libavcodec/rdft.c

   1 /*
   2  * (I)RDFT transforms
   3  * Copyright (c) 2009 Alex Converse <alex dot converse at gmail dot com>
   4  *
   5  * This file is part of FFmpeg.
   6  *
   7  * FFmpeg is free software; you can redistribute it and/or
   8  * modify it under the terms of the GNU Lesser General Public
   9  * License as published by the Free Software Foundation; either
  10  * version 2.1 of the License, or (at your option) any later version.
  11  *
  12  * FFmpeg is distributed in the hope that it will be useful,
  13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  15  * Lesser General Public License for more details.
  16  *
  17  * You should have received a copy of the GNU Lesser General Public
  18  * License along with FFmpeg; if not, write to the Free Software
  19  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
  20  */
  21 #include <math.h>
  22 #include "dsputil.h"
  23
  24 /**
  25  * @file libavcodec/rdft.c
  26  * (Inverse) Real Discrete Fourier Transforms.
  27  */
  28
  29 /* sin(2*pi*x/n) for 0<=x<n/4, followed by n/2<=x<3n/4 */
  30 DECLARE_ALIGNED_16(FFTSample, ff_sin_16[8]);
  31 DECLARE_ALIGNED_16(FFTSample, ff_sin_32[16]);
  32 DECLARE_ALIGNED_16(FFTSample, ff_sin_64[32]);
  33 DECLARE_ALIGNED_16(FFTSample, ff_sin_128[64]);
  34 DECLARE_ALIGNED_16(FFTSample, ff_sin_256[128]);
  35 DECLARE_ALIGNED_16(FFTSample, ff_sin_512[256]);
  36 DECLARE_ALIGNED_16(FFTSample, ff_sin_1024[512]);
  37 DECLARE_ALIGNED_16(FFTSample, ff_sin_2048[1024]);
  38 DECLARE_ALIGNED_16(FFTSample, ff_sin_4096[2048]);
  39 DECLARE_ALIGNED_16(FFTSample, ff_sin_8192[4096]);
  40 DECLARE_ALIGNED_16(FFTSample, ff_sin_16384[8192]);
  41 DECLARE_ALIGNED_16(FFTSample, ff_sin_32768[16384]);
  42 DECLARE_ALIGNED_16(FFTSample, ff_sin_65536[32768]);
  43 FFTSample * const ff_sin_tabs[] = {
  44     ff_sin_16, ff_sin_32, ff_sin_64, ff_sin_128, ff_sin_256, ff_sin_512, ff_sin_1024,
  45     ff_sin_2048, ff_sin_4096, ff_sin_8192, ff_sin_16384, ff_sin_32768, ff_sin_65536,
  46 };
  47
  48 av_cold int ff_rdft_init(RDFTContext *s, int nbits, enum RDFTransformType trans)
  49 {
  50     int n = 1 << nbits;
  51     int i;
  52     const double theta = (trans == RDFT || trans == IRIDFT ? -1 : 1)*2*M_PI/n;
  53
  54     s->nbits           = nbits;
  55     s->inverse         = trans == IRDFT || trans == IRIDFT;
  56     s->sign_convention = trans == RIDFT || trans == IRIDFT ? 1 : -1;
  57
  58     if (nbits < 4 || nbits > 16)
  59         return -1;
  60
  61     if (ff_fft_init(&s->fft, nbits-1, trans == IRDFT || trans == RIDFT) < 0)
  62         return -1;
  63
  64     s->tcos = ff_cos_tabs[nbits-4];
  65     s->tsin = ff_sin_tabs[nbits-4]+(trans == RDFT || trans == IRIDFT)*(n>>2);
  66     for (i = 0; i < (n>>2); i++) {
  67         s->tcos[i] = cos(i*theta);
  68         s->tsin[i] = sin(i*theta);
  69     }
  70     return 0;
  71 }
  72
  73 /** Map one real FFT into two parallel real even and odd FFTs. Then interleave
  74  * the two real FFTs into one complex FFT. Unmangle the results.
  75  * ref: http://www.engineeringproductivitytools.com/stuff/T0001/PT10.HTM
  76  */
  77 void ff_rdft_calc_c(RDFTContext* s, FFTSample* data)
  78 {
  79     int i, i1, i2;
  80     FFTComplex ev, od;
  81     const int n = 1 << s->nbits;
  82     const float k1 = 0.5;
  83     const float k2 = 0.5 - s->inverse;
  84     const FFTSample *tcos = s->tcos;
  85     const FFTSample *tsin = s->tsin;
  86
  87     if (!s->inverse) {
  88         ff_fft_permute(&s->fft, (FFTComplex*)data);
  89         ff_fft_calc(&s->fft, (FFTComplex*)data);
  90     }
  91     /* i=0 is a special case because of packing, the DC term is real, so we
  92        are going to throw the N/2 term (also real) in with it. */
  93     ev.re = data[0];
  94     data[0] = ev.re+data[1];
  95     data[1] = ev.re-data[1];
  96     for (i = 1; i < (n>>2); i++) {
  97         i1 = 2*i;
  98         i2 = n-i1;
  99         /* Separate even and odd FFTs */
 100         ev.re =  k1*(data[i1  ]+data[i2  ]);
 101         od.im = -k2*(data[i1  ]-data[i2  ]);
 102         ev.im =  k1*(data[i1+1]-data[i2+1]);
 103         od.re =  k2*(data[i1+1]+data[i2+1]);
 104         /* Apply twiddle factors to the odd FFT and add to the even FFT */
 105         data[i1  ] =  ev.re + od.re*tcos[i] - od.im*tsin[i];
 106         data[i1+1] =  ev.im + od.im*tcos[i] + od.re*tsin[i];
 107         data[i2  ] =  ev.re - od.re*tcos[i] + od.im*tsin[i];
 108         data[i2+1] = -ev.im + od.im*tcos[i] + od.re*tsin[i];
 109     }
 110     data[2*i+1]=s->sign_convention*data[2*i+1];
 111     if (s->inverse) {
 112         data[0] *= k1;
 113         data[1] *= k1;
 114         ff_fft_permute(&s->fft, (FFTComplex*)data);
 115         ff_fft_calc(&s->fft, (FFTComplex*)data);
 116     }
 117 }
 118
 119 void ff_rdft_calc(RDFTContext *s, FFTSample *data)
 120 {
 121     ff_rdft_calc_c(s, data);
 122 }
 123
 124 av_cold void ff_rdft_end(RDFTContext *s)
 125 {
 126     ff_fft_end(&s->fft);
 127 }