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