summaryrefslogtreecommitdiffstats
path: root/libFDK/src/dct.cpp
blob: d05a26fc1acfb320ecdef34be098ad1b43b06c67 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
/****************************************************************************

                       (C) copyright Fraunhofer IIS (2004)
                               All Rights Reserved

    Please be advised that this software and/or program delivery is
    Confidential Information of Fraunhofer and subject to and covered by the

    Fraunhofer IIS Software Evaluation Agreement
    between Google Inc. and  Fraunhofer
    effective and in full force since March 1, 2012.

    You may use this software and/or program only under the terms and
    conditions described in the above mentioned Fraunhofer IIS Software
    Evaluation Agreement. Any other and/or further use requires a separate agreement.



 $Id$

*******************************************************************************/
/*!
  \file   dct.cpp
  \brief  DCT Implementations  $Revision: 36871 $
  Library functions to calculate standard DCTs. This will most likely be replaced by hand-optimized
  functions for the specific target processor.

  Three different implementations of the dct type II and the dct type III transforms are provided.

  By default implementations which are based on a single, standard complex FFT-kernel are used (dctII_f() and dctIII_f()).
  These are specifically helpful in cases where optimized FFT libraries are already available. The FFT used in these
  implementation is FFT rad2 from FDK_tools.

  Of course, one might also use DCT-libraries should they be available. The DCT and DST
  type IV implementations are only available in a version based on a complex FFT kernel.
*/

#include "dct.h"


#include "FDK_tools_rom.h"
#include "fft.h"


#if defined(__arm__)
#include "arm/dct_arm.cpp"
#endif


/*!
 *
 * \brief Perform dct type 3
 * The dct 3 is calculated by a inverse real fft, with
 * some pre twiddeling before the inverse real fft, as discribed by Takuya OOURA.
 * (http://momonga.t.u-tokyo.ac.jp/~ooura/fftman/ftmn2_32.html#sec2_3_2)
 * The real inverse fft is calculated by a inverse complex fft, as described
 * in numerical recipes in C, Cambridge University press
 * the auxiliary function is built by reversing the odd samples
 *
 * Instead of doing 2 times the conjugation to calculate the
 * inverse cfft with the cfft, one can also swap elements before
 * calling the cfft to get the same result:
 * swap
 * r(1),i(1) with r(n-1),i(n-1),
 * r(2),i(2) with r(n-2),i(n-2), ...
 * r(n/2-1),i(n/2-1) with r(n/2+1),i(n/2+1)
 *
 *
 * Scaling 1 shift in pre twiddeling,
 *         log2(L)-1 in cfft
 */
#if !defined(FUNCTION_dct_III)
void dct_III(FIXP_DBL *pDat, /*!< pointer to input/output */
             FIXP_DBL *tmp,  /*!< pointer to temporal working buffer */
             int L,          /*!< lenght of transform */
             int *pDat_e
             )
{
  FDK_ASSERT(L == 64 || L == 32);
  int  i;
  FIXP_DBL xr, accu1, accu2;
  int inc;
  int M = L>>1;
  int ld_M;

  if (L == 64)  ld_M = 5;
  else          ld_M = 4;

  /* This loop performs multiplication for index i (i*inc) */
  inc = (64/2) >> ld_M; /* 64/L */

  FIXP_DBL *pTmp_0 = &tmp[2];
  FIXP_DBL *pTmp_1 = &tmp[(M-1)*2];

  for(i=1; i<M>>1; i++,pTmp_0+=2,pTmp_1-=2) {

    FIXP_DBL accu3,accu4,accu5,accu6;

    cplxMultDiv2(&accu2, &accu1, pDat[L - i], pDat[i], sin_twiddle_L64[i*inc]);
    cplxMultDiv2(&accu4, &accu3, pDat[M+i], pDat[M-i], sin_twiddle_L64[(M-i)*inc]);
    accu3 >>= 1; accu4 >>= 1;

    /* This method is better for ARM926, that uses operand2 shifted right by 1 always */
    cplxMultDiv2(&accu6, &accu5, (accu3 - (accu1>>1)), ((accu2>>1) + accu4), sin_twiddle_L64[(4*i)*inc]);
    xr = (accu1>>1) + accu3;
    pTmp_0[0] = (xr>>1) - accu5;
    pTmp_1[0] = (xr>>1) + accu5;

    xr = (accu2>>1) - accu4;
    pTmp_0[1] =  (xr>>1) - accu6;
    pTmp_1[1] = -((xr>>1) + accu6);

  }

  xr     = fMultDiv2(pDat[M], sin_twiddle_L64[64/2].v.re );/* cos((PI/(2*L))*M); */
  tmp[0] = ((pDat[0]>>1) + xr)>>1;
  tmp[1] = ((pDat[0]>>1) - xr)>>1;

  cplxMultDiv2(&accu2, &accu1, pDat[L - (M/2)], pDat[M/2], sin_twiddle_L64[64/4]);
  tmp[M]   = accu1>>1;
  tmp[M+1] = accu2>>1;

  /* dit_fft expects 1 bit scaled input values */
  fft(M, tmp, pDat_e);

  /* ARM926: 12 cycles per 2-iteration, no overhead code by compiler */
  pTmp_1 = &tmp[L];
  for (i = M>>1; i--;)
  {
    FIXP_DBL tmp1, tmp2, tmp3, tmp4;
    tmp1 = *tmp++;
    tmp2 = *tmp++;
    tmp3 = *--pTmp_1;
    tmp4 = *--pTmp_1;
    *pDat++ = tmp1;
    *pDat++ = tmp3;
    *pDat++ = tmp2;
    *pDat++ = tmp4;
  }

  *pDat_e += 2;
}
#endif

/*!
 *
 * \brief Perform dct type 2
 * The dct 2 is calculated by a real inverse fft, with
 * some pre twiddeling after the  fft, as discribed by Takuya OOURA.
 * (http://momonga.t.u-tokyo.ac.jp/~ooura/fftman/ftmn2_32.html#sec2_3_2)
 * The real inverse fft is calculated by a inverse complex fft, as described
 * in numerical recipes in C, Cambridge University press
 * the auxilery function is build by reversing the odd samples
 *
 * Scaling 1 shift in pre twiddeling,
 *         5 in cfft
 */
#if !defined(FUNCTION_dct_II)
void dct_II(FIXP_DBL *pDat, /*!< pointer to input/output */
            FIXP_DBL *tmp,  /*!< pointer to temporal working buffer */
            int L,          /*!< lenght of transform */
            int *pDat_e
            )
{
    FDK_ASSERT(L == 64 || L == 32);
    FIXP_DBL accu1,accu2;
    FIXP_DBL *pTmp_0, *pTmp_1;

    int i;
    int inc;
    int M =  L>>1;
    int ld_M;

    FDK_ASSERT(L == 64 || L == 32);
    ld_M = 4 + (L >> 6);  /* L=64: 5,  L=32: 4 */

    inc = (64/2) >> ld_M; /* L=64: 1,  L=32: 2 */

    FIXP_DBL *pdat  = &pDat[0];
    FIXP_DBL accu3, accu4;
    pTmp_0 = &tmp[0];
    pTmp_1 = &tmp[L-1];
    for (i = M>>1; i--; )
    {
      accu1 = *pdat++;
      accu2 = *pdat++;
      accu3 = *pdat++;
      accu4 = *pdat++;
      accu1 >>= 1;
      accu2 >>= 1;
      accu3 >>= 1;
      accu4 >>= 1;
      *pTmp_0++ = accu1;
      *pTmp_0++ = accu3;
      *pTmp_1-- = accu2;
      *pTmp_1-- = accu4;
    }


    fft(M, tmp, pDat_e);

    pTmp_0 = &tmp[2];
    pTmp_1 = &tmp[(M-1)*2];

    for (i=1; i<M>>1; i++,pTmp_0+=2,pTmp_1-=2) {

      FIXP_DBL a1,a2;
      FIXP_DBL accu3, accu4;

      a1 = ((pTmp_0[1]>>1) + (pTmp_1[1]>>1));
      a2 = ((pTmp_1[0]>>1) - (pTmp_0[0]>>1));

      cplxMultDiv2(&accu1, &accu2, a2, a1, sin_twiddle_L64[(4*i)*inc]);
      accu1<<=1; accu2<<=1;

      a1 = ((pTmp_0[0]>>1) + (pTmp_1[0]>>1));
      a2 = ((pTmp_0[1]>>1) - (pTmp_1[1]>>1));

      cplxMultDiv2(&accu3, &accu4, (a1 + accu2), -(accu1 + a2), sin_twiddle_L64[i*inc]);
      pDat[L - i] = accu4;
      pDat[i]     = accu3;

      cplxMultDiv2(&accu3, &accu4, (a1 - accu2), -(accu1 - a2), sin_twiddle_L64[(M-i)*inc]);
      pDat[M + i] = accu4;
      pDat[M - i] = accu3;

    }

    cplxMultDiv2(&accu1, &accu2, tmp[M], tmp[M+1], sin_twiddle_L64[(M/2)*inc]);
    pDat[L - (M/2)] = accu2;
    pDat[M/2]       = accu1;

    pDat[0] = (tmp[0]>>1)+(tmp[1]>>1);
    pDat[M] =  fMult(((tmp[0]>>1)-(tmp[1]>>1)), sin_twiddle_L64[64/2].v.re);/* cos((PI/(2*L))*M); */

    *pDat_e += 2;
}
#endif

static
void getTables(const FIXP_WTP **twiddle, const FIXP_STP **sin_twiddle, int *sin_step, int length)
{
  int ld2_length;

 /* Get ld2 of length - 2 + 1
     -2: because first table entry is window of size 4
     +1: because we already include +1 because of ceil(log2(length)) */
  ld2_length = DFRACT_BITS-1-fNormz((FIXP_DBL)length) - 1;

  /* Extract sort of "eigenvalue" (the 4 left most bits) of length. */
  switch ( (length) >> (ld2_length-1) ) {
    case 0x4: /* radix 2 */
      *sin_twiddle = SineTable512;
      *sin_step = 1<<(9 - ld2_length);
      *twiddle = windowSlopes[0][0][ld2_length-1];
      break;
    case 0x7: /* 10 ms */
      *sin_twiddle = SineTable480;
      *sin_step = 1<<(8 - ld2_length);
      *twiddle = windowSlopes[0][1][ld2_length];
      break;
    default:
      *sin_twiddle = NULL;
      *sin_step = 0;
      *twiddle = NULL;
      break;
  }

  FDK_ASSERT(*twiddle != NULL);

  FDK_ASSERT(*sin_step > 0);

}

#if !defined(FUNCTION_dct_IV)

void dct_IV(FIXP_DBL *pDat,
            int L,
            int *pDat_e)
{
  int sin_step = 0;
  int M = L >> 1;

  const FIXP_WTP *twiddle;
  const FIXP_STP *sin_twiddle;

  FDK_ASSERT(L >= 4);

  getTables(&twiddle, &sin_twiddle, &sin_step, L);

#ifdef FUNCTION_dct_IV_func1
  if (M>=4 && (M&3) == 0) {
     /* ARM926: 44 cycles for 2 iterations = 22 cycles/iteration */
    dct_IV_func1(M>>2, twiddle,  &pDat[0], &pDat[L-1]);
  } else
#endif /* FUNCTION_dct_IV_func1 */
  {
    FIXP_DBL *RESTRICT pDat_0 = &pDat[0];
    FIXP_DBL *RESTRICT pDat_1 = &pDat[L - 2];
    register int i;

    /* 29 cycles on ARM926 */
    for (i = 0; i < M-1; i+=2,pDat_0+=2,pDat_1-=2)
    {
      register FIXP_DBL accu1,accu2,accu3,accu4;

      accu1 = pDat_1[1]; accu2 = pDat_0[0];
      accu3 = pDat_0[1]; accu4 = pDat_1[0];

      cplxMultDiv2(&accu1, &accu2, accu1, accu2, twiddle[i]);
      cplxMultDiv2(&accu3, &accu4, accu4, accu3, twiddle[i+1]);

      pDat_0[0] = accu2; pDat_0[1] = accu1;
      pDat_1[0] = accu4; pDat_1[1] = -accu3;
    }
    if (M&1)
    {
      register FIXP_DBL accu1,accu2;

      accu1 = pDat_1[1]; accu2 = pDat_0[0];

      cplxMultDiv2(&accu1, &accu2, accu1, accu2, twiddle[i]);

      pDat_0[0] = accu2; pDat_0[1] = accu1;
    }
  }

  fft(M, pDat, pDat_e);

#ifdef FUNCTION_dct_IV_func2
  if (M>=4 && (M&3) == 0) {
     /* ARM926: 42 cycles for 2 iterations = 21 cycles/iteration */
    dct_IV_func2(M>>2, sin_twiddle, &pDat[0], &pDat[L], sin_step);
  } else
#endif /* FUNCTION_dct_IV_func2 */
  {
    FIXP_DBL *RESTRICT pDat_0 = &pDat[0];
    FIXP_DBL *RESTRICT pDat_1 = &pDat[L - 2];
    register FIXP_DBL accu1,accu2,accu3,accu4;
    int idx, i;

    /* Sin and Cos values are 0.0f and 1.0f */
    accu1 = pDat_1[0];
    accu2 = pDat_1[1];

    pDat_1[1] = -(pDat_0[1]>>1);
    pDat_0[0] = (pDat_0[0]>>1);


    /* 28 cycles for ARM926 */  
    for (idx = sin_step,i=1; i<(M+1)>>1; i++, idx+=sin_step)
    {
      FIXP_STP twd = sin_twiddle[idx];
      cplxMultDiv2(&accu3, &accu4, accu1, accu2, twd);
      pDat_0[1] =  accu3;
      pDat_1[0] =  accu4;
      
      pDat_0+=2;
      pDat_1-=2;

      cplxMultDiv2(&accu3, &accu4, pDat_0[1], pDat_0[0], twd);

      accu1 = pDat_1[0];
      accu2 = pDat_1[1];

      pDat_1[1] = -accu3;
      pDat_0[0] =  accu4;
    }

    if ( (M&1) == 0 )
    {
      /* Last Sin and Cos value pair are the same */
      accu1 = fMultDiv2(accu1, WTC(0x5a82799a));
      accu2 = fMultDiv2(accu2, WTC(0x5a82799a));

      pDat_1[0] = accu1 + accu2;
      pDat_0[1] = accu1 - accu2;
    }
  }

  /* Add twiddeling scale. */
  *pDat_e += 2;
}
#endif /* defined (FUNCTION_dct_IV) */

#if !defined(FUNCTION_dst_IV)
void dst_IV(FIXP_DBL *pDat,
            int L,
            int *pDat_e )
{
  int sin_step = 0;
  int M = L >> 1;

  const FIXP_WTP *twiddle;
  const FIXP_STP *sin_twiddle;

#ifdef DSTIV2_ENABLE
  if (L == 2) {
    const FIXP_STP tab = STCP(0x7641AF3D, 0x30FB9452);
    FIXP_DBL tmp1, tmp2;

    cplxMultDiv2(&tmp2, &tmp1, pDat[0], pDat[1], tab);

    pDat[0] = tmp1;
    pDat[1] = tmp2;

    *pDat_e += 1;

    return;
  }
#else
  FDK_ASSERT(L >= 4);
#endif

  getTables(&twiddle, &sin_twiddle, &sin_step, L);

#ifdef FUNCTION_dst_IV_func1
  if ( (M>=4) && ((M&3) == 0) ) {
    dst_IV_func1(M, twiddle, &pDat[0], &pDat[L]);
  } else 
#endif
  {
    FIXP_DBL *RESTRICT pDat_0 = &pDat[0];
    FIXP_DBL *RESTRICT pDat_1 = &pDat[L - 2];
  
    register int i;

    /* 34 cycles on ARM926 */
    for (i = 0; i < M-1; i+=2,pDat_0+=2,pDat_1-=2) 
    {
      register FIXP_DBL accu1,accu2,accu3,accu4;

      accu1 =  pDat_1[1]; accu2 = -pDat_0[0];
      accu3 =  pDat_0[1]; accu4 = -pDat_1[0];
    
      cplxMultDiv2(&accu1, &accu2, accu1, accu2, twiddle[i]);
      cplxMultDiv2(&accu3, &accu4, accu4, accu3, twiddle[i+1]);

      pDat_0[0] = accu2; pDat_0[1] = accu1;
      pDat_1[0] = accu4; pDat_1[1] = -accu3;
    }
    if (M&1)
    {
      register FIXP_DBL accu1,accu2;

      accu1 =  pDat_1[1]; accu2 = -pDat_0[0];
    
      cplxMultDiv2(&accu1, &accu2, accu1, accu2, twiddle[i]);

      pDat_0[0] = accu2; pDat_0[1] = accu1;
    }
  }

  fft(M, pDat, pDat_e);

#ifdef FUNCTION_dst_IV_func2
  if ( (M>=4) && ((M&3) == 0) ) {
    dst_IV_func2(M>>2, sin_twiddle + sin_step, &pDat[0], &pDat[L - 1], sin_step);
  } else
#endif /* FUNCTION_dst_IV_func2 */
  {
    FIXP_DBL *RESTRICT pDat_0;
    FIXP_DBL *RESTRICT pDat_1;
    register FIXP_DBL accu1,accu2,accu3,accu4;
    int idx, i;

    pDat_0 = &pDat[0];
    pDat_1 = &pDat[L - 2];

    /* Sin and Cos values are 0.0f and 1.0f */
    accu1 = pDat_1[0];
    accu2 = pDat_1[1];

    pDat_1[1] = -(pDat_0[0]>>1);
    pDat_0[0] = (pDat_0[1]>>1);

    for (idx = sin_step,i=1; i<(M+1)>>1; i++, idx+=sin_step)
    {
      FIXP_STP twd = sin_twiddle[idx];

      cplxMultDiv2(&accu3, &accu4, accu1, accu2, twd);
      pDat_1[0] =  -accu3;
      pDat_0[1] =  -accu4;

      pDat_0+=2;
      pDat_1-=2;

      cplxMultDiv2(&accu3, &accu4, pDat_0[1], pDat_0[0], twd);

      accu1 = pDat_1[0];
      accu2 = pDat_1[1];

      pDat_0[0] =  accu3;
      pDat_1[1] = -accu4;
    }

    if ( (M&1) == 0 )
    {
      /* Last Sin and Cos value pair are the same */
      accu1 = fMultDiv2(accu1, WTC(0x5a82799a));
      accu2 = fMultDiv2(accu2, WTC(0x5a82799a));

      pDat_0[1] = - accu1 - accu2;
      pDat_1[0] =   accu2 - accu1;
    }
  }

  /* Add twiddeling scale. */
  *pDat_e += 2;
}
#endif /* !defined(FUNCTION_dst_IV) */