yading@10: /*
yading@10:  * (I)RDFT transforms
yading@10:  * Copyright (c) 2009 Alex Converse <alex dot converse at gmail dot com>
yading@10:  *
yading@10:  * This file is part of FFmpeg.
yading@10:  *
yading@10:  * FFmpeg is free software; you can redistribute it and/or
yading@10:  * modify it under the terms of the GNU Lesser General Public
yading@10:  * License as published by the Free Software Foundation; either
yading@10:  * version 2.1 of the License, or (at your option) any later version.
yading@10:  *
yading@10:  * FFmpeg is distributed in the hope that it will be useful,
yading@10:  * but WITHOUT ANY WARRANTY; without even the implied warranty of
yading@10:  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
yading@10:  * Lesser General Public License for more details.
yading@10:  *
yading@10:  * You should have received a copy of the GNU Lesser General Public
yading@10:  * License along with FFmpeg; if not, write to the Free Software
yading@10:  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
yading@10:  */
yading@10: #include <stdlib.h>
yading@10: #include <math.h>
yading@10: #include "libavutil/mathematics.h"
yading@10: #include "rdft.h"
yading@10: 
yading@10: /**
yading@10:  * @file
yading@10:  * (Inverse) Real Discrete Fourier Transforms.
yading@10:  */
yading@10: 
yading@10: /* sin(2*pi*x/n) for 0<=x<n/4, followed by n/2<=x<3n/4 */
yading@10: #if !CONFIG_HARDCODED_TABLES
yading@10: SINTABLE(16);
yading@10: SINTABLE(32);
yading@10: SINTABLE(64);
yading@10: SINTABLE(128);
yading@10: SINTABLE(256);
yading@10: SINTABLE(512);
yading@10: SINTABLE(1024);
yading@10: SINTABLE(2048);
yading@10: SINTABLE(4096);
yading@10: SINTABLE(8192);
yading@10: SINTABLE(16384);
yading@10: SINTABLE(32768);
yading@10: SINTABLE(65536);
yading@10: #endif
yading@10: static SINTABLE_CONST FFTSample * const ff_sin_tabs[] = {
yading@10:     NULL, NULL, NULL, NULL,
yading@10:     ff_sin_16, ff_sin_32, ff_sin_64, ff_sin_128, ff_sin_256, ff_sin_512, ff_sin_1024,
yading@10:     ff_sin_2048, ff_sin_4096, ff_sin_8192, ff_sin_16384, ff_sin_32768, ff_sin_65536,
yading@10: };
yading@10: 
yading@10: /** Map one real FFT into two parallel real even and odd FFTs. Then interleave
yading@10:  * the two real FFTs into one complex FFT. Unmangle the results.
yading@10:  * ref: http://www.engineeringproductivitytools.com/stuff/T0001/PT10.HTM
yading@10:  */
yading@10: static void ff_rdft_calc_c(RDFTContext* s, FFTSample* data)
yading@10: {
yading@10:     int i, i1, i2;
yading@10:     FFTComplex ev, od;
yading@10:     const int n = 1 << s->nbits;
yading@10:     const float k1 = 0.5;
yading@10:     const float k2 = 0.5 - s->inverse;
yading@10:     const FFTSample *tcos = s->tcos;
yading@10:     const FFTSample *tsin = s->tsin;
yading@10: 
yading@10:     if (!s->inverse) {
yading@10:         s->fft.fft_permute(&s->fft, (FFTComplex*)data);
yading@10:         s->fft.fft_calc(&s->fft, (FFTComplex*)data);
yading@10:     }
yading@10:     /* i=0 is a special case because of packing, the DC term is real, so we
yading@10:        are going to throw the N/2 term (also real) in with it. */
yading@10:     ev.re = data[0];
yading@10:     data[0] = ev.re+data[1];
yading@10:     data[1] = ev.re-data[1];
yading@10:     for (i = 1; i < (n>>2); i++) {
yading@10:         i1 = 2*i;
yading@10:         i2 = n-i1;
yading@10:         /* Separate even and odd FFTs */
yading@10:         ev.re =  k1*(data[i1  ]+data[i2  ]);
yading@10:         od.im = -k2*(data[i1  ]-data[i2  ]);
yading@10:         ev.im =  k1*(data[i1+1]-data[i2+1]);
yading@10:         od.re =  k2*(data[i1+1]+data[i2+1]);
yading@10:         /* Apply twiddle factors to the odd FFT and add to the even FFT */
yading@10:         data[i1  ] =  ev.re + od.re*tcos[i] - od.im*tsin[i];
yading@10:         data[i1+1] =  ev.im + od.im*tcos[i] + od.re*tsin[i];
yading@10:         data[i2  ] =  ev.re - od.re*tcos[i] + od.im*tsin[i];
yading@10:         data[i2+1] = -ev.im + od.im*tcos[i] + od.re*tsin[i];
yading@10:     }
yading@10:     data[2*i+1]=s->sign_convention*data[2*i+1];
yading@10:     if (s->inverse) {
yading@10:         data[0] *= k1;
yading@10:         data[1] *= k1;
yading@10:         s->fft.fft_permute(&s->fft, (FFTComplex*)data);
yading@10:         s->fft.fft_calc(&s->fft, (FFTComplex*)data);
yading@10:     }
yading@10: }
yading@10: 
yading@10: av_cold int ff_rdft_init(RDFTContext *s, int nbits, enum RDFTransformType trans)
yading@10: {
yading@10:     int n = 1 << nbits;
yading@10:     int i;
yading@10:     const double theta = (trans == DFT_R2C || trans == DFT_C2R ? -1 : 1)*2*M_PI/n;
yading@10: 
yading@10:     s->nbits           = nbits;
yading@10:     s->inverse         = trans == IDFT_C2R || trans == DFT_C2R;
yading@10:     s->sign_convention = trans == IDFT_R2C || trans == DFT_C2R ? 1 : -1;
yading@10: 
yading@10:     if (nbits < 4 || nbits > 16)
yading@10:         return -1;
yading@10: 
yading@10:     if (ff_fft_init(&s->fft, nbits-1, trans == IDFT_C2R || trans == IDFT_R2C) < 0)
yading@10:         return -1;
yading@10: 
yading@10:     ff_init_ff_cos_tabs(nbits);
yading@10:     s->tcos = ff_cos_tabs[nbits];
yading@10:     s->tsin = ff_sin_tabs[nbits]+(trans == DFT_R2C || trans == DFT_C2R)*(n>>2);
yading@10: #if !CONFIG_HARDCODED_TABLES
yading@10:     for (i = 0; i < (n>>2); i++) {
yading@10:         s->tsin[i] = sin(i*theta);
yading@10:     }
yading@10: #endif
yading@10:     s->rdft_calc   = ff_rdft_calc_c;
yading@10: 
yading@10:     if (ARCH_ARM) ff_rdft_init_arm(s);
yading@10: 
yading@10:     return 0;
yading@10: }
yading@10: 
yading@10: av_cold void ff_rdft_end(RDFTContext *s)
yading@10: {
yading@10:     ff_fft_end(&s->fft);
yading@10: }