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, see file COPYING.LIB.
  11  */
  12
  13 /**
  14  * \file imdct.c Inverse modified discrete cosine transform.
  15  */
  16
  17 #include <math.h>
  18 #include <regex.h>
  19
  20 #include "para.h"
  21 #include "error.h"
  22 #include "string.h"
  23 #include "imdct.h"
  24 #include "wma.h"
  25
  26 typedef float fftsample_t;
  27
  28 /** Canonical representation of a complex number. */
  29 struct fft_complex {
  30         /** Real part. */
  31         fftsample_t re;
  32         /** Imaginary part. */
  33         fftsample_t im;
  34 };
  35
  36 /** FFT Lookup table. */
  37 struct fft_context {
  38         /** Number of bits of this instance of the FFT. */
  39         int nbits;
  40         /** The lookup table for cosine values. */
  41         uint16_t *revtab;
  42 };
  43
  44 struct mdct_context {
  45         /** Size of MDCT (number of input data * 2). */
  46         int n;
  47         /** n = 2^n bits. */
  48         int nbits;
  49         /** Cosine table for pre/post rotation. */
  50         fftsample_t *tcos;
  51         /** Sine table for pre/post rotation. */
  52         fftsample_t *tsin;
  53         /** The context for the underlying fast Fourier transform. */
  54         struct fft_context fft;
  55 };
  56
  57 /** \cond cosine_tabs */
  58
  59 /* cos(2 * pi * x / n) for 0 <= x <= n / 4, followed by its reverse */
  60 #define COSINE_TAB(n) static fftsample_t cos_ ## n[n / 2] __a_aligned(16)
  61
  62 COSINE_TAB(16);
  63 COSINE_TAB(32);
  64 COSINE_TAB(64);
  65 COSINE_TAB(128);
  66 COSINE_TAB(256);
  67 COSINE_TAB(512);
  68 COSINE_TAB(1024);
  69 COSINE_TAB(2048);
  70 COSINE_TAB(4096);
  71 COSINE_TAB(8192);
  72 COSINE_TAB(16384);
  73 COSINE_TAB(32768);
  74 COSINE_TAB(65536);
  75
  76 static fftsample_t *cos_tabs[] = {
  77         cos_16, cos_32, cos_64, cos_128, cos_256, cos_512, cos_1024, cos_2048,
  78         cos_4096, cos_8192, cos_16384, cos_32768, cos_65536,
  79 };
  80 /** \endcond cosine_tabs */
  81
  82 __a_const static int split_radix_permutation(int i, int n)
  83 {
  84         int m;
  85         if (n <= 2)
  86                 return i & 1;
  87         m = n >> 1;
  88         if ((i & m) == 0)
  89                 return split_radix_permutation(i, m) * 2;
  90         m >>= 1;
  91         if ((i & m) == 0)
  92                 return split_radix_permutation(i, m) * 4 + 1;
  93         else
  94                 return split_radix_permutation(i, m) * 4 - 1;
  95 }
  96
  97 #define BF(x, y, a, b) {\
  98         x = a - b;\
  99         y = a + b;\
 100 }
 101
 102 #define BUTTERFLIES(a0, a1, a2, a3) {\
 103         BF(t3, t5, t5, t1);\
 104         BF(a2.re, a0.re, a0.re, t5);\
 105         BF(a3.im, a1.im, a1.im, t3);\
 106         BF(t4, t6, t2, t6);\
 107         BF(a3.re, a1.re, a1.re, t4);\
 108         BF(a2.im, a0.im, a0.im, t6);\
 109 }
 110
 111 /*
 112  * Force loading all the inputs before storing any. This is slightly slower for
 113  * small data, but avoids store->load aliasing for addresses separated by large
 114  * powers of 2.
 115  */
 116 #define BUTTERFLIES_BIG(a0, a1, a2, a3) {\
 117         fftsample_t r0 = a0.re, i0 = a0.im, r1 = a1.re, i1 = a1.im;\
 118         BF(t3, t5, t5, t1);\
 119         BF(a2.re, a0.re, r0, t5);\
 120         BF(a3.im, a1.im, i1, t3);\
 121         BF(t4, t6, t2, t6);\
 122         BF(a3.re, a1.re, r1, t4);\
 123         BF(a2.im, a0.im, i0, t6);\
 124 }
 125
 126 #define TRANSFORM(a0, a1, a2, a3, wre,wim) {\
 127         t1 = a2.re * wre + a2.im * wim;\
 128         t2 = a2.im * wre - a2.re * wim;\
 129         t5 = a3.re * wre - a3.im * wim;\
 130         t6 = a3.im * wre + a3.re * wim;\
 131         BUTTERFLIES(a0, a1, a2, a3)\
 132 }
 133
 134 #define TRANSFORM_ZERO(a0, a1, a2, a3) {\
 135         t1 = a2.re;\
 136         t2 = a2.im;\
 137         t5 = a3.re;\
 138         t6 = a3.im;\
 139         BUTTERFLIES(a0, a1, a2, a3)\
 140 }
 141
 142 /* z[0...8n - 1], w[1...2n - 1] */
 143 static void pass(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
 151         n--;
 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 #undef BUTTERFLIES
 164 #define BUTTERFLIES BUTTERFLIES_BIG
 165
 166 #define DECL_FFT(n, n2, n4)\
 167 static void fft##n(struct fft_complex *z)\
 168 {\
 169         fft ## n2(z);\
 170         fft ## n4(z + n4 * 2);\
 171         fft ## n4(z + n4 * 3);\
 172         pass(z, cos_ ## n, n4 / 2);\
 173 }
 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], M_SQRT1_2, M_SQRT1_2);
 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], M_SQRT1_2, M_SQRT1_2);
 219         TRANSFORM(z[1], z[5], z[9], z[13], cos_16[1], cos_16[3]);
 220         TRANSFORM(z[3], z[7], z[11], z[15], cos_16[3], 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         for (k = 0; k < n8; k++) {
 294                 fftsample_t r0, i0, r1, i1;
 295                 CMUL(r0, i1, z[n8 - k - 1].im, z[n8 - k - 1].re,
 296                         tsin[n8 - k - 1], tcos[n8 - k - 1]);
 297                 CMUL(r1, i0, z[n8 + k].im, z[n8 + k].re, tsin[n8 + k],
 298                         tcos[n8 + k]);
 299                 z[n8 - k - 1].re = r0;
 300                 z[n8 - k - 1].im = i0;
 301                 z[n8 + k].re = r1;
 302                 z[n8 + k].im = i1;
 303         }
 304 }
 305
 306 /**
 307  * Compute the inverse MDCT.
 308  *
 309  * \param ctx The initialized context structure.
 310  * \param output N samples.
 311  * \param input N/2 samples.
 312  *
 313  * \sa \ref imdct_init().
 314  */
 315 void imdct(struct mdct_context *ctx, float *output, const float *input)
 316 {
 317         int k;
 318         int n = 1 << ctx->nbits;
 319         int n2 = n >> 1;
 320         int n4 = n >> 2;
 321
 322         imdct_half(ctx, output + n4, input);
 323
 324         for (k = 0; k < n4; k++) {
 325                 output[k] = -output[n2 - k - 1];
 326                 output[n - k - 1] = output[n2 + k];
 327         }
 328 }
 329
 330 static int fft_init(struct fft_context *s, int nbits)
 331 {
 332         int i, j, n;
 333
 334         if (nbits < 2 || nbits > 16)
 335                 return -E_FFT_BAD_PARAMS;
 336         s->nbits = nbits;
 337         n = 1 << nbits;
 338
 339         s->revtab = para_malloc(n * sizeof(uint16_t));
 340         for (j = 4; j <= nbits; j++) {
 341                 int k = 1 << j;
 342                 double freq = 2 * M_PI / k;
 343                 fftsample_t *tab = cos_tabs[j - 4];
 344                 for (i = 0; i <= k / 4; i++)
 345                         tab[i] = cos(i * freq);
 346                 for (i = 1; i < k / 4; i++)
 347                         tab[k / 2 - i] = tab[i];
 348         }
 349         for (i = 0; i < n; i++)
 350                 s->revtab[-split_radix_permutation(i, n) & (n - 1)] = i;
 351         return 0;
 352 }
 353
 354 /**
 355  * Initialize the inverse modified cosine transform.
 356  *
 357  * \param nbits The number of bits to use (4 <= \a nbits <= 18).
 358  *
 359  * \param result Opaque structure that must be passed to \ref imdct().
 360  *
 361  * \return Standard.
 362  */
 363 int imdct_init(int nbits, struct mdct_context **result)
 364 {
 365         int ret, n, n4, i;
 366         double alpha;
 367         struct mdct_context *s;
 368
 369         s = para_calloc(sizeof(*s));
 370         n = 1 << nbits;
 371         s->nbits = nbits;
 372         s->n = n;
 373         n4 = n >> 2;
 374         s->tcos = para_malloc(n4 * sizeof(fftsample_t));
 375         s->tsin = para_malloc(n4 * sizeof(fftsample_t));
 376
 377         for (i = 0; i < n4; i++) {
 378                 alpha = 2 * M_PI * (i + 1.0 / 8.0) / n;
 379                 s->tcos[i] = -cos(alpha);
 380                 s->tsin[i] = -sin(alpha);
 381         }
 382         ret = fft_init(&s->fft, s->nbits - 2);
 383         if (ret < 0)
 384                 goto fail;
 385         *result = s;
 386         return 0;
 387 fail:
 388         freep(&s->tcos);
 389         freep(&s->tsin);
 390         free(s);
 391         return ret;
 392 }
 393
 394 /**
 395  * Deallocate imdct resources.
 396  *
 397  * \param ctx The pointer obtained by imdct_init().
 398  */
 399 void imdct_end(struct mdct_context *ctx)
 400 {
 401         free(ctx->tcos);
 402         free(ctx->tsin);
 403         free(ctx->fft.revtab);
 404         free(ctx);
 405 }