fft.c

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/* fft.c: Iterative implementation of a FFT
 * Copyright (C) 1999 Richard Boulton <[e-mail]>
 * Convolution stuff by Ralph Loader <[e-mail]>
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 */

/*
 * TODO
 * Remove compiling in of FFT_BUFFER_SIZE?  (Might slow things down, but would
 * be nice to be able to change size at runtime.)
 * Finish making / checking thread-safety.
 * More optimisations.
 */

#include "config.h"
#include "fft.h"

#include <glib.h>
#include <stdlib.h>
#include <math.h>
#ifndef PI
 #ifdef M_PI
  #define PI M_PI
 #else
  #define PI            3.14159265358979323846  /* pi */
 #endif
#endif

/* ########### */
/* # Structs # */
/* ########### */

struct _struct_fft_state {
    /* Temporary data stores to perform FFT in. */
    float real[FFT_BUFFER_SIZE];
    float imag[FFT_BUFFER_SIZE];
};

/* ############################# */
/* # Local function prototypes # */
/* ############################# */

static void fft_prepare(const sound_sample *input, float * re, float * im);
static void fft_calculate(float * re, float * im);
static void fft_output(const float *re, const float *im, float *output);
static int reverseBits(unsigned int initial);

/* #################### */
/* # Global variables # */
/* #################### */

/* Table to speed up bit reverse copy */
static unsigned int bitReverse[FFT_BUFFER_SIZE];

/* The next two tables could be made to use less space in memory, since they
 * overlap hugely, but hey. */
static float sintable[FFT_BUFFER_SIZE / 2];
static float costable[FFT_BUFFER_SIZE / 2];

/* ############################## */
/* # Externally called routines # */
/* ############################## */

/* --------- */
/* FFT stuff */
/* --------- */

/*
 * Initialisation routine - sets up tables and space to work in.
 * Returns a pointer to internal state, to be used when performing calls.
 * On error, returns NULL.
 * The pointer should be freed when it is finished with, by fft_close().
 */
fft_state *fft_init(void) {
    fft_state *state;
    unsigned int i;

    state = (fft_state *) g_malloc (sizeof(fft_state));
    if(!state) return NULL;

    for(i = 0; i < FFT_BUFFER_SIZE; i++) {
	bitReverse[i] = reverseBits(i);
    }
    for(i = 0; i < FFT_BUFFER_SIZE / 2; i++) {
	float j = 2 * PI * i / FFT_BUFFER_SIZE;
	costable[i] = cos(j);
	sintable[i] = sin(j);
    }

    return state;
}

/*
 * Do all the steps of the FFT, taking as input sound data (as described in
 * sound.h) and returning the intensities of each frequency as floats in the
 * range 0 to ((FFT_BUFFER_SIZE / 2) * 32768) ^ 2
 *
 * FIXME - the above range assumes no frequencies present have an amplitude
 * larger than that of the sample variation.  But this is false: we could have
 * a wave such that its maximums are always between samples, and it's just
 * inside the representable range at the places samples get taken.
 * Question: what _is_ the maximum value possible.  Twice that value?  Root
 * two times that value?  Hmmm.  Think it depends on the frequency, too.
 *
 * The input array is assumed to have FFT_BUFFER_SIZE elements,
 * and the output array is assumed to have (FFT_BUFFER_SIZE / 2 + 1) elements.
 * state is a (non-NULL) pointer returned by fft_init.
 */
void fft_perform(const sound_sample *input, float *output, fft_state *state) {
    /* Convert data from sound format to be ready for FFT */
    fft_prepare(input, state->real, state->imag);

    /* Do the actual FFT */
    fft_calculate(state->real, state->imag);

    /* Convert the FFT output into intensities */
    fft_output(state->real, state->imag, output);
}

/*
 * Free the state.
 */
void fft_close(fft_state *state) {
    if(state) free(state);
}

/* ########################### */
/* # Locally called routines # */
/* ########################### */

/*
 * Prepare data to perform an FFT on
 */
static void fft_prepare(const sound_sample *input, float * re, float * im) {
    unsigned int i;
    float *realptr = re;
    float *imagptr = im;
    
    /* Get input, in reverse bit order */
    for(i = 0; i < FFT_BUFFER_SIZE; i++) {
	*realptr++ = input[bitReverse[i]];
	*imagptr++ = 0;
    }
}

/*
 * Take result of an FFT and calculate the intensities of each frequency
 * Note: only produces half as many data points as the input had.
 * This is roughly a consequence of the Nyquist sampling theorm thingy.
 * (FIXME - make this comment better, and helpful.)
 * 
 * The two divisions by 4 are also a consequence of this: the contributions
 * returned for each frequency are split into two parts, one at i in the
 * table, and the other at FFT_BUFFER_SIZE - i, except for i = 0 and
 * FFT_BUFFER_SIZE which would otherwise get float (and then 4* when squared)
 * the contributions.
 */
static void fft_output(const float * re, const float * im, float *output) {
    float *outputptr = output;
    const float *realptr   = re;
    const float *imagptr   = im;
    float *endptr    = output + FFT_BUFFER_SIZE / 2;
 
#ifdef DEBUG
    unsigned int i, j;
#endif
 
    while(outputptr <= endptr) {
	*outputptr = (*realptr * *realptr) + (*imagptr * *imagptr);
	outputptr++; realptr++; imagptr++;
    }
    /* Do divisions to keep the constant and highest frequency terms in scale
     * with the other terms. */
    *output /= 4;
    *endptr /= 4;

#ifdef DEBUG
    printf("Recalculated input:\n");
    for(i = 0; i < FFT_BUFFER_SIZE; i++) {
        float val_real = 0;
        float val_imag = 0;
	for(j = 0; j < FFT_BUFFER_SIZE; j++) {
	    float fact_real = cos(- 2 * j * i * PI / FFT_BUFFER_SIZE);
	    float fact_imag = sin(- 2 * j * i * PI / FFT_BUFFER_SIZE);
	    val_real += fact_real * re[j] - fact_imag * im[j];
	    val_imag += fact_real * im[j] + fact_imag * re[j];
	}
	printf("%5d = %8f + i * %8f\n", i,
	       val_real / FFT_BUFFER_SIZE,
	       val_imag / FFT_BUFFER_SIZE);
    }
    printf("\n");
#endif
}

/*
 * Actually perform the FFT
 */
static void fft_calculate(float * re, float * im) {
    unsigned int i, j, k;
    unsigned int exchanges;
    float fact_real, fact_imag;
    float tmp_real, tmp_imag;
    unsigned int factfact;
    
    /* Set up some variables to reduce calculation in the loops */
    exchanges = 1;
    factfact = FFT_BUFFER_SIZE / 2;

    /* Loop through the divide and conquer steps */
    for(i = FFT_BUFFER_SIZE_LOG; i != 0; i--) {
	/* In this step, we have 2 ^ (i - 1) exchange groups, each with
	 * 2 ^ (FFT_BUFFER_SIZE_LOG - i) exchanges
	 */
	/* Loop through the exchanges in a group */
	for(j = 0; j != exchanges; j++) {
	    /* Work out factor for this exchange
	     * factor ^ (exchanges) = -1
	     * So, real = cos(j * PI / exchanges),
	     *     imag = sin(j * PI / exchanges)
	     */
	    fact_real = costable[j * factfact];
	    fact_imag = sintable[j * factfact];
	    
	    /* Loop through all the exchange groups */
	    for(k = j; k < FFT_BUFFER_SIZE; k += exchanges << 1) {
		int k1 = k + exchanges;
		/* newval[k]  := val[k] + factor * val[k1]
		 * newval[k1] := val[k] - factor * val[k1]
		 **/
#ifdef DEBUG
		printf("%d %d %d\n", i,j,k);
		printf("Exchange %d with %d\n", k, k1);
		printf("Factor %9f + i * %8f\n", fact_real, fact_imag);
#endif
		/* FIXME - potential scope for more optimization here? */
		tmp_real = fact_real * re[k1] - fact_imag * im[k1];
		tmp_imag = fact_real * im[k1] + fact_imag * re[k1];
		re[k1] = re[k] - tmp_real;
		im[k1] = im[k] - tmp_imag;
		re[k]  += tmp_real;
		im[k]  += tmp_imag;
#ifdef DEBUG
		for(k1 = 0; k1 < FFT_BUFFER_SIZE; k1++) {
		    printf("%5d = %8f + i * %8f\n", k1, real[k1], imag[k1]);
		}
#endif
	    }
	}
	exchanges <<= 1;
	factfact >>= 1;
    }
}

static int reverseBits(unsigned int initial) {
    unsigned int reversed = 0, loop;
    for(loop = 0; loop < FFT_BUFFER_SIZE_LOG; loop++) {
	reversed <<= 1;
	reversed += (initial & 1);
	initial >>= 1;
    }
    return reversed;
}