474 lines
13 KiB
C
474 lines
13 KiB
C
/*
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* FFT/IFFT transforms converted to integer precision
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* Copyright (c) 2010 Dave Hooper, Mohamed Tarek, Michael Giacomelli
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* Copyright (c) 2008 Loren Merritt
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* Copyright (c) 2002 Fabrice Bellard
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* Partly based on libdjbfft by D. J. Bernstein
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*
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* This file is part of FFmpeg.
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*
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* FFmpeg is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* FFmpeg is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with FFmpeg; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*/
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/**
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* @file libavcodec/fft.c
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* FFT/IFFT transforms.
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*/
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#ifdef CPU_ARM
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// we definitely want CONFIG_SMALL undefined for ipod
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// so we get the inlined version of fft16 (which is measurably faster)
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#undef CONFIG_SMALL
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#else
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#undef CONFIG_SMALL
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#endif
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#include "fft.h"
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#include <string.h>
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#include <stdlib.h>
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#include <math.h>
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#include <inttypes.h>
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#include <time.h>
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#include <codecs/lib/codeclib.h>
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#include "codeclib_misc.h"
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#include "mdct_lookup.h"
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/* constants for fft_16 (same constants as in mdct_arm.S ... ) */
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#define cPI1_8 (0x7641af3d) /* cos(pi/8) s.31 */
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#define cPI2_8 (0x5a82799a) /* cos(2pi/8) = 1/sqrt(2) s.31 */
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#define cPI3_8 (0x30fbc54d) /* cos(3pi/8) s.31 */
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/* asm-optimised functions and/or macros */
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#include "fft-ffmpeg_arm.h"
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#include "fft-ffmpeg_cf.h"
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#ifndef ICODE_ATTR_TREMOR_MDCT
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#define ICODE_ATTR_TREMOR_MDCT ICODE_ATTR
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#endif
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#if 0
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static int split_radix_permutation(int i, int n, int inverse)
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{
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int m;
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if(n <= 2) return i&1;
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m = n >> 1;
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if(!(i&m)) return split_radix_permutation(i, m, inverse)*2;
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m >>= 1;
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if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
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else return split_radix_permutation(i, m, inverse)*4 - 1;
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}
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static void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
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{
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int j, k, np;
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FFTComplex tmp;
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//const uint16_t *revtab = s->revtab;
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np = 1 << s->nbits;
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const int revtab_shift = (12 - s->nbits);
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/* reverse */
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for(j=0;j<np;j++) {
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k = revtab[j]>>revtab_shift;
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if (k < j) {
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tmp = z[k];
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z[k] = z[j];
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z[j] = tmp;
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}
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}
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}
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#endif
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#define BF(x,y,a,b) {\
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x = a - b;\
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y = a + b;\
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}
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#define BF_REV(x,y,a,b) {\
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x = a + b;\
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y = a - b;\
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}
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#ifndef FFT_FFMPEG_INCL_OPTIMISED_BUTTERFLIES
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#define BUTTERFLIES(a0,a1,a2,a3) {\
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{\
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FFTSample temp1,temp2;\
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BF(temp1, temp2, t5, t1);\
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BF(a2.re, a0.re, a0.re, temp2);\
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BF(a3.im, a1.im, a1.im, temp1);\
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}\
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{\
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FFTSample temp1,temp2;\
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BF(temp1, temp2, t2, t6);\
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BF(a3.re, a1.re, a1.re, temp1);\
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BF(a2.im, a0.im, a0.im, temp2);\
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}\
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}
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// force loading all the inputs before storing any.
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// this is slightly slower for small data, but avoids store->load aliasing
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// for addresses separated by large powers of 2.
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#define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
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FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
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{\
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FFTSample temp1, temp2;\
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BF(temp1, temp2, t5, t1);\
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BF(a2.re, a0.re, r0, temp2);\
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BF(a3.im, a1.im, i1, temp1);\
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}\
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{\
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FFTSample temp1, temp2;\
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BF(temp1, temp2, t2, t6);\
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BF(a3.re, a1.re, r1, temp1);\
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BF(a2.im, a0.im, i0, temp2);\
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}\
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}
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#endif
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/*
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see conjugate pair description in
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http://www.fftw.org/newsplit.pdf
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a0 = z[k]
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a1 = z[k+N/4]
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a2 = z[k+2N/4]
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a3 = z[k+3N/4]
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result:
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y[k] = z[k]+w(z[k+2N/4])+w'(z[k+3N/4])
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y[k+N/4] = z[k+N/4]-iw(z[k+2N/4])+iw'(z[k+3N/4])
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y[k+2N/4] = z[k]-w(z[k+2N/4])-w'(z[k+3N/4])
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y[k+3N/4] = z[k+N/4]+iw(z[k+2N/4])-iw'(z[k+3N/4])
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i.e.
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a0 = a0 + (w.a2 + w'.a3)
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a1 = a1 - i(w.a2 - w'.a3)
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a2 = a0 - (w.a2 + w'.a3)
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a3 = a1 + i(w.a2 - w'.a3)
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note re(w') = re(w) and im(w') = -im(w)
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so therefore
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re(a0) = re(a0) + re(w.a2) + re(w.a3)
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im(a0) = im(a0) + im(w.a2) - im(w.a3) etc
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and remember also that
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Re([s+it][u+iv]) = su-tv
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Im([s+it][u+iv]) = sv+tu
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so
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Re(w'.(s+it)) = Re(w').s - Im(w').t = Re(w).s + Im(w).t
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Im(w'.(s+it)) = Re(w').t + Im(w').s = Re(w).t - Im(w).s
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For inverse dft we take the complex conjugate of all twiddle factors.
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Hence
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a0 = a0 + (w'.a2 + w.a3)
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a1 = a1 - i(w'.a2 - w.a3)
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a2 = a0 - (w'.a2 + w.a3)
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a3 = a1 + i(w'.a2 - w.a3)
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Define t1 = Re(w'.a2) = Re(w)*Re(a2) + Im(w)*Im(a2)
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t2 = Im(w'.a2) = Re(w)*Im(a2) - Im(w)*Re(a2)
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t5 = Re(w.a3) = Re(w)*Re(a3) - Im(w)*Im(a3)
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t6 = Im(w.a3) = Re(w)*Im(a3) + Im(w)*Re(a3)
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Then we just output:
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a0.re = a0.re + ( t1 + t5 )
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a0.im = a0.im + ( t2 + t6 )
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a1.re = a1.re + ( t2 - t6 ) // since we multiply by -i and i(-i) = 1
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a1.im = a1.im - ( t1 - t5 ) // since we multiply by -i and 1(-i) = -i
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a2.re = a0.re - ( t1 + t5 )
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a2.im = a0.im - ( t1 + t5 )
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a3.re = a1.re - ( t2 - t6 ) // since we multiply by +i and i(+i) = -1
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a3.im = a1.im + ( t1 - t5 ) // since we multiply by +i and 1(+i) = i
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*/
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#ifndef FFT_FFMPEG_INCL_OPTIMISED_TRANSFORM
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static inline FFTComplex* TRANSFORM(FFTComplex * z, unsigned int n, FFTSample wre, FFTSample wim)
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{
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register FFTSample t1,t2,t5,t6,r_re,r_im;
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r_re = z[n*2].re;
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r_im = z[n*2].im;
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XPROD31_R(r_re, r_im, wre, wim, t1,t2);
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r_re = z[n*3].re;
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r_im = z[n*3].im;
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XNPROD31_R(r_re, r_im, wre, wim, t5,t6);
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BUTTERFLIES(z[0],z[n],z[n*2],z[n*3]);
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return z+1;
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}
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static inline FFTComplex* TRANSFORM_W01(FFTComplex * z, unsigned int n, const FFTSample * w)
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{
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register const FFTSample wre=w[0],wim=w[1];
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register FFTSample t1,t2,t5,t6,r_re,r_im;
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r_re = z[n*2].re;
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r_im = z[n*2].im;
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XPROD31_R(r_re, r_im, wre, wim, t1,t2);
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r_re = z[n*3].re;
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r_im = z[n*3].im;
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XNPROD31_R(r_re, r_im, wre, wim, t5,t6);
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BUTTERFLIES(z[0],z[n],z[n*2],z[n*3]);
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return z+1;
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}
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static inline FFTComplex* TRANSFORM_W10(FFTComplex * z, unsigned int n, const FFTSample * w)
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{
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register const FFTSample wim=w[0],wre=w[1];
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register FFTSample t1,t2,t5,t6,r_re,r_im;
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r_re = z[n*2].re;
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r_im = z[n*2].im;
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XPROD31_R(r_re, r_im, wre, wim, t1,t2);
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r_re = z[n*3].re;
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r_im = z[n*3].im;
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XNPROD31_R(r_re, r_im, wre, wim, t5,t6);
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BUTTERFLIES(z[0],z[n],z[n*2],z[n*3]);
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return z+1;
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}
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static inline FFTComplex* TRANSFORM_EQUAL(FFTComplex * z, unsigned int n)
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{
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register FFTSample t1,t2,t5,t6,temp1,temp2;
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register FFTSample * my_z = (FFTSample *)(z);
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my_z += n*4;
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t2 = MULT31(my_z[0], cPI2_8);
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temp1 = MULT31(my_z[1], cPI2_8);
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my_z += n*2;
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temp2 = MULT31(my_z[0], cPI2_8);
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t5 = MULT31(my_z[1], cPI2_8);
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t1 = ( temp1 + t2 );
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t2 = ( temp1 - t2 );
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t6 = ( temp2 + t5 );
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t5 = ( temp2 - t5 );
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my_z -= n*6;
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BUTTERFLIES(z[0],z[n],z[n*2],z[n*3]);
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return z+1;
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}
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static inline FFTComplex* TRANSFORM_ZERO(FFTComplex * z, unsigned int n)
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{
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FFTSample t1,t2,t5,t6;
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t1 = z[n*2].re;
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t2 = z[n*2].im;
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t5 = z[n*3].re;
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t6 = z[n*3].im;
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BUTTERFLIES(z[0],z[n],z[n*2],z[n*3]);
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return z+1;
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}
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#endif
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/* z[0...8n-1], w[1...2n-1] */
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static void pass(FFTComplex *z_arg, unsigned int STEP_arg, unsigned int n_arg) ICODE_ATTR_TREMOR_MDCT;
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static void pass(FFTComplex *z_arg, unsigned int STEP_arg, unsigned int n_arg)
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{
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register FFTComplex * z = z_arg;
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register unsigned int STEP = STEP_arg;
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register unsigned int n = n_arg;
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register const FFTSample *w = sincos_lookup0+STEP;
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/* wre = *(wim+1) . ordering is sin,cos */
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register const FFTSample *w_end = sincos_lookup0+1024;
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/* first two are special (well, first one is special, but we need to do pairs) */
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z = TRANSFORM_ZERO(z,n);
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z = TRANSFORM_W10(z,n,w);
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w += STEP;
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/* first pass forwards through sincos_lookup0*/
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do {
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z = TRANSFORM_W10(z,n,w);
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w += STEP;
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z = TRANSFORM_W10(z,n,w);
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w += STEP;
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} while(LIKELY(w < w_end));
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/* second half: pass backwards through sincos_lookup0*/
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/* wim and wre are now in opposite places so ordering now [0],[1] */
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w_end=sincos_lookup0;
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while(LIKELY(w>w_end))
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{
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z = TRANSFORM_W01(z,n,w);
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w -= STEP;
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z = TRANSFORM_W01(z,n,w);
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w -= STEP;
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}
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}
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/* what is STEP?
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sincos_lookup0 has sin,cos pairs for 1/4 cycle, in 1024 points
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so half cycle would be 2048 points
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ff_cos_16 has 8 elements corresponding to 4 cos points and 4 sin points
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so each of the 4 points pairs corresponds to a 256*2-byte jump in sincos_lookup0
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8192/16 (from "ff_cos_16") is 512 bytes.
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i.e. for fft16, STEP = 8192/16 */
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#define DECL_FFT(n,n2,n4)\
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static void fft##n(FFTComplex *z) ICODE_ATTR_TREMOR_MDCT;\
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static void fft##n(FFTComplex *z)\
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{\
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fft##n2(z);\
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fft##n4(z+n4*2);\
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fft##n4(z+n4*3);\
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pass(z,8192/n,n4);\
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}
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#ifndef FFT_FFMPEG_INCL_OPTIMISED_FFT4
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static inline void fft4(FFTComplex *z)
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{
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FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
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BF(t3, t1, z[0].re, z[1].re); // t3=r1-r3 ; t1 = r1+r3
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BF(t8, t6, z[3].re, z[2].re); // t8=r7-r5 ; t6 = r7+r5
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BF(z[2].re, z[0].re, t1, t6); // r5=t1-t6 ; r1 = t1+t6
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BF(t4, t2, z[0].im, z[1].im); // t4=r2-r4 ; t2 = r2+r4
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BF(t7, t5, z[2].im, z[3].im); // t7=r6-r8 ; t5 = r6+r8
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BF(z[3].im, z[1].im, t4, t8); // r8=t4-t8 ; r4 = t4+t8
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BF(z[3].re, z[1].re, t3, t7); // r7=t3-t7 ; r3 = t3+t7
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BF(z[2].im, z[0].im, t2, t5); // r6=t2-t5 ; r2 = t2+t5
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}
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#endif
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static void fft4_dispatch(FFTComplex *z)
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{
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fft4(z);
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}
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#ifndef FFT_FFMPEG_INCL_OPTIMISED_FFT8
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static inline void fft8(FFTComplex *z)
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{
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fft4(z);
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FFTSample t1,t2,t3,t4,t7,t8;
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BF(t1, z[5].re, z[4].re, -z[5].re);
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BF(t2, z[5].im, z[4].im, -z[5].im);
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BF(t3, z[7].re, z[6].re, -z[7].re);
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BF(t4, z[7].im, z[6].im, -z[7].im);
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BF(t8, t1, t3, t1);
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BF(t7, t2, t2, t4);
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BF(z[4].re, z[0].re, z[0].re, t1);
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BF(z[4].im, z[0].im, z[0].im, t2);
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BF(z[6].re, z[2].re, z[2].re, t7);
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BF(z[6].im, z[2].im, z[2].im, t8);
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z++;
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TRANSFORM_EQUAL(z,2);
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}
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#endif
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static void fft8_dispatch(FFTComplex *z)
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{
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fft8(z);
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}
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#ifndef CONFIG_SMALL
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static void fft16(FFTComplex *z) ICODE_ATTR_TREMOR_MDCT;
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static void fft16(FFTComplex *z)
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{
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fft8(z);
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fft4(z+8);
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fft4(z+12);
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TRANSFORM_ZERO(z,4);
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z+=2;
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TRANSFORM_EQUAL(z,4);
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z-=1;
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TRANSFORM(z,4,cPI1_8,cPI3_8);
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z+=2;
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TRANSFORM(z,4,cPI3_8,cPI1_8);
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}
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#else
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DECL_FFT(16,8,4)
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#endif
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DECL_FFT(32,16,8)
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DECL_FFT(64,32,16)
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DECL_FFT(128,64,32)
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DECL_FFT(256,128,64)
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DECL_FFT(512,256,128)
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DECL_FFT(1024,512,256)
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DECL_FFT(2048,1024,512)
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DECL_FFT(4096,2048,1024)
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static void (*fft_dispatch[])(FFTComplex*) = {
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fft4_dispatch, fft8_dispatch, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
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fft2048, fft4096
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};
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void ff_fft_calc_c(int nbits, FFTComplex *z)
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{
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fft_dispatch[nbits-2](z);
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}
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#if 0
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int main (void)
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{
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#define PRECISION 16
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#define FFT_SIZE 1024
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#define ftofix32(x) ((fixed32)((x) * (float)(1 << PRECISION) + ((x) < 0 ? -0.5 : 0.5)))
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#define itofix32(x) ((x) << PRECISION)
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#define fixtoi32(x) ((x) >> PRECISION)
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int j;
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const long N = FFT_SIZE;
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double r[FFT_SIZE] = {0.0}, i[FFT_SIZE] = {0.0};
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long n;
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double t;
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double amp, phase;
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clock_t start, end;
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double exec_time = 0;
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FFTContext s;
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FFTComplex z[FFT_SIZE];
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memset(z, 0, 64*sizeof(FFTComplex));
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/* Generate saw-tooth test data */
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for (n = 0; n < FFT_SIZE; n++)
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{
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t = (2 * M_PI * n)/N;
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/*z[n].re = 1.1 + sin( t) +
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0.5 * sin(2.0 * t) +
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(1.0/3.0) * sin(3.0 * t) +
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0.25 * sin(4.0 * t) +
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0.2 * sin(5.0 * t) +
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(1.0/6.0) * sin(6.0 * t) +
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(1.0/7.0) * sin(7.0 * t) ;*/
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z[n].re = ftofix32(cos(2*M_PI*n/64));
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//printf("z[%d] = %f\n", n, z[n].re);
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//getchar();
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}
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ff_fft_init(&s, 10, 1);
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//start = clock();
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//for(n = 0; n < 1000000; n++)
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ff_fft_permute_c(&s, z);
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ff_fft_calc_c(&s, z);
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//end = clock();
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//exec_time = (((double)end-(double)start)/CLOCKS_PER_SEC);
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for(j = 0; j < FFT_SIZE; j++)
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{
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printf("%8.4f\n", sqrt(pow(fixtof32(z[j].re),2)+ pow(fixtof32(z[j].im), 2)));
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//getchar();
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}
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printf("muls = %d, adds = %d\n", muls, adds);
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//printf(" Time elapsed = %f\n", exec_time);
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//ff_fft_end(&s);
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}
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#endif
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