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 */ 30DECLARE_ALIGNED_16(FFTSample, ff_sin_16[8]); 31DECLARE_ALIGNED_16(FFTSample, ff_sin_32[16]); 32DECLARE_ALIGNED_16(FFTSample, ff_sin_64[32]); 33DECLARE_ALIGNED_16(FFTSample, ff_sin_128[64]); 34DECLARE_ALIGNED_16(FFTSample, ff_sin_256[128]); 35DECLARE_ALIGNED_16(FFTSample, ff_sin_512[256]); 36DECLARE_ALIGNED_16(FFTSample, ff_sin_1024[512]); 37DECLARE_ALIGNED_16(FFTSample, ff_sin_2048[1024]); 38DECLARE_ALIGNED_16(FFTSample, ff_sin_4096[2048]); 39DECLARE_ALIGNED_16(FFTSample, ff_sin_8192[4096]); 40DECLARE_ALIGNED_16(FFTSample, ff_sin_16384[8192]); 41DECLARE_ALIGNED_16(FFTSample, ff_sin_32768[16384]); 42DECLARE_ALIGNED_16(FFTSample, ff_sin_65536[32768]); 43FFTSample *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 48av_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 */ 77void 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 119void ff_rdft_calc(RDFTContext *s, FFTSample *data) 120{ 121 ff_rdft_calc_c(s, data); 122} 123 124av_cold void ff_rdft_end(RDFTContext *s) 125{ 126 ff_fft_end(&s->fft); 127} 128