imdct.c

   1 /*
   2  * FFT/IFFT transforms.
   3  *
   4  * Extracted 2009 from mplayer 2009-02-10 libavcodec/fft.c and libavcodec/mdct.c
   5  *
   6  * Copyright (c) 2008 Loren Merritt
   7  * Copyright (c) 2002 Fabrice Bellard
   8  * Partly based on libdjbfft by D. J. Bernstein
   9  *
  10  * Licensed under the GNU Lesser General Public License.
  11  * For licencing details see COPYING.LIB.
  12  */
  13
  14 /**
  15  * \file imdct.c Inverse modified discrete cosine transform.
  16  */
  17
  18 #include <inttypes.h>
  19 #include <math.h>
  20 #include <string.h>
  21 #include <stdlib.h>
  22 #include <regex.h>
  23
  24 #include "para.h"
  25 #include "error.h"
  26 #include "string.h"
  27 #include "imdct.h"
  28 #include "wma.h"
  29
  30 typedef float fftsample_t;
  31
  32 #define DECLARE_ALIGNED(n,t,v)      t v __attribute__ ((aligned (n)))
  33 #define DECLARE_ALIGNED_16(t, v) DECLARE_ALIGNED(16, t, v)
  34 #define M_SQRT1_2      0.70710678118654752440   /* 1/sqrt(2) */
  35
  36 struct fft_complex {
  37         fftsample_t re, im;
  38 };
  39
  40 struct fft_context {
  41         int nbits;
  42         int inverse;
  43         uint16_t *revtab;
  44         struct fft_complex *exptab;
  45         struct fft_complex *exptab1;    /* only used by SSE code */
  46         struct fft_complex *tmp_buf;
  47 };
  48
  49 struct mdct_context {
  50         /** Size of MDCT (i.e. number of input data * 2). */
  51         int n;
  52         /** n = 2^n bits. */
  53         int nbits;
  54         /** pre/post rotation tables */
  55         fftsample_t *tcos;
  56         fftsample_t *tsin;
  57         struct fft_context fft;
  58 };
  59
  60 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
  61 DECLARE_ALIGNED_16(fftsample_t, ff_cos_16[8]);
  62 DECLARE_ALIGNED_16(fftsample_t, ff_cos_32[16]);
  63 DECLARE_ALIGNED_16(fftsample_t, ff_cos_64[32]);
  64 DECLARE_ALIGNED_16(fftsample_t, ff_cos_128[64]);
  65 DECLARE_ALIGNED_16(fftsample_t, ff_cos_256[128]);
  66 DECLARE_ALIGNED_16(fftsample_t, ff_cos_512[256]);
  67 DECLARE_ALIGNED_16(fftsample_t, ff_cos_1024[512]);
  68 DECLARE_ALIGNED_16(fftsample_t, ff_cos_2048[1024]);
  69 DECLARE_ALIGNED_16(fftsample_t, ff_cos_4096[2048]);
  70 DECLARE_ALIGNED_16(fftsample_t, ff_cos_8192[4096]);
  71 DECLARE_ALIGNED_16(fftsample_t, ff_cos_16384[8192]);
  72 DECLARE_ALIGNED_16(fftsample_t, ff_cos_32768[16384]);
  73 DECLARE_ALIGNED_16(fftsample_t, ff_cos_65536[32768]);
  74
  75 static fftsample_t *ff_cos_tabs[] = {
  76         ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256,
  77         ff_cos_512, ff_cos_1024, ff_cos_2048, ff_cos_4096, ff_cos_8192,
  78         ff_cos_16384, ff_cos_32768, ff_cos_65536,
  79 };
  80
  81 static int split_radix_permutation(int i, int n, int inverse)
  82 {
  83         int m;
  84         if (n <= 2)
  85                 return i & 1;
  86         m = n >> 1;
  87         if (!(i & m))
  88                 return split_radix_permutation(i, m, inverse) * 2;
  89         m >>= 1;
  90         if (inverse == !(i & m))
  91                 return split_radix_permutation(i, m, inverse) * 4 + 1;
  92         else
  93                 return split_radix_permutation(i, m, inverse) * 4 - 1;
  94 }
  95
  96 #define sqrthalf (float)M_SQRT1_2
  97
  98 #define BF(x,y,a,b) {\
  99     x = a - b;\
 100     y = a + b;\
 101 }
 102
 103 #define BUTTERFLIES(a0,a1,a2,a3) {\
 104     BF(t3, t5, t5, t1);\
 105     BF(a2.re, a0.re, a0.re, t5);\
 106     BF(a3.im, a1.im, a1.im, t3);\
 107     BF(t4, t6, t2, t6);\
 108     BF(a3.re, a1.re, a1.re, t4);\
 109     BF(a2.im, a0.im, a0.im, t6);\
 110 }
 111
 112 // force loading all the inputs before storing any.
 113 // this is slightly slower for small data, but avoids store->load aliasing
 114 // for addresses separated by large powers of 2.
 115 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
 116     fftsample_t r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
 117     BF(t3, t5, t5, t1);\
 118     BF(a2.re, a0.re, r0, t5);\
 119     BF(a3.im, a1.im, i1, t3);\
 120     BF(t4, t6, t2, t6);\
 121     BF(a3.re, a1.re, r1, t4);\
 122     BF(a2.im, a0.im, i0, t6);\
 123 }
 124
 125 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
 126     t1 = a2.re * wre + a2.im * wim;\
 127     t2 = a2.im * wre - a2.re * wim;\
 128     t5 = a3.re * wre - a3.im * wim;\
 129     t6 = a3.im * wre + a3.re * wim;\
 130     BUTTERFLIES(a0,a1,a2,a3)\
 131 }
 132
 133 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
 134     t1 = a2.re;\
 135     t2 = a2.im;\
 136     t5 = a3.re;\
 137     t6 = a3.im;\
 138     BUTTERFLIES(a0,a1,a2,a3)\
 139 }
 140
 141 /* z[0...8n-1], w[1...2n-1] */
 142 #define PASS(name)\
 143 static void name(struct fft_complex *z, const fftsample_t *wre, unsigned int n)\
 144 {\
 145     fftsample_t t1, t2, t3, t4, t5, t6;\
 146     int o1 = 2*n;\
 147     int o2 = 4*n;\
 148     int o3 = 6*n;\
 149     const fftsample_t *wim = wre+o1;\
 150     n--;\
 151 \
 152     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
 153     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 154     do {\
 155         z += 2;\
 156         wre += 2;\
 157         wim -= 2;\
 158         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
 159         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 160     } while(--n);\
 161 }
 162
 163 PASS(pass)
 164 #undef BUTTERFLIES
 165 #define BUTTERFLIES BUTTERFLIES_BIG
 166
 167 #define DECL_FFT(n,n2,n4)\
 168 static void fft##n(struct fft_complex *z)\
 169 {\
 170     fft##n2(z);\
 171     fft##n4(z+n4*2);\
 172     fft##n4(z+n4*3);\
 173     pass(z,ff_cos_##n,n4/2);\
 174 }
 175 static void fft4(struct fft_complex *z)
 176 {
 177         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 178
 179         BF(t3, t1, z[0].re, z[1].re);
 180         BF(t8, t6, z[3].re, z[2].re);
 181         BF(z[2].re, z[0].re, t1, t6);
 182         BF(t4, t2, z[0].im, z[1].im);
 183         BF(t7, t5, z[2].im, z[3].im);
 184         BF(z[3].im, z[1].im, t4, t8);
 185         BF(z[3].re, z[1].re, t3, t7);
 186         BF(z[2].im, z[0].im, t2, t5);
 187 }
 188
 189 static void fft8(struct fft_complex *z)
 190 {
 191         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 192
 193         fft4(z);
 194
 195         BF(t1, z[5].re, z[4].re, -z[5].re);
 196         BF(t2, z[5].im, z[4].im, -z[5].im);
 197         BF(t3, z[7].re, z[6].re, -z[7].re);
 198         BF(t4, z[7].im, z[6].im, -z[7].im);
 199         BF(t8, t1, t3, t1);
 200         BF(t7, t2, t2, t4);
 201         BF(z[4].re, z[0].re, z[0].re, t1);
 202         BF(z[4].im, z[0].im, z[0].im, t2);
 203         BF(z[6].re, z[2].re, z[2].re, t7);
 204         BF(z[6].im, z[2].im, z[2].im, t8);
 205
 206         TRANSFORM(z[1], z[3], z[5], z[7], sqrthalf, sqrthalf);
 207 }
 208
 209 static void fft16(struct fft_complex *z)
 210 {
 211         fftsample_t t1, t2, t3, t4, t5, t6;
 212
 213         fft8(z);
 214         fft4(z + 8);
 215         fft4(z + 12);
 216
 217         TRANSFORM_ZERO(z[0], z[4], z[8], z[12]);
 218         TRANSFORM(z[2], z[6], z[10], z[14], sqrthalf, sqrthalf);
 219         TRANSFORM(z[1], z[5], z[9], z[13], ff_cos_16[1], ff_cos_16[3]);
 220         TRANSFORM(z[3], z[7], z[11], z[15], ff_cos_16[3], ff_cos_16[1]);
 221 }
 222
 223 DECL_FFT(32, 16, 8)
 224 DECL_FFT(64, 32, 16)
 225 DECL_FFT(128, 64, 32)
 226 DECL_FFT(256, 128, 64)
 227 DECL_FFT(512, 256, 128)
 228
 229 DECL_FFT(1024, 512, 256)
 230 DECL_FFT(2048, 1024, 512)
 231 DECL_FFT(4096, 2048, 1024)
 232 DECL_FFT(8192, 4096, 2048)
 233 DECL_FFT(16384, 8192, 4096)
 234 DECL_FFT(32768, 16384, 8192)
 235 DECL_FFT(65536, 32768, 16384)
 236
 237 static void (*fft_dispatch[]) (struct fft_complex *) = {
 238         fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
 239         fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
 240 };
 241
 242 static void fft(struct fft_context *s, struct fft_complex *z)
 243 {
 244         fft_dispatch[s->nbits - 2] (z);
 245 }
 246
 247 /* complex multiplication: p = a * b */
 248 #define CMUL(pre, pim, are, aim, bre, bim) \
 249 {\
 250         fftsample_t _are = (are);\
 251         fftsample_t _aim = (aim);\
 252         fftsample_t _bre = (bre);\
 253         fftsample_t _bim = (bim);\
 254         (pre) = _are * _bre - _aim * _bim;\
 255         (pim) = _are * _bim + _aim * _bre;\
 256 }
 257
 258 /**
 259  * Compute the middle half of the inverse MDCT of size N = 2^nbits
 260  *
 261  * Thus excluding the parts that can be derived by symmetry.
 262  *
 263  * \param output N/2 samples.
 264  * \param input N/2 samples.
 265  */
 266 static void imdct_half(struct mdct_context *s, fftsample_t *output,
 267                 const fftsample_t *input)
 268 {
 269         int k, n8, n4, n2, n, j;
 270         const uint16_t *revtab = s->fft.revtab;
 271         const fftsample_t *tcos = s->tcos;
 272         const fftsample_t *tsin = s->tsin;
 273         const fftsample_t *in1, *in2;
 274         struct fft_complex *z = (struct fft_complex *)output;
 275
 276         n = 1 << s->nbits;
 277         n2 = n >> 1;
 278         n4 = n >> 2;
 279         n8 = n >> 3;
 280
 281         /* pre rotation */
 282         in1 = input;
 283         in2 = input + n2 - 1;
 284         for (k = 0; k < n4; k++) {
 285                 j = revtab[k];
 286                 CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
 287                 in1 += 2;
 288                 in2 -= 2;
 289         }
 290         fft(&s->fft, z);
 291
 292         /* post rotation + reordering */
 293         output += n4;
 294         for (k = 0; k < n8; k++) {
 295                 fftsample_t r0, i0, r1, i1;
 296                 CMUL(r0, i1, z[n8 - k - 1].im, z[n8 - k - 1].re,
 297                         tsin[n8 - k - 1], tcos[n8 - k - 1]);
 298                 CMUL(r1, i0, z[n8 + k].im, z[n8 + k].re, tsin[n8 + k],
 299                         tcos[n8 + k]);
 300                 z[n8 - k - 1].re = r0;
 301                 z[n8 - k - 1].im = i0;
 302                 z[n8 + k].re = r1;
 303                 z[n8 + k].im = i1;
 304         }
 305 }
 306
 307 /**
 308  * Compute the inverse MDCT of size N = 2^nbits.
 309  *
 310  * \param output N samples.
 311  * \param input N/2 samples.
 312  */
 313 void imdct(struct mdct_context *s, float *output, const float *input)
 314 {
 315         int k;
 316         int n = 1 << s->nbits;
 317         int n2 = n >> 1;
 318         int n4 = n >> 2;
 319
 320         imdct_half(s, output + n4, input);
 321
 322         for (k = 0; k < n4; k++) {
 323                 output[k] = -output[n2 - k - 1];
 324                 output[n - k - 1] = output[n2 + k];
 325         }
 326 }
 327
 328 static int fft_init(struct fft_context *s, int nbits, int inverse)
 329 {
 330         int i, j, m, n;
 331         float alpha, c1, s1, s2;
 332         int split_radix = 1;
 333
 334         if (nbits < 2 || nbits > 16)
 335                 return -E_FFT_BAD_PARAMS;
 336         s->nbits = nbits;
 337         n = 1 << nbits;
 338
 339         s->tmp_buf = NULL;
 340         s->exptab = para_malloc((n / 2) * sizeof(struct fft_complex));
 341         s->revtab = para_malloc(n * sizeof(uint16_t));
 342         s->inverse = inverse;
 343
 344         s2 = inverse ? 1.0 : -1.0;
 345
 346         s->exptab1 = NULL;
 347
 348         if (split_radix) {
 349                 for (j = 4; j <= nbits; j++) {
 350                         int k = 1 << j;
 351                         double freq = 2 * M_PI / k;
 352                         fftsample_t *tab = ff_cos_tabs[j - 4];
 353                         for (i = 0; i <= k / 4; i++)
 354                                 tab[i] = cos(i * freq);
 355                         for (i = 1; i < k / 4; i++)
 356                                 tab[k / 2 - i] = tab[i];
 357                 }
 358                 for (i = 0; i < n; i++)
 359                         s->revtab[-split_radix_permutation(
 360                                 i, n, s->inverse) & (n - 1)] = i;
 361                 s->tmp_buf = para_malloc(n * sizeof(struct fft_complex));
 362         } else {
 363                 int np, nblocks, np2, l;
 364                 struct fft_complex *q;
 365
 366                 for (i = 0; i < (n / 2); i++) {
 367                         alpha = 2 * M_PI * (float) i / (float) n;
 368                         c1 = cos(alpha);
 369                         s1 = sin(alpha) * s2;
 370                         s->exptab[i].re = c1;
 371                         s->exptab[i].im = s1;
 372                 }
 373
 374                 np = 1 << nbits;
 375                 nblocks = np >> 3;
 376                 np2 = np >> 1;
 377                 s->exptab1 = para_malloc(np * 2 * sizeof(struct fft_complex));
 378                 q = s->exptab1;
 379                 do {
 380                         for (l = 0; l < np2; l += 2 * nblocks) {
 381                                 *q++ = s->exptab[l];
 382                                 *q++ = s->exptab[l + nblocks];
 383
 384                                 q->re = -s->exptab[l].im;
 385                                 q->im = s->exptab[l].re;
 386                                 q++;
 387                                 q->re = -s->exptab[l + nblocks].im;
 388                                 q->im = s->exptab[l + nblocks].re;
 389                                 q++;
 390                         }
 391                         nblocks = nblocks >> 1;
 392                 } while (nblocks != 0);
 393                 freep(&s->exptab);
 394                 /* compute bit reverse table */
 395                 for (i = 0; i < n; i++) {
 396                         m = 0;
 397                         for (j = 0; j < nbits; j++)
 398                                 m |= ((i >> j) & 1) << (nbits - j - 1);
 399                         s->revtab[i] = m;
 400                 }
 401         }
 402         return 0;
 403 }
 404
 405 static void fft_end(struct fft_context *ctx)
 406 {
 407         freep(&ctx->revtab);
 408         freep(&ctx->exptab);
 409         freep(&ctx->exptab1);
 410         freep(&ctx->tmp_buf);
 411 }
 412
 413 DECLARE_ALIGNED(16, float, ff_sine_128[128]);
 414 DECLARE_ALIGNED(16, float, ff_sine_256[256]);
 415 DECLARE_ALIGNED(16, float, ff_sine_512[512]);
 416 DECLARE_ALIGNED(16, float, ff_sine_1024[1024]);
 417 DECLARE_ALIGNED(16, float, ff_sine_2048[2048]);
 418 DECLARE_ALIGNED(16, float, ff_sine_4096[4096]);
 419
 420 float *ff_sine_windows[6] = {
 421         ff_sine_128, ff_sine_256, ff_sine_512, ff_sine_1024,
 422         ff_sine_2048, ff_sine_4096
 423 };
 424
 425 // Generate a sine window.
 426 void sine_window_init(float *window, int n)
 427 {
 428         int i;
 429
 430         for (i = 0; i < n; i++)
 431                 window[i] = sinf((i + 0.5) * (M_PI / (2.0 * n)));
 432 }
 433
 434 /**
 435  * Init MDCT or IMDCT computation.
 436  */
 437 int imdct_init(int nbits, int inverse, struct mdct_context **result)
 438 {
 439         int ret, n, n4, i;
 440         double alpha;
 441         struct mdct_context *s;
 442
 443         s = para_calloc(sizeof(*s));
 444         n = 1 << nbits;
 445         s->nbits = nbits;
 446         s->n = n;
 447         n4 = n >> 2;
 448         s->tcos = para_malloc(n4 * sizeof(fftsample_t));
 449         s->tsin = para_malloc(n4 * sizeof(fftsample_t));
 450
 451         for (i = 0; i < n4; i++) {
 452                 alpha = 2 * M_PI * (i + 1.0 / 8.0) / n;
 453                 s->tcos[i] = -cos(alpha);
 454                 s->tsin[i] = -sin(alpha);
 455         }
 456         ret = fft_init(&s->fft, s->nbits - 2, inverse);
 457         if (ret < 0)
 458                 goto fail;
 459         *result = s;
 460         return 0;
 461 fail:
 462         freep(&s->tcos);
 463         freep(&s->tsin);
 464         free(s);
 465         return ret;
 466 }
 467
 468 void imdct_end(struct mdct_context *ctx)
 469 {
 470         freep(&ctx->tcos);
 471         freep(&ctx->tsin);
 472         fft_end(&ctx->fft);
 473         free(ctx);
 474 }