5 = ( TI11 * cr5 ) + ( TI12 * cr4 ); + ti5 = ( TI11 * ci5 ) + ( TI12 * ci4 ); + tr4 = ( TI12 * cr5 ) - ( TI11 * cr4 ); + ti4 = ( TI12 * ci5 ) - ( TI11 * ci4 ); + + // Output column 2 (real part) + io = optr( i-1, 2, k, M, so, oo ); + out[ io ] = tr2 + tr5; + + // Output column 1 (real part) + io = optr( im-1, 1, k, M, so, oo ); + out[ io ] = tr2 - tr5; + + // Output column 2 (imag part) + io = optr( i, 2, k, M, so, oo ); + out[ io ] = ti2 + ti5; + + // Output column 1 (imag part) + io = optr( im, 1, k, M, so, oo ); + out[ io ] = ti5 - ti2; + + // Output column 4 (real part) + io = optr( i-1, 4, k, M, so, oo ); + out[ io ] = tr3 + tr4; + + // Output column 3 (real part) + io = optr( im-1, 3, k, M, so, oo ); + out[ io ] = tr3 - tr4; + + // Output column 4 (imag part) + io = optr( i, 4, k, M, so, oo ); + out[ io ] = ti3 + ti4; + + // Output column 3 (imag part) + io = optr( im, 3, k, M, so, oo ); + out[ io ] = ti4 - ti3; + } + } +} + + +// EXPORTS // + +module.exports = radf5; From 5f3fc63cf0db06f23c35f665b887db06f0caac93 Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Tue, 12 May 2026 00:49:35 +0530 Subject: [PATCH 04/19] refactor: use sinpi and cospi --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../@stdlib/fft/base/fftpack/rfftf/lib/radf3.js | 13 +++++++++++-- 1 file changed, 11 insertions(+), 2 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js index 54783ad72d3b..914ca19853df 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js @@ -60,10 +60,19 @@ 'use strict'; +// MODULES // + +var cospi = require( '@stdlib/math/base/special/cospi' ); +var sinpi = require( '@stdlib/math/base/special/sinpi' ); + + // VARIABLES // -var TAUR = -0.5; // cos( 2π/3 ) -var TAUI = 0.866025403784439; // sin( 2π/3 ) +// cos( 2π/3 ) = -0.5 +var TAUR = cospi( 2.0 / 3.0 ); + +// sin( 2π/3 ) = 0.866025403784439 +var TAUI = sinpi( 2.0 / 3.0 ); // FUNCTIONS // From dd6338d1fdde9ebea792d0adccae7cb85b9750ed Mon Sep 17 00:00:00 2001 From: GUNJ JOSHI Date: Wed, 20 May 2026 01:55:20 +0530 Subject: [PATCH 05/19] feat: add radfg --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rfftf/lib/radfg.js | 761 ++++++++++++++++++ 1 file changed, 761 insertions(+) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js new file mode 100644 index 000000000000..c6f7dfc925a8 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js @@ -0,0 +1,761 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/0b4ee12c4ba45a4a8e567550c16d96d1679f50ce/src/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, max-lines-per-function */ + +'use strict'; + +// MODULES // + +var cospi = require( '@stdlib/math/base/special/cospi' ); +var sinpi = require( '@stdlib/math/base/special/sinpi' ); +var floor = require( '@stdlib/math/base/special/floor' ); + + +// FUNCTIONS // + +/** +* Resolves an index into the input array. +* +* ## Notes +* +* In a forward real FFT, the previous stage writes its results as `R` "rows" per sub-sequence. +* +* Thus, when reading from an input array stored in linear memory, we can reinterpret the array as a three-dimensional logical view containing `L` independent sub-sequences having `R` "rows" (components 0, 1, 2, ..., R-1) and where each "row" is arranged as `M*L` contiguous elements corresponding to interleaved real and imaginary components. +* +* Accordingly, the following is a logical view of an input array (zero-based indexing) which contains `L = 3` transforms and in which each sub-sequence has length `M = 4`: +* +* ```text +* │ k = 0 k = 1 k = 2 +* │ ─────────────────────────────────────────────────────────────────────────────────────→ k +* j = 0 │ cc(0,0,0) ... cc(3,0,0) cc(0,1,0) ... cc(3,1,0) cc(0,2,0) ... cc(3,2,0) +* │ +* j = 1 │ cc(0,0,1) ... cc(3,0,1) cc(0,1,1) ... cc(3,1,1) cc(0,2,1) ... cc(3,2,1) +* │ +* j = 2 │ cc(0,0,2) ... cc(3,0,2) cc(0,1,2) ... cc(3,1,2) cc(0,2,2) ... cc(3,2,2) +* │ +* j = 3 │ cc(0,0,3) ... cc(3,0,3) cc(0,1,3) ... cc(3,1,3) cc(0,2,3) ... cc(3,2,3) +* │ +* ... │ ... ... ... +* │ +* j=R-1 │ cc(0,0,R-1) ... cc(3,0,R-1) cc(0,1,R-1) ... cc(3,1,R-1) cc(0,2,R-1) ... cc(3,2,R-1) +* └──────────────────────────────────────────────────────────────────────────────────────→ i +* ↑ ↑ ↑ ↑ ↑ ↑ +* i = 0 M-1 0 M-1 0 M-1 +* ``` +* +* In the above, +* +* - `i` is the fastest varying index, which walks within one short sub-sequence corresponding to one of the R component rows. +* - `j` selects between the R component rows (0, 1, 2, ..., R-1). +* - `k` specifies the index of one of the `L` independent transforms we are processing. +* +* In linear memory, the three-dimensional logical view is arranged as follows: +* +* ```text +* | cc(0,0,0)...cc(3,0,0) ... cc(0,2,0)...cc(3,2,0) | cc(0,0,1)...cc(3,0,1) ... cc(0,2,1)...cc(3,2,1) | ... | cc(0,0,R-1)...cc(3,0,R-1) ... cc(0,2,R-1)...cc(3,2,R-1) | +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* 0 M-1 LM LM-1 (L+1)M (L+1)M-1 (2L-1)M 2LM-1 (R-1)LM ((R-1)L+1)M-1 (RL-1)M RLM-1 +* ``` +* +* @private +* @param {NonNegativeInteger} i - index of an element within a sub-sequence +* @param {NonNegativeInteger} k - index of the sub-sequence being transformed +* @param {NonNegativeInteger} j - input row +* @param {NonNegativeInteger} L - number of sub-sequences +* @param {NonNegativeInteger} M - sub-sequence length +* @param {integer} stride - stride length of the input array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the input array +* @returns {NonNegativeInteger} computed index +* +* @example +* var stride = 1; +* var offset = 0; +* +* var M = 4; // sub-sequence length +* var L = 3; // number of sub-sequences +* +* var idx = iptr( 0, 0, 0, L, M, stride, offset ); +* // returns 0 +* +* idx = iptr( 1, 0, 0, L, M, stride, offset ); +* // returns 1 +* +* idx = iptr( M-1, 0, 0, L, M, stride, offset ); +* // returns 3 +* +* idx = iptr( 0, 1, 0, L, M, stride, offset ); +* // returns 4 +* +* // ... +* +* idx = iptr( M-1, L-1, 6, L, M, stride, offset ); +* // returns 83 +*/ +function iptr( i, k, j, L, M, stride, offset ) { + var n = i + ( ( k+(j*L) ) * M ); + return ( n*stride ) + offset; +} + +/** +* Resolves an index into the output array. +* +* ## Notes +* +* When writing to an output array stored in linear memory, we can reinterpret the array as a three-dimensional logical view containing `L` independent sub-sequences having `R` "columns" corresponding to the `R` components of a radix-R stage (with real and imaginary parts of each component interleaved along each sub-sequence) and where each "column" has `M` elements. +* +* Accordingly, the following is a logical view of an output array (zero-based indexing) which contains `L = 3` transforms and in which each "column" sub-sequence has length `M = 4` for an arbitrary radix `R`: +* +* ```text +* j = 0 (component 0) j = 1 (component 1) j = 2 (component 2) ... j = R-1 (component R-1) +* k = 0 ─┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────────────┐ +* │ out(0,0,0) out(1,0,0) ... out(3,0,0) │ out(0,1,0) out(1,1,0) ... out(3,1,0) │ out(0,2,0) out(1,2,0) ... out(3,2,0) │ ... │ out(0,R-1,0) out(1,R-1,0) ... out(3,R-1,0) │ +* └───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────────────┤ +* k = 1 ─┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────────────┤ +* │ out(0,0,1) out(1,0,1) ... out(3,0,1) │ out(0,1,1) out(1,1,1) ... out(3,1,1) │ out(0,2,1) out(1,2,1) ... out(3,2,1) │ ... │ out(0,R-1,1) out(1,R-1,1) ... out(3,R-1,1) │ +* └───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────────────┤ +* k = 2 ─┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────────────────────┤ +* │ out(0,0,2) out(1,0,2) ... out(3,0,2) │ out(0,1,2) out(1,1,2) ... out(3,1,2) │ out(0,2,2) out(1,2,2) ... out(3,2,2) │ ... │ out(0,R-1,2) out(1,R-1,2) ... out(3,R-1,2) │ +* └───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────────────────────┘ +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* i = 0 1 M-1 0 1 M-1 0 1 M-1 0 1 M-1 +* ``` +* +* In the above, +* +* - `i` is the fastest varying index, which walks within one short "column" sub-sequence. +* - `j` selects which of the R components we are in (0, 1, 2, ..., R-1). +* - `k` specifies the index of one of the `L` independent transforms we are processing. +* +* In linear memory, the three-dimensional logical view is arranged as follows: +* +* ```text +* | out(0,0,0)...out(3,0,0) | out(0,1,0)...out(3,1,0) | out(0,2,0)...out(3,2,0) | ... | out(0,R-1,0)...out(3,R-1,0) | out(0,0,1)...out(3,0,1) | ... | out(0,R-1,2)...out(3,R-1,2) | +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* 0 M-1 M 2M-1 2M 3M-1 (R-1)M RM-1 RM (R+1)M-1 (RL-1)M RLM-1 +* ``` +* +* As may be observed, when resolving an index in the output array, the `j` and `k` dimensions are swapped relative index resolution in the input array. This stems from `radfg` being only one stage in a multi-stage driver which alternates between using `cc` and `out` as workspace buffers. After each stage, the next stage reads what the previous stage wrote. +* +* Each stage expects a transpose, and, in order to avoid explicit transposition between the stages, we swap the last two logical dimensions while still maintaining cache locality within the inner loop logical dimension, as indexed by `i`. +* +* @private +* @param {NonNegativeInteger} i - index of an element within a sub-sequence +* @param {NonNegativeInteger} j - index specifying which of the R complex components we are in (0, 1, ..., R-1) +* @param {NonNegativeInteger} k - index of the sub-sequence being transformed +* @param {NonNegativeInteger} R - radix +* @param {NonNegativeInteger} M - sub-sequence length +* @param {integer} stride - stride length of the output array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the output array +* @returns {NonNegativeInteger} computed index +* +* @example +* var stride = 1; +* var offset = 0; +* +* var M = 4; // sub-sequence length +* var L = 3; // number of sub-sequences +* +* var idx = optr( 0, 0, 0, 7, M, stride, offset ); +* // returns 0 +* +* idx = optr( 1, 0, 0, 7, M, stride, offset ); +* // returns 1 +* +* idx = optr( M-1, 0, 0, 7, M, stride, offset ); +* // returns 3 +* +* idx = optr( 0, 1, 0, 7, M, stride, offset ); +* // returns 4 +* +* // ... +* +* idx = optr( M-1, 6, L-1, 7, M, stride, offset ); +* // returns 83 +*/ +function optr( i, j, k, R, M, stride, offset ) { + var n = i + ( ( j+(k*R) ) * M ); + return ( n*stride ) + offset; +} + +/** +* Resolves an index into a flattened workspace array. +* +* ## Notes +* +* During the general radix stage, flattened workspace arrays store `ML = M * L` elements for each of the `R` component columns. Both the flattened input and output workspace arrays share the same `[ML, R]` logical layout. +* +* Thus, when accessing a flattened workspace array stored in linear memory, we can reinterpret the array as a two-dimensional logical view having `R` component columns, where each column has `ML` elements. +* +* Accordingly, the following is a logical view of a flattened workspace array (zero-based indexing) having flattened dimension `ML` and arbitrary radix `R`: +* +* ```text +* │ j = 0 j = 1 j = 2 ... j = R-1 +* │ ────────────────────────────────────────────────────────────────────────→ j +* ik = 0 │ ws(0,0) ws(0,1) ws(0,2) ... ws(0,R-1) +* │ +* ik = 1 │ ws(1,0) ws(1,1) ws(1,2) ... ws(1,R-1) +* │ +* ik = 2 │ ws(2,0) ws(2,1) ws(2,2) ... ws(2,R-1) +* │ +* ik = 3 │ ws(3,0) ws(3,1) ws(3,2) ... ws(3,R-1) +* │ +* ... │ ... ... ... ... ... +* │ +* ik = ML-1 │ ws(ML-1,0) ws(ML-1,1) ws(ML-1,2) ... ws(ML-1,R-1) +* ``` +* +* In the above, +* +* - `ik` is the fastest varying index, which walks along the flattened sub-sequence dimension. +* - `j` selects between the `R` workspace component columns (0, 1, 2, ..., R-1). +* +* In linear memory, the two-dimensional logical view is arranged as follows: +* +* ```text +* | ws(0,0)...ws(ML-1,0) | ws(0,1)...ws(ML-1,1) | ws(0,2)...ws(ML-1,2) | ... | ws(0,R-1)...ws(ML-1,R-1) | +* ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ +* 0 ML-1 ML 2ML-1 2ML 3ML-1 (R-1)ML RML-1 +* ``` +* +* Here, the original `M` and `L` dimensions have been collapsed into the single flattened `ik` dimension. Each workspace component `j` therefore occupies one contiguous block of `ML` elements in linear memory. +* +* @private +* @param {NonNegativeInteger} ik - index of an element within a flattened sub-sequence +* @param {NonNegativeInteger} j - index specifying which of the R workspace component columns we are in (0, 1, ..., R-1) +* @param {NonNegativeInteger} ML - flattened sub-sequence length +* @param {integer} stride - stride length of the flattened workspace array +* @param {NonNegativeInteger} offset - index specifying the first indexed element in the flattened workspace array +* @returns {NonNegativeInteger} computed index +* +* @example +* var stride = 1; +* var offset = 0; +* +* var M = 4; // sub-sequence length +* var L = 3; // number of sub-sequences +* var ML = M * L; // flattened dimension ( 4*3 = 12 ) +* +* var idx = fptr( 0, 0, ML, stride, offset ); +* // returns 0 +* +* idx = fptr( 1, 0, ML, stride, offset ); +* // returns 1 +* +* idx = fptr( ML-1, 0, ML, stride, offset ); +* // returns 11 +* +* idx = fptr( 0, 1, ML, stride, offset ); +* // returns 12 +* +* // ... +* +* idx = fptr( ML-1, 6, ML, stride, offset ); +* // returns 83 +*/ +function fptr( ik, j, ML, stride, offset ) { + var n = ik + ( j*ML ); + return ( n*stride ) + offset; +} + + +// MAIN // + +/** +* Performs one general radix stage within a forward Fourier transform for a real-valued sequence. +* +* @private +* @param {NonNegativeInteger} M - number of elements in each sub-sequence to be transformed +* @param {NonNegativeInteger} R - radix of the transform +* @param {NonNegativeInteger} L - number of sub-sequences to be transformed +* @param {NonNegativeInteger} ML - number of elements in each flattened sub-sequence (`M*L`) +* @param {Float64Array} cc - input array containing the sub-sequences to be transformed +* @param {integer} sc - stride length for `cc` +* @param {NonNegativeInteger} oc - index offset for `cc` +* @param {Float64Array} c1 - input workspace array containing intermediate sub-sequences to be transformed +* @param {integer} sc1 - stride length for `c1` +* @param {NonNegativeInteger} oc1 - index offset for `c1` +* @param {Float64Array} c2 - flattened input workspace array containing intermediate sub-sequences +* @param {integer} sc2 - stride length for `c2` +* @param {NonNegativeInteger} oc2 - index offset for `c2` +* @param {Float64Array} ch - output array containing transformed sequences +* @param {integer} sch - stride length for `ch` +* @param {NonNegativeInteger} och - index offset for `ch` +* @param {Float64Array} ch2 - flattened output workspace array containing intermediate sub-sequences +* @param {integer} sch2 - stride length for `ch2` +* @param {NonNegativeInteger} och2 - index offset for `ch2` +* @param {Float64Array} twiddles - array of twiddle factors +* @param {integer} stw - stride length for `twiddles` +* @param {NonNegativeInteger} otw - index offset for `twiddles` +* @returns {void} +*/ +function radfg( M, R, L, ML, cc, sc, oc, c1, sc1, oc1, c2, sc2, oc2, ch, sch, och, ch2, sch2, och2, twiddles, stw, otw ) { // eslint-disable-line max-params + var ar1h; + var ar2h; + var idij; + var ic2o; + var ic1o; + var ich; + var icc; + var Rph; + var Rp1; + var ih1; + var ih2; + var ih3; + var ih4; + var ic1; + var ic2; + var ic3; + var ic4; + var it1; + var it2; + var io1; + var io2; + var io3; + var io4; + var dc2; + var ai1; + var ai2; + var ar1; + var ar2; + var ds2; + var nbd; + var dcp; + var dsp; + var im; + var ik; + var is; + var jc; + var lc; + var j2; + var i; + var j; + var k; + var l; + + // Compute the basic rotation angle for the radix-R DFT matrix: + dcp = cospi( 2.0 / R ); // cos(2π/R) + dsp = sinpi( 2.0 / R ); // sin(2π/R) + + // Compute half the radix, rounded up, which is used as the exclusive upper bound for conjugate-symmetric component loops: + Rph = floor( ( R + 1 ) / 2 ); + Rp1 = R + 1; + + // Compute the number of non-DC complex harmonics in each sub-sequence: + nbd = floor( ( M - 1 ) / 2 ); + + /* + * First, initialize the work arrays for the general-radix butterfly. + * + * At this stage, each sub-sequence has already been split into `R` radix components. The `j = 0` component is carried in the flattened work arrays, while the remaining components `j = 1, ..., R-1` are carried in the three-dimensional work arrays. + * + * For harmonic `n = 0`, we only copy the DC terms. + * + * For harmonics `n = 1, ..., floor((M-1)/2)`, each nonzero radix component is multiplied by its stage twiddle factor and stored in `ch`. + */ + if ( M === 1 ) { + // Copy the DC column from the flattened output workspace back to the flattened input workspace... + for ( ik = 0; ik < ML; ik++ ) { + ic2o = fptr( ik, 0, ML, sc2, oc2 ); + ich = fptr( ik, 0, ML, sch2, och2 ); + c2[ ic2o ] = ch2[ ich ]; + } + } else { + // Copy the DC column into the flattened output workspace... + for ( ik = 0; ik < ML; ik++ ) { + ich = fptr( ik, 0, ML, sch2, och2 ); + ic2o = fptr( ik, 0, ML, sc2, oc2 ); + ch2[ ich ] = c2[ ic2o ]; + } + + // Copy the DC terms for the remaining radix components... + for ( j = 1; j < R; j++ ) { + for ( k = 0; k < L; k++ ) { + ih1 = optr( 0, k, j, L, M, sch, och ); + ic1 = iptr( 0, k, j, L, M, sc1, oc1 ); + ch[ ih1 ] = c1[ ic1 ]; + } + } + + // Apply twiddle factors to the non-DC harmonics of the remaining radix components... + if ( nbd <= L ) { + // Loop over harmonics before sub-sequences... + is = 0; + for ( j = 1; j < R; j++ ) { + idij = is; + for ( i = 2; i < M; i += 2 ) { + for ( k = 0; k < L; k++ ) { + // Resolve output indices in ch: + ih1 = optr( i-1, k, j, L, M, sch, och ); // real part + ih2 = optr( i, k, j, L, M, sch, och ); // imaginary part + + // Resolve indices in the input workspace: + ic1 = iptr( i-1, k, j, L, M, sc1, oc1 ); // real part + ic2 = iptr( i, k, j, L, M, sc1, oc1 ); // imaginary part + + // Resolve twiddle factor indices: + it1 = ( idij * stw ) + otw; // cos(θ) + it2 = ( (idij+1) * stw ) + otw; // sin(θ) + + // Apply the twiddle factor: + ch[ ih1 ] = ( twiddles[ it1 ] * c1[ ic1 ] ) + ( twiddles[ it2 ] * c1[ ic2 ] ); // Re(ch) + ch[ ih2 ] = ( twiddles[ it1 ] * c1[ ic2 ] ) - ( twiddles[ it2 ] * c1[ ic1 ] ); // Im(ch) + } + idij += 2; + } + is += M; + } + } else { + // Loop over sub-sequences before harmonics... + is = 0; + for ( j = 1; j < R; j++ ) { + for ( k = 0; k < L; k++ ) { + idij = is; + for ( i = 2; i < M; i += 2 ) { + // Resolve output indices in ch: + ih1 = optr( i-1, k, j, L, M, sch, och ); // real part + ih2 = optr( i, k, j, L, M, sch, och ); // imaginary part + + // Resolve indices in the input workspace: + ic1 = iptr( i-1, k, j, L, M, sc1, oc1 ); // real part + ic2 = iptr( i, k, j, L, M, sc1, oc1 ); // imaginary part + + // Resolve twiddle factor indices: + it1 = ( idij * stw ) + otw; // cos(θ) + it2 = ( (idij+1) * stw ) + otw; // sin(θ) + + // Apply the twiddle factor: + ch[ ih1 ] = ( twiddles[ it1 ] * c1[ ic1 ] ) + ( twiddles[ it2 ] * c1[ ic2 ] ); // Re(ch) + ch[ ih2 ] = ( twiddles[ it1 ] * c1[ ic2 ] ) - ( twiddles[ it2 ] * c1[ ic1 ] ); // Im(ch) + + idij += 2; + } + } + is += M; + } + } + + /* + * Next, combine mirrored radix components, storing their sums and differences in c1. + */ + if ( nbd >= L ) { + // Loop over sub-sequences before harmonics... + for ( j = 1; j < Rph; j++ ) { + jc = Rp1 - j - 1; // "mirror" index + for ( k = 0; k < L; k++ ) { + for ( i = 2; i < M; i += 2 ) { + // Resolve ch indices for component j: + ih1 = optr( i-1, k, j, L, M, sch, och ); // Re(ch[j]) + ih2 = optr( i, k, j, L, M, sch, och ); // Im(ch[j]) + + // Resolve ch indices for conjugate component jc: + ih3 = optr( i-1, k, jc, L, M, sch, och ); // Re(ch[jc]) + ih4 = optr( i, k, jc, L, M, sch, och ); // Im(ch[jc]) + + // Resolve input-workspace indices for component j: + ic1 = iptr( i-1, k, j, L, M, sc1, oc1 ); // Re(component j) + ic2 = iptr( i, k, j, L, M, sc1, oc1 ); // Im(component j) + + // Resolve input-workspace indices for component jc: + ic3 = iptr( i-1, k, jc, L, M, sc1, oc1 ); // Re(component jc) + ic4 = iptr( i, k, jc, L, M, sc1, oc1 ); // Im(component jc) + + // Form the sum and difference combinations: + c1[ ic1 ] = ch[ ih1 ] + ch[ ih3 ]; // Re(j) + Re(jc) + c1[ ic3 ] = ch[ ih2 ] - ch[ ih4 ]; // Im(j) - Im(jc) + c1[ ic2 ] = ch[ ih2 ] + ch[ ih4 ]; // Im(j) + Im(jc) + c1[ ic4 ] = ch[ ih3 ] - ch[ ih1 ]; // Re(jc) - Re(j) + } + } + } + } else { + // Loop over harmonics before sub-sequences... + for ( j = 1; j < Rph; j++ ) { + jc = Rp1 - j - 1; // "mirror" index + for ( i = 2; i < M; i += 2 ) { + for ( k = 0; k < L; k++ ) { + // Resolve ch indices for component j: + ih1 = optr( i-1, k, j, L, M, sch, och ); // Re(ch[j]) + ih2 = optr( i, k, j, L, M, sch, och ); // Im(ch[j]) + + // Resolve ch indices for conjugate component jc: + ih3 = optr( i-1, k, jc, L, M, sch, och ); // Re(ch[jc]) + ih4 = optr( i, k, jc, L, M, sch, och ); // Im(ch[jc]) + + // Resolve input-workspace indices for component j: + ic1 = iptr( i-1, k, j, L, M, sc1, oc1 ); // Re(component j) + ic2 = iptr( i, k, j, L, M, sc1, oc1 ); // Im(component j) + + // Resolve input-workspace indices for component jc: + ic3 = iptr( i-1, k, jc, L, M, sc1, oc1 ); // Re(component jc) + ic4 = iptr( i, k, jc, L, M, sc1, oc1 ); // Im(component jc) + + // Form the sum and difference combinations: + c1[ ic1 ] = ch[ ih1 ] + ch[ ih3 ]; // Re(j) + Re(jc) + c1[ ic3 ] = ch[ ih2 ] - ch[ ih4 ]; // Im(j) - Im(jc) + c1[ ic2 ] = ch[ ih2 ] + ch[ ih4 ]; // Im(j) + Im(jc) + c1[ ic4 ] = ch[ ih3 ] - ch[ ih1 ]; // Re(jc) - Re(j) + } + } + } + } + } + + // Combine the DC terms for each conjugate-symmetric component pair... + for ( j = 1; j < Rph; j++ ) { + jc = Rp1 - j - 1; // "mirror" index + for ( k = 0; k < L; k++ ) { + ih1 = optr( 0, k, j, L, M, sch, och ); + ih2 = optr( 0, k, jc, L, M, sch, och ); + + ic1 = iptr( 0, k, j, L, M, sc1, oc1 ); + ic2 = iptr( 0, k, jc, L, M, sc1, oc1 ); + + c1[ ic1 ] = ch[ ih1 ] + ch[ ih2 ]; + c1[ ic2 ] = ch[ ih2 ] - ch[ ih1 ]; + } + } + + /* + * Next, apply the radix-`R` DFT matrix. + * + * For each mirrored output pair, accumulate the contributions of the radix components in the flattened work array. + * + * The required rotation factors are generated recursively from the previous ones: + * + * W_l = W_{l-1} ⋅ W_1 + * W_{lj} = W_{l(j-1)} ⋅ W_l + * + * Here, `W_1` is the basic radix-`R` rotation, `W_{l-1}` and `W_l` are the previous and current outer factors, and `W_{l(j-1)}` and `W_{lj}` are the previous and current inner factors. + */ + ar1 = 1.0; // Re(W_0) + ai1 = 0.0; // Im(W_0) + for ( l = 1; l < Rph; l++ ) { + lc = Rp1 - l - 1; // "mirror" index + + // Advance the rotation factor by one step: W_l = W_{l-1} ⋅ W_1 + ar1h = ( dcp * ar1 ) - ( dsp * ai1 ); // Re(W_l) + ai1 = ( dcp * ai1 ) + ( dsp * ar1 ); // Im(W_l) + ar1 = ar1h; + + // Accumulate the contributions from components 1 and R-1: + for ( ik = 0; ik < ML; ik++ ) { + ich = fptr( ik, l, ML, sch2, och2 ); + ic1o = fptr( ik, lc, ML, sch2, och2 ); + + ic2o = fptr( ik, 0, ML, sc2, oc2 ); + ic1 = fptr( ik, 1, ML, sc2, oc2 ); + ic2 = fptr( ik, R-1, ML, sc2, oc2 ); + + ch2[ ich ] = c2[ ic2o ] + ( ar1 * c2[ ic1 ] ); + ch2[ ic1o ] = ai1 * c2[ ic2 ]; + } + + // Save W_l for the inner recurrence: + dc2 = ar1; + ds2 = ai1; + + // Initialize W_{l·1}: + ar2 = ar1; + ai2 = ai1; + + // Accumulate the remaining component pairs: + for ( j = 2; j < Rph; j++ ) { + jc = Rp1 - j - 1; // "mirror" index + + // Advance the nested rotation factor by one step: W_{l*j} = W_{l*(j-1)} ⋅ W_l + ar2h = ( dc2 * ar2 ) - ( ds2 * ai2 ); // Re(W_{l*j}) + ai2 = ( dc2 * ai2 ) + ( ds2 * ar2 ); // Im(W_{l*j}) + ar2 = ar2h; + + // Accumulate the contributions from components j and jc: + for ( ik = 0; ik < ML; ik++ ) { + ich = fptr( ik, l, ML, sch2, och2 ); + ic1o = fptr( ik, lc, ML, sch2, och2 ); + + ic1 = fptr( ik, j, ML, sc2, oc2 ); + ic2 = fptr( ik, jc, ML, sc2, oc2 ); + + ch2[ ich ] += ar2 * c2[ ic1 ]; + ch2[ ic1o ] += ai2 * c2[ ic2 ]; + } + } + } + + // Accumulate the nonzero radix components into the DC output... + for ( j = 1; j < Rph; j++ ) { + for ( ik = 0; ik < ML; ik++ ) { + ich = fptr( ik, 0, ML, sch2, och2 ); + ic1 = fptr( ik, j, ML, sc2, oc2 ); + ch2[ ich ] += c2[ ic1 ]; + } + } + + // Copy the first output column from ch to cc... + if ( M >= L ) { + for ( k = 0; k < L; k++ ) { + for ( i = 0; i < M; i++ ) { + icc = iptr( i, k, 0, L, M, sc, oc ); + ih1 = optr( i, k, 0, L, M, sch, och ); + cc[ icc ] = ch[ ih1 ]; + } + } + } else { + for ( i = 0; i < M; i++ ) { + for ( k = 0; k < L; k++ ) { + icc = iptr( i, k, 0, L, M, sc, oc ); + ih1 = optr( i, k, 0, L, M, sch, och ); + cc[ icc ] = ch[ ih1 ]; + } + } + } + + // Store DC harmonics for conjugate pairs in the output array... + for ( j = 1; j < Rph; j++ ) { + jc = Rp1 - j - 1; // "mirror" index + j2 = 2 * j; // output column index + for ( k = 0; k < L; k++ ) { + io1 = iptr( M-1, k, j2-1, L, M, sc, oc ); + io2 = iptr( 0, k, j2, L, M, sc, oc ); + + ih1 = optr( 0, k, j, L, M, sch, och ); + ih2 = optr( 0, k, jc, L, M, sch, och ); + + cc[ io1 ] = ch[ ih1 ]; + cc[ io2 ] = ch[ ih2 ]; + } + } + + // When M = 1, there are no non-DC harmonics to process, so we're done... + if ( M === 1 ) { + return; + } + + /* + * Finally, store the non-DC harmonics in folded format. + * + * For each mirror pair, write the non-DC harmonics from `ch` to the two output columns as the required sum and difference combinations. + */ + if ( nbd >= L ) { + // Loop over sub-sequences before harmonics... + for ( j = 1; j < Rph; j++ ) { + jc = Rp1 - j - 1; // "mirror" index + j2 = 2 * j; // output column index + for ( k = 0; k < L; k++ ) { + for ( i = 2; i < M; i += 2 ) { + im = M - i; // "mirror" harmonic index + + // Resolve ch indices for component j: + ih1 = optr( i-1, k, j, L, M, sch, och ); // Re(ch[j]) + ih2 = optr( i, k, j, L, M, sch, och ); // Im(ch[j]) + + // Resolve ch indices for conjugate component jc: + ih3 = optr( i-1, k, jc, L, M, sch, och ); // Re(ch[jc]) + ih4 = optr( i, k, jc, L, M, sch, och ); // Im(ch[jc]) + + // Resolve cc output indices: + io1 = iptr( i-1, k, j2, L, M, sc, oc ); + io2 = iptr( im-1, k, j2-1, L, M, sc, oc ); + io3 = iptr( i, k, j2, L, M, sc, oc ); + io4 = iptr( im, k, j2-1, L, M, sc, oc ); + + // Store the sum and difference combinations: + cc[ io1 ] = ch[ ih1 ] + ch[ ih3 ]; + cc[ io2 ] = ch[ ih1 ] - ch[ ih3 ]; + cc[ io3 ] = ch[ ih2 ] + ch[ ih4 ]; + cc[ io4 ] = ch[ ih4 ] - ch[ ih2 ]; + } + } + } + } else { + // Loop over harmonics before sub-sequences... + for ( j = 1; j < Rph; j++ ) { + jc = Rp1 - j - 1; // "mirror" index + j2 = 2 * j; // output column index + for ( i = 2; i < M; i += 2 ) { + im = M - i; // "mirror" harmonic index + for ( k = 0; k < L; k++ ) { + // Resolve ch indices for component j: + ih1 = optr( i-1, k, j, L, M, sch, och ); // Re(ch[j]) + ih2 = optr( i, k, j, L, M, sch, och ); // Im(ch[j]) + + // Resolve ch indices for conjugate component jc: + ih3 = optr( i-1, k, jc, L, M, sch, och ); // Re(ch[jc]) + ih4 = optr( i, k, jc, L, M, sch, och ); // Im(ch[jc]) + + // Resolve cc output indices: + io1 = iptr( i-1, k, j2, L, M, sc, oc ); + io2 = iptr( im-1, k, j2-1, L, M, sc, oc ); + io3 = iptr( i, k, j2, L, M, sc, oc ); + io4 = iptr( im, k, j2-1, L, M, sc, oc ); + + // Store the sum and difference combinations: + cc[ io1 ] = ch[ ih1 ] + ch[ ih3 ]; + cc[ io2 ] = ch[ ih1 ] - ch[ ih3 ]; + cc[ io3 ] = ch[ ih2 ] + ch[ ih4 ]; + cc[ io4 ] = ch[ ih4 ] - ch[ ih2 ]; + } + } + } + } +} + + +// EXPORTS // + +module.exports = radfg; From 2c9f317e5b70443f3d15909d7c7aef8ae8713fe1 Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Sat, 23 May 2026 13:26:14 +0530 Subject: [PATCH 06/19] feat: add rfftf1 --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rfftf/lib/rfftf1.js | 178 ++++++++++++++++++ 1 file changed, 178 insertions(+) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/rfftf1.js diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/rfftf1.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/rfftf1.js new file mode 100644 index 000000000000..73ecae7b4248 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/rfftf1.js @@ -0,0 +1,178 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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/0b4ee12c4ba45a4a8e567550c16d96d1679f50ce/src/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 */ + +'use strict'; + +// MODULES // + +var floor = require( '@stdlib/math/base/special/floor' ); +var dcopy = require( '@stdlib/blas/base/dcopy' ).ndarray; +var radf2 = require( './radf2.js' ); +var radf3 = require( './radf3.js' ); +var radf4 = require( './radf4.js' ); +var radf5 = require( './radf5.js' ); +var radfg = require( './radfg.js' ); + + +// MAIN // + +/** +* Performs the forward real-valued Fourier transform. +* +* @private +* @param {NonNegativeInteger} N - length of the sequence to transform +* @param {Float64Array} c - input array containing the sequence to be transformed +* @param {NonNegativeInteger} cOffset - starting index for `c` +* @param {Float64Array} ch - working array for intermediate results +* @param {NonNegativeInteger} chOffset - starting index for `ch` +* @param {Float64Array} wa - workspace array for storing twiddle factors +* @param {NonNegativeInteger} waOffset - starting index for `wa` +* @param {Int32Array} ifac - workspace array for storing factorization results +* @param {NonNegativeInteger} ifacOffset - starting index for `ifac` +* @returns {void} +*/ +function rfftf1( N, c, cOffset, ch, chOffset, wa, waOffset, ifac, ifacOffset ) { + var factor; + var idl1; + var FLG; + var ido; + var ix4; + var ix3; + var ix2; + var nf; + var l2; + var l1; + var kh; + var iw; + var k1; + + // Resolve the number of factors: + nf = ifac[ ifacOffset+1 ]; + + FLG = 1; // Flag to track whether the latest stage output resides in `c` or `ch`. + l2 = N; + + // Initialize an index offset to the last element in each workspace: + iw = N - 1; + + for ( k1 = 1; k1 <= nf; k1++ ) { + kh = nf - k1; + + // Resolve the next factor: + factor = ifac[ ifacOffset+kh+2 ]; + + // Compute a sub-transform length: + l1 = floor( l2 / factor ); + + ido = floor( N / l2 ); + idl1 = ido * l1; + + // Adjust the index offset + iw -= ( (factor-1) * ido ); + + // Toggle the flag to swap the input and output work buffers for the next stage: + FLG = 1 - FLG; + + switch ( factor ) { + case 4: + ix2 = iw + ido; + ix3 = ix2 + ido; + radf4( ido, l1, ( FLG ) ? ch : c, 1, ( FLG ) ? chOffset : cOffset, ( FLG ) ? c : ch, 1, ( FLG ) ? cOffset : chOffset, wa, 1, iw+waOffset, wa, 1, ix2+waOffset, wa, 1, ix3+waOffset ); + break; + case 2: + radf2( ido, l1, ( FLG ) ? ch : c, 1, ( FLG ) ? chOffset : cOffset, ( FLG ) ? c : ch, 1, ( FLG ) ? cOffset : chOffset, wa, 1, iw+waOffset ); + break; + case 3: + ix2 = iw + ido; + radf3( ido, l1, ( FLG ) ? ch : c, 1, ( FLG ) ? chOffset : cOffset, ( FLG ) ? c : ch, 1, ( FLG ) ? cOffset : chOffset, wa, 1, iw+waOffset, wa, 1, ix2+waOffset ); + break; + case 5: + ix2 = iw + ido; + ix3 = ix2 + ido; + ix4 = ix3 + ido; + radf5( ido, l1, ( FLG ) ? ch : c, 1, ( FLG ) ? chOffset : cOffset, ( FLG ) ? c : ch, 1, ( FLG ) ? cOffset : chOffset, wa, 1, iw+waOffset, wa, 1, ix2+waOffset, wa, 1, ix3+waOffset, wa, 1, ix4+waOffset ); + break; + default: + if ( ido === 1 ) { + FLG = 1 - FLG; + } + if ( FLG === 0 ) { + radfg( ido, factor, l1, idl1, c, 1, cOffset, c, 1, cOffset, c, 1, cOffset, ch, 1, chOffset, ch, 1, chOffset, wa, 1, iw+waOffset ); + FLG = 1; + } else { + radfg( ido, factor, l1, idl1, ch, 1, chOffset, ch, 1, chOffset, ch, 1, chOffset, c, 1, cOffset, c, 1, cOffset, wa, 1, iw+waOffset ); + FLG = 0; + } + break; + } + l2 = l1; + } + if ( FLG === 1 ) { + return; + } + + // Now that we've finished computing the transforms, copy over the final results to the input array... + dcopy( N, ch, 1, chOffset, c, 1, cOffset ); +} + + +// EXPORTS // + +module.exports = rfftf1; From ddd4f97fcb9432ffac59d8193c90b3ab9c627f0a Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Sat, 23 May 2026 13:27:44 +0530 Subject: [PATCH 07/19] refactor: remove argument validation from main.js --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../@stdlib/fft/base/fftpack/rfftf/lib/main.js | 17 +++-------------- 1 file changed, 3 insertions(+), 14 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js index 0e54338933a1..37577ba9f86c 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js @@ -18,7 +18,7 @@ * * ## 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. +* The original C code and copyright notice are from the [PFFFT library]{@link https://github.com/marton78/pffft/blob/0b4ee12c4ba45a4a8e567550c16d96d1679f50ce/src/fftpack.c}. The implementation follows the original, but has been modified for JavaScript. * * ```text * Copyright (c) 2004 the University Corporation for Atmospheric @@ -60,9 +60,6 @@ // MODULES // -var isNonNegativeInteger = require( '@stdlib/assert/is-nonnegative-integer' ); -var isFloat64Array = require( '@stdlib/assert/is-float64array' ); -var isInteger = require( '@stdlib/assert/is-integer' ); var rfftf1 = require( './rfftf1.js' ); @@ -98,22 +95,14 @@ function rfftf( N, r, strideR, offsetR, workspace, strideW, offsetW ) { var offsetT; var offsetF; - if ( !isNonNegativeInteger( N ) || !isFloat64Array( r ) || - !isInteger( strideR ) || !isNonNegativeInteger( offsetR ) || - !isFloat64Array( workspace ) || !isInteger( strideW ) || - !isNonNegativeInteger( offsetW ) || - workspace.length < offsetW + ( ( ( 2*N ) + 34 ) * strideW ) ) { - return; - } - // When a sub-sequence is a single data point, the FFT is the identity, so no transformation necessary... if ( N === 1 ) { return; } // Resolve the starting indices for storing twiddle factors and factorization results: - offsetT = offsetW + (N * strideW); // index offset for twiddle factors - offsetF = offsetT + (N * strideW); // index offset for factors describing the sub-transforms + offsetT = offsetW + ( N * strideW ); // index offset for twiddle factors + offsetF = offsetT + ( N * strideW ); // index offset for factors describing the sub-transforms rfftf1( N, r, offsetR, workspace, offsetW, workspace, offsetT, workspace, offsetF ); // eslint-disable-line max-len } From 614570def5294999f891dbb511aa424bbc574718 Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Mon, 4 May 2026 07:10:35 +0530 Subject: [PATCH 08/19] build: add recipes for installing fftpack PR-URL: https://github.com/stdlib-js/stdlib/pull/11819 Co-authored-by: Athan Reines Reviewed-by: Athan Reines --- deps/checksums/pffft_1_1_0_tar_gz/sha256 | 1 + deps/test/fftpack/test_install.c | 36 +++++ tools/make/common.mk | 11 ++ tools/make/lib/install/Makefile | 7 +- tools/make/lib/install/fftpack.mk | 177 +++++++++++++++++++++++ tools/make/lib/test-fixtures/c.mk | 4 +- 6 files changed, 231 insertions(+), 5 deletions(-) create mode 100644 deps/checksums/pffft_1_1_0_tar_gz/sha256 create mode 100644 deps/test/fftpack/test_install.c create mode 100644 tools/make/lib/install/fftpack.mk diff --git a/deps/checksums/pffft_1_1_0_tar_gz/sha256 b/deps/checksums/pffft_1_1_0_tar_gz/sha256 new file mode 100644 index 000000000000..d04a825080df --- /dev/null +++ b/deps/checksums/pffft_1_1_0_tar_gz/sha256 @@ -0,0 +1 @@ +ea0701a6bc256405b03975908a6a92d0ffecdd18579e8484b8d789c8bd561787 diff --git a/deps/test/fftpack/test_install.c b/deps/test/fftpack/test_install.c new file mode 100644 index 000000000000..356f0bbe334c --- /dev/null +++ b/deps/test/fftpack/test_install.c @@ -0,0 +1,36 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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. +*/ + +#include +#include + +extern void rffti( int n, double *wsave ); + +int main( void ) { + double wsave[ 2*8 + 15 ]; // 2*n + 15 + int n = 8; + int i; + + rffti( n, wsave ); + + printf( "rffti( %d, wsave )\n", n ); + for ( i = n; i < 2*n; i++ ) { + printf( "wsave[%2d] = %f\n", i, wsave[i] ); + } + printf( "\n" ); +} diff --git a/tools/make/common.mk b/tools/make/common.mk index e5f8e49ba41c..f570982f637e 100644 --- a/tools/make/common.mk +++ b/tools/make/common.mk @@ -688,3 +688,14 @@ DEPS_CPPCHECK_BUILD_OUT ?= $(DEPS_BUILD_DIR)/cppcheck_$(deps_cppcheck_version_sl # Host platform: DEPS_CPPCHECK_PLATFORM := $(shell command -v $(NODE) >/dev/null 2>&1 && $(NODE_HOST_PLATFORM)) + +# FFTPACK... + +# Define the PFFFT version: +DEPS_FFTPACK_VERSION ?= 1.1.0 + +# Generate a version slug: +deps_fftpack_version_slug := $(subst .,_,$(DEPS_FFTPACK_VERSION)) + +# Define the output path when building FFTPACK: +DEPS_FFTPACK_BUILD_OUT ?= $(DEPS_BUILD_DIR)/pffft-$(DEPS_FFTPACK_VERSION) diff --git a/tools/make/lib/install/Makefile b/tools/make/lib/install/Makefile index e66e2bc5aaf8..be8363f97b9a 100644 --- a/tools/make/lib/install/Makefile +++ b/tools/make/lib/install/Makefile @@ -39,6 +39,7 @@ include $(TOOLS_MAKE_LIB_DIR)/install/cephes.mk include $(TOOLS_MAKE_LIB_DIR)/install/cppcheck.mk include $(TOOLS_MAKE_LIB_DIR)/install/electron.mk include $(TOOLS_MAKE_LIB_DIR)/install/emsdk.mk +include $(TOOLS_MAKE_LIB_DIR)/install/fftpack.mk include $(TOOLS_MAKE_LIB_DIR)/install/llvm.mk include $(TOOLS_MAKE_LIB_DIR)/install/node.mk include $(TOOLS_MAKE_LIB_DIR)/install/openblas.mk @@ -157,7 +158,7 @@ clean-deps-tests: clean-deps-openblas-tests # @example # make install-deps-dev #/ -install-deps-dev: install-deps-boost install-deps-cephes install-deps-cppcheck install-deps-python install-deps-r install-deps-shellcheck +install-deps-dev: install-deps-boost install-deps-cephes install-deps-cppcheck install-deps-fftpack install-deps-python install-deps-r install-deps-shellcheck .PHONY: install-deps-dev @@ -167,7 +168,7 @@ install-deps-dev: install-deps-boost install-deps-cephes install-deps-cppcheck i # @example # make clean-deps-dev #/ -clean-deps-dev: clean-deps-boost clean-deps-cephes clean-deps-cppcheck clean-deps-python clean-deps-r clean-deps-shellcheck +clean-deps-dev: clean-deps-boost clean-deps-cephes clean-deps-cppcheck clean-deps-fftpack clean-deps-python clean-deps-r clean-deps-shellcheck .PHONY: clean-deps-dev @@ -177,7 +178,7 @@ clean-deps-dev: clean-deps-boost clean-deps-cephes clean-deps-cppcheck clean-dep # @example # make clean-deps-dev-tests #/ -clean-deps-dev-tests: clean-deps-boost-tests clean-deps-cephes-tests clean-deps-cppcheck-tests clean-deps-shellcheck-tests +clean-deps-dev-tests: clean-deps-boost-tests clean-deps-cephes-tests clean-deps-cppcheck-tests clean-deps-fftpack-tests clean-deps-shellcheck-tests .PHONY: clean-deps-dev-tests diff --git a/tools/make/lib/install/fftpack.mk b/tools/make/lib/install/fftpack.mk new file mode 100644 index 000000000000..b697b4a947d7 --- /dev/null +++ b/tools/make/lib/install/fftpack.mk @@ -0,0 +1,177 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2026 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. +#/ + +# VARIABLES # + +# Define the download URL: +DEPS_FFTPACK_URL ?= https://github.com/marton78/pffft/archive/refs/tags/v$(DEPS_FFTPACK_VERSION).tar.gz + +# Determine the basename for the download: +deps_fftpack_basename := pffft-$(DEPS_FFTPACK_VERSION).tar.gz + +# Define the path to the file containing a checksum to verify a download: +DEPS_FFTPACK_CHECKSUM ?= $(shell $(CAT) $(DEPS_CHECKSUMS_DIR)/$(subst .,_,$(subst -,_,$(deps_fftpack_basename)))/sha256) + +# Define the output path when downloading: +DEPS_FFTPACK_DOWNLOAD_OUT ?= $(DEPS_TMP_DIR)/$(deps_fftpack_basename) + +# Define a list of source files: +deps_fftpack_src := \ + src/fftpack.c + +# Resolve a list of source files to absolute filepaths: +DEPS_FFTPACK_SRC ?= $(addprefix $(DEPS_FFTPACK_BUILD_OUT)/,$(deps_fftpack_src)) + +# Define the path to the directory containing tests: +DEPS_FFTPACK_TEST_DIR ?= $(DEPS_DIR)/test/fftpack + +# Define the output directory path for compiled tests: +DEPS_FFTPACK_TEST_OUT ?= $(DEPS_FFTPACK_TEST_DIR)/build + +# Define the path to a test file for checking an installation: +DEPS_FFTPACK_TEST_INSTALL ?= $(DEPS_FFTPACK_TEST_DIR)/test_install.c + +# Define the output path for a test file: +DEPS_FFTPACK_TEST_INSTALL_OUT ?= $(DEPS_FFTPACK_TEST_OUT)/test_install + + +# RULES # + +#/ +# Downloads an FFTPACK distribution. +# +# @private +#/ +$(DEPS_FFTPACK_DOWNLOAD_OUT): | $(DEPS_TMP_DIR) + $(QUIET) echo 'Downloading FFTPACK...' >&2 + $(QUIET) $(DEPS_DOWNLOAD_BIN) $(DEPS_FFTPACK_URL) $(DEPS_FFTPACK_DOWNLOAD_OUT) + +#/ +# Extracts an FFTPACK gzipped tar archive. +# +# @private +#/ +$(DEPS_FFTPACK_BUILD_OUT): $(DEPS_FFTPACK_DOWNLOAD_OUT) | $(DEPS_BUILD_DIR) + $(QUIET) echo 'Extracting FFTPACK...' >&2 + $(QUIET) $(TAR) -zxf $(DEPS_FFTPACK_DOWNLOAD_OUT) -C $(DEPS_BUILD_DIR) + +#/ +# Creates a directory for storing compiled tests. +# +# @private +#/ +$(DEPS_FFTPACK_TEST_OUT): + $(QUIET) $(MKDIR_RECURSIVE) $(DEPS_FFTPACK_TEST_OUT) + +#/ +# Compiles a test file for testing an FFTPACK installation. +# +# @private +#/ +$(DEPS_FFTPACK_TEST_INSTALL_OUT): $(DEPS_FFTPACK_BUILD_OUT) $(DEPS_FFTPACK_TEST_OUT) + $(QUIET) $(CC) -I $(DEPS_FFTPACK_BUILD_OUT) $(DEPS_FFTPACK_TEST_INSTALL) $(DEPS_FFTPACK_SRC) -o $(DEPS_FFTPACK_TEST_INSTALL_OUT) + +#/ +# Downloads an FFTPACK distribution. +# +# @private +# +# @example +# make deps-download-fftpack +#/ +deps-download-fftpack: $(DEPS_FFTPACK_DOWNLOAD_OUT) + +.PHONY: deps-download-fftpack + +#/ +# Verifies a downloaded FFTPACK distribution. +# +# @private +# +# @example +# make deps-verify-fftpack +#/ +deps-verify-fftpack: deps-download-fftpack + $(QUIET) echo 'Verifying download...' >&2 + $(QUIET) $(DEPS_CHECKSUM_BIN) $(DEPS_FFTPACK_DOWNLOAD_OUT) $(DEPS_FFTPACK_CHECKSUM) >&2 + +.PHONY: deps-verify-fftpack + +#/ +# Extracts a downloaded FFTPACK distribution. +# +# @private +# +# @example +# make deps-extract-fftpack +#/ +deps-extract-fftpack: $(DEPS_FFTPACK_BUILD_OUT) + +.PHONY: deps-extract-fftpack + +#/ +# Tests an installed FFTPACK distribution. +# +# @private +# +# @example +# make deps-test-fftpack +#/ +deps-test-fftpack: $(DEPS_FFTPACK_TEST_INSTALL_OUT) + $(QUIET) echo 'Running tests...' >&2 + $(QUIET) $(DEPS_FFTPACK_TEST_INSTALL_OUT) + $(QUIET) echo '' >&2 + $(QUIET) echo 'Success.' >&2 + +.PHONY: deps-test-fftpack + +#/ +# Installs FFTPACK. +# +# @example +# make install-deps-fftpack +#/ +install-deps-fftpack: deps-download-fftpack deps-verify-fftpack deps-extract-fftpack deps-test-fftpack + +.PHONY: install-deps-fftpack + +#/ +# Removes an installed FFTPACK distribution. +# +# ## Notes +# +# - The rule does **not** remove an FFTPACK download (if one exists). +# +# @example +# make clean-deps-fftpack +#/ +clean-deps-fftpack: clean-deps-fftpack-tests + $(QUIET) $(DELETE) $(DELETE_FLAGS) $(DEPS_FFTPACK_BUILD_OUT) + +.PHONY: clean-deps-fftpack + +#/ +# Removes compiled FFTPACK installation tests. +# +# @example +# make clean-deps-fftpack-tests +#/ +clean-deps-fftpack-tests: + $(QUIET) $(DELETE) $(DELETE_FLAGS) $(DEPS_FFTPACK_TEST_OUT) + +.PHONY: clean-deps-fftpack-tests diff --git a/tools/make/lib/test-fixtures/c.mk b/tools/make/lib/test-fixtures/c.mk index 835c780d8f77..f48c82935cb1 100644 --- a/tools/make/lib/test-fixtures/c.mk +++ b/tools/make/lib/test-fixtures/c.mk @@ -28,7 +28,7 @@ test-fixtures-c: echo "Generating test fixtures: $$file"; \ cd `dirname $$file` && \ $(MAKE) clean && \ - CEPHES="$(DEPS_CEPHES_BUILD_OUT)" CEPHES_SRC="$(DEPS_CEPHES_SRC)" $(MAKE) && \ + CEPHES="$(DEPS_CEPHES_BUILD_OUT)" CEPHES_SRC="$(DEPS_CEPHES_SRC)" FFTPACK_SRC="$(DEPS_FFTPACK_SRC)" $(MAKE) && \ $(MAKE) run || exit 1; \ done @@ -45,7 +45,7 @@ test-fixtures-c-files: echo "Generating test fixtures: $$file"; \ cd `dirname $$file` && \ $(MAKE) clean && \ - CEPHES="$(DEPS_CEPHES_BUILD_OUT)" CEPHES_SRC="$(DEPS_CEPHES_SRC)" $(MAKE) && \ + CEPHES="$(DEPS_CEPHES_BUILD_OUT)" CEPHES_SRC="$(DEPS_CEPHES_SRC)" FFTPACK_SRC="$(DEPS_FFTPACK_SRC)" $(MAKE) && \ $(MAKE) run || exit 1; \ done From 79e83a3a493e2d4db65fe15d4984a740d0cde15f Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Sun, 24 May 2026 11:44:13 +0530 Subject: [PATCH 09/19] feat: add initial fftpack fixtures --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: passed - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../rfftf/test/fixtures/c/fftpack/Makefile | 137 ++++++++ .../rfftf/test/fixtures/c/fftpack/large.json | 1 + .../rfftf/test/fixtures/c/fftpack/medium.json | 1 + .../rfftf/test/fixtures/c/fftpack/runner.c | 318 ++++++++++++++++++ .../rfftf/test/fixtures/c/fftpack/small.json | 1 + 5 files changed, 458 insertions(+) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/Makefile create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/large.json create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/medium.json create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/runner.c create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/small.json diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/Makefile b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/Makefile new file mode 100644 index 000000000000..7ce16281940d --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/Makefile @@ -0,0 +1,137 @@ +#/ +# @license Apache-2.0 +# +# Copyright (c) 2026 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. +#/ + +# VARIABLES # + +ifndef VERBOSE + QUIET := @ +endif + +# Specify the path to FFTPACK: +FFTPACK ?= + +# Specify a list of FFTPACK source files: +FFTPACK_SRC ?= + +# Determine the OS: +# +# [1]: https://en.wikipedia.org/wiki/Uname#Examples +# [2]: http://stackoverflow.com/a/27776822/2225624 +OS ?= $(shell uname) +ifneq (, $(findstring MINGW,$(OS))) + OS := WINNT +else +ifneq (, $(findstring MSYS,$(OS))) + OS := WINNT +else +ifneq (, $(findstring CYGWIN,$(OS))) + OS := WINNT +endif +endif +endif + +# Define the program used for compiling C source files: +ifdef C_COMPILER + CC := $(C_COMPILER) +else + CC := gcc +endif + +# Define the command-line options when compiling C files: +CFLAGS ?= \ + -std=c99 \ + -O3 \ + -Wall \ + -pedantic + +# Determine whether to generate [position independent code][1]: +# +# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options +# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option +ifeq ($(OS), WINNT) + fPIC ?= +else + fPIC ?= -fPIC +endif + +# List of C targets: +c_targets := runner.out + + +# RULES # + +#/ +# Compiles C source files. +# +# @param {string} [C_COMPILER] - C compiler +# @param {string} [CFLAGS] - C compiler flags +# @param {(string|void)} [fPIC] - flag indicating whether to generate position independent code +# +# @example +# make +# +# @example +# make all +#/ +all: $(c_targets) + +.PHONY: all + +#/ +# Compiles C source files. +# +# @private +# @param {string} CC - C compiler +# @param {string} CFLAGS - C compiler flags +# @param {(string|void)} fPIC - flag indicating whether to generate position independent code +#/ +$(c_targets): %.out: %.c + $(QUIET) $(CC) $(CFLAGS) -DFFTPACK_DOUBLE_PRECISION $(fPIC) -o $@ $(FFTPACK_SRC) $< -lm + +#/ +# Generates test fixtures. +# +# @example +# make run +#/ +run: $(c_targets) + $(QUIET) ./$< + +.PHONY: run + +#/ +# Removes generated files. +# +# @example +# make clean +#/ +clean: + $(QUIET) -rm -f *.o *.out + +.PHONY: clean + +#/ +# Removes generated test fixtures. +# +# @example +# make clean-fixtures +#/ +clean-fixtures: + $(QUIET) -rm -f *.json + +.PHONY: clean-fixtures diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/large.json b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/large.json new file mode 100644 index 000000000000..003f72d330e9 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/large.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/medium.json b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/medium.json new file mode 100644 index 000000000000..412133370358 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/medium.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/runner.c b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/runner.c new file mode 100644 index 000000000000..83735d958f19 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/runner.c @@ -0,0 +1,318 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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. +*/ + +/** +* Generate FFTPACK test fixtures. +* +* ## Notes +* +* - Run this script from the directory in which fixtures should be written. +* +*/ + +#include +#include +#include + +/** +* Define prototypes for external functions. +*/ +extern void rffti( int n, double *wsave ); +extern void rfftf( int n, double *r, double *wsave ); + +/** +* Generates a random number on the interval [0,1]. +* +* @return random number +*/ +double rand_double( void ) { + int r = rand(); + return (double)r / ( (double)RAND_MAX + 1.0 ); +} + +/** +* Generates an array of pseudorandom integers drawn from a uniform distribution. +* +* ## Notes +* +* - WARNING: the method used here is not particularly robust, as some integer values may be sampled more frequently than others. +* +* +* @param out output array +* @param len array length +* @param a lower bound (inclusive) +* @param b upper bound (exclusive) +*/ +void rand_array_i32( int *out, const unsigned int len, const int a, const int b ) { + unsigned int i; + unsigned int r; + double delta; + + delta = (double)b - (double)a; + + for ( i = 0; i < len; i++ ) { + r = (unsigned int)( delta * rand_double() ); // truncation + out[ i ] = (int)( a + r ); + } +} + +/** +* Generates an array of pseudorandom numbers drawn from a uniform distribution. +* +* @param out output array +* @param len array length +* @param a lower bound (inclusive) +* @param b upper bound (exclusive) +*/ +void rand_array_f64( double *out, const unsigned int len, const double a, const double b ) { + unsigned int i; + double delta; + + delta = b - a; + + for ( i = 0; i < len; i++ ) { + out[ i ] = a + ( rand_double()*delta ); + } +} + +/** +* Writes an array of doubles to a file as a series of comma-separated values. +* +* @param f file to write to +* @param x array of doubles +* @param len array length +*/ +void write_array_f64( FILE *f, const double *x, const unsigned int len ) { + unsigned int i; + + for ( i = 0; i < len; i++ ) { + fprintf( f, "%.17g", x[ i ] ); + if ( i < len-1 ) { + fprintf( f, "," ); + } + } +} + +/** +* Writes an array of integers to a file as a series of comma-separated values. +* +* @param f file to write to +* @param x array of integers +* @param len array length +*/ +void write_array_i32( FILE *f, const int *x, const unsigned int len ) { + unsigned int i; + + for ( i = 0; i < len; i++ ) { + fprintf( f, "%d", x[ i ] ); + if ( i < len-1 ) { + fprintf( f, "," ); + } + } +} + +/** +* Writes a named array of doubles to a file as JSON. +* +* @param f file to write to +* @param name array name +* @param x data +* @param len array length +*/ +void write_named_array_f64( FILE *f, const char *name, const double *x, const unsigned int len ) { + fprintf( f, "\"%s\":[", name ); + write_array_f64( f, x, len ); + fprintf( f, "]" ); +} + +/** +* Writes a named array of integers to a file as JSON. +* +* @param f file to write to +* @param name array name +* @param x data +* @param len array length +*/ +void write_named_array_i32( FILE *f, const char *name, const int *x, const unsigned int len ) { + fprintf( f, "\"%s\":[", name ); + write_array_i32( f, x, len ); + fprintf( f, "]" ); +} + +/** +* Writes data to a file as JSON. +* +* ## Notes +* +* - This function SHOULD be tailored to the input data (e.g., input types, output types, number of arguments, etc) and may vary from use case to use case. +* +* +* @param f file to write to +* @param lengths sequence lengths +* @param offsets offsets +* @param input input values +* @param expected results +* @param num number of sequence lengths +* @param total total array length +*/ +void write_data_as_json( FILE *f, const int *lengths, const int *offsets, const double *input, const double *expected, const unsigned int num, const unsigned int total ) { + fprintf( f, "{" ); + write_named_array_i32( f, "lengths", lengths, num ); + fprintf( f, "," ); + write_named_array_i32( f, "offsets", offsets, num ); + fprintf( f, "," ); + write_named_array_f64( f, "input", input, total ); + fprintf( f, "," ); + write_named_array_f64( f, "expected", expected, total ); + fprintf( f, "}\n" ); +} + +/** +* Generates test fixtures. +* +* @param lengths sequence lengths +* @param offsets input offsets into flat arrays +* @param num number of sequence lengths +* @param total total number of input and output values +* @param name output filename +*/ +void generate( const int *lengths, const int *offsets, const unsigned int num, const unsigned int total, const char *name ) { + unsigned int i; + unsigned int j; + double *expected; + double *input; + double *wsave; + FILE *f; + int off; + int n; + + // Allocate output arrays: + input = (double*) malloc( total * sizeof(double) ); + if ( input == NULL ) { + printf( "Error allocating memory.\n" ); + exit( 1 ); + } + expected = (double*) malloc( total * sizeof(double) ); + if ( expected == NULL ) { + printf( "Error allocating memory.\n" ); + exit( 1 ); + } + + // Generate fixture data: + for ( i = 0; i < num; i++ ) { + n = lengths[ i ]; + off = offsets[ i ]; + + rand_array_f64( input + off, (unsigned int)n, -10.0, 10.0 ); + for ( j = 0; j < (unsigned int)n; j++ ) { + expected[ off + j ] = input[ off + j ]; + } + + wsave = (double*) calloc( 2*n + 15, sizeof(double) ); + if ( wsave == NULL ) { + printf( "Error allocating memory.\n" ); + exit( 1 ); + } + rffti( n, wsave ); + rfftf( n, expected + off, wsave ); + free( wsave ); + } + // Open a new file: + f = fopen( name, "w" ); + if ( f == NULL ) { + printf( "Error opening file.\n" ); + exit( 1 ); + } + + // Write data as JSON: + write_data_as_json( f, lengths, offsets, input, expected, num, total ); + + // Close the file: + fclose( f ); + + // Free allocated memory: + free( input ); + free( expected ); +} + +/** +* Computes offsets into flat input and output arrays for each sequence length. +* +* @param offsets output array of offsets +* @param lengths sequence lengths +* @param num number of sequence lengths +* @return total number of values +*/ +unsigned int compute_offsets( int *offsets, const int *lengths, const unsigned int num ) { + unsigned int total; + unsigned int i; + + total = 0; + for ( i = 0; i < num; i++ ) { + offsets[ i ] = total; + total += lengths[ i ]; + } + return total; +} + +/** +* Main execution sequence. +*/ +int main( void ) { + unsigned int total; + unsigned int num; + int *lengths; + int *offsets; + + // Use the current time to seed the random number generator: + srand( time( NULL ) ); + + // Define the number of sequence lengths per range: + num = 10; + + // Allocate arrays: + lengths = (int*) malloc( num * sizeof(int) ); + if ( lengths == NULL ) { + printf( "Error allocating memory.\n" ); + exit( 1 ); + } + offsets = (int*) malloc( num * sizeof(int) ); + if ( offsets == NULL ) { + printf( "Error allocating memory.\n" ); + exit( 1 ); + } + + // Generate fixture data: + rand_array_i32( lengths, num, 2, 16 ); + total = compute_offsets( offsets, lengths, num ); + generate( lengths, offsets, num, total, "small.json" ); + + rand_array_i32( lengths, num, 16, 128 ); + total = compute_offsets( offsets, lengths, num ); + generate( lengths, offsets, num, total, "medium.json" ); + + rand_array_i32( lengths, num, 128, 1024 ); + total = compute_offsets( offsets, lengths, num ); + generate( lengths, offsets, num, total, "large.json" ); + + // Free allocated memory: + free( lengths ); + free( offsets ); + + return 0; +} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/small.json b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/small.json new file mode 100644 index 000000000000..57b79850e380 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/small.json @@ -0,0 +1 @@ +{"lengths":[13,13,11,2,10,5,2,10,10,9],"offsets":[0,13,26,37,39,49,54,56,66,76],"input":[0.89892103336751461,8.1658930983394384,4.1654459573328495,8.6503157485276461,5.8569314610213041,-2.5528105162084103,-5.0862876325845718,-5.2362023945897818,-4.8536085896193981,5.4004745371639729,5.7756666373461485,-8.3707026578485966,-6.3995577115565538,2.6335700415074825,2.4117864854633808,-5.1044416800141335,9.6487223077565432,6.0759802348911762,-1.0000663716346025,-8.1154376268386841,3.8398204650729895,-4.137335205450654,3.8072478678077459,8.4150222968310118,-8.7201130390167236,1.0601632576435804,-1.8360422272235155,1.6383509431034327,-4.2356081772595644,-7.8665900882333517,6.2204037513583899,6.3259760197252035,0.67909128963947296,-6.5126114524900913,2.5393452867865562,-1.2236668448895216,-6.1685933731496334,4.4512074533849955,-8.5562178585678339,-4.3535376526415348,-9.9072837550193071,8.2819301076233387,-5.600538095459342,-8.2437359541654587,7.5298320781439543,-6.1121254414319992,-6.4922637213021517,4.5236635208129883,9.212907962501049,1.3442761171609163,-6.75121009349823,-7.5880159996449947,8.2151128351688385,-8.5984367597848177,6.073389258235693,-4.546611038967967,5.1083107385784388,-4.6212984714657068,9.8366321623325348,4.2769075650721788,1.9855578988790512,-8.7282997369766235,3.4663305804133415,-1.3818296045064926,-4.4100954942405224,-0.47492795623838902,-2.1140859555453062,8.557406859472394,4.3372323829680681,-4.1352272499352694,-0.76434376649558544,-6.3256112113595009,5.452399430796504,-1.5226456709206104,8.8942751754075289,6.0830209404230118,-2.6669284421950579,-3.0662705842405558,5.1903449278324842,-5.8726790361106396,-2.1165276132524014,7.5204657576978207,-3.5318732541054487,-0.19373113289475441,3.960926178842783],"expected":[6.4144789706915617,13.387325639756353,-21.928023159213939,-29.072416633192926,-21.740203696122322,13.566472080239153,-16.552310855726809,18.878112433369161,-3.7491472312635481,-6.5631348955019266,1.4585744125270956,-7.5606113931267442,-1.1929519180426831,10.814919034019113,4.5240653055954922,-6.1690899057242099,-19.833546830362998,-5.7253623090062646,19.102546057824817,5.3466877778085831,31.495461146592756,-9.6332047876495039,-3.999038984352814,14.856967070745597,-19.578740942508169,-12.395630761446979,-10.439944872632623,-13.686801011432884,-2.3948586896435407,10.903168971775433,7.8994841094889532,-2.9993672325729852,-29.193233050805333,0.616389351330208,-1.7062234540582542,0.28835010748720563,10.029382864118968,-4.1050104051828384,13.007425311952829,-11.161150950938463,6.8630316157481648,8.0690905410139795,-2.0511453240953905,14.472190355472936,-36.248225998378459,22.944861839971143,15.572456863320673,12.711879949701993,-0.64645988866686821,-13.378273900598288,-3.9063576152150148,7.5320291111354711,13.956184858416449,-16.115441248286185,1.5267782192677259,10.62000029720366,5.0572876818478107,6.0852700183592532,-15.623670249201187,-10.242411035426388,-2.5127599655273629,15.048164125489459,17.051869870244605,-1.3362053014929742,9.7344634097243343,26.916184090077877,18.462420934811234,18.100303029150734,9.0184203948204562,-8.5940664319131805,-7.1228293551532778,-14.145756689340839,-0.65500619424010331,-21.736386952754454,-6.9578100280660662,13.148533599451184,-0.77627319842576981,-1.4896942678591465,4.5379582892306223,1.6350786910462221,-3.1427618177595837,-17.719084499403834,19.09435863406452,5.9606586855518833,-1.5991282893642211]} From ffeafb70f280ef6e12c53cc69237a2db712ced57 Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Tue, 26 May 2026 02:49:02 +0530 Subject: [PATCH 10/19] refactor: handle strides correctly --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: na - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rfftf/lib/main.js | 2 +- .../fft/base/fftpack/rfftf/lib/radfg.js | 27 ++++++++------- .../fft/base/fftpack/rfftf/lib/rfftf1.js | 34 +++++++++++-------- 3 files changed, 35 insertions(+), 28 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js index 37577ba9f86c..7383a0611504 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js @@ -104,7 +104,7 @@ function rfftf( N, r, strideR, offsetR, workspace, strideW, offsetW ) { offsetT = offsetW + ( N * strideW ); // index offset for twiddle factors offsetF = offsetT + ( N * strideW ); // index offset for factors describing the sub-transforms - rfftf1( N, r, offsetR, workspace, offsetW, workspace, offsetT, workspace, offsetF ); // eslint-disable-line max-len + rfftf1( N, r, strideR, offsetR, workspace, strideW, offsetW, workspace, strideW, offsetT, workspace, strideW, offsetF ); // eslint-disable-line max-len } diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js index c6f7dfc925a8..49e8103f81af 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js @@ -650,7 +650,7 @@ function radfg( M, R, L, ML, cc, sc, oc, c1, sc1, oc1, c2, sc2, oc2, ch, sch, oc if ( M >= L ) { for ( k = 0; k < L; k++ ) { for ( i = 0; i < M; i++ ) { - icc = iptr( i, k, 0, L, M, sc, oc ); + icc = optr( i, 0, k, R, M, sc, oc ); ih1 = optr( i, k, 0, L, M, sch, och ); cc[ icc ] = ch[ ih1 ]; } @@ -658,20 +658,23 @@ function radfg( M, R, L, ML, cc, sc, oc, c1, sc1, oc1, c2, sc2, oc2, ch, sch, oc } else { for ( i = 0; i < M; i++ ) { for ( k = 0; k < L; k++ ) { - icc = iptr( i, k, 0, L, M, sc, oc ); + icc = optr( i, 0, k, R, M, sc, oc ); ih1 = optr( i, k, 0, L, M, sch, och ); cc[ icc ] = ch[ ih1 ]; } } } + /* + * `cc` is stored in output order, where the component index comes before the sub-sequence index. Accordingly, writes to `cc` use `optr`, not `iptr`. + */ // Store DC harmonics for conjugate pairs in the output array... for ( j = 1; j < Rph; j++ ) { jc = Rp1 - j - 1; // "mirror" index j2 = 2 * j; // output column index for ( k = 0; k < L; k++ ) { - io1 = iptr( M-1, k, j2-1, L, M, sc, oc ); - io2 = iptr( 0, k, j2, L, M, sc, oc ); + io1 = optr( M-1, j2-1, k, R, M, sc, oc ); + io2 = optr( 0, j2, k, R, M, sc, oc ); ih1 = optr( 0, k, j, L, M, sch, och ); ih2 = optr( 0, k, jc, L, M, sch, och ); @@ -709,10 +712,10 @@ function radfg( M, R, L, ML, cc, sc, oc, c1, sc1, oc1, c2, sc2, oc2, ch, sch, oc ih4 = optr( i, k, jc, L, M, sch, och ); // Im(ch[jc]) // Resolve cc output indices: - io1 = iptr( i-1, k, j2, L, M, sc, oc ); - io2 = iptr( im-1, k, j2-1, L, M, sc, oc ); - io3 = iptr( i, k, j2, L, M, sc, oc ); - io4 = iptr( im, k, j2-1, L, M, sc, oc ); + io1 = optr( i-1, j2, k, R, M, sc, oc ); + io2 = optr( im-1, j2-1, k, R, M, sc, oc ); + io3 = optr( i, j2, k, R, M, sc, oc ); + io4 = optr( im, j2-1, k, R, M, sc, oc ); // Store the sum and difference combinations: cc[ io1 ] = ch[ ih1 ] + ch[ ih3 ]; @@ -739,10 +742,10 @@ function radfg( M, R, L, ML, cc, sc, oc, c1, sc1, oc1, c2, sc2, oc2, ch, sch, oc ih4 = optr( i, k, jc, L, M, sch, och ); // Im(ch[jc]) // Resolve cc output indices: - io1 = iptr( i-1, k, j2, L, M, sc, oc ); - io2 = iptr( im-1, k, j2-1, L, M, sc, oc ); - io3 = iptr( i, k, j2, L, M, sc, oc ); - io4 = iptr( im, k, j2-1, L, M, sc, oc ); + io1 = optr( i-1, j2, k, R, M, sc, oc ); + io2 = optr( im-1, j2-1, k, R, M, sc, oc ); + io3 = optr( i, j2, k, R, M, sc, oc ); + io4 = optr( im, j2-1, k, R, M, sc, oc ); // Store the sum and difference combinations: cc[ io1 ] = ch[ ih1 ] + ch[ ih3 ]; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/rfftf1.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/rfftf1.js index 73ecae7b4248..745341fa5551 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/rfftf1.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/rfftf1.js @@ -79,16 +79,20 @@ var radfg = require( './radfg.js' ); * @private * @param {NonNegativeInteger} N - length of the sequence to transform * @param {Float64Array} c - input array containing the sequence to be transformed -* @param {NonNegativeInteger} cOffset - starting index for `c` +* @param {integer} sc - stride length for `c` +* @param {NonNegativeInteger} oc - starting index for `c` * @param {Float64Array} ch - working array for intermediate results -* @param {NonNegativeInteger} chOffset - starting index for `ch` +* @param {integer} sch - stride length for `ch` +* @param {NonNegativeInteger} och - starting index for `ch` * @param {Float64Array} wa - workspace array for storing twiddle factors -* @param {NonNegativeInteger} waOffset - starting index for `wa` +* @param {integer} swa - stride length for `wa` +* @param {NonNegativeInteger} owa - starting index for `wa` * @param {Int32Array} ifac - workspace array for storing factorization results -* @param {NonNegativeInteger} ifacOffset - starting index for `ifac` +* @param {integer} si - stride length for `ifac` +* @param {NonNegativeInteger} oi - starting index for `ifac` * @returns {void} */ -function rfftf1( N, c, cOffset, ch, chOffset, wa, waOffset, ifac, ifacOffset ) { +function rfftf1( N, c, sc, oc, ch, sch, och, wa, swa, owa, ifac, si, oi ) { // eslint-disable-line max-params var factor; var idl1; var FLG; @@ -104,7 +108,7 @@ function rfftf1( N, c, cOffset, ch, chOffset, wa, waOffset, ifac, ifacOffset ) { var k1; // Resolve the number of factors: - nf = ifac[ ifacOffset+1 ]; + nf = ifac[ oi + si ]; FLG = 1; // Flag to track whether the latest stage output resides in `c` or `ch`. l2 = N; @@ -116,7 +120,7 @@ function rfftf1( N, c, cOffset, ch, chOffset, wa, waOffset, ifac, ifacOffset ) { kh = nf - k1; // Resolve the next factor: - factor = ifac[ ifacOffset+kh+2 ]; + factor = ifac[ oi + ( ( kh + 2 ) * si ) ]; // Compute a sub-transform length: l1 = floor( l2 / factor ); @@ -125,7 +129,7 @@ function rfftf1( N, c, cOffset, ch, chOffset, wa, waOffset, ifac, ifacOffset ) { idl1 = ido * l1; // Adjust the index offset - iw -= ( (factor-1) * ido ); + iw -= ( ( factor - 1 ) * ido ); // Toggle the flag to swap the input and output work buffers for the next stage: FLG = 1 - FLG; @@ -134,30 +138,30 @@ function rfftf1( N, c, cOffset, ch, chOffset, wa, waOffset, ifac, ifacOffset ) { case 4: ix2 = iw + ido; ix3 = ix2 + ido; - radf4( ido, l1, ( FLG ) ? ch : c, 1, ( FLG ) ? chOffset : cOffset, ( FLG ) ? c : ch, 1, ( FLG ) ? cOffset : chOffset, wa, 1, iw+waOffset, wa, 1, ix2+waOffset, wa, 1, ix3+waOffset ); + radf4( ido, l1, ( FLG ) ? ch : c, ( FLG ) ? sch : sc, ( FLG ) ? och : oc, ( FLG ) ? c : ch, ( FLG ) ? sc : sch, ( FLG ) ? oc : och, wa, swa, owa + ( ( iw + 1 ) * swa ), wa, swa, owa + ( ( ix2 + 1 ) * swa ), wa, swa, owa + ( ( ix3 + 1 ) * swa ) ); break; case 2: - radf2( ido, l1, ( FLG ) ? ch : c, 1, ( FLG ) ? chOffset : cOffset, ( FLG ) ? c : ch, 1, ( FLG ) ? cOffset : chOffset, wa, 1, iw+waOffset ); + radf2( ido, l1, ( FLG ) ? ch : c, ( FLG ) ? sch : sc, ( FLG ) ? och : oc, ( FLG ) ? c : ch, ( FLG ) ? sc : sch, ( FLG ) ? oc : och, wa, swa, owa + ( ( iw + 1 ) * swa ) ); break; case 3: ix2 = iw + ido; - radf3( ido, l1, ( FLG ) ? ch : c, 1, ( FLG ) ? chOffset : cOffset, ( FLG ) ? c : ch, 1, ( FLG ) ? cOffset : chOffset, wa, 1, iw+waOffset, wa, 1, ix2+waOffset ); + radf3( ido, l1, ( FLG ) ? ch : c, ( FLG ) ? sch : sc, ( FLG ) ? och : oc, ( FLG ) ? c : ch, ( FLG ) ? sc : sch, ( FLG ) ? oc : och, wa, swa, owa + ( ( iw + 1 ) * swa ), wa, swa, owa + ( ( ix2 + 1 ) * swa ) ); break; case 5: ix2 = iw + ido; ix3 = ix2 + ido; ix4 = ix3 + ido; - radf5( ido, l1, ( FLG ) ? ch : c, 1, ( FLG ) ? chOffset : cOffset, ( FLG ) ? c : ch, 1, ( FLG ) ? cOffset : chOffset, wa, 1, iw+waOffset, wa, 1, ix2+waOffset, wa, 1, ix3+waOffset, wa, 1, ix4+waOffset ); + radf5( ido, l1, ( FLG ) ? ch : c, ( FLG ) ? sch : sc, ( FLG ) ? och : oc, ( FLG ) ? c : ch, ( FLG ) ? sc : sch, ( FLG ) ? oc : och, wa, swa, owa + ( ( iw + 1 ) * swa ), wa, swa, owa + ( ( ix2 + 1 ) * swa ), wa, swa, owa + ( ( ix3 + 1 ) * swa ), wa, swa, owa + ( ( ix4 + 1 ) * swa ) ); break; default: if ( ido === 1 ) { FLG = 1 - FLG; } if ( FLG === 0 ) { - radfg( ido, factor, l1, idl1, c, 1, cOffset, c, 1, cOffset, c, 1, cOffset, ch, 1, chOffset, ch, 1, chOffset, wa, 1, iw+waOffset ); + radfg( ido, factor, l1, idl1, c, sc, oc, c, sc, oc, c, sc, oc, ch, sch, och, ch, sch, och, wa, swa, owa + ( ( iw + 1 ) * swa ) ); FLG = 1; } else { - radfg( ido, factor, l1, idl1, ch, 1, chOffset, ch, 1, chOffset, ch, 1, chOffset, c, 1, cOffset, c, 1, cOffset, wa, 1, iw+waOffset ); + radfg( ido, factor, l1, idl1, ch, sch, och, ch, sch, och, ch, sch, och, c, sc, oc, c, sc, oc, wa, swa, owa + ( ( iw + 1 ) * swa ) ); FLG = 0; } break; @@ -169,7 +173,7 @@ function rfftf1( N, c, cOffset, ch, chOffset, wa, waOffset, ifac, ifacOffset ) { } // Now that we've finished computing the transforms, copy over the final results to the input array... - dcopy( N, ch, 1, chOffset, c, 1, cOffset ); + dcopy( N, ch, sch, och, c, sc, oc ); } From 19a6a79587e6ab37b948362bfe1416a82415e3f7 Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Tue, 26 May 2026 02:49:55 +0530 Subject: [PATCH 11/19] test: add initial tests --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: na - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: passed - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rfftf/package.json | 58 +++ .../fft/base/fftpack/rfftf/test/test.js | 368 ++++++++++++++++++ 2 files changed, 426 insertions(+) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/package.json create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/test.js diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/package.json b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/package.json new file mode 100644 index 000000000000..11923965b83e --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/package.json @@ -0,0 +1,58 @@ +{ + "name": "@stdlib/fft/base/fftpack/rfftf", + "version": "0.0.0", + "description": "Compute the forward real-valued fast Fourier transform (FFT).", + "license": "Apache-2.0", + "author": { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + }, + "contributors": [ + { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + } + ], + "main": "./lib", + "directories": { + "lib": "./lib", + "test": "./test" + }, + "scripts": {}, + "homepage": "https://github.com/stdlib-js/stdlib", + "repository": { + "type": "git", + "url": "git://github.com/stdlib-js/stdlib.git" + }, + "bugs": { + "url": "https://github.com/stdlib-js/stdlib/issues" + }, + "dependencies": {}, + "devDependencies": {}, + "engines": { + "node": ">=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "fft", + "fftpack", + "rfftf", + "fourier", + "transform", + "forward", + "real" + ], + "__stdlib__": {} +} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/test.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/test.js new file mode 100644 index 000000000000..2443949b6998 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/test.js @@ -0,0 +1,368 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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. +*/ + +'use strict'; + +// MODULES // + +var tape = require( 'tape' ); +var Float64Array = require( '@stdlib/array/float64' ); +var isAlmostSameValue = require( '@stdlib/number/float64/base/assert/is-almost-same-value' ); +var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); +var rfftf = require( './../lib' ); + + +// FIXTURES // + +var small = require( './fixtures/c/fftpack/small.json' ); +var medium = require( './fixtures/c/fftpack/medium.json' ); +var large = require( './fixtures/c/fftpack/large.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof rfftf, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'the function has an arity of 7', function test( t ) { + t.strictEqual( rfftf.length, 7, 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns all zeros for a zero sequence', function test( t ) { + var workspace; + var expected; + var N; + var r; + + N = 4; + r = new Float64Array( [ 0.0, 0.0, 0.0, 0.0 ] ); + expected = new Float64Array( [ 0.0, 0.0, 0.0, 0.0 ] ); + workspace = new Float64Array( ( 2 * N ) + 34 ); + + rffti( N, workspace, 1, 0 ); + rfftf( N, r, 1, 0, workspace, 1, 0 ); + + t.deepEqual( r, expected, 'returns expected value' ); + t.end(); +}); + +tape( 'the function returns only a zero-frequency term for a constant sequence', function test( t ) { + var workspace; + var expected; + var N; + var r; + + N = 4; + r = new Float64Array( [ 1.0, 1.0, 1.0, 1.0 ] ); + expected = new Float64Array( [ 4.0, 0.0, 0.0, 0.0 ] ); + workspace = new Float64Array( ( 2 * N ) + 34 ); + + rffti( N, workspace, 1, 0 ); + rfftf( N, r, 1, 0, workspace, 1, 0 ); + + t.deepEqual( r, expected, 'returns expected value' ); + t.end(); +}); + +tape( 'the function computes the exact two-point real FFT', function test( t ) { + var workspace; + var expected; + var N; + var r; + + N = 2; + r = new Float64Array( [ 3.0, -1.0 ] ); + + // For [ a, b ], output is [ a+b, a-b ]... + expected = new Float64Array( [ 2.0, 4.0 ] ); + workspace = new Float64Array( ( 2 * N ) + 34 ); + + rffti( N, workspace, 1, 0 ); + rfftf( N, r, 1, 0, workspace, 1, 0 ); + + t.deepEqual( r, expected, 'returns expected value' ); + t.end(); +}); + +tape( 'the function computes a forward real-valued FFT (small sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var input; + var ulps; + var off; + var y; + var e; + var N; + var i; + var k; + var r; + + lengths = small.lengths; + offsets = small.offsets; + input = small.input; + expected = small.expected; + + ulps = 32; + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + r = new Float64Array( N ); + for ( i = 0; i < N; i++ ) { + r[ i ] = input[ off + i ]; + } + workspace = new Float64Array( ( 2 * N ) + 34 ); + + rffti( N, workspace, 1, 0 ); + rfftf( N, r, 1, 0, workspace, 1, 0 ); + + for ( i = 0; i < N; i++ ) { + y = r[ i ]; + e = expected[ off + i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within tolerance. N: '+N+'. index: '+i+'. y: '+y+'. E: '+e+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a forward real-valued FFT (medium sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var input; + var ulps; + var off; + var y; + var e; + var N; + var i; + var k; + var r; + + lengths = medium.lengths; + offsets = medium.offsets; + input = medium.input; + expected = medium.expected; + + ulps = 8163; + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + r = new Float64Array( N ); + for ( i = 0; i < N; i++ ) { + r[ i ] = input[ off + i ]; + } + workspace = new Float64Array( ( 2 * N ) + 34 ); + + rffti( N, workspace, 1, 0 ); + rfftf( N, r, 1, 0, workspace, 1, 0 ); + + for ( i = 0; i < N; i++ ) { + y = r[ i ]; + e = expected[ off + i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within tolerance. N: '+N+'. index: '+i+'. y: '+y+'. E: '+e+'.' ); + } + } + t.end(); +}); + +tape( 'the function computes a forward real-valued FFT (large sequence lengths)', function test( t ) { + var workspace; + var expected; + var lengths; + var offsets; + var input; + var ulps; + var off; + var y; + var e; + var N; + var i; + var k; + var r; + + lengths = large.lengths; + offsets = large.offsets; + input = large.input; + expected = large.expected; + + ulps = 40987; + for ( k = 0; k < lengths.length; k++ ) { + N = lengths[ k ]; + off = offsets[ k ]; + r = new Float64Array( N ); + for ( i = 0; i < N; i++ ) { + r[ i ] = input[ off + i ]; + } + workspace = new Float64Array( ( 2 * N ) + 34 ); + + rffti( N, workspace, 1, 0 ); + rfftf( N, r, 1, 0, workspace, 1, 0 ); + + for ( i = 0; i < N; i++ ) { + y = r[ i ]; + e = expected[ off + i ]; + t.strictEqual( isAlmostSameValue( y, e, ulps ), true, 'within tolerance. N: '+N+'. index: '+i+'. y: '+y+'. E: '+e+'.' ); + } + } + t.end(); +}); + +tape( 'the function leaves a length-one sequence unchanged', function test( t ) { + var workspace; + var N; + var r; + + N = 1; + r = new Float64Array( [ 5.0 ] ); + workspace = new Float64Array( ( 2 * N ) + 34 ); + + rffti( N, workspace, 1, 0 ); + rfftf( N, r, 1, 0, workspace, 1, 0 ); + t.strictEqual( r[ 0 ], 5.0, 'returns expected value' ); + t.end(); +}); + +tape( 'the function supports specifying a stride', function test( t ) { + var workspace; + var expected; + var v; + var i; + var N; + var r; + + N = 4; + r = new Float64Array([ + 1.0, // 0 + -999.0, + 2.0, // 1 + -999.0, + 3.0, // 2 + -999.0, + 4.0, // 3 + -999.0 + ]); + expected = new Float64Array([ + 10.0, // 0 + -999.0, + -2.0, // 1 + -999.0, + 2.0, // 2 + -999.0, + -2.0, // 3 + -999.0 + ]); + + workspace = new Float64Array( ( ( 2 * N ) + 34 ) * 2 ); + rffti( N, workspace, 2, 0 ); + rfftf( N, r, 2, 0, workspace, 2, 0 ); + + for ( i = 0; i < r.length; i++ ) { + v = r[ i ]; + t.strictEqual( isAlmostSameValue( v, expected[ i ], 1 ), true, 'within tolerance. index: '+i+'. y: '+v+'. E: '+expected[ i ]+'.' ); + } + t.end(); +}); + +tape( 'the function supports specifying a negative stride', function test( t ) { + var workspace; + var expected; + var v; + var i; + var N; + var r; + + N = 4; + r = new Float64Array([ + 4.0, // 3 + -999.0, + 3.0, // 2 + -999.0, + 2.0, // 1 + -999.0, + 1.0 // 0 + ]); + expected = new Float64Array([ + -2.0, // 3 + -999.0, + 2.0, // 2 + -999.0, + -2.0, // 1 + -999.0, + 10.0 // 0 + ]); + + workspace = new Float64Array( ( 2 * N ) + 34 ); + rffti( N, workspace, -1, workspace.length-1 ); + rfftf( N, r, -2, r.length-1, workspace, -1, workspace.length-1 ); + + for ( i = 0; i < r.length; i++ ) { + v = r[ i ]; + t.strictEqual( isAlmostSameValue( v, expected[ i ], 1 ), true, 'within tolerance. index: '+i+'. y: '+v+'. E: '+expected[ i ]+'.' ); + } + t.end(); +}); + +tape( 'the function supports an offset parameter', function test( t ) { + var workspace; + var expected; + var v; + var i; + var N; + var r; + + N = 4; + r = new Float64Array([ + -999.0, + 1.0, // 0 + -999.0, + 2.0, // 1 + -999.0, + 3.0, // 2 + -999.0, + 4.0, // 3 + -999.0 + ]); + expected = new Float64Array([ + -999.0, + 10.0, // 0 + -999.0, + -2.0, // 1 + -999.0, + 2.0, // 2 + -999.0, + -2.0, // 3 + -999.0 + ]); + + workspace = new Float64Array( 3 + ( ( ( 2 * N ) + 34 ) * 2 ) ); + rffti( N, workspace, 2, 3 ); + rfftf( N, r, 2, 1, workspace, 2, 3 ); + + for ( i = 0; i < r.length; i++ ) { + v = r[ i ]; + t.strictEqual( isAlmostSameValue( v, expected[ i ], 1 ), true, 'within tolerance. index: '+i+'. y: '+v+'. E: '+expected[ i ]+'.' ); + } + t.end(); +}); From 5baaac3e51450b6dc0e82ba5e071b31026fca0f3 Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Wed, 27 May 2026 00:47:54 +0530 Subject: [PATCH 12/19] docs: add README --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: passed - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../@stdlib/fft/base/fftpack/rfftf/README.md | 152 ++++++++++++++++++ 1 file changed, 152 insertions(+) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/README.md diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/README.md new file mode 100644 index 000000000000..9e0fa4cce33b --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/README.md @@ -0,0 +1,152 @@ + + +# rfftf + +> Compute the forward real-valued fast Fourier transform (FFT). + + + +
+ +
+ + + + + +
+ +## Usage + +```javascript +var rfftf = require( '@stdlib/fft/base/fftpack/rfftf' ); +``` + +#### rfftf( N, r, strideR, offsetR, workspace, strideW, offsetW ) + +Computes the forward real-valued fast Fourier transform (FFT). + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); +var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); + +var N = 4; +var workspace = new Float64Array( ( 2*N ) + 34 ); + +rffti( N, workspace, 1, 0 ); + +var r = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] ); + +rfftf( N, r, 1, 0, workspace, 1, 0 ); + +var out = r.slice( 0, N ); +// returns [ 10.0, -2.0, 2.0, -2.0 ] +``` + +The function accepts the following arguments: + +- **N**: length of the sequence to transform. +- **r**: input array containing the sequence to transform. +- **strideR**: stride length for `r`. +- **offsetR**: starting index for `r`. +- **workspace**: workspace array containing pre-computed values. +- **strideW**: stride length for `workspace`. +- **offsetW**: starting index for `workspace`. + +
+ + + + + +
+ +## Notes + +- Before calling this function, initialize the workspace by calling [`rffti`][@stdlib/fft/base/fftpack/rffti] with the same sequence length and workspace layout. + +- For `N = 4`, the output + + ```text + [ 10.0, -2.0, 2.0, -2.0 ] + ``` + + corresponds to a zero-frequency term `10.0`, a complex coefficient `-2.0 + 2.0i` at frequency `1`, and a Nyquist term `-2.0`. + +- If `N` equals `1`, the function returns early without modifying the input, as a single data point is its own Fourier transform. + +
+ + + +
+ +## Examples + + + +```javascript +var Float64Array = require( '@stdlib/array/float64' ); +var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); +var rfftf = require( '@stdlib/fft/base/fftpack/rfftf' ); + +var N = 4; +var r = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] ); +var workspace = new Float64Array( ( 2*N ) + 34 ); + +rffti( N, workspace, 1, 0 ); + +console.log( 'Input sequence: %s', r ); + +rfftf( N, r, 1, 0, workspace, 1, 0 ); + +console.log( 'Packed output: %s', r.slice( 0, N ) ); +``` + +
+ + + + + +
+ +
+ + + + + +
+ +
+ + + + + +
+ +[@stdlib/fft/base/fftpack/rffti]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/fft/base/fftpack/rffti + +
+ + From 6ea739c0cbef861617d5ceb71ff7bd8a91c63c02 Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Wed, 27 May 2026 22:01:58 +0530 Subject: [PATCH 13/19] docs: add examples --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: na - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: passed - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: passed - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rfftf/examples/index.js | 35 +++++++++++++++++++ .../fft/base/fftpack/rfftf/package.json | 1 + 2 files changed, 36 insertions(+) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/examples/index.js diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/examples/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/examples/index.js new file mode 100644 index 000000000000..a9561fc6155b --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/examples/index.js @@ -0,0 +1,35 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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. +*/ + +'use strict'; + +var Float64Array = require( '@stdlib/array/float64' ); +var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); +var rfftf = require( './../lib' ); + +var N = 4; +var r = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] ); +var workspace = new Float64Array( ( 2*N ) + 34 ); + +rffti( N, workspace, 1, 0 ); + +console.log( 'Input sequence: %s', r ); + +rfftf( N, r, 1, 0, workspace, 1, 0 ); + +console.log( 'Packed output: %s', r.slice( 0, N ) ); diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/package.json b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/package.json index 11923965b83e..f0617e07afbb 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/package.json +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/package.json @@ -15,6 +15,7 @@ ], "main": "./lib", "directories": { + "example": "./examples", "lib": "./lib", "test": "./test" }, From 84c46609c90084b1785cabe82457eb844cb2c006 Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Wed, 27 May 2026 22:03:30 +0530 Subject: [PATCH 14/19] refactor: replace functions by hardcoded fftpack constants --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: na - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rfftf/lib/radf3.js | 14 ++++-------- .../fft/base/fftpack/rfftf/lib/radf5.js | 22 +++++++------------ .../fft/base/fftpack/rfftf/lib/radfg.js | 9 ++++---- 3 files changed, 17 insertions(+), 28 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js index 914ca19853df..2f2994203a2e 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js @@ -60,19 +60,13 @@ 'use strict'; -// MODULES // - -var cospi = require( '@stdlib/math/base/special/cospi' ); -var sinpi = require( '@stdlib/math/base/special/sinpi' ); - - // VARIABLES // -// cos( 2π/3 ) = -0.5 -var TAUR = cospi( 2.0 / 3.0 ); +// cos( 2π/3 ): +var TAUR = -0.5; -// sin( 2π/3 ) = 0.866025403784439 -var TAUI = sinpi( 2.0 / 3.0 ); +// sin( 2π/3 ): +var TAUI = 0.866025403784439; // FUNCTIONS // diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf5.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf5.js index 6ad5dea1f911..b2c119e9f673 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf5.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf5.js @@ -60,25 +60,19 @@ 'use strict'; -// MODULES // - -var cospi = require( '@stdlib/math/base/special/cospi' ); -var sinpi = require( '@stdlib/math/base/special/sinpi' ); - - // VARIABLES // -// cos( 2π/5 ) = 0.30901699437494734 -var TR11 = cospi( 2.0 / 5.0 ); +// cos( 2π/5 ): +var TR11 = 0.309016994374947; -// sin( 2π/5 ) = 0.9510565162951536 -var TI11 = sinpi( 2.0 / 5.0 ); +// sin( 2π/5 ): +var TI11 = 0.951056516295154; -// cos( 4π/5 ) = -0.8090169943749475 -var TR12 = cospi( 4.0 / 5.0 ); +// cos( 4π/5 ): +var TR12 = -0.809016994374947; -// sin( 4π/5 ) = 0.587785252292473 -var TI12 = sinpi( 4.0 / 5.0 ); +// sin( 4π/5 ): +var TI12 = 0.587785252292473; // FUNCTIONS // diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js index 49e8103f81af..890ae2120058 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js @@ -62,8 +62,9 @@ // MODULES // -var cospi = require( '@stdlib/math/base/special/cospi' ); -var sinpi = require( '@stdlib/math/base/special/sinpi' ); +var TWO_PI = require( '@stdlib/constants/float64/two-pi' ); +var cos = require( '@stdlib/math/base/special/cos' ); +var sin = require( '@stdlib/math/base/special/sin' ); var floor = require( '@stdlib/math/base/special/floor' ); @@ -389,8 +390,8 @@ function radfg( M, R, L, ML, cc, sc, oc, c1, sc1, oc1, c2, sc2, oc2, ch, sch, oc var l; // Compute the basic rotation angle for the radix-R DFT matrix: - dcp = cospi( 2.0 / R ); // cos(2π/R) - dsp = sinpi( 2.0 / R ); // sin(2π/R) + dcp = cos( TWO_PI / R ); // cos(2π/R) + dsp = sin( TWO_PI / R ); // sin(2π/R) // Compute half the radix, rounded up, which is used as the exclusive upper bound for conjugate-symmetric component loops: Rph = floor( ( R + 1 ) / 2 ); From b5c2ad393adf701a409e653154f589a78647e0a9 Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Wed, 27 May 2026 22:05:15 +0530 Subject: [PATCH 15/19] test: regenerate fixtures with ffp contract off --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: na - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rfftf/test/fixtures/c/fftpack/Makefile | 1 + .../fft/base/fftpack/rfftf/test/fixtures/c/fftpack/large.json | 2 +- .../base/fftpack/rfftf/test/fixtures/c/fftpack/medium.json | 2 +- .../fft/base/fftpack/rfftf/test/fixtures/c/fftpack/small.json | 2 +- lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/test.js | 4 ++-- 5 files changed, 6 insertions(+), 5 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/Makefile b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/Makefile index 7ce16281940d..4b8cac6acbd2 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/Makefile +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/Makefile @@ -56,6 +56,7 @@ endif CFLAGS ?= \ -std=c99 \ -O3 \ + -ffp-contract=off \ -Wall \ -pedantic diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/large.json b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/large.json index 003f72d330e9..bb503d1af6b9 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/large.json +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/large.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/medium.json b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/medium.json index 412133370358..6f956976e745 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/medium.json +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/medium.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/small.json b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/small.json index 57b79850e380..8d557d1163b5 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/small.json +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/fixtures/c/fftpack/small.json @@ -1 +1 @@ -{"lengths":[13,13,11,2,10,5,2,10,10,9],"offsets":[0,13,26,37,39,49,54,56,66,76],"input":[0.89892103336751461,8.1658930983394384,4.1654459573328495,8.6503157485276461,5.8569314610213041,-2.5528105162084103,-5.0862876325845718,-5.2362023945897818,-4.8536085896193981,5.4004745371639729,5.7756666373461485,-8.3707026578485966,-6.3995577115565538,2.6335700415074825,2.4117864854633808,-5.1044416800141335,9.6487223077565432,6.0759802348911762,-1.0000663716346025,-8.1154376268386841,3.8398204650729895,-4.137335205450654,3.8072478678077459,8.4150222968310118,-8.7201130390167236,1.0601632576435804,-1.8360422272235155,1.6383509431034327,-4.2356081772595644,-7.8665900882333517,6.2204037513583899,6.3259760197252035,0.67909128963947296,-6.5126114524900913,2.5393452867865562,-1.2236668448895216,-6.1685933731496334,4.4512074533849955,-8.5562178585678339,-4.3535376526415348,-9.9072837550193071,8.2819301076233387,-5.600538095459342,-8.2437359541654587,7.5298320781439543,-6.1121254414319992,-6.4922637213021517,4.5236635208129883,9.212907962501049,1.3442761171609163,-6.75121009349823,-7.5880159996449947,8.2151128351688385,-8.5984367597848177,6.073389258235693,-4.546611038967967,5.1083107385784388,-4.6212984714657068,9.8366321623325348,4.2769075650721788,1.9855578988790512,-8.7282997369766235,3.4663305804133415,-1.3818296045064926,-4.4100954942405224,-0.47492795623838902,-2.1140859555453062,8.557406859472394,4.3372323829680681,-4.1352272499352694,-0.76434376649558544,-6.3256112113595009,5.452399430796504,-1.5226456709206104,8.8942751754075289,6.0830209404230118,-2.6669284421950579,-3.0662705842405558,5.1903449278324842,-5.8726790361106396,-2.1165276132524014,7.5204657576978207,-3.5318732541054487,-0.19373113289475441,3.960926178842783],"expected":[6.4144789706915617,13.387325639756353,-21.928023159213939,-29.072416633192926,-21.740203696122322,13.566472080239153,-16.552310855726809,18.878112433369161,-3.7491472312635481,-6.5631348955019266,1.4585744125270956,-7.5606113931267442,-1.1929519180426831,10.814919034019113,4.5240653055954922,-6.1690899057242099,-19.833546830362998,-5.7253623090062646,19.102546057824817,5.3466877778085831,31.495461146592756,-9.6332047876495039,-3.999038984352814,14.856967070745597,-19.578740942508169,-12.395630761446979,-10.439944872632623,-13.686801011432884,-2.3948586896435407,10.903168971775433,7.8994841094889532,-2.9993672325729852,-29.193233050805333,0.616389351330208,-1.7062234540582542,0.28835010748720563,10.029382864118968,-4.1050104051828384,13.007425311952829,-11.161150950938463,6.8630316157481648,8.0690905410139795,-2.0511453240953905,14.472190355472936,-36.248225998378459,22.944861839971143,15.572456863320673,12.711879949701993,-0.64645988866686821,-13.378273900598288,-3.9063576152150148,7.5320291111354711,13.956184858416449,-16.115441248286185,1.5267782192677259,10.62000029720366,5.0572876818478107,6.0852700183592532,-15.623670249201187,-10.242411035426388,-2.5127599655273629,15.048164125489459,17.051869870244605,-1.3362053014929742,9.7344634097243343,26.916184090077877,18.462420934811234,18.100303029150734,9.0184203948204562,-8.5940664319131805,-7.1228293551532778,-14.145756689340839,-0.65500619424010331,-21.736386952754454,-6.9578100280660662,13.148533599451184,-0.77627319842576981,-1.4896942678591465,4.5379582892306223,1.6350786910462221,-3.1427618177595837,-17.719084499403834,19.09435863406452,5.9606586855518833,-1.5991282893642211]} +{"lengths":[4,13,5,5,15,10,10,2,10,15],"offsets":[0,4,17,22,27,42,52,62,64,74],"input":[-9.116728724911809,-4.8596726823598146,3.4812678024172783,9.668060727417469,-8.9032003656029701,3.9114638883620501,-0.026319427415728569,-2.3505385220050812,-5.5008794739842415,6.7187159508466721,1.4591167215257883,3.3748283609747887,0.74036757461726665,3.3579106442630291,-3.5956973303109407,7.115019578486681,2.1341895684599876,9.3241720646619797,-8.6399579886347055,8.2260956522077322,-4.010230703279376,0.05261685699224472,4.3315941374748945,1.1027806997299194,-5.564692746847868,-5.7909615617245436,-8.6909349635243416,-8.5439217090606689,2.3078472074121237,7.9881112929433584,-3.8133587222546339,8.8800034765154123,6.2185775488615036,-4.3670093547552824,3.6738187074661255,5.8711233921349049,-4.0290241781622171,4.1906843520700932,-7.1679836977273226,7.6980144530534744,0.52905097603797913,-8.2401633262634277,7.5749892555177212,-7.1554449666291475,-1.5635318774729967,1.7198013328015804,4.7010921128094196,-8.7447449564933777,7.0715260319411755,-8.8618475571274757,-1.0718837380409241,4.8500846140086651,-4.6277761366218328,0.96651383675634861,4.1981401853263378,-1.8577941041439772,-3.9454446267336607,8.9122058637440205,7.4440999515354633,-7.0119780208915472,9.685426251962781,2.9591707978397608,-5.2162992861121893,9.6579357422888279,0.92617449350655079,6.2147978693246841,-7.8920833580195904,-2.2449817415326834,8.5919307451695204,4.5801795646548271,-0.92194274067878723,4.9084284529089928,-4.0428752824664116,-8.6048257909715176,-1.3070579431951046,-7.7227832470089197,3.1819853372871876,-0.37233305163681507,2.1984764840453863,9.7943628113716841,-6.1440743599087,-3.4577368106693029,5.8174742758274078,-5.7097223773598671,-3.3039627131074667,-9.7012667916715145,-9.1909652855247259,7.446452509611845,-7.4725344125181437],"expected":[-0.8270728774368763,-12.597996527329087,14.527733409777284,-10.443848967552185,8.4349771682173014,-9.7567153511884861,8.5923802120769253,4.57425773203913,4.0866333108592272,-14.22715060271884,-6.6576554982603335,-26.372765919953665,2.8296022954701328,-8.980587583926571,-6.8431158070115705,-7.3253292347795274,-19.352006438403265,4.952695881947875,3.259831328816762,1.0747977763238268,17.574250891864249,16.746805214608187,-14.612214434891939,11.173642831905873,-9.4473745727180862,6.9614497292273327,-5.541407201183806,11.195770418271422,-14.991257708546126,-15.946231614575851,-17.300471915627686,-4.6130790288011587,-19.788622037389842,-4.3067661197842559,-5.5157193718121711,-30.002457820459789,-25.180834475904703,-12.913945229888764,18.854087307931454,19.383661310646723,-5.7544798257416492,19.640630053430741,-1.47995974868536,6.3230358066860246,-1.1461816305236983,9.6659206372041417,15.672241202115009,17.024128064244636,19.603107401239232,-11.850330015300589,-4.8679641623852099,34.904343318194151,16.722563998773694,-6.1633397371209089,8.1826596782807925,2.5224321416795537,-2.68207208227156,-32.079778889875975,12.531437445164677,-0.17263982326092409,-15.643991329488166,8.7863272521644831,4.4416364561766386,-14.874235028401017,1.5148022118955851,-16.303884263575817,-3.8387589572180141,14.638762167581284,-6.9882295533190071,11.265068834141644,-29.609707780796953,-1.6302781281256387,0.023841251436460542,-8.1923944968730211,-25.943685574457049,-6.2112734554560713,-26.110422946311445,-2.2624743686374584,8.8755320203980546,-8.2645672629549143,25.11030762650708,-12.000561912417531,-15.582412082646586,-21.114386739209294,5.5941560454209212,34.194765437856233,-13.8671250199453,18.827406514084274,-0.55489016140835545]} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/test.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/test.js index 2443949b6998..fce285b902ea 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/test.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/test.js @@ -165,7 +165,7 @@ tape( 'the function computes a forward real-valued FFT (medium sequence lengths) input = medium.input; expected = medium.expected; - ulps = 8163; + ulps = 150; for ( k = 0; k < lengths.length; k++ ) { N = lengths[ k ]; off = offsets[ k ]; @@ -207,7 +207,7 @@ tape( 'the function computes a forward real-valued FFT (large sequence lengths)' input = large.input; expected = large.expected; - ulps = 40987; + ulps = 1800; for ( k = 0; k < lengths.length; k++ ) { N = lengths[ k ]; off = offsets[ k ]; From fa5a56ae7ba2bb42d91d3f34bcbe280e928ff362 Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Sun, 31 May 2026 16:11:24 +0530 Subject: [PATCH 16/19] refactor: return the input array and use Collection --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: na - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: passed - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../@stdlib/fft/base/fftpack/rfftf/lib/main.js | 10 ++++++---- .../@stdlib/fft/base/fftpack/rfftf/lib/radf2.js | 6 +++--- .../@stdlib/fft/base/fftpack/rfftf/lib/radf3.js | 8 ++++---- .../@stdlib/fft/base/fftpack/rfftf/lib/radf4.js | 10 +++++----- .../@stdlib/fft/base/fftpack/rfftf/lib/radf5.js | 12 ++++++------ .../@stdlib/fft/base/fftpack/rfftf/lib/radfg.js | 12 ++++++------ .../@stdlib/fft/base/fftpack/rfftf/lib/rfftf1.js | 8 ++++---- 7 files changed, 34 insertions(+), 32 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js index 7383a0611504..1dbfbd084cfb 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/main.js @@ -69,13 +69,13 @@ var rfftf1 = require( './rfftf1.js' ); * Computes the forward real-valued fast Fourier transform (FFT). * * @param {NonNegativeInteger} N - length of the sequence to transform -* @param {Float64Array} r - input array containing the sequence to transform +* @param {Collection} r - input array * @param {integer} strideR - stride length for `r` * @param {NonNegativeInteger} offsetR - starting index for `r` -* @param {Float64Array} workspace - workspace array containing pre-computed values +* @param {Collection} workspace - workspace array containing pre-computed values * @param {integer} strideW - stride length for `workspace` * @param {NonNegativeInteger} offsetW - starting index for `workspace` -* @returns {void} +* @returns {Collection} input array * * @example * var Float64Array = require( '@stdlib/array/float64' ); @@ -97,7 +97,7 @@ function rfftf( N, r, strideR, offsetR, workspace, strideW, offsetW ) { // When a sub-sequence is a single data point, the FFT is the identity, so no transformation necessary... if ( N === 1 ) { - return; + return r; } // Resolve the starting indices for storing twiddle factors and factorization results: @@ -105,6 +105,8 @@ function rfftf( N, r, strideR, offsetR, workspace, strideW, offsetW ) { offsetF = offsetT + ( N * strideW ); // index offset for factors describing the sub-transforms rfftf1( N, r, strideR, offsetR, workspace, strideW, offsetW, workspace, strideW, offsetT, workspace, strideW, offsetF ); // eslint-disable-line max-len + + return r; } diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js index d7ac34b18d32..7e7871ca0ebf 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf2.js @@ -226,13 +226,13 @@ function optr( i, j, k, M, stride, offset ) { * @private * @param {NonNegativeInteger} M - number of elements in each sub-sequence to be transformed * @param {NonNegativeInteger} L - number of sub-sequences to be transformed -* @param {Float64Array} cc - input array containing the sub-sequences to be transformed +* @param {Collection} cc - input array containing the sub-sequences to be transformed * @param {integer} sc - stride length for `cc` * @param {NonNegativeInteger} oc - index offset for `cc` -* @param {Float64Array} out - output array containing transformed sub-sequences +* @param {Collection} out - output array containing transformed sub-sequences * @param {integer} so - stride length for `out` * @param {NonNegativeInteger} oo - index offset for `out` -* @param {Float64Array} twiddles - array containing twiddle factors +* @param {Collection} twiddles - array containing twiddle factors * @param {integer} st - stride length for `twiddles` * @param {NonNegativeInteger} ot - index offset for `twiddles` * @returns {void} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js index 2f2994203a2e..e0361c31120c 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf3.js @@ -237,16 +237,16 @@ function optr( i, j, k, M, stride, offset ) { * @private * @param {NonNegativeInteger} M - number of elements in each sub-sequence to be transformed * @param {NonNegativeInteger} L - number of sub-sequences to be transformed -* @param {Float64Array} cc - input array containing the sub-sequences to be transformed +* @param {Collection} cc - input array containing the sub-sequences to be transformed * @param {integer} sc - stride length for `cc` * @param {NonNegativeInteger} oc - index offset for `cc` -* @param {Float64Array} out - output array containing transformed sub-sequences +* @param {Collection} out - output array containing transformed sub-sequences * @param {integer} so - stride length for `out` * @param {NonNegativeInteger} oo - index offset for `out` -* @param {Float64Array} twiddles1 - first array containing twiddle factors +* @param {Collection} twiddles1 - first array containing twiddle factors * @param {integer} st1 - stride length for `twiddles1` * @param {NonNegativeInteger} ot1 - index offset for `twiddles1` -* @param {Float64Array} twiddles2 - second array containing twiddle factors +* @param {Collection} twiddles2 - second array containing twiddle factors * @param {integer} st2 - stride length for `twiddles2` * @param {NonNegativeInteger} ot2 - index offset for `twiddles2` * @returns {void} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf4.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf4.js index d657a5cf8005..65fa22ef79c3 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf4.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf4.js @@ -235,19 +235,19 @@ function optr( i, j, k, M, stride, offset ) { * @private * @param {NonNegativeInteger} M - number of elements in each sub-sequence to be transformed * @param {NonNegativeInteger} L - number of sub-sequences to be transformed -* @param {Float64Array} cc - input array containing the sub-sequences to be transformed +* @param {Collection} cc - input array containing the sub-sequences to be transformed * @param {integer} sc - stride length for `cc` * @param {NonNegativeInteger} oc - index offset for `cc` -* @param {Float64Array} out - output array containing transformed sub-sequences +* @param {Collection} out - output array containing transformed sub-sequences * @param {integer} so - stride length for `out` * @param {NonNegativeInteger} oo - index offset for `out` -* @param {Float64Array} twiddles1 - first array containing twiddle factors +* @param {Collection} twiddles1 - first array containing twiddle factors * @param {integer} st1 - stride length for `twiddles1` * @param {NonNegativeInteger} ot1 - index offset for `twiddles1` -* @param {Float64Array} twiddles2 - second array containing twiddle factors +* @param {Collection} twiddles2 - second array containing twiddle factors * @param {integer} st2 - stride length for `twiddles2` * @param {NonNegativeInteger} ot2 - index offset for `twiddles2` -* @param {Float64Array} twiddles3 - third array containing twiddle factors +* @param {Collection} twiddles3 - third array containing twiddle factors * @param {integer} st3 - stride length for `twiddles3` * @param {NonNegativeInteger} ot3 - index offset for `twiddles3` * @returns {void} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf5.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf5.js index b2c119e9f673..dec092981317 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf5.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radf5.js @@ -247,22 +247,22 @@ function optr( i, j, k, M, stride, offset ) { * @private * @param {NonNegativeInteger} M - number of elements in each sub-sequence to be transformed * @param {NonNegativeInteger} L - number of sub-sequences to be transformed -* @param {Float64Array} cc - input array containing the sub-sequences to be transformed +* @param {Collection} cc - input array containing the sub-sequences to be transformed * @param {integer} sc - stride length for `cc` * @param {NonNegativeInteger} oc - index offset for `cc` -* @param {Float64Array} out - output array containing transformed sub-sequences +* @param {Collection} out - output array containing transformed sub-sequences * @param {integer} so - stride length for `out` * @param {NonNegativeInteger} oo - index offset for `out` -* @param {Float64Array} twiddles1 - first array containing twiddle factors +* @param {Collection} twiddles1 - first array containing twiddle factors * @param {integer} st1 - stride length for `twiddles1` * @param {NonNegativeInteger} ot1 - index offset for `twiddles1` -* @param {Float64Array} twiddles2 - second array containing twiddle factors +* @param {Collection} twiddles2 - second array containing twiddle factors * @param {integer} st2 - stride length for `twiddles2` * @param {NonNegativeInteger} ot2 - index offset for `twiddles2` -* @param {Float64Array} twiddles3 - third array containing twiddle factors +* @param {Collection} twiddles3 - third array containing twiddle factors * @param {integer} st3 - stride length for `twiddles3` * @param {NonNegativeInteger} ot3 - index offset for `twiddles3` -* @param {Float64Array} twiddles4 - fourth array containing twiddle factors +* @param {Collection} twiddles4 - fourth array containing twiddle factors * @param {integer} st4 - stride length for `twiddles4` * @param {NonNegativeInteger} ot4 - index offset for `twiddles4` * @returns {void} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js index 890ae2120058..8e00218e2186 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/radfg.js @@ -325,22 +325,22 @@ function fptr( ik, j, ML, stride, offset ) { * @param {NonNegativeInteger} R - radix of the transform * @param {NonNegativeInteger} L - number of sub-sequences to be transformed * @param {NonNegativeInteger} ML - number of elements in each flattened sub-sequence (`M*L`) -* @param {Float64Array} cc - input array containing the sub-sequences to be transformed +* @param {Collection} cc - input array containing the sub-sequences to be transformed * @param {integer} sc - stride length for `cc` * @param {NonNegativeInteger} oc - index offset for `cc` -* @param {Float64Array} c1 - input workspace array containing intermediate sub-sequences to be transformed +* @param {Collection} c1 - input workspace array containing intermediate sub-sequences to be transformed * @param {integer} sc1 - stride length for `c1` * @param {NonNegativeInteger} oc1 - index offset for `c1` -* @param {Float64Array} c2 - flattened input workspace array containing intermediate sub-sequences +* @param {Collection} c2 - flattened input workspace array containing intermediate sub-sequences * @param {integer} sc2 - stride length for `c2` * @param {NonNegativeInteger} oc2 - index offset for `c2` -* @param {Float64Array} ch - output array containing transformed sequences +* @param {Collection} ch - output array containing transformed sequences * @param {integer} sch - stride length for `ch` * @param {NonNegativeInteger} och - index offset for `ch` -* @param {Float64Array} ch2 - flattened output workspace array containing intermediate sub-sequences +* @param {Collection} ch2 - flattened output workspace array containing intermediate sub-sequences * @param {integer} sch2 - stride length for `ch2` * @param {NonNegativeInteger} och2 - index offset for `ch2` -* @param {Float64Array} twiddles - array of twiddle factors +* @param {Collection} twiddles - array of twiddle factors * @param {integer} stw - stride length for `twiddles` * @param {NonNegativeInteger} otw - index offset for `twiddles` * @returns {void} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/rfftf1.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/rfftf1.js index 745341fa5551..01854653d35d 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/rfftf1.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/lib/rfftf1.js @@ -78,16 +78,16 @@ var radfg = require( './radfg.js' ); * * @private * @param {NonNegativeInteger} N - length of the sequence to transform -* @param {Float64Array} c - input array containing the sequence to be transformed +* @param {Collection} c - input array containing the sequence to be transformed * @param {integer} sc - stride length for `c` * @param {NonNegativeInteger} oc - starting index for `c` -* @param {Float64Array} ch - working array for intermediate results +* @param {Collection} ch - working array for intermediate results * @param {integer} sch - stride length for `ch` * @param {NonNegativeInteger} och - starting index for `ch` -* @param {Float64Array} wa - workspace array for storing twiddle factors +* @param {Collection} wa - workspace array for storing twiddle factors * @param {integer} swa - stride length for `wa` * @param {NonNegativeInteger} owa - starting index for `wa` -* @param {Int32Array} ifac - workspace array for storing factorization results +* @param {Collection} ifac - workspace array for storing factorization results * @param {integer} si - stride length for `ifac` * @param {NonNegativeInteger} oi - starting index for `ifac` * @returns {void} From 3ad34a01322ed8bf675e44dcb79678dc47dc2648 Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Sun, 31 May 2026 16:18:29 +0530 Subject: [PATCH 17/19] docs: add docs, update README and examples --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: passed - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: passed - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: passed - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: passed - task: lint_license_headers status: passed --- --- .../@stdlib/fft/base/fftpack/rfftf/README.md | 26 +-- .../fft/base/fftpack/rfftf/docs/repl.txt | 54 +++++++ .../base/fftpack/rfftf/docs/types/index.d.ts | 56 +++++++ .../fft/base/fftpack/rfftf/docs/types/test.ts | 148 ++++++++++++++++++ .../fft/base/fftpack/rfftf/examples/index.js | 17 +- 5 files changed, 283 insertions(+), 18 deletions(-) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/docs/repl.txt create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/docs/types/index.d.ts create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/docs/types/test.ts diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/README.md b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/README.md index 9e0fa4cce33b..60f25003f647 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/README.md +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/README.md @@ -57,14 +57,13 @@ var r = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] ); rfftf( N, r, 1, 0, workspace, 1, 0 ); -var out = r.slice( 0, N ); -// returns [ 10.0, -2.0, 2.0, -2.0 ] +// r => [ 10.0, -2.0, 2.0, -2.0 ] ``` The function accepts the following arguments: - **N**: length of the sequence to transform. -- **r**: input array containing the sequence to transform. +- **r**: input array. - **strideR**: stride length for `r`. - **offsetR**: starting index for `r`. - **workspace**: workspace array containing pre-computed values. @@ -83,6 +82,8 @@ The function accepts the following arguments: - Before calling this function, initialize the workspace by calling [`rffti`][@stdlib/fft/base/fftpack/rffti] with the same sequence length and workspace layout. +- The function performs the transform in-place and returns the same input array reference. + - For `N = 4`, the output ```text @@ -91,7 +92,7 @@ The function accepts the following arguments: corresponds to a zero-frequency term `10.0`, a complex coefficient `-2.0 + 2.0i` at frequency `1`, and a Nyquist term `-2.0`. -- If `N` equals `1`, the function returns early without modifying the input, as a single data point is its own Fourier transform. +- If `N` equals `1`, the function returns early without modifying the input, as a single data point is its own Fourier transform. In that case, the function still returns the same input array reference. @@ -104,21 +105,24 @@ The function accepts the following arguments: ```javascript -var Float64Array = require( '@stdlib/array/float64' ); +var zeros = require( '@stdlib/array/zeros' ); +var discreteUniform = require( '@stdlib/random/array/discrete-uniform' ); var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); var rfftf = require( '@stdlib/fft/base/fftpack/rfftf' ); var N = 4; -var r = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] ); -var workspace = new Float64Array( ( 2*N ) + 34 ); +var opts = { + 'dtype': 'float64' +}; +var r = discreteUniform( N, -10, 10, opts ); +var workspace = zeros( ( 2*N ) + 34 ); -rffti( N, workspace, 1, 0 ); - -console.log( 'Input sequence: %s', r ); +console.log( r ); +rffti( N, workspace, 1, 0 ); rfftf( N, r, 1, 0, workspace, 1, 0 ); -console.log( 'Packed output: %s', r.slice( 0, N ) ); +console.log( r ); ``` diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/docs/repl.txt b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/docs/repl.txt new file mode 100644 index 000000000000..c117bdc2cd0f --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/docs/repl.txt @@ -0,0 +1,54 @@ + +{{alias}}( N, r, strideR, offsetR, workspace, strideW, offsetW ) + Computes the forward real-valued fast Fourier transform (FFT). + + Before calling this function, initialize the workspace by calling + `@stdlib/fft/base/fftpack/rffti` with the same sequence length and workspace + layout. + + Parameters + ---------- + N: integer + Length of the sequence to transform. + + r: ArrayLikeObject + Input array. + + strideR: integer + Stride length for `r`. + + offsetR: integer + Starting index for `r`. + + workspace: ArrayLikeObject + Workspace array containing pre-computed values. + + strideW: integer + Stride length for `workspace`. + + offsetW: integer + Starting index for `workspace`. + + Returns + ------- + r: ArrayLikeObject + Input array. + + Examples + -------- + > var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); + > var N = 4; + > var r = new {{alias:@stdlib/array/float64}}( [ 1.0, 2.0, 3.0, 4.0 ] ); + > var workspace = new {{alias:@stdlib/array/float64}}( ( 2*N ) + 34 ); + > rffti( N, workspace, 1, 0 ) + + > var out = {{alias}}( N, r, 1, 0, workspace, 1, 0 ) + + > var bool = ( out === r ) + true + > r + [ 10.0, -2.0, 2.0, -2.0 ] + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/docs/types/index.d.ts b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/docs/types/index.d.ts new file mode 100644 index 000000000000..a95ed2ed1a44 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/docs/types/index.d.ts @@ -0,0 +1,56 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 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. +*/ + +// TypeScript Version: 4.1 + +/// + +import { Collection } from '@stdlib/types/array'; + +/** +* Computes the forward real-valued fast Fourier transform (FFT). +* +* @param N - length of the sequence to transform +* @param r - input array +* @param strideR - stride length for `r` +* @param offsetR - starting index for `r` +* @param workspace - workspace array containing pre-computed values +* @param strideW - stride length for `workspace` +* @param offsetW - starting index for `workspace` +* @returns input array +* +* @example +* var Float64Array = require( '@stdlib/array/float64' ); +* var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); +* +* var N = 4; +* +* var workspace = new Float64Array( ( 2*N ) + 34 ); +* rffti( N, workspace, 1, 0 ); +* +* var r = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] ); +* +* rfftf( N, r, 1, 0, workspace, 1, 0 ); +* // r => [ 10.0, -2.0, 2.0, -2.0 ] +*/ +declare function rfftf>( N: number, r: T, strideR: number, offsetR: number, workspace: Collection, strideW: number, offsetW: number ): T; + + +// EXPORTS // + +export = rfftf; diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/docs/types/test.ts b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/docs/types/test.ts new file mode 100644 index 000000000000..135116bb4667 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/docs/types/test.ts @@ -0,0 +1,148 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2026 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. +*/ + +import rfftf = require( './index' ); + + +// TESTS // + +// The function returns a collection... +{ + const r = new Float64Array( 4 ); + const workspace = new Float64Array( ( 2*4 ) + 34 ); + + rfftf( 4, r, 1, 0, workspace, 1, 0 ); // $ExpectType Float64Array +} + +// The compiler throws an error if the function is provided a first argument which is not a number... +{ + const r = new Float64Array( 4 ); + const workspace = new Float64Array( ( 2*4 ) + 34 ); + + rfftf( '4', r, 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( true, r, 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( false, r, 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( null, r, 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( void 0, r, 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( [], r, 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( {}, r, 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( ( x: number ): number => x, r, 1, 0, workspace, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a second argument which is not a collection... +{ + const workspace = new Float64Array( ( 2*4 ) + 34 ); + + rfftf( 4, '4', 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, 4, 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, true, 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, false, 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, null, 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, void 0, 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, {}, 1, 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, ( x: number ): number => x, 1, 0, workspace, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a third argument which is not a number... +{ + const r = new Float64Array( 4 ); + const workspace = new Float64Array( ( 2*4 ) + 34 ); + + rfftf( 4, r, '1', 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, true, 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, false, 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, null, 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, void 0, 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, [], 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, {}, 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, ( x: number ): number => x, 0, workspace, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a fourth argument which is not a number... +{ + const r = new Float64Array( 4 ); + const workspace = new Float64Array( ( 2*4 ) + 34 ); + + rfftf( 4, r, 1, '0', workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, true, workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, false, workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, null, workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, void 0, workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, [], workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, {}, workspace, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, ( x: number ): number => x, workspace, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a fifth argument which is not a collection... +{ + const r = new Float64Array( 4 ); + + rfftf( 4, r, 1, 0, '42', 1, 0 ); // $ExpectError + rfftf( 4, r, 1, 0, 42, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, 0, true, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, 0, false, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, 0, null, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, 0, void 0, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, 0, {}, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, 0, ( x: number ): number => x, 1, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a sixth argument which is not a number... +{ + const r = new Float64Array( 4 ); + const workspace = new Float64Array( ( 2*4 ) + 34 ); + + rfftf( 4, r, 1, 0, workspace, '1', 0 ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, true, 0 ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, false, 0 ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, null, 0 ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, void 0, 0 ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, [], 0 ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, {}, 0 ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, ( x: number ): number => x, 0 ); // $ExpectError +} + +// The compiler throws an error if the function is provided a seventh argument which is not a number... +{ + const r = new Float64Array( 4 ); + const workspace = new Float64Array( ( 2*4 ) + 34 ); + + rfftf( 4, r, 1, 0, workspace, 1, '0' ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, 1, true ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, 1, false ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, 1, null ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, 1, void 0 ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, 1, [] ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, 1, {} ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, 1, ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided an unsupported number of arguments... +{ + const r = new Float64Array( 4 ); + const workspace = new Float64Array( ( 2*4 ) + 34 ); + + rfftf(); // $ExpectError + rfftf( 4 ); // $ExpectError + rfftf( 4, r ); // $ExpectError + rfftf( 4, r, 1 ); // $ExpectError + rfftf( 4, r, 1, 0 ); // $ExpectError + rfftf( 4, r, 1, 0, workspace ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, 1 ); // $ExpectError + rfftf( 4, r, 1, 0, workspace, 1, 0, 123 ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/examples/index.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/examples/index.js index a9561fc6155b..b2b4f1218523 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/examples/index.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/examples/index.js @@ -18,18 +18,21 @@ 'use strict'; -var Float64Array = require( '@stdlib/array/float64' ); +var zeros = require( '@stdlib/array/zeros' ); +var discreteUniform = require( '@stdlib/random/array/discrete-uniform' ); var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); var rfftf = require( './../lib' ); var N = 4; -var r = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] ); -var workspace = new Float64Array( ( 2*N ) + 34 ); +var opts = { + 'dtype': 'float64' +}; +var r = discreteUniform( N, -10, 10, opts ); +var workspace = zeros( ( 2*N ) + 34 ); -rffti( N, workspace, 1, 0 ); - -console.log( 'Input sequence: %s', r ); +console.log( r ); +rffti( N, workspace, 1, 0 ); rfftf( N, r, 1, 0, workspace, 1, 0 ); -console.log( 'Packed output: %s', r.slice( 0, N ) ); +console.log( r ); From d4af2f606739e8e14acdbcbca6fadce7d73d4002 Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Sun, 31 May 2026 16:20:26 +0530 Subject: [PATCH 18/19] bench: add benchmark, update package.json --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: na - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: passed - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: na - task: lint_javascript_benchmarks status: passed - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../base/fftpack/rfftf/benchmark/benchmark.js | 138 ++++++++++++++++++ .../fft/base/fftpack/rfftf/package.json | 3 + 2 files changed, 141 insertions(+) create mode 100644 lib/node_modules/@stdlib/fft/base/fftpack/rfftf/benchmark/benchmark.js diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/benchmark/benchmark.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/benchmark/benchmark.js new file mode 100644 index 000000000000..ec2747300307 --- /dev/null +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/benchmark/benchmark.js @@ -0,0 +1,138 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2026 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. +*/ + +'use strict'; + +// MODULES // + +var bench = require( '@stdlib/bench' ); +var slice = require( '@stdlib/array/slice' ); +var uniform = require( '@stdlib/random/array/uniform' ); +var floor = require( '@stdlib/math/base/special/floor' ); +var pow = require( '@stdlib/math/base/special/pow' ); +var format = require( '@stdlib/string/format' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var Float64Array = require( '@stdlib/array/float64' ); +var dcopy = require( '@stdlib/blas/base/dcopy' ); +var rffti = require( '@stdlib/fft/base/fftpack/rffti' ); +var pkg = require( './../package.json' ).name; +var rfftf = require( './../lib' ); + + +// VARIABLES // + +var options = { + 'dtype': 'float64' +}; + + +// FUNCTIONS // + +/** +* Creates a benchmark function. +* +* @private +* @param {PositiveInteger} iter - number of iterations +* @param {PositiveInteger} N - sequence length +* @returns {Function} benchmark function +*/ +function createBenchmark( iter, N ) { + var workspace = new Float64Array( ( 2*N ) + 34 ); + var x; + var i; + + x = []; + for ( i = 0; i < iter; i++ ) { + x.push( uniform( N, -100.0, 100.0, options ) ); + } + + rffti( N, workspace, 1, 0 ); + return benchmark; + + /** + * Benchmark function. + * + * @private + * @param {Benchmark} b - benchmark instance + */ + function benchmark( b ) { + var xc; + var y; + var i; + + xc = slice( x ); + for ( i = 0; i < iter; i++ ) { + xc[ i ] = dcopy( N, x[ i ], 1, new Float64Array( N ), 1 ); + } + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = rfftf( N, xc[ i ], 1, 0, workspace, 1, 0 ); + if ( isnan( y[ i%N ] ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( y[ i%N ] ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); + } +} + + +// MAIN // + +/** +* Main execution sequence. +* +* @private +*/ +function main() { + var lengths; + var opts; + var iter; + var N; + var f; + var i; + + lengths = [ + 8, + 16, + 32, + 64, + 128, + 256, + 512, + 1024 + ]; + + iter = 1e6; + + for ( i = 0; i < lengths.length; i++ ) { + N = lengths[ i ]; + f = createBenchmark( iter, N ); + opts = { + 'iterations': iter + }; + bench( format( '%s:N=%d', pkg, N ), opts, f ); + iter = floor( pow( iter, 3.0/4.0 ) ); + } +} + +main(); diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/package.json b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/package.json index f0617e07afbb..1ef3db1b49a7 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/package.json +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/package.json @@ -15,10 +15,13 @@ ], "main": "./lib", "directories": { + "benchmark": "./benchmark", + "doc": "./docs", "example": "./examples", "lib": "./lib", "test": "./test" }, + "types": "./docs/types", "scripts": {}, "homepage": "https://github.com/stdlib-js/stdlib", "repository": { From 88aacde32eb914c26ff4e8907750871a1504509d Mon Sep 17 00:00:00 2001 From: Gunj Joshi Date: Sun, 31 May 2026 16:43:03 +0530 Subject: [PATCH 19/19] test: reduce tolerance, add a test --- type: pre_commit_static_analysis_report description: Results of running static analysis checks when committing changes. report: - task: lint_filenames status: passed - task: lint_editorconfig status: passed - task: lint_markdown_pkg_readmes status: na - task: lint_markdown_docs status: na - task: lint_markdown status: na - task: lint_package_json status: na - task: lint_repl_help status: na - task: lint_javascript_src status: na - task: lint_javascript_cli status: na - task: lint_javascript_examples status: na - task: lint_javascript_tests status: passed - task: lint_javascript_benchmarks status: na - task: lint_python status: na - task: lint_r status: na - task: lint_c_src status: na - task: lint_c_examples status: na - task: lint_c_benchmarks status: na - task: lint_c_tests_fixtures status: na - task: lint_shell status: na - task: lint_typescript_declarations status: passed - task: lint_typescript_tests status: na - task: lint_license_headers status: passed --- --- .../fft/base/fftpack/rfftf/test/test.js | 27 ++++++++++++++++--- 1 file changed, 23 insertions(+), 4 deletions(-) diff --git a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/test.js b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/test.js index fce285b902ea..344e70a53fef 100644 --- a/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/test.js +++ b/lib/node_modules/@stdlib/fft/base/fftpack/rfftf/test/test.js @@ -47,6 +47,23 @@ tape( 'the function has an arity of 7', function test( t ) { t.end(); }); +tape( 'the function returns a reference to the input array', function test( t ) { + var workspace; + var out; + var N; + var r; + + N = 4; + r = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] ); + workspace = new Float64Array( ( 2 * N ) + 34 ); + + rffti( N, workspace, 1, 0 ); + out = rfftf( N, r, 1, 0, workspace, 1, 0 ); + + t.strictEqual( out, r, 'same reference' ); + t.end(); +}); + tape( 'the function returns all zeros for a zero sequence', function test( t ) { var workspace; var expected; @@ -123,7 +140,7 @@ tape( 'the function computes a forward real-valued FFT (small sequence lengths)' input = small.input; expected = small.expected; - ulps = 32; + ulps = 20; for ( k = 0; k < lengths.length; k++ ) { N = lengths[ k ]; off = offsets[ k ]; @@ -165,7 +182,7 @@ tape( 'the function computes a forward real-valued FFT (medium sequence lengths) input = medium.input; expected = medium.expected; - ulps = 150; + ulps = 130; for ( k = 0; k < lengths.length; k++ ) { N = lengths[ k ]; off = offsets[ k ]; @@ -207,7 +224,7 @@ tape( 'the function computes a forward real-valued FFT (large sequence lengths)' input = large.input; expected = large.expected; - ulps = 1800; + ulps = 800; for ( k = 0; k < lengths.length; k++ ) { N = lengths[ k ]; off = offsets[ k ]; @@ -231,6 +248,7 @@ tape( 'the function computes a forward real-valued FFT (large sequence lengths)' tape( 'the function leaves a length-one sequence unchanged', function test( t ) { var workspace; + var out; var N; var r; @@ -239,7 +257,8 @@ tape( 'the function leaves a length-one sequence unchanged', function test( t ) workspace = new Float64Array( ( 2 * N ) + 34 ); rffti( N, workspace, 1, 0 ); - rfftf( N, r, 1, 0, workspace, 1, 0 ); + out = rfftf( N, r, 1, 0, workspace, 1, 0 ); + t.strictEqual( out, r, 'same reference' ); t.strictEqual( r[ 0 ], 5.0, 'returns expected value' ); t.end(); });