Chris@32: /* 
Chris@32:  * Free FFT and convolution (C)
Chris@32:  * 
Chris@32:  * Copyright (c) 2014 Project Nayuki
Chris@32:  * http://www.nayuki.io/page/free-small-fft-in-multiple-languages
Chris@32:  * 
Chris@32:  * (MIT License)
Chris@32:  * Permission is hereby granted, free of charge, to any person obtaining a copy of
Chris@32:  * this software and associated documentation files (the "Software"), to deal in
Chris@32:  * the Software without restriction, including without limitation the rights to
Chris@32:  * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
Chris@32:  * the Software, and to permit persons to whom the Software is furnished to do so,
Chris@32:  * subject to the following conditions:
Chris@32:  * - The above copyright notice and this permission notice shall be included in
Chris@32:  *   all copies or substantial portions of the Software.
Chris@32:  * - The Software is provided "as is", without warranty of any kind, express or
Chris@32:  *   implied, including but not limited to the warranties of merchantability,
Chris@32:  *   fitness for a particular purpose and noninfringement. In no event shall the
Chris@32:  *   authors or copyright holders be liable for any claim, damages or other
Chris@32:  *   liability, whether in an action of contract, tort or otherwise, arising from,
Chris@32:  *   out of or in connection with the Software or the use or other dealings in the
Chris@32:  *   Software.
Chris@32:  */
Chris@32: 
Chris@32: #include <math.h>
Chris@32: #include <stdlib.h>
Chris@32: #include <string.h>
Chris@32: #include <stdio.h>
Chris@32: #include "fft.h"
Chris@32: 
Chris@32: 
Chris@32: // Private function prototypes
Chris@32: static size_t reverse_bits(size_t x, unsigned int n);
Chris@32: static void *memdup(const void *src, size_t n);
Chris@32: 
Chris@32: #define SIZE_MAX ((size_t)-1)
Chris@32: 
Chris@32: 
Chris@32: int transform(double real[], double imag[], size_t n) {
Chris@32: 	if (n == 0)
Chris@32: 		return 1;
Chris@32: 	else if ((n & (n - 1)) == 0)  // Is power of 2
Chris@32: 		return transform_radix2(real, imag, n);
Chris@32: 	else  // More complicated algorithm for arbitrary sizes
Chris@32: 		return transform_bluestein(real, imag, n);
Chris@32: }
Chris@32: 
Chris@32: 
Chris@32: int inverse_transform(double real[], double imag[], size_t n) {
Chris@32: 	return transform(imag, real, n);
Chris@32: }
Chris@32: 
Chris@32: tables *precalc(size_t n) {
Chris@32:     unsigned int levels;
Chris@32:     // Compute levels = floor(log2(n))
Chris@32:     {
Chris@32: 	size_t temp = n;
Chris@32: 	levels = 0;
Chris@32: 	while (temp > 1) {
Chris@32: 	    levels++;
Chris@32: 	    temp >>= 1;
Chris@32: 	}
Chris@32: 	if (1u << levels != n)
Chris@32: 	    return 0;  // n is not a power of 2
Chris@32:     }
Chris@32:     if (SIZE_MAX / sizeof(double) < n / 2) return 0;
Chris@32:     tables *tables = malloc(sizeof(tables));
Chris@32:     if (!tables) return tables;
Chris@32:     tables->levels = levels;
Chris@32:     size_t size = (n / 2) * sizeof(double);
Chris@32:     tables->cos = malloc(size);
Chris@32:     if (!tables->cos) {
Chris@32: 	free(tables);
Chris@32: 	return 0;
Chris@32:     }
Chris@32:     tables->sin = malloc(size);
Chris@32:     if (!tables->sin) {
Chris@32: 	free(tables->cos);
Chris@32: 	free(tables);
Chris@32: 	return 0;
Chris@32:     }
Chris@32:     int i;
Chris@32:     for (i = 0; i < n / 2; i++) {
Chris@32: 	tables->cos[i] = cos(2 * M_PI * i / n);
Chris@32: 	tables->sin[i] = sin(2 * M_PI * i / n);
Chris@32:     }
Chris@32:     return tables;
Chris@32: }
Chris@32: 
Chris@33: tables_f *precalc_f(size_t n) {
Chris@33:     unsigned int levels;
Chris@33:     // Compute levels = floor(log2(n))
Chris@33:     {
Chris@33: 	size_t temp = n;
Chris@33: 	levels = 0;
Chris@33: 	while (temp > 1) {
Chris@33: 	    levels++;
Chris@33: 	    temp >>= 1;
Chris@33: 	}
Chris@33: 	if (1u << levels != n)
Chris@33: 	    return 0;  // n is not a power of 2
Chris@33:     }
Chris@33:     if (SIZE_MAX / sizeof(float) < n / 2) return 0;
Chris@33:     tables_f *tables = malloc(sizeof(tables_f));
Chris@33:     if (!tables) return tables;
Chris@33:     tables->levels = levels;
Chris@33:     size_t size = (n / 2) * sizeof(float);
Chris@33:     tables->cos = malloc(size);
Chris@33:     if (!tables->cos) {
Chris@33: 	free(tables);
Chris@33: 	return 0;
Chris@33:     }
Chris@33:     tables->sin = malloc(size);
Chris@33:     if (!tables->sin) {
Chris@33: 	free(tables->cos);
Chris@33: 	free(tables);
Chris@33: 	return 0;
Chris@33:     }
Chris@33:     int i;
Chris@33:     for (i = 0; i < n / 2; i++) {
Chris@33: 	tables->cos[i] = cos(2 * M_PI * i / n);
Chris@33: 	tables->sin[i] = sin(2 * M_PI * i / n);
Chris@33:     }
Chris@33:     return tables;
Chris@33: }
Chris@33: 
Chris@32: void dispose(tables *tables) {
Chris@32:     if (!tables) return;
Chris@32:     free(tables->cos);
Chris@32:     free(tables->sin);
Chris@32:     free(tables);
Chris@32: }
Chris@32: 
Chris@33: void dispose_f(tables_f *tables) {
Chris@33:     if (!tables) return;
Chris@33:     free(tables->cos);
Chris@33:     free(tables->sin);
Chris@33:     free(tables);
Chris@33: }
Chris@33: 
Chris@32: void transform_radix2_precalc(double real[], double imag[], int n, tables *tables) {
Chris@32: 	double *cos_table, *sin_table;
Chris@32: 	int size;
Chris@32: 	int i;
Chris@32: 	
Chris@32: 	// Trignometric tables
Chris@32: 	cos_table = tables->cos;
Chris@32: 	sin_table = tables->sin;
Chris@32: 
Chris@32: 	// Bit-reversed addressing permutation
Chris@32: 	for (i = 0; i < n; i++) {
Chris@32: 		int j = reverse_bits(i, tables->levels);
Chris@32: 		if (j > i) {
Chris@32: 			double temp = real[i];
Chris@32: 			real[i] = real[j];
Chris@32: 			real[j] = temp;
Chris@32: 			temp = imag[i];
Chris@32: 			imag[i] = imag[j];
Chris@32: 			imag[j] = temp;
Chris@32: 		}
Chris@32: 	}
Chris@32: 	
Chris@32: 	// Cooley-Tukey decimation-in-time radix-2 FFT
Chris@32: 	for (size = 2; size <= n; size *= 2) {
Chris@32: 		int halfsize = size / 2;
Chris@32: 		int tablestep = n / size;
Chris@32: 		for (i = 0; i < n; i += size) {
Chris@32: 			int j;
Chris@32: 			int k;
Chris@32: 			for (j = i, k = 0; j < i + halfsize; j++, k += tablestep) {
Chris@32: 				double tpre =  real[j+halfsize] * cos_table[k] + imag[j+halfsize] * sin_table[k];
Chris@32: 				double tpim = -real[j+halfsize] * sin_table[k] + imag[j+halfsize] * cos_table[k];
Chris@32: 				real[j + halfsize] = real[j] - tpre;
Chris@32: 				imag[j + halfsize] = imag[j] - tpim;
Chris@32: 				real[j] += tpre;
Chris@32: 				imag[j] += tpim;
Chris@32: 			}
Chris@32: 		}
Chris@32: 		if (size == n)  // Prevent overflow in 'size *= 2'
Chris@32: 			break;
Chris@32: 	}
Chris@32: }
Chris@32: 
Chris@33: void transform_radix2_precalc_f(float real[], float imag[], int n, tables_f *tables) {
Chris@33: 	float *cos_table, *sin_table;
Chris@33: 	int size;
Chris@33: 	int i;
Chris@33: 	
Chris@33: 	// Trignometric tables
Chris@33: 	cos_table = tables->cos;
Chris@33: 	sin_table = tables->sin;
Chris@33: 
Chris@33: 	// Bit-reversed addressing permutation
Chris@33: 	for (i = 0; i < n; i++) {
Chris@33: 		int j = reverse_bits(i, tables->levels);
Chris@33: 		if (j > i) {
Chris@33: 			float temp = real[i];
Chris@33: 			real[i] = real[j];
Chris@33: 			real[j] = temp;
Chris@33: 			temp = imag[i];
Chris@33: 			imag[i] = imag[j];
Chris@33: 			imag[j] = temp;
Chris@33: 		}
Chris@33: 	}
Chris@33: 	
Chris@33: 	// Cooley-Tukey decimation-in-time radix-2 FFT
Chris@33: 	for (size = 2; size <= n; size *= 2) {
Chris@33: 		int halfsize = size / 2;
Chris@33: 		int tablestep = n / size;
Chris@33: 		for (i = 0; i < n; i += size) {
Chris@33: 			int j;
Chris@33: 			int k;
Chris@33: 			for (j = i, k = 0; j < i + halfsize; j++, k += tablestep) {
Chris@33: 				float tpre =  real[j+halfsize] * cos_table[k] + imag[j+halfsize] * sin_table[k];
Chris@33: 				float tpim = -real[j+halfsize] * sin_table[k] + imag[j+halfsize] * cos_table[k];
Chris@33: 				real[j + halfsize] = real[j] - tpre;
Chris@33: 				imag[j + halfsize] = imag[j] - tpim;
Chris@33: 				real[j] += tpre;
Chris@33: 				imag[j] += tpim;
Chris@33: 			}
Chris@33: 		}
Chris@33: 		if (size == n)  // Prevent overflow in 'size *= 2'
Chris@33: 			break;
Chris@33: 	}
Chris@33: }
Chris@33: 
Chris@32: int transform_radix2(double real[], double imag[], size_t n) {
Chris@32: 	// Variables
Chris@32: 	int status = 0;
Chris@32: 	unsigned int levels;
Chris@32: 	double *cos_table, *sin_table;
Chris@32: 	size_t size;
Chris@32: 	size_t i;
Chris@32: 	
Chris@32: 	// Compute levels = floor(log2(n))
Chris@32: 	{
Chris@32: 		size_t temp = n;
Chris@32: 		levels = 0;
Chris@32: 		while (temp > 1) {
Chris@32: 			levels++;
Chris@32: 			temp >>= 1;
Chris@32: 		}
Chris@32: 		if (1u << levels != n)
Chris@32: 			return 0;  // n is not a power of 2
Chris@32: 	}
Chris@32: 	
Chris@32: 	// Trignometric tables
Chris@32: 	if (SIZE_MAX / sizeof(double) < n / 2)
Chris@32: 		return 0;
Chris@32: 	size = (n / 2) * sizeof(double);
Chris@32: 	cos_table = malloc(size);
Chris@32: 	sin_table = malloc(size);
Chris@32: 	if (cos_table == NULL || sin_table == NULL)
Chris@32: 		goto cleanup;
Chris@32: 	for (i = 0; i < n / 2; i++) {
Chris@32: 		cos_table[i] = cos(2 * M_PI * i / n);
Chris@32: 		sin_table[i] = sin(2 * M_PI * i / n);
Chris@32: 	}
Chris@32: 	
Chris@32: 	// Bit-reversed addressing permutation
Chris@32: 	for (i = 0; i < n; i++) {
Chris@32: 		size_t j = reverse_bits(i, levels);
Chris@32: 		if (j > i) {
Chris@32: 			double temp = real[i];
Chris@32: 			real[i] = real[j];
Chris@32: 			real[j] = temp;
Chris@32: 			temp = imag[i];
Chris@32: 			imag[i] = imag[j];
Chris@32: 			imag[j] = temp;
Chris@32: 		}
Chris@32: 	}
Chris@32: 	
Chris@32: 	// Cooley-Tukey decimation-in-time radix-2 FFT
Chris@32: 	for (size = 2; size <= n; size *= 2) {
Chris@32: 		size_t halfsize = size / 2;
Chris@32: 		size_t tablestep = n / size;
Chris@32: 		for (i = 0; i < n; i += size) {
Chris@32: 			size_t j;
Chris@32: 			size_t k;
Chris@32: 			for (j = i, k = 0; j < i + halfsize; j++, k += tablestep) {
Chris@32: 				double tpre =  real[j+halfsize] * cos_table[k] + imag[j+halfsize] * sin_table[k];
Chris@32: 				double tpim = -real[j+halfsize] * sin_table[k] + imag[j+halfsize] * cos_table[k];
Chris@32: 				real[j + halfsize] = real[j] - tpre;
Chris@32: 				imag[j + halfsize] = imag[j] - tpim;
Chris@32: 				real[j] += tpre;
Chris@32: 				imag[j] += tpim;
Chris@32: 			}
Chris@32: 		}
Chris@32: 		if (size == n)  // Prevent overflow in 'size *= 2'
Chris@32: 			break;
Chris@32: 	}
Chris@32: 	status = 1;
Chris@32: 	
Chris@32: cleanup:
Chris@32: 	free(sin_table);
Chris@32: 	free(cos_table);
Chris@32: 	return status;
Chris@32: }
Chris@32: 
Chris@32: 
Chris@32: int transform_bluestein(double real[], double imag[], size_t n) {
Chris@32: 	// Variables
Chris@32: 	int status = 0;
Chris@32: 	double *cos_table, *sin_table;
Chris@32: 	double *areal, *aimag;
Chris@32: 	double *breal, *bimag;
Chris@32: 	double *creal, *cimag;
Chris@32: 	size_t m;
Chris@32: 	size_t size_n, size_m;
Chris@32: 	size_t i;
Chris@32: 	
Chris@32: 	// Find a power-of-2 convolution length m such that m >= n * 2 + 1
Chris@32: 	{
Chris@32: 		size_t target;
Chris@32: 		if (n > (SIZE_MAX - 1) / 2)
Chris@32: 			return 0;
Chris@32: 		target = n * 2 + 1;
Chris@32: 		for (m = 1; m < target; m *= 2) {
Chris@32: 			if (SIZE_MAX / 2 < m)
Chris@32: 				return 0;
Chris@32: 		}
Chris@32: 	}
Chris@32: 	
Chris@32: 	// Allocate memory
Chris@32: 	if (SIZE_MAX / sizeof(double) < n || SIZE_MAX / sizeof(double) < m)
Chris@32: 		return 0;
Chris@32: 	size_n = n * sizeof(double);
Chris@32: 	size_m = m * sizeof(double);
Chris@32: 	cos_table = malloc(size_n);
Chris@32: 	sin_table = malloc(size_n);
Chris@32: 	areal = calloc(m, sizeof(double));
Chris@32: 	aimag = calloc(m, sizeof(double));
Chris@32: 	breal = calloc(m, sizeof(double));
Chris@32: 	bimag = calloc(m, sizeof(double));
Chris@32: 	creal = malloc(size_m);
Chris@32: 	cimag = malloc(size_m);
Chris@32: 	if (cos_table == NULL || sin_table == NULL
Chris@32: 			|| areal == NULL || aimag == NULL
Chris@32: 			|| breal == NULL || bimag == NULL
Chris@32: 			|| creal == NULL || cimag == NULL)
Chris@32: 		goto cleanup;
Chris@32: 	
Chris@32: 	// Trignometric tables
Chris@32: 	for (i = 0; i < n; i++) {
Chris@32: 		double temp = M_PI * (size_t)((unsigned long long)i * i % ((unsigned long long)n * 2)) / n;
Chris@32: 		// Less accurate version if long long is unavailable: double temp = M_PI * i * i / n;
Chris@32: 		cos_table[i] = cos(temp);
Chris@32: 		sin_table[i] = sin(temp);
Chris@32: 	}
Chris@32: 	
Chris@32: 	// Temporary vectors and preprocessing
Chris@32: 	for (i = 0; i < n; i++) {
Chris@32: 		areal[i] =  real[i] * cos_table[i] + imag[i] * sin_table[i];
Chris@32: 		aimag[i] = -real[i] * sin_table[i] + imag[i] * cos_table[i];
Chris@32: 	}
Chris@32: 	breal[0] = cos_table[0];
Chris@32: 	bimag[0] = sin_table[0];
Chris@32: 	for (i = 1; i < n; i++) {
Chris@32: 		breal[i] = breal[m - i] = cos_table[i];
Chris@32: 		bimag[i] = bimag[m - i] = sin_table[i];
Chris@32: 	}
Chris@32: 	
Chris@32: 	// Convolution
Chris@32: 	if (!convolve_complex(areal, aimag, breal, bimag, creal, cimag, m))
Chris@32: 		goto cleanup;
Chris@32: 	
Chris@32: 	// Postprocessing
Chris@32: 	for (i = 0; i < n; i++) {
Chris@32: 		real[i] =  creal[i] * cos_table[i] + cimag[i] * sin_table[i];
Chris@32: 		imag[i] = -creal[i] * sin_table[i] + cimag[i] * cos_table[i];
Chris@32: 	}
Chris@32: 	status = 1;
Chris@32: 	
Chris@32: 	// Deallocation
Chris@32: cleanup:
Chris@32: 	free(cimag);
Chris@32: 	free(creal);
Chris@32: 	free(bimag);
Chris@32: 	free(breal);
Chris@32: 	free(aimag);
Chris@32: 	free(areal);
Chris@32: 	free(sin_table);
Chris@32: 	free(cos_table);
Chris@32: 	return status;
Chris@32: }
Chris@32: 
Chris@32: 
Chris@32: int convolve_real(const double x[], const double y[], double out[], size_t n) {
Chris@32: 	double *ximag, *yimag, *zimag;
Chris@32: 	int status = 0;
Chris@32: 	ximag = calloc(n, sizeof(double));
Chris@32: 	yimag = calloc(n, sizeof(double));
Chris@32: 	zimag = calloc(n, sizeof(double));
Chris@32: 	if (ximag == NULL || yimag == NULL || zimag == NULL)
Chris@32: 		goto cleanup;
Chris@32: 	
Chris@32: 	status = convolve_complex(x, ximag, y, yimag, out, zimag, n);
Chris@32: cleanup:
Chris@32: 	free(zimag);
Chris@32: 	free(yimag);
Chris@32: 	free(ximag);
Chris@32: 	return status;
Chris@32: }
Chris@32: 
Chris@32: 
Chris@32: int convolve_complex(const double xreal[], const double ximag[], const double yreal[], const double yimag[], double outreal[], double outimag[], size_t n) {
Chris@32: 	int status = 0;
Chris@32: 	size_t size;
Chris@32: 	size_t i;
Chris@32: 	double *xr, *xi, *yr, *yi;
Chris@32: 	if (SIZE_MAX / sizeof(double) < n)
Chris@32: 		return 0;
Chris@32: 	size = n * sizeof(double);
Chris@32: 	xr = memdup(xreal, size);
Chris@32: 	xi = memdup(ximag, size);
Chris@32: 	yr = memdup(yreal, size);
Chris@32: 	yi = memdup(yimag, size);
Chris@32: 	if (xr == NULL || xi == NULL || yr == NULL || yi == NULL)
Chris@32: 		goto cleanup;
Chris@32: 	
Chris@32: 	if (!transform(xr, xi, n))
Chris@32: 		goto cleanup;
Chris@32: 	if (!transform(yr, yi, n))
Chris@32: 		goto cleanup;
Chris@32: 	for (i = 0; i < n; i++) {
Chris@32: 		double temp = xr[i] * yr[i] - xi[i] * yi[i];
Chris@32: 		xi[i] = xi[i] * yr[i] + xr[i] * yi[i];
Chris@32: 		xr[i] = temp;
Chris@32: 	}
Chris@32: 	if (!inverse_transform(xr, xi, n))
Chris@32: 		goto cleanup;
Chris@32: 	for (i = 0; i < n; i++) {  // Scaling (because this FFT implementation omits it)
Chris@32: 		outreal[i] = xr[i] / n;
Chris@32: 		outimag[i] = xi[i] / n;
Chris@32: 	}
Chris@32: 	status = 1;
Chris@32: 	
Chris@32: cleanup:
Chris@32: 	free(yi);
Chris@32: 	free(yr);
Chris@32: 	free(xi);
Chris@32: 	free(xr);
Chris@32: 	return status;
Chris@32: }
Chris@32: 
Chris@32: 
Chris@32: static size_t reverse_bits(size_t x, unsigned int n) {
Chris@32: 	size_t result = 0;
Chris@32: 	unsigned int i;
Chris@32: 	for (i = 0; i < n; i++, x >>= 1)
Chris@32: 		result = (result << 1) | (x & 1);
Chris@32: 	return result;
Chris@32: }
Chris@32: 
Chris@32: 
Chris@32: static void *memdup(const void *src, size_t n) {
Chris@32: 	void *dest = malloc(n);
Chris@32: 	if (dest != NULL)
Chris@32: 		memcpy(dest, src, n);
Chris@32: 	return dest;
Chris@32: }