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 /** Canonical representation of a complex number. */
  33 struct fft_complex {
  34         /** Real part. */
  35         fftsample_t re;
  36         /** Imaginary part. */
  37         fftsample_t im;
  38 };
  39
  40 /** FFT Lookup table. */
  41 struct fft_context {
  42         /** Number of bits of this instance of the FFT. */
  43         int nbits;
  44         /** The lookup table for cosine values. */
  45         uint16_t *revtab;
  46 };
  47
  48 struct mdct_context {
  49         /** Size of MDCT (number of input data * 2). */
  50         int n;
  51         /** n = 2^n bits. */
  52         int nbits;
  53         /** Cosine table for pre/post rotation. */
  54         fftsample_t *tcos;
  55         /** Sine table for pre/post rotation. */
  56         fftsample_t *tsin;
  57         /** The context for the underlying fast Fourier transform. */
  58         struct fft_context fft;
  59 };
  60
  61 /** cos(2 * pi * x / n) for 0 <= x <= n / 4, followed by its reverse */
  62 #define COSINE_TAB(n) static fftsample_t cos_ ## n[n / 2] __a_aligned(16)
  63
  64 COSINE_TAB(16);
  65 COSINE_TAB(32);
  66 COSINE_TAB(64);
  67 COSINE_TAB(128);
  68 COSINE_TAB(256);
  69 COSINE_TAB(512);
  70 COSINE_TAB(1024);
  71 COSINE_TAB(2048);
  72 COSINE_TAB(4096);
  73 COSINE_TAB(8192);
  74 COSINE_TAB(16384);
  75 COSINE_TAB(32768);
  76 COSINE_TAB(65536);
  77
  78 static fftsample_t *cos_tabs[] = {
  79         cos_16, cos_32, cos_64, cos_128, cos_256, cos_512, cos_1024, cos_2048,
  80         cos_4096, cos_8192, cos_16384, cos_32768, cos_65536,
  81 };
  82
  83 static int split_radix_permutation(int i, int n)
  84 {
  85         int m;
  86         if (n <= 2)
  87                 return i & 1;
  88         m = n >> 1;
  89         if ((i & m) == 0)
  90                 return split_radix_permutation(i, m) * 2;
  91         m >>= 1;
  92         if ((i & m) == 0)
  93                 return split_radix_permutation(i, m) * 4 + 1;
  94         else
  95                 return split_radix_permutation(i, m) * 4 - 1;
  96 }
  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 /*
 113  * Force loading all the inputs before storing any. This is slightly slower for
 114  * small data, but avoids store->load aliasing for addresses separated by large
 115  * powers of 2.
 116  */
 117 #define BUTTERFLIES_BIG(a0, a1, a2, a3) {\
 118         fftsample_t r0 = a0.re, i0 = a0.im, r1 = a1.re, i1 = a1.im;\
 119         BF(t3, t5, t5, t1);\
 120         BF(a2.re, a0.re, r0, t5);\
 121         BF(a3.im, a1.im, i1, t3);\
 122         BF(t4, t6, t2, t6);\
 123         BF(a3.re, a1.re, r1, t4);\
 124         BF(a2.im, a0.im, i0, t6);\
 125 }
 126
 127 #define TRANSFORM(a0, a1, a2, a3, wre,wim) {\
 128         t1 = a2.re * wre + a2.im * wim;\
 129         t2 = a2.im * wre - a2.re * wim;\
 130         t5 = a3.re * wre - a3.im * wim;\
 131         t6 = a3.im * wre + a3.re * wim;\
 132         BUTTERFLIES(a0, a1, a2, a3)\
 133 }
 134
 135 #define TRANSFORM_ZERO(a0, a1, a2, a3) {\
 136         t1 = a2.re;\
 137         t2 = a2.im;\
 138         t5 = a3.re;\
 139         t6 = a3.im;\
 140         BUTTERFLIES(a0, a1, a2, a3)\
 141 }
 142
 143 /* z[0...8n - 1], w[1...2n - 1] */
 144 #define PASS(name)\
 145 static void name(struct fft_complex *z, const fftsample_t *wre, unsigned int n)\
 146 {\
 147         fftsample_t t1, t2, t3, t4, t5, t6;\
 148         int o1 = 2 * n;\
 149         int o2 = 4 * n;\
 150         int o3 = 6 * n;\
 151         const fftsample_t *wim = wre + o1;\
 152         n--;\
 153 \
 154         TRANSFORM_ZERO(z[0], z[o1], z[o2], z[o3]);\
 155         TRANSFORM(z[1], z[o1 + 1], z[o2 + 1], z[o3 + 1], wre[1], wim[-1]);\
 156         do {\
 157                 z += 2;\
 158                 wre += 2;\
 159                 wim -= 2;\
 160                 TRANSFORM(z[0], z[o1], z[o2], z[o3], wre[0], wim[0]);\
 161                 TRANSFORM(z[1], z[o1 + 1], z[o2 + 1], z[o3 + 1], wre[1], wim[-1]);\
 162         } while (--n);\
 163 }
 164
 165 PASS(pass)
 166 #undef BUTTERFLIES
 167 #define BUTTERFLIES BUTTERFLIES_BIG
 168
 169 #define DECL_FFT(n, n2, n4)\
 170 static void fft##n(struct fft_complex *z)\
 171 {\
 172         fft ## n2(z);\
 173         fft ## n4(z + n4 * 2);\
 174         fft ## n4(z + n4 * 3);\
 175         pass(z, cos_ ## n, n4 / 2);\
 176 }
 177
 178 static void fft4(struct fft_complex *z)
 179 {
 180         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 181
 182         BF(t3, t1, z[0].re, z[1].re);
 183         BF(t8, t6, z[3].re, z[2].re);
 184         BF(z[2].re, z[0].re, t1, t6);
 185         BF(t4, t2, z[0].im, z[1].im);
 186         BF(t7, t5, z[2].im, z[3].im);
 187         BF(z[3].im, z[1].im, t4, t8);
 188         BF(z[3].re, z[1].re, t3, t7);
 189         BF(z[2].im, z[0].im, t2, t5);
 190 }
 191
 192 static void fft8(struct fft_complex *z)
 193 {
 194         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 195
 196         fft4(z);
 197
 198         BF(t1, z[5].re, z[4].re, -z[5].re);
 199         BF(t2, z[5].im, z[4].im, -z[5].im);
 200         BF(t3, z[7].re, z[6].re, -z[7].re);
 201         BF(t4, z[7].im, z[6].im, -z[7].im);
 202         BF(t8, t1, t3, t1);
 203         BF(t7, t2, t2, t4);
 204         BF(z[4].re, z[0].re, z[0].re, t1);
 205         BF(z[4].im, z[0].im, z[0].im, t2);
 206         BF(z[6].re, z[2].re, z[2].re, t7);
 207         BF(z[6].im, z[2].im, z[2].im, t8);
 208
 209         TRANSFORM(z[1], z[3], z[5], z[7], M_SQRT1_2, M_SQRT1_2);
 210 }
 211
 212 static void fft16(struct fft_complex *z)
 213 {
 214         fftsample_t t1, t2, t3, t4, t5, t6;
 215
 216         fft8(z);
 217         fft4(z + 8);
 218         fft4(z + 12);
 219
 220         TRANSFORM_ZERO(z[0], z[4], z[8], z[12]);
 221         TRANSFORM(z[2], z[6], z[10], z[14], M_SQRT1_2, M_SQRT1_2);
 222         TRANSFORM(z[1], z[5], z[9], z[13], cos_16[1], cos_16[3]);
 223         TRANSFORM(z[3], z[7], z[11], z[15], cos_16[3], cos_16[1]);
 224 }
 225
 226 DECL_FFT(32, 16, 8)
 227 DECL_FFT(64, 32, 16)
 228 DECL_FFT(128, 64, 32)
 229 DECL_FFT(256, 128, 64)
 230 DECL_FFT(512, 256, 128)
 231
 232 DECL_FFT(1024, 512, 256)
 233 DECL_FFT(2048, 1024, 512)
 234 DECL_FFT(4096, 2048, 1024)
 235 DECL_FFT(8192, 4096, 2048)
 236 DECL_FFT(16384, 8192, 4096)
 237 DECL_FFT(32768, 16384, 8192)
 238 DECL_FFT(65536, 32768, 16384)
 239
 240 static void (*fft_dispatch[]) (struct fft_complex *) = {
 241         fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
 242         fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
 243 };
 244
 245 static void fft(struct fft_context *s, struct fft_complex *z)
 246 {
 247         fft_dispatch[s->nbits - 2] (z);
 248 }
 249
 250 /* complex multiplication: p = a * b */
 251 #define CMUL(pre, pim, are, aim, bre, bim) \
 252 {\
 253         fftsample_t _are = (are);\
 254         fftsample_t _aim = (aim);\
 255         fftsample_t _bre = (bre);\
 256         fftsample_t _bim = (bim);\
 257         (pre) = _are * _bre - _aim * _bim;\
 258         (pim) = _are * _bim + _aim * _bre;\
 259 }
 260
 261 /**
 262  * Compute the middle half of the inverse MDCT of size N = 2^nbits
 263  *
 264  * Thus excluding the parts that can be derived by symmetry.
 265  *
 266  * \param output N/2 samples.
 267  * \param input N/2 samples.
 268  */
 269 static void imdct_half(struct mdct_context *s, fftsample_t *output,
 270                 const fftsample_t *input)
 271 {
 272         int k, n8, n4, n2, n, j;
 273         const uint16_t *revtab = s->fft.revtab;
 274         const fftsample_t *tcos = s->tcos;
 275         const fftsample_t *tsin = s->tsin;
 276         const fftsample_t *in1, *in2;
 277         struct fft_complex *z = (struct fft_complex *)output;
 278
 279         n = 1 << s->nbits;
 280         n2 = n >> 1;
 281         n4 = n >> 2;
 282         n8 = n >> 3;
 283
 284         /* pre rotation */
 285         in1 = input;
 286         in2 = input + n2 - 1;
 287         for (k = 0; k < n4; k++) {
 288                 j = revtab[k];
 289                 CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
 290                 in1 += 2;
 291                 in2 -= 2;
 292         }
 293         fft(&s->fft, z);
 294
 295         /* post rotation + reordering */
 296         output += n4;
 297         for (k = 0; k < n8; k++) {
 298                 fftsample_t r0, i0, r1, i1;
 299                 CMUL(r0, i1, z[n8 - k - 1].im, z[n8 - k - 1].re,
 300                         tsin[n8 - k - 1], tcos[n8 - k - 1]);
 301                 CMUL(r1, i0, z[n8 + k].im, z[n8 + k].re, tsin[n8 + k],
 302                         tcos[n8 + k]);
 303                 z[n8 - k - 1].re = r0;
 304                 z[n8 - k - 1].im = i0;
 305                 z[n8 + k].re = r1;
 306                 z[n8 + k].im = i1;
 307         }
 308 }
 309
 310 /**
 311  * Compute the inverse MDCT.
 312  *
 313  * \param ctx The initialized context structure.
 314  * \param output N samples.
 315  * \param input N/2 samples.
 316  *
 317  * \sa \ref imdct_init().
 318  */
 319 void imdct(struct mdct_context *ctx, float *output, const float *input)
 320 {
 321         int k;
 322         int n = 1 << ctx->nbits;
 323         int n2 = n >> 1;
 324         int n4 = n >> 2;
 325
 326         imdct_half(ctx, output + n4, input);
 327
 328         for (k = 0; k < n4; k++) {
 329                 output[k] = -output[n2 - k - 1];
 330                 output[n - k - 1] = output[n2 + k];
 331         }
 332 }
 333
 334 static int fft_init(struct fft_context *s, int nbits)
 335 {
 336         int i, j, n;
 337
 338         if (nbits < 2 || nbits > 16)
 339                 return -E_FFT_BAD_PARAMS;
 340         s->nbits = nbits;
 341         n = 1 << nbits;
 342
 343         s->revtab = para_malloc(n * sizeof(uint16_t));
 344         for (j = 4; j <= nbits; j++) {
 345                 int k = 1 << j;
 346                 double freq = 2 * M_PI / k;
 347                 fftsample_t *tab = cos_tabs[j - 4];
 348                 for (i = 0; i <= k / 4; i++)
 349                         tab[i] = cos(i * freq);
 350                 for (i = 1; i < k / 4; i++)
 351                         tab[k / 2 - i] = tab[i];
 352         }
 353         for (i = 0; i < n; i++)
 354                 s->revtab[-split_radix_permutation(i, n) & (n - 1)] = i;
 355         return 0;
 356 }
 357
 358 /**
 359  * Initialize the inverse modified cosine transform.
 360  *
 361  * \param nbits The number of bits to use (4 <= \a nbits <= 18).
 362  *
 363  * \param result Opaque structure that must be passed to \ref imdct().
 364  *
 365  * \return Standard.
 366  */
 367 int imdct_init(int nbits, struct mdct_context **result)
 368 {
 369         int ret, n, n4, i;
 370         double alpha;
 371         struct mdct_context *s;
 372
 373         s = para_calloc(sizeof(*s));
 374         n = 1 << nbits;
 375         s->nbits = nbits;
 376         s->n = n;
 377         n4 = n >> 2;
 378         s->tcos = para_malloc(n4 * sizeof(fftsample_t));
 379         s->tsin = para_malloc(n4 * sizeof(fftsample_t));
 380
 381         for (i = 0; i < n4; i++) {
 382                 alpha = 2 * M_PI * (i + 1.0 / 8.0) / n;
 383                 s->tcos[i] = -cos(alpha);
 384                 s->tsin[i] = -sin(alpha);
 385         }
 386         ret = fft_init(&s->fft, s->nbits - 2);
 387         if (ret < 0)
 388                 goto fail;
 389         *result = s;
 390         return 0;
 391 fail:
 392         freep(&s->tcos);
 393         freep(&s->tsin);
 394         free(s);
 395         return ret;
 396 }
 397
 398 /**
 399  * Deallocate imdct resources.
 400  *
 401  * \param ctx The pointer obtained by imdct_init().
 402  */
 403 void imdct_end(struct mdct_context *ctx)
 404 {
 405         free(ctx->tcos);
 406         free(ctx->tsin);
 407         free(ctx->fft.revtab);
 408         free(ctx);
 409 }