apps/codecs/lib/fft-ffmpeg.c

   1 /*
   2  * FFT/IFFT transforms converted to integer precision
   3  * Copyright (c) 2010 Dave Hooper, Mohamed Tarek, Michael Giacomelli
   4  * Copyright (c) 2008 Loren Merritt
   5  * Copyright (c) 2002 Fabrice Bellard
   6  * Partly based on libdjbfft by D. J. Bernstein
   7  *
   8  * This file is part of FFmpeg.
   9  *
  10  * FFmpeg is free software; you can redistribute it and/or
  11  * modify it under the terms of the GNU Lesser General Public
  12  * License as published by the Free Software Foundation; either
  13  * version 2.1 of the License, or (at your option) any later version.
  14  *
  15  * FFmpeg is distributed in the hope that it will be useful,
  16  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  17  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  18  * Lesser General Public License for more details.
  19  *
  20  * You should have received a copy of the GNU Lesser General Public
  21  * License along with FFmpeg; if not, write to the Free Software
  22  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
  23  */
  24
  25 /**
  26  * @file libavcodec/fft.c
  27  * FFT/IFFT transforms.
  28  */
  29
  30
  31 #ifdef CPU_ARM
  32 // we definitely want CONFIG_SMALL undefined for ipod
  33 // so we get the inlined version of fft16 (which is measurably faster)
  34 #undef CONFIG_SMALL
  35 #else
  36 #undef CONFIG_SMALL
  37 #endif
  38
  39 #include "fft.h"
  40 #include <string.h>
  41 #include <stdlib.h>
  42 #include <math.h>
  43 #include <inttypes.h>
  44 #include <time.h>
  45 #include <codecs/lib/codeclib.h>
  46
  47 #include "codeclib_misc.h"
  48 #include "mdct_lookup.h"
  49
  50 /* constants for fft_16 (same constants as in mdct_arm.S ... ) */
  51 #define cPI1_8 (0x7641af3d) /* cos(pi/8) s.31 */
  52 #define cPI2_8 (0x5a82799a) /* cos(2pi/8) = 1/sqrt(2) s.31 */
  53 #define cPI3_8 (0x30fbc54d) /* cos(3pi/8) s.31 */
  54
  55 /* asm-optimised functions and/or macros */
  56 #include "fft-ffmpeg_arm.h"
  57 #include "fft-ffmpeg_cf.h"
  58
  59 #ifndef ICODE_ATTR_TREMOR_MDCT
  60 #define ICODE_ATTR_TREMOR_MDCT ICODE_ATTR
  61 #endif
  62
  63 #if 0
  64 static int split_radix_permutation(int i, int n, int inverse)
  65 {
  66     int m;
  67     if(n <= 2) return i&1;
  68     m = n >> 1;
  69     if(!(i&m))            return split_radix_permutation(i, m, inverse)*2;
  70     m >>= 1;
  71     if(inverse == !(i&m)) return split_radix_permutation(i, m, inverse)*4 + 1;
  72     else                  return split_radix_permutation(i, m, inverse)*4 - 1;
  73 }
  74
  75 static void ff_fft_permute_c(FFTContext *s, FFTComplex *z)
  76 {
  77     int j, k, np;
  78     FFTComplex tmp;
  79     //const uint16_t *revtab = s->revtab;
  80     np = 1 << s->nbits;
  81
  82     const int revtab_shift = (12 - s->nbits);
  83
  84     /* reverse */
  85     for(j=0;j<np;j++) {
  86         k = revtab[j]>>revtab_shift;
  87         if (k < j) {
  88             tmp = z[k];
  89             z[k] = z[j];
  90             z[j] = tmp;
  91         }
  92     }
  93 }
  94 #endif
  95
  96 #define BF(x,y,a,b) {\
  97     x = a - b;\
  98     y = a + b;\
  99 }
 100
 101 #define BF_REV(x,y,a,b) {\
 102     x = a + b;\
 103     y = a - b;\
 104 }
 105
 106 #ifndef FFT_FFMPEG_INCL_OPTIMISED_BUTTERFLIES
 107 #define BUTTERFLIES(a0,a1,a2,a3) {\
 108     {\
 109         FFTSample temp1,temp2;\
 110         BF(temp1, temp2, t5, t1);\
 111         BF(a2.re, a0.re, a0.re, temp2);\
 112         BF(a3.im, a1.im, a1.im, temp1);\
 113     }\
 114     {\
 115         FFTSample temp1,temp2;\
 116         BF(temp1, temp2, t2, t6);\
 117         BF(a3.re, a1.re, a1.re, temp1);\
 118         BF(a2.im, a0.im, a0.im, temp2);\
 119     }\
 120 }
 121
 122 // force loading all the inputs before storing any.
 123 // this is slightly slower for small data, but avoids store->load aliasing
 124 // for addresses separated by large powers of 2.
 125 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
 126     FFTSample r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
 127     {\
 128         FFTSample temp1, temp2;\
 129         BF(temp1, temp2, t5, t1);\
 130         BF(a2.re, a0.re, r0, temp2);\
 131         BF(a3.im, a1.im, i1, temp1);\
 132     }\
 133     {\
 134         FFTSample temp1, temp2;\
 135         BF(temp1, temp2, t2, t6);\
 136         BF(a3.re, a1.re, r1, temp1);\
 137         BF(a2.im, a0.im, i0, temp2);\
 138     }\
 139 }
 140 #endif
 141
 142 /*
 143   see conjugate pair description in
 144   http://www.fftw.org/newsplit.pdf
 145
 146   a0 = z[k]
 147   a1 = z[k+N/4]
 148   a2 = z[k+2N/4]
 149   a3 = z[k+3N/4]
 150
 151   result:
 152   y[k]      = z[k]+w(z[k+2N/4])+w'(z[k+3N/4])
 153   y[k+N/4]  = z[k+N/4]-iw(z[k+2N/4])+iw'(z[k+3N/4])
 154   y[k+2N/4] = z[k]-w(z[k+2N/4])-w'(z[k+3N/4])
 155   y[k+3N/4] = z[k+N/4]+iw(z[k+2N/4])-iw'(z[k+3N/4])
 156
 157   i.e.
 158
 159   a0        = a0 +  (w.a2 + w'.a3)
 160   a1        = a1 - i(w.a2 - w'.a3)
 161   a2        = a0 -  (w.a2 + w'.a3)
 162   a3        = a1 + i(w.a2 - w'.a3)
 163
 164   note re(w') = re(w) and im(w') = -im(w)
 165
 166   so therefore
 167
 168   re(a0)   = re(a0) + re(w.a2) + re(w.a3)
 169   im(a0)   = im(a0) + im(w.a2) - im(w.a3) etc
 170
 171   and remember also that
 172   Re([s+it][u+iv]) = su-tv
 173   Im([s+it][u+iv]) = sv+tu
 174
 175   so
 176   Re(w'.(s+it)) = Re(w').s - Im(w').t = Re(w).s + Im(w).t
 177   Im(w'.(s+it)) = Re(w').t + Im(w').s = Re(w).t - Im(w).s
 178
 179   For inverse dft we take the complex conjugate of all twiddle factors.
 180   Hence
 181
 182   a0        = a0 +  (w'.a2 + w.a3)
 183   a1        = a1 - i(w'.a2 - w.a3)
 184   a2        = a0 -  (w'.a2 + w.a3)
 185   a3        = a1 + i(w'.a2 - w.a3)
 186
 187   Define t1 = Re(w'.a2)  =  Re(w)*Re(a2) + Im(w)*Im(a2)
 188          t2 = Im(w'.a2)  =  Re(w)*Im(a2) - Im(w)*Re(a2)
 189          t5 = Re(w.a3)   =  Re(w)*Re(a3) - Im(w)*Im(a3)
 190          t6 = Im(w.a3)   =  Re(w)*Im(a3) + Im(w)*Re(a3)
 191
 192   Then we just output:
 193   a0.re = a0.re + ( t1 + t5 )
 194   a0.im = a0.im + ( t2 + t6 )
 195   a1.re = a1.re + ( t2 - t6 )   // since we multiply by -i and i(-i) = 1
 196   a1.im = a1.im - ( t1 - t5 )   // since we multiply by -i and 1(-i) = -i
 197   a2.re = a0.re - ( t1 + t5 )
 198   a2.im = a0.im - ( t1 + t5 )
 199   a3.re = a1.re - ( t2 - t6 )   // since we multiply by +i and i(+i) = -1
 200   a3.im = a1.im + ( t1 - t5 )   // since we multiply by +i and 1(+i) = i
 201
 202
 203 */
 204
 205 #ifndef FFT_FFMPEG_INCL_OPTIMISED_TRANSFORM
 206 static inline FFTComplex* TRANSFORM(FFTComplex * z, unsigned int n, FFTSample wre, FFTSample wim)
 207 {
 208     register FFTSample t1,t2,t5,t6,r_re,r_im;
 209     r_re = z[n*2].re;
 210     r_im = z[n*2].im;
 211     XPROD31_R(r_re, r_im, wre, wim, t1,t2);
 212     r_re = z[n*3].re;
 213     r_im = z[n*3].im;
 214     XNPROD31_R(r_re, r_im, wre, wim, t5,t6);
 215     BUTTERFLIES(z[0],z[n],z[n*2],z[n*3]);
 216     return z+1;
 217 }
 218
 219 static inline FFTComplex* TRANSFORM_W01(FFTComplex * z, unsigned int n, const FFTSample * w)
 220 {
 221     register const FFTSample wre=w[0],wim=w[1];
 222     register FFTSample t1,t2,t5,t6,r_re,r_im;
 223     r_re = z[n*2].re;
 224     r_im = z[n*2].im;
 225     XPROD31_R(r_re, r_im, wre, wim, t1,t2);
 226     r_re = z[n*3].re;
 227     r_im = z[n*3].im;
 228     XNPROD31_R(r_re, r_im, wre, wim, t5,t6);
 229     BUTTERFLIES(z[0],z[n],z[n*2],z[n*3]);
 230     return z+1;
 231 }
 232
 233 static inline FFTComplex* TRANSFORM_W10(FFTComplex * z, unsigned int n, const FFTSample * w)
 234 {
 235     register const FFTSample wim=w[0],wre=w[1];
 236     register FFTSample t1,t2,t5,t6,r_re,r_im;
 237     r_re = z[n*2].re;
 238     r_im = z[n*2].im;
 239     XPROD31_R(r_re, r_im, wre, wim, t1,t2);
 240     r_re = z[n*3].re;
 241     r_im = z[n*3].im;
 242     XNPROD31_R(r_re, r_im, wre, wim, t5,t6);
 243     BUTTERFLIES(z[0],z[n],z[n*2],z[n*3]);
 244     return z+1;
 245 }
 246
 247 static inline FFTComplex* TRANSFORM_EQUAL(FFTComplex * z, unsigned int n)
 248 {
 249     register FFTSample t1,t2,t5,t6,temp1,temp2;
 250     register FFTSample * my_z = (FFTSample *)(z);
 251     my_z += n*4;
 252     t2    = MULT31(my_z[0], cPI2_8);
 253     temp1 = MULT31(my_z[1], cPI2_8);
 254     my_z += n*2;
 255     temp2 = MULT31(my_z[0], cPI2_8);
 256     t5    = MULT31(my_z[1], cPI2_8);
 257     t1 = ( temp1 + t2 );
 258     t2 = ( temp1 - t2 );
 259     t6 = ( temp2 + t5 );
 260     t5 = ( temp2 - t5 );
 261     my_z -= n*6;
 262     BUTTERFLIES(z[0],z[n],z[n*2],z[n*3]);
 263     return z+1;
 264 }
 265
 266 static inline FFTComplex* TRANSFORM_ZERO(FFTComplex * z, unsigned int n)
 267 {
 268     FFTSample t1,t2,t5,t6;
 269     t1 = z[n*2].re;
 270     t2 = z[n*2].im;
 271     t5 = z[n*3].re;
 272     t6 = z[n*3].im;
 273     BUTTERFLIES(z[0],z[n],z[n*2],z[n*3]);
 274     return z+1;
 275 }
 276 #endif
 277
 278 /* z[0...8n-1], w[1...2n-1] */
 279 void pass(FFTComplex *z_arg, unsigned int STEP_arg, unsigned int n_arg) ICODE_ATTR_TREMOR_MDCT;
 280 void pass(FFTComplex *z_arg, unsigned int STEP_arg, unsigned int n_arg)
 281 {
 282     register FFTComplex * z = z_arg;
 283     register unsigned int STEP = STEP_arg;
 284     register unsigned int n = n_arg;
 285
 286     register const FFTSample *w = sincos_lookup0+STEP;
 287     /* wre = *(wim+1) .  ordering is sin,cos */
 288     register const FFTSample *w_end = sincos_lookup0+1024;
 289
 290     /* first two are special (well, first one is special, but we need to do pairs) */
 291     z = TRANSFORM_ZERO(z,n);
 292     z = TRANSFORM_W10(z,n,w);
 293     w += STEP;
 294     /* first pass forwards through sincos_lookup0*/
 295     do {
 296         z = TRANSFORM_W10(z,n,w);
 297         w += STEP;
 298         z = TRANSFORM_W10(z,n,w);
 299         w += STEP;
 300     } while(LIKELY(w < w_end));
 301     /* second half: pass backwards through sincos_lookup0*/
 302     /* wim and wre are now in opposite places so ordering now [0],[1] */
 303     w_end=sincos_lookup0;
 304     while(LIKELY(w>w_end))
 305     {
 306         z = TRANSFORM_W01(z,n,w);
 307         w -= STEP;
 308         z = TRANSFORM_W01(z,n,w);
 309         w -= STEP;
 310     }
 311 }
 312
 313 /* what is STEP?
 314    sincos_lookup0 has sin,cos pairs for 1/4 cycle, in 1024 points
 315    so half cycle would be 2048 points
 316    ff_cos_16 has 8 elements corresponding to 4 cos points and 4 sin points
 317    so each of the 4 points pairs corresponds to a 256*2-byte jump in sincos_lookup0
 318    8192/16 (from "ff_cos_16") is 512 bytes.
 319    i.e.  for fft16, STEP = 8192/16 */
 320 #define DECL_FFT(n,n2,n4)\
 321 void fft##n(FFTComplex *z) ICODE_ATTR_TREMOR_MDCT;\
 322 void fft##n(FFTComplex *z)\
 323 {\
 324     fft##n2(z);\
 325     fft##n4(z+n4*2);\
 326     fft##n4(z+n4*3);\
 327     pass(z,8192/n,n4);\
 328 }
 329
 330 #ifndef FFT_FFMPEG_INCL_OPTIMISED_FFT4
 331 static inline void fft4(FFTComplex *z)
 332 {
 333     FFTSample t1, t2, t3, t4, t5, t6, t7, t8;
 334
 335     BF(t3, t1, z[0].re, z[1].re); // t3=r1-r3 ; t1 = r1+r3
 336     BF(t8, t6, z[3].re, z[2].re); // t8=r7-r5 ; t6 = r7+r5
 337
 338     BF(z[2].re, z[0].re, t1, t6); // r5=t1-t6 ; r1 = t1+t6
 339
 340     BF(t4, t2, z[0].im, z[1].im); // t4=r2-r4 ; t2 = r2+r4
 341     BF(t7, t5, z[2].im, z[3].im); // t7=r6-r8 ; t5 = r6+r8
 342
 343     BF(z[3].im, z[1].im, t4, t8); // r8=t4-t8 ; r4 = t4+t8
 344     BF(z[3].re, z[1].re, t3, t7); // r7=t3-t7 ; r3 = t3+t7
 345     BF(z[2].im, z[0].im, t2, t5); // r6=t2-t5 ; r2 = t2+t5
 346 }
 347 #endif
 348
 349 static void fft4_dispatch(FFTComplex *z)
 350 {
 351     fft4(z);
 352 }
 353
 354 #ifndef FFT_FFMPEG_INCL_OPTIMISED_FFT8
 355 static inline void fft8(FFTComplex *z)
 356 {
 357     fft4(z);
 358     FFTSample t1,t2,t3,t4,t7,t8;
 359
 360     BF(t1, z[5].re, z[4].re, -z[5].re);
 361     BF(t2, z[5].im, z[4].im, -z[5].im);
 362     BF(t3, z[7].re, z[6].re, -z[7].re);
 363     BF(t4, z[7].im, z[6].im, -z[7].im);
 364     BF(t8, t1, t3, t1);
 365     BF(t7, t2, t2, t4);
 366     BF(z[4].re, z[0].re, z[0].re, t1);
 367     BF(z[4].im, z[0].im, z[0].im, t2);
 368     BF(z[6].re, z[2].re, z[2].re, t7);
 369     BF(z[6].im, z[2].im, z[2].im, t8);
 370
 371     z++;
 372     TRANSFORM_EQUAL(z,2);
 373 }
 374 #endif
 375
 376 static void fft8_dispatch(FFTComplex *z)
 377 {
 378     fft8(z);
 379 }
 380
 381 #ifndef CONFIG_SMALL
 382 void fft16(FFTComplex *z) ICODE_ATTR_TREMOR_MDCT;
 383 void fft16(FFTComplex *z)
 384 {
 385     fft8(z);
 386     fft4(z+8);
 387     fft4(z+12);
 388
 389     TRANSFORM_ZERO(z,4);
 390     z+=2;
 391     TRANSFORM_EQUAL(z,4);
 392     z-=1;
 393     TRANSFORM(z,4,cPI1_8,cPI3_8);
 394     z+=2;
 395     TRANSFORM(z,4,cPI3_8,cPI1_8);
 396 }
 397 #else
 398 DECL_FFT(16,8,4)
 399 #endif
 400 DECL_FFT(32,16,8)
 401 DECL_FFT(64,32,16)
 402 DECL_FFT(128,64,32)
 403 DECL_FFT(256,128,64)
 404 DECL_FFT(512,256,128)
 405 DECL_FFT(1024,512,256)
 406 DECL_FFT(2048,1024,512)
 407 DECL_FFT(4096,2048,1024)
 408
 409 static void (*fft_dispatch[])(FFTComplex*) = {
 410     fft4_dispatch, fft8_dispatch, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
 411     fft2048, fft4096
 412 };
 413
 414 void ff_fft_calc_c(int nbits, FFTComplex *z)
 415 {
 416     fft_dispatch[nbits-2](z);
 417 }
 418
 419 #if 0
 420 int main (void)
 421 {
 422 #define PRECISION       16
 423 #define FFT_SIZE 1024
 424 #define ftofix32(x)       ((fixed32)((x) * (float)(1 << PRECISION) + ((x) < 0 ? -0.5 : 0.5)))
 425 #define itofix32(x)       ((x) << PRECISION)
 426 #define fixtoi32(x)       ((x) >> PRECISION)
 427
 428     int             j;
 429     const long      N = FFT_SIZE;
 430     double          r[FFT_SIZE] = {0.0}, i[FFT_SIZE] = {0.0};
 431     long            n;
 432     double          t;
 433     double          amp, phase;
 434     clock_t         start, end;
 435     double          exec_time = 0;
 436     FFTContext      s;
 437     FFTComplex      z[FFT_SIZE];
 438     memset(z, 0, 64*sizeof(FFTComplex));
 439
 440     /* Generate saw-tooth test data */
 441     for (n = 0; n < FFT_SIZE; n++)
 442     {
 443         t = (2 * M_PI * n)/N;
 444         /*z[n].re =  1.1      + sin(      t) +
 445                    0.5      * sin(2.0 * t) +
 446                   (1.0/3.0) * sin(3.0 * t) +
 447                    0.25     * sin(4.0 * t) +
 448                    0.2      * sin(5.0 * t) +
 449                   (1.0/6.0) * sin(6.0 * t) +
 450                   (1.0/7.0) * sin(7.0 * t) ;*/
 451         z[n].re  =  ftofix32(cos(2*M_PI*n/64));
 452         //printf("z[%d] = %f\n", n, z[n].re);
 453         //getchar();
 454     }
 455
 456     ff_fft_init(&s, 10, 1);
 457 //start = clock();
 458 //for(n = 0; n < 1000000; n++)
 459     ff_fft_permute_c(&s, z);
 460     ff_fft_calc_c(&s, z);
 461 //end   = clock();
 462 //exec_time = (((double)end-(double)start)/CLOCKS_PER_SEC);
 463     for(j = 0; j < FFT_SIZE; j++)
 464     {
 465         printf("%8.4f\n", sqrt(pow(fixtof32(z[j].re),2)+ pow(fixtof32(z[j].im), 2)));
 466         //getchar();
 467     }
 468     printf("muls = %d, adds = %d\n", muls, adds);
 469 //printf(" Time elapsed = %f\n", exec_time);
 470     //ff_fft_end(&s);
 471
 472 }
 473 #endif