NanoVNA/fft.h

/* 
 * fft.h is Based on
 * Free FFT and convolution (C)
 * 
 * Copyright (c) 2019 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 <math.h>
#include <stdint.h>

// Use table increase transform speed from 6500 tick to 2025, increase code size on 700 bytes
// Use compact table, increase code size on 208 bytes, and not decrease speed
#define FFT_USE_SIN_COS_TABLE

static uint16_t reverse_bits(uint16_t x, int n) {
	uint16_t result = 0;
	int i;
	for (i = 0; i < n; i++, x >>= 1)
		result = (result << 1) | (x & 1U);
	return result;
}
#ifdef FFT_USE_SIN_COS_TABLE
static const float sin_table[] = {
	/*
	 * float has about 7.2 digits of precision
		for (uint8_t i = 0; i < FFT_SIZE - (FFT_SIZE / 4); i++) {
			printf("% .8f,%c", sin(2 * M_PI * i / FFT_SIZE), i % 8 == 7 ? '\n' : ' ');
		}
	*/
	 // for FFT_SIZE = 256
	 0.00000000,  0.02454123,  0.04906767,  0.07356456,  0.09801714,  0.12241068,  0.14673047,  0.17096189,
	 0.19509032,  0.21910124,  0.24298018,  0.26671276,  0.29028468,  0.31368174,  0.33688985,  0.35989504,
	 0.38268343,  0.40524131,  0.42755509,  0.44961133,  0.47139674,  0.49289819,  0.51410274,  0.53499762,
	 0.55557023,  0.57580819,  0.59569930,  0.61523159,  0.63439328,  0.65317284,  0.67155895,  0.68954054,
	 0.70710678,  0.72424708,  0.74095113,  0.75720885,  0.77301045,  0.78834643,  0.80320753,  0.81758481,
	 0.83146961,  0.84485357,  0.85772861,  0.87008699,  0.88192126,  0.89322430,  0.90398929,  0.91420976,
	 0.92387953,  0.93299280,  0.94154407,  0.94952818,  0.95694034,  0.96377607,  0.97003125,  0.97570213,
	 0.98078528,  0.98527764,  0.98917651,  0.99247953,  0.99518473,  0.99729046,  0.99879546,  0.99969882,
	 1.00000000,/*  0.99969882,  0.99879546,  0.99729046,  0.99518473,  0.99247953,  0.98917651,  0.98527764,
	 0.98078528,  0.97570213,  0.97003125,  0.96377607,  0.95694034,  0.94952818,  0.94154407,  0.93299280,
	 0.92387953,  0.91420976,  0.90398929,  0.89322430,  0.88192126,  0.87008699,  0.85772861,  0.84485357,
	 0.83146961,  0.81758481,  0.80320753,  0.78834643,  0.77301045,  0.75720885,  0.74095113,  0.72424708,
	 0.70710678,  0.68954054,  0.67155895,  0.65317284,  0.63439328,  0.61523159,  0.59569930,  0.57580819,
	 0.55557023,  0.53499762,  0.51410274,  0.49289819,  0.47139674,  0.44961133,  0.42755509,  0.40524131,
	 0.38268343,  0.35989504,  0.33688985,  0.31368174,  0.29028468,  0.26671276,  0.24298018,  0.21910124,
	 0.19509032,  0.17096189,  0.14673047,  0.12241068,  0.09801714,  0.07356456,  0.04906767,  0.02454123,
	 0.00000000, -0.02454123, -0.04906767, -0.07356456, -0.09801714, -0.12241068, -0.14673047, -0.17096189,
	-0.19509032, -0.21910124, -0.24298018, -0.26671276, -0.29028468, -0.31368174, -0.33688985, -0.35989504,
	-0.38268343, -0.40524131, -0.42755509, -0.44961133, -0.47139674, -0.49289819, -0.51410274, -0.53499762,
	-0.55557023, -0.57580819, -0.59569930, -0.61523159, -0.63439328, -0.65317284, -0.67155895, -0.68954054,
	-0.70710678, -0.72424708, -0.74095113, -0.75720885, -0.77301045, -0.78834643, -0.80320753, -0.81758481,
	-0.83146961, -0.84485357, -0.85772861, -0.87008699, -0.88192126, -0.89322430, -0.90398929, -0.91420976,
	-0.92387953, -0.93299280, -0.94154407, -0.94952818, -0.95694034, -0.96377607, -0.97003125, -0.97570213,
	-0.98078528, -0.98527764, -0.98917651, -0.99247953, -0.99518473, -0.99729046, -0.99879546, -0.99969882,*/
};
// full size table:
//   sin = sin_table[i   ]
//   cos = sin_table[i+64]
//#define SIN(i) sin_table[(i)]
//#define COS(i) sin_table[(i)+64]

// for size use only 0-64 indexes
//   sin = i > 64 ? sin_table[128-i] : sin_table[   i];
//   cos = i > 64 ?-sin_table[ i-64] : sin_table[64-i];
#define SIN(i) ((i) > 64 ? sin_table[128-(i)] : sin_table[   (i)])
#define COS(i) ((i) > 64 ?-sin_table[ (i)-64] : sin_table[64-(i)])
#endif

/***
 * dir = forward: 0, inverse: 1
 * https://www.nayuki.io/res/free-small-fft-in-multiple-languages/fft.c
 */
static void fft256(float array[][2], const uint8_t dir) {
	const uint16_t n = 256;
	const uint8_t levels = 8; // log2(n)

	const uint8_t real =   dir & 1;
	const uint8_t imag = ~real & 1;
	uint16_t i;

	for (i = 0; i < n; i++) {
		uint16_t j = reverse_bits(i, levels);
		if (j > i) {
			float temp = array[i][real];
			array[i][real] = array[j][real];
			array[j][real] = temp;
			temp = array[i][imag];
			array[i][imag] = array[j][imag];
			array[j][imag] = temp;
		}
	}
	const uint16_t size = 2;
	uint16_t halfsize = size / 2;
	uint16_t tablestep = n / size;
	uint16_t j, k;
	// Cooley-Tukey decimation-in-time radix-2 FFT
	for (;tablestep; tablestep>>=1, halfsize<<=1) {
		for (i = 0; i < n; i+=2*halfsize) {
			for (j = i, k = 0; j < i + halfsize; j++, k += tablestep) {
				uint16_t l = j + halfsize;
#ifdef FFT_USE_SIN_COS_TABLE
				float s = SIN(k);
				float c = COS(k);
#else
				float c = cos(2 * VNA_PI * k / 256);
				float s = sin(2 * VNA_PI * k / 256);
#endif
				float tpre =  array[l][real] * c + array[l][imag] * s;
				float tpim = -array[l][real] * s + array[l][imag] * c;
				array[l][real] = array[j][real] - tpre;
				array[l][imag] = array[j][imag] - tpim;
				array[j][real] += tpre;
				array[j][imag] += tpim;
			}
		}
	}
}

static inline void fft256_forward(float array[][2]) {
	fft256(array, 0);
}

static inline void fft256_inverse(float array[][2]) {
	fft256(array, 1);
}