feat: FDCT

.github/workflows/cmake-single-platform.yml

@@ -17,7 +17,7 @@ jobs:
     # The CMake configure and build commands are platform agnostic and should work equally well on Windows or Mac.
     # You can convert this to a matrix build if you need cross-platform coverage.
     # See: https://docs.github.com/en/free-pro-team@latest/actions/learn-github-actions/managing-complex-workflows#using-a-build-matrix
-    runs-on: ubuntu-latest
+    runs-on: ubuntu-24.04
     strategy:
       fail-fast: false
 
@@ -29,7 +29,8 @@ jobs:
         python-version: ${{ matrix.python-version }}
     - name: Install dependencies
       run: |
-        sudo apt install python3-pybind11
+        sudo apt -y update
+        sudo apt -y install python3-pybind11 libfftw3-dev cmake python3-dev
         python -m pip install --upgrade pip
         python -m pip install pytest
         if [ -f requirements.txt ]; then pip install -r requirements.txt; fi

.gitignore

@@ -1 +1,6 @@
 compile_commands.json
+build/
+.vscode/
+.cache/
+*.so
+

CMakeLists.txt

@@ -8,7 +8,16 @@ include_directories(${PYTHON_INCLUDE_DIRS})
 # Find Pybind11
 find_package(pybind11 REQUIRED)
 
-pybind11_add_module(fdct src/fdct.cpp)
+find_package(PkgConfig REQUIRED)
+pkg_search_module(FFTW REQUIRED fftw3 IMPORTED_TARGET)
+include_directories(PkgConfig::FFTW)
+link_libraries(PkgConfig::FFTW)
+
+pybind11_add_module(fdct 
+    src/fdct_module.cpp
+    src/fft.cpp
+    src/fdct_inner.cpp
+)
 
 # Link the module with Python
 target_link_libraries(fdct PRIVATE ${PYTHON_LIBRARIES})

ref/FastDctFft.hpp

@@ -0,0 +1,36 @@
+/* 
+ * Fast discrete cosine transform algorithms (C++)
+ * 
+ * Copyright (c) 2017 Project Nayuki. (MIT License)
+ * https://www.nayuki.io/page/fast-discrete-cosine-transform-algorithms
+ * 
+ * Permission is hereby granted, free of charge, to any person obtaining a copy of
+ * this software and associated documentation files (the "Software"), to deal in
+ * the Software without restriction, including without limitation the rights to
+ * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
+ * the Software, and to permit persons to whom the Software is furnished to do so,
+ * subject to the following conditions:
+ * - The above copyright notice and this permission notice shall be included in
+ *   all copies or substantial portions of the Software.
+ * - The 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
+ *   authors or copyright holders be liable for any claim, 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 in the
+ *   Software.
+ */
+
+#pragma once
+
+#include <vector>
+
+
+namespace FastDctFft {
+
+	void transform(std::vector<double> &vec);
+
+	void inverseTransform(std::vector<double> &vec);
+
+}
+

ref/FastDctFtt.cpp

@@ -0,0 +1,75 @@
+/* 
+ * Fast discrete cosine transform algorithms (C++)
+ * 
+ * Copyright (c) 2017 Project Nayuki. (MIT License)
+ * https://www.nayuki.io/page/fast-discrete-cosine-transform-algorithms
+ * 
+ * Permission is hereby granted, free of charge, to any person obtaining a copy of
+ * this software and associated documentation files (the "Software"), to deal in
+ * the Software without restriction, including without limitation the rights to
+ * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
+ * the Software, and to permit persons to whom the Software is furnished to do so,
+ * subject to the following conditions:
+ * - The above copyright notice and this permission notice shall be included in
+ *   all copies or substantial portions of the Software.
+ * - The 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
+ *   authors or copyright holders be liable for any claim, 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 in the
+ *   Software.
+ */
+
+#include <algorithm>
+#include <cmath>
+#include <cstddef>
+#include "FastDctFft.hpp"
+#include "FftRealPair.hpp"
+
+using std::size_t;
+using std::vector;
+
+
+// DCT type II, unscaled
+void FastDctFft::transform(vector<double> &vec) {
+	size_t len = vec.size();
+	size_t halfLen = len / 2;
+	vector<double> real(len);
+	for (size_t i = 0; i < halfLen; i++) {
+		real.at(i) = vec.at(i * 2);
+		real.at(len - 1 - i) = vec.at(i * 2 + 1);
+	}
+	if (len % 2 == 1)
+		real.at(halfLen) = vec.at(len - 1);
+	std::fill(vec.begin(), vec.end(), 0.0);
+	Fft::transform(real, vec);
+	for (size_t i = 0; i < len; i++) {
+		double temp = i * M_PI / (len * 2);
+		vec.at(i) = real.at(i) * std::cos(temp) + vec.at(i) * std::sin(temp);
+	}
+}
+
+
+// DCT type III, unscaled
+void FastDctFft::inverseTransform(vector<double> &vec) {
+	size_t len = vec.size();
+	if (len > 0)
+		vec.at(0) /= 2;
+	vector<double> real(len);
+	for (size_t i = 0; i < len; i++) {
+		double temp = i * M_PI / (len * 2);
+		real.at(i) = vec.at(i) * std::cos(temp);
+		vec.at(i) *= -std::sin(temp);
+	}
+	Fft::transform(real, vec);
+
+	size_t halfLen = len / 2;
+	for (size_t i = 0; i < halfLen; i++) {
+		vec.at(i * 2 + 0) = real.at(i);
+		vec.at(i * 2 + 1) = real.at(len - 1 - i);
+	}
+	if (len % 2 == 1)
+		vec.at(len - 1) = real.at(halfLen);
+}
+

ref/FftComplex.cpp

@@ -0,0 +1,149 @@
+/* 
+ * Free FFT and convolution (C++)
+ * 
+ * Copyright (c) 2021 Project Nayuki. (MIT License)
+ * https://www.nayuki.io/page/free-small-fft-in-multiple-languages
+ * 
+ * Permission is hereby granted, free of charge, to any person obtaining a copy of
+ * this software and associated documentation files (the "Software"), to deal in
+ * the Software without restriction, including without limitation the rights to
+ * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
+ * the Software, and to permit persons to whom the Software is furnished to do so,
+ * subject to the following conditions:
+ * - The above copyright notice and this permission notice shall be included in
+ *   all copies or substantial portions of the Software.
+ * - The 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
+ *   authors or copyright holders be liable for any claim, 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 in the
+ *   Software.
+ */
+
+#include <cstddef>
+#include <cstdint>
+#include <stdexcept>
+#include <utility>
+#include "FftComplex.hpp"
+
+using std::complex;
+using std::size_t;
+using std::uintmax_t;
+using std::vector;
+
+
+// Private function prototypes
+static size_t reverseBits(size_t val, int width);
+
+
+void Fft::transform(vector<complex<double> > &vec, bool inverse) {
+	size_t n = vec.size();
+	if (n == 0)
+		return;
+	else if ((n & (n - 1)) == 0)  // Is power of 2
+		transformRadix2(vec, inverse);
+	else  // More complicated algorithm for arbitrary sizes
+		transformBluestein(vec, inverse);
+}
+
+
+void Fft::transformRadix2(vector<complex<double> > &vec, bool inverse) {
+	// Length variables
+	size_t n = vec.size();
+	int levels = 0;  // Compute levels = floor(log2(n))
+	for (size_t temp = n; temp > 1U; temp >>= 1)
+		levels++;
+	if (static_cast<size_t>(1U) << levels != n)
+		throw std::domain_error("Length is not a power of 2");
+
+	// Trigonometric table
+	vector<complex<double> > expTable(n / 2);
+	for (size_t i = 0; i < n / 2; i++)
+		expTable[i] = std::polar(1.0, (inverse ? 2 : -2) * M_PI * i / n);
+
+	// Bit-reversed addressing permutation
+	for (size_t i = 0; i < n; i++) {
+		size_t j = reverseBits(i, levels);
+		if (j > i)
+			std::swap(vec[i], vec[j]);
+	}
+
+	// Cooley-Tukey decimation-in-time radix-2 FFT
+	for (size_t size = 2; size <= n; size *= 2) {
+		size_t halfsize = size / 2;
+		size_t tablestep = n / size;
+		for (size_t i = 0; i < n; i += size) {
+			for (size_t j = i, k = 0; j < i + halfsize; j++, k += tablestep) {
+				complex<double> temp = vec[j + halfsize] * expTable[k];
+				vec[j + halfsize] = vec[j] - temp;
+				vec[j] += temp;
+			}
+		}
+		if (size == n)  // Prevent overflow in 'size *= 2'
+			break;
+	}
+}
+
+
+void Fft::transformBluestein(vector<complex<double> > &vec, bool inverse) {
+	// Find a power-of-2 convolution length m such that m >= n * 2 + 1
+	size_t n = vec.size();
+	size_t m = 1;
+	while (m / 2 <= n) {
+		if (m > SIZE_MAX / 2)
+			throw std::length_error("Vector too large");
+		m *= 2;
+	}
+
+	// Trigonometric table
+	vector<complex<double> > expTable(n);
+	for (size_t i = 0; i < n; i++) {
+		uintmax_t temp = static_cast<uintmax_t>(i) * i;
+		temp %= static_cast<uintmax_t>(n) * 2;
+		double angle = (inverse ? M_PI : -M_PI) * temp / n;
+		expTable[i] = std::polar(1.0, angle);
+	}
+
+	// Temporary vectors and preprocessing
+	vector<complex<double> > avec(m);
+	for (size_t i = 0; i < n; i++)
+		avec[i] = vec[i] * expTable[i];
+	vector<complex<double> > bvec(m);
+	bvec[0] = expTable[0];
+	for (size_t i = 1; i < n; i++)
+		bvec[i] = bvec[m - i] = std::conj(expTable[i]);
+
+	// Convolution
+	vector<complex<double> > cvec = convolve(std::move(avec), std::move(bvec));
+
+	// Postprocessing
+	for (size_t i = 0; i < n; i++)
+		vec[i] = cvec[i] * expTable[i];
+}
+
+
+vector<complex<double> > Fft::convolve(
+		vector<complex<double> > xvec,
+		vector<complex<double> > yvec) {
+
+	size_t n = xvec.size();
+	if (n != yvec.size())
+		throw std::domain_error("Mismatched lengths");
+	transform(xvec, false);
+	transform(yvec, false);
+	for (size_t i = 0; i < n; i++)
+		xvec[i] *= yvec[i];
+	transform(xvec, true);
+	for (size_t i = 0; i < n; i++)  // Scaling (because this FFT implementation omits it)
+		xvec[i] /= static_cast<double>(n);
+	return xvec;
+}
+
+
+static size_t reverseBits(size_t val, int width) {
+	size_t result = 0;
+	for (int i = 0; i < width; i++, val >>= 1)
+		result = (result << 1) | (val & 1U);
+	return result;
+}

ref/FftComplex.hpp

@@ -0,0 +1,61 @@
+/* 
+ * Free FFT and convolution (C++)
+ * 
+ * Copyright (c) 2021 Project Nayuki. (MIT License)
+ * https://www.nayuki.io/page/free-small-fft-in-multiple-languages
+ * 
+ * Permission is hereby granted, free of charge, to any person obtaining a copy of
+ * this software and associated documentation files (the "Software"), to deal in
+ * the Software without restriction, including without limitation the rights to
+ * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
+ * the Software, and to permit persons to whom the Software is furnished to do so,
+ * subject to the following conditions:
+ * - The above copyright notice and this permission notice shall be included in
+ *   all copies or substantial portions of the Software.
+ * - The 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
+ *   authors or copyright holders be liable for any claim, 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 in the
+ *   Software.
+ */
+
+#pragma once
+
+#include <complex>
+#include <vector>
+using Complex = std::complex<double>;
+
+namespace Fft {
+
+	/* 
+	 * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
+	 * The vector can have any length. This is a wrapper function. The inverse transform does not perform scaling, so it is not a true inverse.
+	 */
+	void transform(std::vector<std::complex<double> > &vec, bool inverse);
+
+
+	/* 
+	 * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
+	 * The vector's length must be a power of 2. Uses the Cooley-Tukey decimation-in-time radix-2 algorithm.
+	 */
+	void transformRadix2(std::vector<std::complex<double> > &vec, bool inverse);
+
+
+	/* 
+	 * Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
+	 * The vector can have any length. This requires the convolution function, which in turn requires the radix-2 FFT function.
+	 * Uses Bluestein's chirp z-transform algorithm.
+	 */
+	void transformBluestein(std::vector<std::complex<double> > &vec, bool inverse);
+
+
+	/* 
+	 * Computes the circular convolution of the given complex vectors. Each vector's length must be the same.
+	 */
+	std::vector<std::complex<double> > convolve(
+		std::vector<std::complex<double> > xvec,
+		std::vector<std::complex<double> > yvec);
+
+}