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 #if !CONFIG_HARDCODED_TABLES
  31 SINTABLE(16);
  32 SINTABLE(32);
  33 SINTABLE(64);
  34 SINTABLE(128);
  35 SINTABLE(256);
  36 SINTABLE(512);
  37 SINTABLE(1024);
  38 SINTABLE(2048);
  39 SINTABLE(4096);
  40 SINTABLE(8192);
  41 SINTABLE(16384);
  42 SINTABLE(32768);
  43 SINTABLE(65536);
  44 #endif
  45 SINTABLE_CONST FFTSample * const ff_sin_tabs[] = {
  46     NULL, NULL, NULL, NULL,
  47     ff_sin_16, ff_sin_32, ff_sin_64, ff_sin_128, ff_sin_256, ff_sin_512, ff_sin_1024,
  48     ff_sin_2048, ff_sin_4096, ff_sin_8192, ff_sin_16384, ff_sin_32768, ff_sin_65536,
  49 };
  50
  51 av_cold int ff_rdft_init(RDFTContext *s, int nbits, enum RDFTransformType trans)
  52 {
  53     int n = 1 << nbits;
  54     int i;
  55     const double theta = (trans == RDFT || trans == IRIDFT ? -1 : 1)*2*M_PI/n;
  56
  57     s->nbits           = nbits;
  58     s->inverse         = trans == IRDFT || trans == IRIDFT;
  59     s->sign_convention = trans == RIDFT || trans == IRIDFT ? 1 : -1;
  60
  61     if (nbits < 4 || nbits > 16)
  62         return -1;
  63
  64     if (ff_fft_init(&s->fft, nbits-1, trans == IRDFT || trans == RIDFT) < 0)
  65         return -1;
  66
  67     ff_init_ff_cos_tabs(nbits);
  68     s->tcos = ff_cos_tabs[nbits];
  69     s->tsin = ff_sin_tabs[nbits]+(trans == RDFT || trans == IRIDFT)*(n>>2);
  70 #if !CONFIG_HARDCODED_TABLES
  71     for (i = 0; i < (n>>2); i++) {
  72         s->tsin[i] = sin(i*theta);
  73     }
  74 #endif
  75     return 0;
  76 }
  77
  78 /** Map one real FFT into two parallel real even and odd FFTs. Then interleave
  79  * the two real FFTs into one complex FFT. Unmangle the results.
  80  * ref: http://www.engineeringproductivitytools.com/stuff/T0001/PT10.HTM
  81  */
  82 void ff_rdft_calc_c(RDFTContext* s, FFTSample* data)
  83 {
  84     int i, i1, i2;
  85     FFTComplex ev, od;
  86     const int n = 1 << s->nbits;
  87     const float k1 = 0.5;
  88     const float k2 = 0.5 - s->inverse;
  89     const FFTSample *tcos = s->tcos;
  90     const FFTSample *tsin = s->tsin;
  91
  92     if (!s->inverse) {
  93         ff_fft_permute(&s->fft, (FFTComplex*)data);
  94         ff_fft_calc(&s->fft, (FFTComplex*)data);
  95     }
  96     /* i=0 is a special case because of packing, the DC term is real, so we
  97        are going to throw the N/2 term (also real) in with it. */
  98     ev.re = data[0];
  99     data[0] = ev.re+data[1];
 100     data[1] = ev.re-data[1];
 101     for (i = 1; i < (n>>2); i++) {
 102         i1 = 2*i;
 103         i2 = n-i1;
 104         /* Separate even and odd FFTs */
 105         ev.re =  k1*(data[i1  ]+data[i2  ]);
 106         od.im = -k2*(data[i1  ]-data[i2  ]);
 107         ev.im =  k1*(data[i1+1]-data[i2+1]);
 108         od.re =  k2*(data[i1+1]+data[i2+1]);
 109         /* Apply twiddle factors to the odd FFT and add to the even FFT */
 110         data[i1  ] =  ev.re + od.re*tcos[i] - od.im*tsin[i];
 111         data[i1+1] =  ev.im + od.im*tcos[i] + od.re*tsin[i];
 112         data[i2  ] =  ev.re - od.re*tcos[i] + od.im*tsin[i];
 113         data[i2+1] = -ev.im + od.im*tcos[i] + od.re*tsin[i];
 114     }
 115     data[2*i+1]=s->sign_convention*data[2*i+1];
 116     if (s->inverse) {
 117         data[0] *= k1;
 118         data[1] *= k1;
 119         ff_fft_permute(&s->fft, (FFTComplex*)data);
 120         ff_fft_calc(&s->fft, (FFTComplex*)data);
 121     }
 122 }
 123
 124 void ff_rdft_calc(RDFTContext *s, FFTSample *data)
 125 {
 126     ff_rdft_calc_c(s, data);
 127 }
 128
 129 av_cold void ff_rdft_end(RDFTContext *s)
 130 {
 131     ff_fft_end(&s->fft);
 132 }