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) fftsample_t cos_ ## n[n / 2] __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 /** 1 / sqrt(2). */
  99 #define SQRTHALF (float)0.70710678118654752440
 100
 101 #define BF(x, y, a, b) {\
 102         x = a - b;\
 103         y = a + b;\
 104 }
 105
 106 #define BUTTERFLIES(a0, a1, a2, a3) {\
 107         BF(t3, t5, t5, t1);\
 108         BF(a2.re, a0.re, a0.re, t5);\
 109         BF(a3.im, a1.im, a1.im, t3);\
 110         BF(t4, t6, t2, t6);\
 111         BF(a3.re, a1.re, a1.re, t4);\
 112         BF(a2.im, a0.im, a0.im, t6);\
 113 }
 114
 115 /*
 116  * Force loading all the inputs before storing any. This is slightly slower for
 117  * small data, but avoids store->load aliasing for addresses separated by large
 118  * powers of 2.
 119  */
 120 #define BUTTERFLIES_BIG(a0, a1, a2, a3) {\
 121         fftsample_t r0 = a0.re, i0 = a0.im, r1 = a1.re, i1 = a1.im;\
 122         BF(t3, t5, t5, t1);\
 123         BF(a2.re, a0.re, r0, t5);\
 124         BF(a3.im, a1.im, i1, t3);\
 125         BF(t4, t6, t2, t6);\
 126         BF(a3.re, a1.re, r1, t4);\
 127         BF(a2.im, a0.im, i0, t6);\
 128 }
 129
 130 #define TRANSFORM(a0, a1, a2, a3, wre,wim) {\
 131         t1 = a2.re * wre + a2.im * wim;\
 132         t2 = a2.im * wre - a2.re * wim;\
 133         t5 = a3.re * wre - a3.im * wim;\
 134         t6 = a3.im * wre + a3.re * wim;\
 135         BUTTERFLIES(a0, a1, a2, a3)\
 136 }
 137
 138 #define TRANSFORM_ZERO(a0, a1, a2, a3) {\
 139         t1 = a2.re;\
 140         t2 = a2.im;\
 141         t5 = a3.re;\
 142         t6 = a3.im;\
 143         BUTTERFLIES(a0, a1, a2, a3)\
 144 }
 145
 146 /* z[0...8n - 1], w[1...2n - 1] */
 147 #define PASS(name)\
 148 static void name(struct fft_complex *z, const fftsample_t *wre, unsigned int n)\
 149 {\
 150         fftsample_t t1, t2, t3, t4, t5, t6;\
 151         int o1 = 2 * n;\
 152         int o2 = 4 * n;\
 153         int o3 = 6 * n;\
 154         const fftsample_t *wim = wre + o1;\
 155         n--;\
 156 \
 157         TRANSFORM_ZERO(z[0], z[o1], z[o2], z[o3]);\
 158         TRANSFORM(z[1], z[o1 + 1], z[o2 + 1], z[o3 + 1], wre[1], wim[-1]);\
 159         do {\
 160                 z += 2;\
 161                 wre += 2;\
 162                 wim -= 2;\
 163                 TRANSFORM(z[0], z[o1], z[o2], z[o3], wre[0], wim[0]);\
 164                 TRANSFORM(z[1], z[o1 + 1], z[o2 + 1], z[o3 + 1], wre[1], wim[-1]);\
 165         } while (--n);\
 166 }
 167
 168 PASS(pass)
 169 #undef BUTTERFLIES
 170 #define BUTTERFLIES BUTTERFLIES_BIG
 171
 172 #define DECL_FFT(n, n2, n4)\
 173 static void fft##n(struct fft_complex *z)\
 174 {\
 175         fft ## n2(z);\
 176         fft ## n4(z + n4 * 2);\
 177         fft ## n4(z + n4 * 3);\
 178         pass(z, cos_ ## n, n4 / 2);\
 179 }
 180
 181 static void fft4(struct fft_complex *z)
 182 {
 183         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 184
 185         BF(t3, t1, z[0].re, z[1].re);
 186         BF(t8, t6, z[3].re, z[2].re);
 187         BF(z[2].re, z[0].re, t1, t6);
 188         BF(t4, t2, z[0].im, z[1].im);
 189         BF(t7, t5, z[2].im, z[3].im);
 190         BF(z[3].im, z[1].im, t4, t8);
 191         BF(z[3].re, z[1].re, t3, t7);
 192         BF(z[2].im, z[0].im, t2, t5);
 193 }
 194
 195 static void fft8(struct fft_complex *z)
 196 {
 197         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 198
 199         fft4(z);
 200
 201         BF(t1, z[5].re, z[4].re, -z[5].re);
 202         BF(t2, z[5].im, z[4].im, -z[5].im);
 203         BF(t3, z[7].re, z[6].re, -z[7].re);
 204         BF(t4, z[7].im, z[6].im, -z[7].im);
 205         BF(t8, t1, t3, t1);
 206         BF(t7, t2, t2, t4);
 207         BF(z[4].re, z[0].re, z[0].re, t1);
 208         BF(z[4].im, z[0].im, z[0].im, t2);
 209         BF(z[6].re, z[2].re, z[2].re, t7);
 210         BF(z[6].im, z[2].im, z[2].im, t8);
 211
 212         TRANSFORM(z[1], z[3], z[5], z[7], SQRTHALF, SQRTHALF);
 213 }
 214
 215 static void fft16(struct fft_complex *z)
 216 {
 217         fftsample_t t1, t2, t3, t4, t5, t6;
 218
 219         fft8(z);
 220         fft4(z + 8);
 221         fft4(z + 12);
 222
 223         TRANSFORM_ZERO(z[0], z[4], z[8], z[12]);
 224         TRANSFORM(z[2], z[6], z[10], z[14], SQRTHALF, SQRTHALF);
 225         TRANSFORM(z[1], z[5], z[9], z[13], cos_16[1], cos_16[3]);
 226         TRANSFORM(z[3], z[7], z[11], z[15], cos_16[3], cos_16[1]);
 227 }
 228
 229 DECL_FFT(32, 16, 8)
 230 DECL_FFT(64, 32, 16)
 231 DECL_FFT(128, 64, 32)
 232 DECL_FFT(256, 128, 64)
 233 DECL_FFT(512, 256, 128)
 234
 235 DECL_FFT(1024, 512, 256)
 236 DECL_FFT(2048, 1024, 512)
 237 DECL_FFT(4096, 2048, 1024)
 238 DECL_FFT(8192, 4096, 2048)
 239 DECL_FFT(16384, 8192, 4096)
 240 DECL_FFT(32768, 16384, 8192)
 241 DECL_FFT(65536, 32768, 16384)
 242
 243 static void (*fft_dispatch[]) (struct fft_complex *) = {
 244         fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
 245         fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
 246 };
 247
 248 static void fft(struct fft_context *s, struct fft_complex *z)
 249 {
 250         fft_dispatch[s->nbits - 2] (z);
 251 }
 252
 253 /* complex multiplication: p = a * b */
 254 #define CMUL(pre, pim, are, aim, bre, bim) \
 255 {\
 256         fftsample_t _are = (are);\
 257         fftsample_t _aim = (aim);\
 258         fftsample_t _bre = (bre);\
 259         fftsample_t _bim = (bim);\
 260         (pre) = _are * _bre - _aim * _bim;\
 261         (pim) = _are * _bim + _aim * _bre;\
 262 }
 263
 264 /**
 265  * Compute the middle half of the inverse MDCT of size N = 2^nbits
 266  *
 267  * Thus excluding the parts that can be derived by symmetry.
 268  *
 269  * \param output N/2 samples.
 270  * \param input N/2 samples.
 271  */
 272 static void imdct_half(struct mdct_context *s, fftsample_t *output,
 273                 const fftsample_t *input)
 274 {
 275         int k, n8, n4, n2, n, j;
 276         const uint16_t *revtab = s->fft.revtab;
 277         const fftsample_t *tcos = s->tcos;
 278         const fftsample_t *tsin = s->tsin;
 279         const fftsample_t *in1, *in2;
 280         struct fft_complex *z = (struct fft_complex *)output;
 281
 282         n = 1 << s->nbits;
 283         n2 = n >> 1;
 284         n4 = n >> 2;
 285         n8 = n >> 3;
 286
 287         /* pre rotation */
 288         in1 = input;
 289         in2 = input + n2 - 1;
 290         for (k = 0; k < n4; k++) {
 291                 j = revtab[k];
 292                 CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
 293                 in1 += 2;
 294                 in2 -= 2;
 295         }
 296         fft(&s->fft, z);
 297
 298         /* post rotation + reordering */
 299         output += n4;
 300         for (k = 0; k < n8; k++) {
 301                 fftsample_t r0, i0, r1, i1;
 302                 CMUL(r0, i1, z[n8 - k - 1].im, z[n8 - k - 1].re,
 303                         tsin[n8 - k - 1], tcos[n8 - k - 1]);
 304                 CMUL(r1, i0, z[n8 + k].im, z[n8 + k].re, tsin[n8 + k],
 305                         tcos[n8 + k]);
 306                 z[n8 - k - 1].re = r0;
 307                 z[n8 - k - 1].im = i0;
 308                 z[n8 + k].re = r1;
 309                 z[n8 + k].im = i1;
 310         }
 311 }
 312
 313 /**
 314  * Compute the inverse MDCT.
 315  *
 316  * \param ctx The initialized context structure.
 317  * \param output N samples.
 318  * \param input N/2 samples.
 319  *
 320  * \sa \ref imdct_init().
 321  */
 322 void imdct(struct mdct_context *ctx, float *output, const float *input)
 323 {
 324         int k;
 325         int n = 1 << ctx->nbits;
 326         int n2 = n >> 1;
 327         int n4 = n >> 2;
 328
 329         imdct_half(ctx, output + n4, input);
 330
 331         for (k = 0; k < n4; k++) {
 332                 output[k] = -output[n2 - k - 1];
 333                 output[n - k - 1] = output[n2 + k];
 334         }
 335 }
 336
 337 static int fft_init(struct fft_context *s, int nbits)
 338 {
 339         int i, j, n;
 340
 341         if (nbits < 2 || nbits > 16)
 342                 return -E_FFT_BAD_PARAMS;
 343         s->nbits = nbits;
 344         n = 1 << nbits;
 345
 346         s->revtab = para_malloc(n * sizeof(uint16_t));
 347         for (j = 4; j <= nbits; j++) {
 348                 int k = 1 << j;
 349                 double freq = 2 * M_PI / k;
 350                 fftsample_t *tab = cos_tabs[j - 4];
 351                 for (i = 0; i <= k / 4; i++)
 352                         tab[i] = cos(i * freq);
 353                 for (i = 1; i < k / 4; i++)
 354                         tab[k / 2 - i] = tab[i];
 355         }
 356         for (i = 0; i < n; i++)
 357                 s->revtab[-split_radix_permutation(i, n) & (n - 1)] = i;
 358         return 0;
 359 }
 360
 361 /**
 362  * Initialize the inverse modified cosine transform.
 363  *
 364  * \param nbits The number of bits to use (4 <= \a nbits <= 18).
 365  *
 366  * \param result Opaque structure that must be passed to \ref imdct().
 367  *
 368  * \return Standard.
 369  */
 370 int imdct_init(int nbits, struct mdct_context **result)
 371 {
 372         int ret, n, n4, i;
 373         double alpha;
 374         struct mdct_context *s;
 375
 376         s = para_calloc(sizeof(*s));
 377         n = 1 << nbits;
 378         s->nbits = nbits;
 379         s->n = n;
 380         n4 = n >> 2;
 381         s->tcos = para_malloc(n4 * sizeof(fftsample_t));
 382         s->tsin = para_malloc(n4 * sizeof(fftsample_t));
 383
 384         for (i = 0; i < n4; i++) {
 385                 alpha = 2 * M_PI * (i + 1.0 / 8.0) / n;
 386                 s->tcos[i] = -cos(alpha);
 387                 s->tsin[i] = -sin(alpha);
 388         }
 389         ret = fft_init(&s->fft, s->nbits - 2);
 390         if (ret < 0)
 391                 goto fail;
 392         *result = s;
 393         return 0;
 394 fail:
 395         freep(&s->tcos);
 396         freep(&s->tsin);
 397         free(s);
 398         return ret;
 399 }
 400
 401 /**
 402  * Deallocate imdct resources.
 403  *
 404  * \param ctx The pointer obtained by imdct_init().
 405  */
 406 void imdct_end(struct mdct_context *ctx)
 407 {
 408         free(ctx->tcos);
 409         free(ctx->tsin);
 410         free(ctx->fft.revtab);
 411         free(ctx);
 412 }