LNXSDK/lib/aura/Backends/common_c/math/fft.c

#include <stdint.h>

#include "fft.h"

#define PI_FLOAT 3.14159265358979323846f

static uint32_t bitReverseUint32(uint32_t value, uint32_t log2N);

static uint32_t log2Unsigned(uint32_t n) {
	uint32_t res = 0;

	while (n >>= 1) {
		res++;
	}

	return res;
}

void aura_ditfft2(const aura_complex_t * times, int t, aura_complex_t * freqs, int f, int n, int step, bool inverse) {
	if (n == 1) {
		aura_copy_complex_elem(freqs, f, times, t);
	}
	else {
		const int halfLen = n >> 1;

		aura_ditfft2(times, t, freqs, f, halfLen, step << 1, inverse);
		aura_ditfft2(times, t + step, freqs, f + halfLen, halfLen, step << 1, inverse);

		const float t_exp = ((inverse ? 1.0f : -1.0f) * 2.0f * PI_FLOAT) / n;
		for (int k = 0; k < halfLen; k++) {
			aura_complex_t even = { 0 };
			aura_complex_t odd = { 0 };
			aura_copy_complex(&even, freqs[f + k]);
			aura_copy_complex(&odd, freqs[f + k + halfLen]);

			const aura_complex_t twiddle = aura_cmult(aura_cexp(t_exp * k), odd);

			aura_copy_complex(&(freqs[f + k]), aura_cadd(even, twiddle));
			aura_copy_complex(&(freqs[f + k + halfLen]), aura_csub(even, twiddle));
		}
	}
}

void aura_ditfft2_iterative(const aura_complex_t * times, aura_complex_t * freqs, int n, bool inverse, const aura_complex_t * exp_lut) {
	// Decimate
	const uint32_t log2N = log2Unsigned(n);
	for (uint32_t i = 0; i < ((uint32_t) n); i++) {
		uint32_t reversedI = bitReverseUint32(i, log2N);

		if (reversedI >= i) {
			aura_copy_complex(&freqs[i], times[reversedI]);
			aura_copy_complex(&freqs[reversedI], times[i]);
		}
		else if (reversedI == i) {
			aura_copy_complex(&freqs[reversedI], times[i]);
		}
	}

	int halfLayerIdx = 0;
	for (int layerSize = 2; layerSize <= n; layerSize <<= 1) {
		const int halfLayerSize = layerSize >> 1;

		aura_complex_t expRotationStep;
		aura_copy_complex(&expRotationStep, exp_lut[halfLayerIdx]);
		if (inverse) {
			expRotationStep = aura_cconj(expRotationStep);
		}

		for (int sectionOffset = 0; sectionOffset < n; sectionOffset += layerSize) {
			aura_complex_t currentExpRotation = {.real = 1.0, .imag = 0.0};

			for (int i = 0; i < halfLayerSize; i++) {
				aura_complex_t even;
				aura_complex_t odd;
				aura_copy_complex(&even, freqs[sectionOffset + i]);
				aura_copy_complex(&odd, freqs[sectionOffset + i + halfLayerSize]);

				const aura_complex_t twiddle = aura_cmult(currentExpRotation, odd);

				aura_copy_complex(&(freqs[sectionOffset + i]), aura_cadd(even, twiddle));
				aura_copy_complex(&(freqs[sectionOffset + i + halfLayerSize]), aura_csub(even, twiddle));

				aura_copy_complex(&currentExpRotation, aura_cmult(currentExpRotation, expRotationStep));
			}
		}
		halfLayerIdx++;
	}
}

/**
	The following bit reversal code is taken (and slightly changed) from
	https://graphics.stanford.edu/~seander/bithacks.html#BitReverseTable.
	The original sources are released in the public domain.
**/

// Lookup table for bit reversal where each entry is one possible byte
static const uint8_t bitReverseTable[] = {
	0x00, 0x80, 0x40, 0xC0, 0x20, 0xA0, 0x60, 0xE0, 0x10, 0x90, 0x50, 0xD0, 0x30, 0xB0, 0x70, 0xF0,
	0x08, 0x88, 0x48, 0xC8, 0x28, 0xA8, 0x68, 0xE8, 0x18, 0x98, 0x58, 0xD8, 0x38, 0xB8, 0x78, 0xF8,
	0x04, 0x84, 0x44, 0xC4, 0x24, 0xA4, 0x64, 0xE4, 0x14, 0x94, 0x54, 0xD4, 0x34, 0xB4, 0x74, 0xF4,
	0x0C, 0x8C, 0x4C, 0xCC, 0x2C, 0xAC, 0x6C, 0xEC, 0x1C, 0x9C, 0x5C, 0xDC, 0x3C, 0xBC, 0x7C, 0xFC,
	0x02, 0x82, 0x42, 0xC2, 0x22, 0xA2, 0x62, 0xE2, 0x12, 0x92, 0x52, 0xD2, 0x32, 0xB2, 0x72, 0xF2,
	0x0A, 0x8A, 0x4A, 0xCA, 0x2A, 0xAA, 0x6A, 0xEA, 0x1A, 0x9A, 0x5A, 0xDA, 0x3A, 0xBA, 0x7A, 0xFA,
	0x06, 0x86, 0x46, 0xC6, 0x26, 0xA6, 0x66, 0xE6, 0x16, 0x96, 0x56, 0xD6, 0x36, 0xB6, 0x76, 0xF6,
	0x0E, 0x8E, 0x4E, 0xCE, 0x2E, 0xAE, 0x6E, 0xEE, 0x1E, 0x9E, 0x5E, 0xDE, 0x3E, 0xBE, 0x7E, 0xFE,
	0x01, 0x81, 0x41, 0xC1, 0x21, 0xA1, 0x61, 0xE1, 0x11, 0x91, 0x51, 0xD1, 0x31, 0xB1, 0x71, 0xF1,
	0x09, 0x89, 0x49, 0xC9, 0x29, 0xA9, 0x69, 0xE9, 0x19, 0x99, 0x59, 0xD9, 0x39, 0xB9, 0x79, 0xF9,
	0x05, 0x85, 0x45, 0xC5, 0x25, 0xA5, 0x65, 0xE5, 0x15, 0x95, 0x55, 0xD5, 0x35, 0xB5, 0x75, 0xF5,
	0x0D, 0x8D, 0x4D, 0xCD, 0x2D, 0xAD, 0x6D, 0xED, 0x1D, 0x9D, 0x5D, 0xDD, 0x3D, 0xBD, 0x7D, 0xFD,
	0x03, 0x83, 0x43, 0xC3, 0x23, 0xA3, 0x63, 0xE3, 0x13, 0x93, 0x53, 0xD3, 0x33, 0xB3, 0x73, 0xF3,
	0x0B, 0x8B, 0x4B, 0xCB, 0x2B, 0xAB, 0x6B, 0xEB, 0x1B, 0x9B, 0x5B, 0xDB, 0x3B, 0xBB, 0x7B, 0xFB,
	0x07, 0x87, 0x47, 0xC7, 0x27, 0xA7, 0x67, 0xE7, 0x17, 0x97, 0x57, 0xD7, 0x37, 0xB7, 0x77, 0xF7,
	0x0F, 0x8F, 0x4F, 0xCF, 0x2F, 0xAF, 0x6F, 0xEF, 0x1F, 0x9F, 0x5F, 0xDF, 0x3F, 0xBF, 0x7F, 0xFF
};

static uint32_t bitReverseUint32(uint32_t value, uint32_t log2N) {
	return ((uint32_t)(
		(bitReverseTable[ value        & 0xff] << 24) |
		(bitReverseTable[(value >> 8 ) & 0xff] << 16) |
		(bitReverseTable[(value >> 16) & 0xff] << 8 ) |
		(bitReverseTable[(value >> 24) & 0xff]      )
	) >> (32 - log2N));
}