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 struct fft_complex {
  33         fftsample_t re, im;
  34 };
  35
  36 struct fft_context {
  37         int nbits;
  38         uint16_t *revtab;
  39 };
  40
  41 struct mdct_context {
  42         /** Size of MDCT (number of input data * 2). */
  43         int n;
  44         /** n = 2^n bits. */
  45         int nbits;
  46         /** Cosine table for pre/post rotation. */
  47         fftsample_t *tcos;
  48         /** Sine table for pre/post rotation. */
  49         fftsample_t *tsin;
  50         /** The context for the underlying fast Fourier transform. */
  51         struct fft_context fft;
  52 };
  53
  54 /** cos(2 * pi * x / n) for 0 <= x <= n / 4, followed by its reverse */
  55 #define COSINE_TAB(n) fftsample_t ff_cos_ ## n[n / 2] __aligned(16)
  56
  57 COSINE_TAB(16);
  58 COSINE_TAB(32);
  59 COSINE_TAB(64);
  60 COSINE_TAB(128);
  61 COSINE_TAB(256);
  62 COSINE_TAB(512);
  63 COSINE_TAB(1024);
  64 COSINE_TAB(2048);
  65 COSINE_TAB(4096);
  66 COSINE_TAB(8192);
  67 COSINE_TAB(16384);
  68 COSINE_TAB(32768);
  69 COSINE_TAB(65536);
  70
  71 static fftsample_t *ff_cos_tabs[] = {
  72         ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256,
  73         ff_cos_512, ff_cos_1024, ff_cos_2048, ff_cos_4096, ff_cos_8192,
  74         ff_cos_16384, ff_cos_32768, ff_cos_65536,
  75 };
  76
  77 static int split_radix_permutation(int i, int n)
  78 {
  79         int m;
  80         if (n <= 2)
  81                 return i & 1;
  82         m = n >> 1;
  83         if ((i & m) == 0)
  84                 return split_radix_permutation(i, m) * 2;
  85         m >>= 1;
  86         if ((i & m) == 0)
  87                 return split_radix_permutation(i, m) * 4 + 1;
  88         else
  89                 return split_radix_permutation(i, m) * 4 - 1;
  90 }
  91
  92 /** 1 / sqrt(2). */
  93 #define SQRTHALF (float)0.70710678118654752440
  94
  95 #define BF(x,y,a,b) {\
  96     x = a - b;\
  97     y = a + b;\
  98 }
  99
 100 #define BUTTERFLIES(a0,a1,a2,a3) {\
 101     BF(t3, t5, t5, t1);\
 102     BF(a2.re, a0.re, a0.re, t5);\
 103     BF(a3.im, a1.im, a1.im, t3);\
 104     BF(t4, t6, t2, t6);\
 105     BF(a3.re, a1.re, a1.re, t4);\
 106     BF(a2.im, a0.im, a0.im, t6);\
 107 }
 108
 109 // force loading all the inputs before storing any.
 110 // this is slightly slower for small data, but avoids store->load aliasing
 111 // for addresses separated by large powers of 2.
 112 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
 113     fftsample_t r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
 114     BF(t3, t5, t5, t1);\
 115     BF(a2.re, a0.re, r0, t5);\
 116     BF(a3.im, a1.im, i1, t3);\
 117     BF(t4, t6, t2, t6);\
 118     BF(a3.re, a1.re, r1, t4);\
 119     BF(a2.im, a0.im, i0, t6);\
 120 }
 121
 122 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
 123     t1 = a2.re * wre + a2.im * wim;\
 124     t2 = a2.im * wre - a2.re * wim;\
 125     t5 = a3.re * wre - a3.im * wim;\
 126     t6 = a3.im * wre + a3.re * wim;\
 127     BUTTERFLIES(a0,a1,a2,a3)\
 128 }
 129
 130 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
 131     t1 = a2.re;\
 132     t2 = a2.im;\
 133     t5 = a3.re;\
 134     t6 = a3.im;\
 135     BUTTERFLIES(a0,a1,a2,a3)\
 136 }
 137
 138 /* z[0...8n-1], w[1...2n-1] */
 139 #define PASS(name)\
 140 static void name(struct fft_complex *z, const fftsample_t *wre, unsigned int n)\
 141 {\
 142     fftsample_t t1, t2, t3, t4, t5, t6;\
 143     int o1 = 2*n;\
 144     int o2 = 4*n;\
 145     int o3 = 6*n;\
 146     const fftsample_t *wim = wre+o1;\
 147     n--;\
 148 \
 149     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
 150     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 151     do {\
 152         z += 2;\
 153         wre += 2;\
 154         wim -= 2;\
 155         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
 156         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 157     } while(--n);\
 158 }
 159
 160 PASS(pass)
 161 #undef BUTTERFLIES
 162 #define BUTTERFLIES BUTTERFLIES_BIG
 163
 164 #define DECL_FFT(n,n2,n4)\
 165 static void fft##n(struct fft_complex *z)\
 166 {\
 167     fft##n2(z);\
 168     fft##n4(z+n4*2);\
 169     fft##n4(z+n4*3);\
 170     pass(z,ff_cos_##n,n4/2);\
 171 }
 172 static void fft4(struct fft_complex *z)
 173 {
 174         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 175
 176         BF(t3, t1, z[0].re, z[1].re);
 177         BF(t8, t6, z[3].re, z[2].re);
 178         BF(z[2].re, z[0].re, t1, t6);
 179         BF(t4, t2, z[0].im, z[1].im);
 180         BF(t7, t5, z[2].im, z[3].im);
 181         BF(z[3].im, z[1].im, t4, t8);
 182         BF(z[3].re, z[1].re, t3, t7);
 183         BF(z[2].im, z[0].im, t2, t5);
 184 }
 185
 186 static void fft8(struct fft_complex *z)
 187 {
 188         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 189
 190         fft4(z);
 191
 192         BF(t1, z[5].re, z[4].re, -z[5].re);
 193         BF(t2, z[5].im, z[4].im, -z[5].im);
 194         BF(t3, z[7].re, z[6].re, -z[7].re);
 195         BF(t4, z[7].im, z[6].im, -z[7].im);
 196         BF(t8, t1, t3, t1);
 197         BF(t7, t2, t2, t4);
 198         BF(z[4].re, z[0].re, z[0].re, t1);
 199         BF(z[4].im, z[0].im, z[0].im, t2);
 200         BF(z[6].re, z[2].re, z[2].re, t7);
 201         BF(z[6].im, z[2].im, z[2].im, t8);
 202
 203         TRANSFORM(z[1], z[3], z[5], z[7], SQRTHALF, SQRTHALF);
 204 }
 205
 206 static void fft16(struct fft_complex *z)
 207 {
 208         fftsample_t t1, t2, t3, t4, t5, t6;
 209
 210         fft8(z);
 211         fft4(z + 8);
 212         fft4(z + 12);
 213
 214         TRANSFORM_ZERO(z[0], z[4], z[8], z[12]);
 215         TRANSFORM(z[2], z[6], z[10], z[14], SQRTHALF, SQRTHALF);
 216         TRANSFORM(z[1], z[5], z[9], z[13], ff_cos_16[1], ff_cos_16[3]);
 217         TRANSFORM(z[3], z[7], z[11], z[15], ff_cos_16[3], ff_cos_16[1]);
 218 }
 219
 220 DECL_FFT(32, 16, 8)
 221 DECL_FFT(64, 32, 16)
 222 DECL_FFT(128, 64, 32)
 223 DECL_FFT(256, 128, 64)
 224 DECL_FFT(512, 256, 128)
 225
 226 DECL_FFT(1024, 512, 256)
 227 DECL_FFT(2048, 1024, 512)
 228 DECL_FFT(4096, 2048, 1024)
 229 DECL_FFT(8192, 4096, 2048)
 230 DECL_FFT(16384, 8192, 4096)
 231 DECL_FFT(32768, 16384, 8192)
 232 DECL_FFT(65536, 32768, 16384)
 233
 234 static void (*fft_dispatch[]) (struct fft_complex *) = {
 235         fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
 236         fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
 237 };
 238
 239 static void fft(struct fft_context *s, struct fft_complex *z)
 240 {
 241         fft_dispatch[s->nbits - 2] (z);
 242 }
 243
 244 /* complex multiplication: p = a * b */
 245 #define CMUL(pre, pim, are, aim, bre, bim) \
 246 {\
 247         fftsample_t _are = (are);\
 248         fftsample_t _aim = (aim);\
 249         fftsample_t _bre = (bre);\
 250         fftsample_t _bim = (bim);\
 251         (pre) = _are * _bre - _aim * _bim;\
 252         (pim) = _are * _bim + _aim * _bre;\
 253 }
 254
 255 /**
 256  * Compute the middle half of the inverse MDCT of size N = 2^nbits
 257  *
 258  * Thus excluding the parts that can be derived by symmetry.
 259  *
 260  * \param output N/2 samples.
 261  * \param input N/2 samples.
 262  */
 263 static void imdct_half(struct mdct_context *s, fftsample_t *output,
 264                 const fftsample_t *input)
 265 {
 266         int k, n8, n4, n2, n, j;
 267         const uint16_t *revtab = s->fft.revtab;
 268         const fftsample_t *tcos = s->tcos;
 269         const fftsample_t *tsin = s->tsin;
 270         const fftsample_t *in1, *in2;
 271         struct fft_complex *z = (struct fft_complex *)output;
 272
 273         n = 1 << s->nbits;
 274         n2 = n >> 1;
 275         n4 = n >> 2;
 276         n8 = n >> 3;
 277
 278         /* pre rotation */
 279         in1 = input;
 280         in2 = input + n2 - 1;
 281         for (k = 0; k < n4; k++) {
 282                 j = revtab[k];
 283                 CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
 284                 in1 += 2;
 285                 in2 -= 2;
 286         }
 287         fft(&s->fft, z);
 288
 289         /* post rotation + reordering */
 290         output += n4;
 291         for (k = 0; k < n8; k++) {
 292                 fftsample_t r0, i0, r1, i1;
 293                 CMUL(r0, i1, z[n8 - k - 1].im, z[n8 - k - 1].re,
 294                         tsin[n8 - k - 1], tcos[n8 - k - 1]);
 295                 CMUL(r1, i0, z[n8 + k].im, z[n8 + k].re, tsin[n8 + k],
 296                         tcos[n8 + k]);
 297                 z[n8 - k - 1].re = r0;
 298                 z[n8 - k - 1].im = i0;
 299                 z[n8 + k].re = r1;
 300                 z[n8 + k].im = i1;
 301         }
 302 }
 303
 304 /**
 305  * Compute the inverse MDCT.
 306  *
 307  * \param ctx The initialized context structure.
 308  * \param output N samples.
 309  * \param input N/2 samples.
 310  *
 311  * \sa \ref imdct_init().
 312  */
 313 void imdct(struct mdct_context *ctx, float *output, const float *input)
 314 {
 315         int k;
 316         int n = 1 << ctx->nbits;
 317         int n2 = n >> 1;
 318         int n4 = n >> 2;
 319
 320         imdct_half(ctx, 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)
 329 {
 330         int i, j, n;
 331
 332         if (nbits < 2 || nbits > 16)
 333                 return -E_FFT_BAD_PARAMS;
 334         s->nbits = nbits;
 335         n = 1 << nbits;
 336
 337         s->revtab = para_malloc(n * sizeof(uint16_t));
 338         for (j = 4; j <= nbits; j++) {
 339                 int k = 1 << j;
 340                 double freq = 2 * M_PI / k;
 341                 fftsample_t *tab = ff_cos_tabs[j - 4];
 342                 for (i = 0; i <= k / 4; i++)
 343                         tab[i] = cos(i * freq);
 344                 for (i = 1; i < k / 4; i++)
 345                         tab[k / 2 - i] = tab[i];
 346         }
 347         for (i = 0; i < n; i++)
 348                 s->revtab[-split_radix_permutation(i, n) & (n - 1)] = i;
 349         return 0;
 350 }
 351
 352 /**
 353  * Initialize the inverse modified cosine transform.
 354  *
 355  * \param nbits The number of bits to use (4 <= \a nbits <= 18).
 356  *
 357  * \param result Opaque structure that must be passed to \ref imdct().
 358  *
 359  * \return Standard.
 360  */
 361 int imdct_init(int nbits, struct mdct_context **result)
 362 {
 363         int ret, n, n4, i;
 364         double alpha;
 365         struct mdct_context *s;
 366
 367         s = para_calloc(sizeof(*s));
 368         n = 1 << nbits;
 369         s->nbits = nbits;
 370         s->n = n;
 371         n4 = n >> 2;
 372         s->tcos = para_malloc(n4 * sizeof(fftsample_t));
 373         s->tsin = para_malloc(n4 * sizeof(fftsample_t));
 374
 375         for (i = 0; i < n4; i++) {
 376                 alpha = 2 * M_PI * (i + 1.0 / 8.0) / n;
 377                 s->tcos[i] = -cos(alpha);
 378                 s->tsin[i] = -sin(alpha);
 379         }
 380         ret = fft_init(&s->fft, s->nbits - 2);
 381         if (ret < 0)
 382                 goto fail;
 383         *result = s;
 384         return 0;
 385 fail:
 386         freep(&s->tcos);
 387         freep(&s->tsin);
 388         free(s);
 389         return ret;
 390 }
 391
 392 /**
 393  * Deallocate imdct resources.
 394  *
 395  * \param ctx The pointer obtained by imdct_init().
 396  */
 397 void imdct_end(struct mdct_context *ctx)
 398 {
 399         free(ctx->tcos);
 400         free(ctx->tsin);
 401         free(ctx->fft.revtab);
 402         free(ctx);
 403 }