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  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 <stdlib.h>
  22. #include <math.h>
  23. #include "libavutil/mathematics.h"
  24. #include "rdft.h"
  25.  
  26. /**
  27.  * @file
  28.  * (Inverse) Real Discrete Fourier Transforms.
  29.  */
  30.  
  31. /* sin(2*pi*x/n) for 0<=x<n/4, followed by n/2<=x<3n/4 */
  32. #if !CONFIG_HARDCODED_TABLES
  33. SINTABLE(16);
  34. SINTABLE(32);
  35. SINTABLE(64);
  36. SINTABLE(128);
  37. SINTABLE(256);
  38. SINTABLE(512);
  39. SINTABLE(1024);
  40. SINTABLE(2048);
  41. SINTABLE(4096);
  42. SINTABLE(8192);
  43. SINTABLE(16384);
  44. SINTABLE(32768);
  45. SINTABLE(65536);
  46. #endif
  47. static SINTABLE_CONST FFTSample * const ff_sin_tabs[] = {
  48.     NULL, NULL, NULL, NULL,
  49.     ff_sin_16, ff_sin_32, ff_sin_64, ff_sin_128, ff_sin_256, ff_sin_512, ff_sin_1024,
  50.     ff_sin_2048, ff_sin_4096, ff_sin_8192, ff_sin_16384, ff_sin_32768, ff_sin_65536,
  51. };
  52.  
  53. /** Map one real FFT into two parallel real even and odd FFTs. Then interleave
  54.  * the two real FFTs into one complex FFT. Unmangle the results.
  55.  * ref: http://www.engineeringproductivitytools.com/stuff/T0001/PT10.HTM
  56.  */
  57. static void rdft_calc_c(RDFTContext *s, FFTSample *data)
  58. {
  59.     int i, i1, i2;
  60.     FFTComplex ev, od;
  61.     const int n = 1 << s->nbits;
  62.     const float k1 = 0.5;
  63.     const float k2 = 0.5 - s->inverse;
  64.     const FFTSample *tcos = s->tcos;
  65.     const FFTSample *tsin = s->tsin;
  66.  
  67.     if (!s->inverse) {
  68.         s->fft.fft_permute(&s->fft, (FFTComplex*)data);
  69.         s->fft.fft_calc(&s->fft, (FFTComplex*)data);
  70.     }
  71.     /* i=0 is a special case because of packing, the DC term is real, so we
  72.        are going to throw the N/2 term (also real) in with it. */
  73.     ev.re = data[0];
  74.     data[0] = ev.re+data[1];
  75.     data[1] = ev.re-data[1];
  76.     for (i = 1; i < (n>>2); i++) {
  77.         i1 = 2*i;
  78.         i2 = n-i1;
  79.         /* Separate even and odd FFTs */
  80.         ev.re =  k1*(data[i1  ]+data[i2  ]);
  81.         od.im = -k2*(data[i1  ]-data[i2  ]);
  82.         ev.im =  k1*(data[i1+1]-data[i2+1]);
  83.         od.re =  k2*(data[i1+1]+data[i2+1]);
  84.         /* Apply twiddle factors to the odd FFT and add to the even FFT */
  85.         data[i1  ] =  ev.re + od.re*tcos[i] - od.im*tsin[i];
  86.         data[i1+1] =  ev.im + od.im*tcos[i] + od.re*tsin[i];
  87.         data[i2  ] =  ev.re - od.re*tcos[i] + od.im*tsin[i];
  88.         data[i2+1] = -ev.im + od.im*tcos[i] + od.re*tsin[i];
  89.     }
  90.     data[2*i+1]=s->sign_convention*data[2*i+1];
  91.     if (s->inverse) {
  92.         data[0] *= k1;
  93.         data[1] *= k1;
  94.         s->fft.fft_permute(&s->fft, (FFTComplex*)data);
  95.         s->fft.fft_calc(&s->fft, (FFTComplex*)data);
  96.     }
  97. }
  98.  
  99. av_cold int ff_rdft_init(RDFTContext *s, int nbits, enum RDFTransformType trans)
  100. {
  101.     int n = 1 << nbits;
  102.     int i;
  103.     const double theta = (trans == DFT_R2C || trans == DFT_C2R ? -1 : 1)*2*M_PI/n;
  104.  
  105.     s->nbits           = nbits;
  106.     s->inverse         = trans == IDFT_C2R || trans == DFT_C2R;
  107.     s->sign_convention = trans == IDFT_R2C || trans == DFT_C2R ? 1 : -1;
  108.  
  109.     if (nbits < 4 || nbits > 16)
  110.         return -1;
  111.  
  112.     if (ff_fft_init(&s->fft, nbits-1, trans == IDFT_C2R || trans == IDFT_R2C) < 0)
  113.         return -1;
  114.  
  115.     ff_init_ff_cos_tabs(nbits);
  116.     s->tcos = ff_cos_tabs[nbits];
  117.     s->tsin = ff_sin_tabs[nbits]+(trans == DFT_R2C || trans == DFT_C2R)*(n>>2);
  118. #if !CONFIG_HARDCODED_TABLES
  119.     for (i = 0; i < (n>>2); i++) {
  120.         s->tsin[i] = sin(i*theta);
  121.     }
  122. #endif
  123.     s->rdft_calc   = rdft_calc_c;
  124.  
  125.     if (ARCH_ARM) ff_rdft_init_arm(s);
  126.  
  127.     return 0;
  128. }
  129.  
  130. av_cold void ff_rdft_end(RDFTContext *s)
  131. {
  132.     ff_fft_end(&s->fft);
  133. }
  134.