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 *tmp_buf;
  46 };
  47
  48 struct mdct_context {
  49         /** Size of MDCT (i.e. number of input data * 2). */
  50         int n;
  51         /** n = 2^n bits. */
  52         int nbits;
  53         /** pre/post rotation tables */
  54         fftsample_t *tcos;
  55         fftsample_t *tsin;
  56         struct fft_context fft;
  57 };
  58
  59 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
  60 DECLARE_ALIGNED_16(fftsample_t, ff_cos_16[8]);
  61 DECLARE_ALIGNED_16(fftsample_t, ff_cos_32[16]);
  62 DECLARE_ALIGNED_16(fftsample_t, ff_cos_64[32]);
  63 DECLARE_ALIGNED_16(fftsample_t, ff_cos_128[64]);
  64 DECLARE_ALIGNED_16(fftsample_t, ff_cos_256[128]);
  65 DECLARE_ALIGNED_16(fftsample_t, ff_cos_512[256]);
  66 DECLARE_ALIGNED_16(fftsample_t, ff_cos_1024[512]);
  67 DECLARE_ALIGNED_16(fftsample_t, ff_cos_2048[1024]);
  68 DECLARE_ALIGNED_16(fftsample_t, ff_cos_4096[2048]);
  69 DECLARE_ALIGNED_16(fftsample_t, ff_cos_8192[4096]);
  70 DECLARE_ALIGNED_16(fftsample_t, ff_cos_16384[8192]);
  71 DECLARE_ALIGNED_16(fftsample_t, ff_cos_32768[16384]);
  72 DECLARE_ALIGNED_16(fftsample_t, ff_cos_65536[32768]);
  73
  74 static fftsample_t *ff_cos_tabs[] = {
  75         ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256,
  76         ff_cos_512, ff_cos_1024, ff_cos_2048, ff_cos_4096, ff_cos_8192,
  77         ff_cos_16384, ff_cos_32768, ff_cos_65536,
  78 };
  79
  80 static int split_radix_permutation(int i, int n, int inverse)
  81 {
  82         int m;
  83         if (n <= 2)
  84                 return i & 1;
  85         m = n >> 1;
  86         if (!(i & m))
  87                 return split_radix_permutation(i, m, inverse) * 2;
  88         m >>= 1;
  89         if (inverse == !(i & m))
  90                 return split_radix_permutation(i, m, inverse) * 4 + 1;
  91         else
  92                 return split_radix_permutation(i, m, inverse) * 4 - 1;
  93 }
  94
  95 #define sqrthalf (float)M_SQRT1_2
  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 // force loading all the inputs before storing any.
 112 // this is slightly slower for small data, but avoids store->load aliasing
 113 // for addresses separated by large powers of 2.
 114 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
 115     fftsample_t r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
 116     BF(t3, t5, t5, t1);\
 117     BF(a2.re, a0.re, r0, t5);\
 118     BF(a3.im, a1.im, i1, t3);\
 119     BF(t4, t6, t2, t6);\
 120     BF(a3.re, a1.re, r1, t4);\
 121     BF(a2.im, a0.im, i0, t6);\
 122 }
 123
 124 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
 125     t1 = a2.re * wre + a2.im * wim;\
 126     t2 = a2.im * wre - a2.re * wim;\
 127     t5 = a3.re * wre - a3.im * wim;\
 128     t6 = a3.im * wre + a3.re * wim;\
 129     BUTTERFLIES(a0,a1,a2,a3)\
 130 }
 131
 132 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
 133     t1 = a2.re;\
 134     t2 = a2.im;\
 135     t5 = a3.re;\
 136     t6 = a3.im;\
 137     BUTTERFLIES(a0,a1,a2,a3)\
 138 }
 139
 140 /* z[0...8n-1], w[1...2n-1] */
 141 #define PASS(name)\
 142 static void name(struct fft_complex *z, const fftsample_t *wre, unsigned int n)\
 143 {\
 144     fftsample_t t1, t2, t3, t4, t5, t6;\
 145     int o1 = 2*n;\
 146     int o2 = 4*n;\
 147     int o3 = 6*n;\
 148     const fftsample_t *wim = wre+o1;\
 149     n--;\
 150 \
 151     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
 152     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 153     do {\
 154         z += 2;\
 155         wre += 2;\
 156         wim -= 2;\
 157         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
 158         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 159     } while(--n);\
 160 }
 161
 162 PASS(pass)
 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,ff_cos_##n,n4/2);\
 173 }
 174 static void fft4(struct fft_complex *z)
 175 {
 176         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 177
 178         BF(t3, t1, z[0].re, z[1].re);
 179         BF(t8, t6, z[3].re, z[2].re);
 180         BF(z[2].re, z[0].re, t1, t6);
 181         BF(t4, t2, z[0].im, z[1].im);
 182         BF(t7, t5, z[2].im, z[3].im);
 183         BF(z[3].im, z[1].im, t4, t8);
 184         BF(z[3].re, z[1].re, t3, t7);
 185         BF(z[2].im, z[0].im, t2, t5);
 186 }
 187
 188 static void fft8(struct fft_complex *z)
 189 {
 190         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 191
 192         fft4(z);
 193
 194         BF(t1, z[5].re, z[4].re, -z[5].re);
 195         BF(t2, z[5].im, z[4].im, -z[5].im);
 196         BF(t3, z[7].re, z[6].re, -z[7].re);
 197         BF(t4, z[7].im, z[6].im, -z[7].im);
 198         BF(t8, t1, t3, t1);
 199         BF(t7, t2, t2, t4);
 200         BF(z[4].re, z[0].re, z[0].re, t1);
 201         BF(z[4].im, z[0].im, z[0].im, t2);
 202         BF(z[6].re, z[2].re, z[2].re, t7);
 203         BF(z[6].im, z[2].im, z[2].im, t8);
 204
 205         TRANSFORM(z[1], z[3], z[5], z[7], sqrthalf, sqrthalf);
 206 }
 207
 208 static void fft16(struct fft_complex *z)
 209 {
 210         fftsample_t t1, t2, t3, t4, t5, t6;
 211
 212         fft8(z);
 213         fft4(z + 8);
 214         fft4(z + 12);
 215
 216         TRANSFORM_ZERO(z[0], z[4], z[8], z[12]);
 217         TRANSFORM(z[2], z[6], z[10], z[14], sqrthalf, sqrthalf);
 218         TRANSFORM(z[1], z[5], z[9], z[13], ff_cos_16[1], ff_cos_16[3]);
 219         TRANSFORM(z[3], z[7], z[11], z[15], ff_cos_16[3], ff_cos_16[1]);
 220 }
 221
 222 DECL_FFT(32, 16, 8)
 223 DECL_FFT(64, 32, 16)
 224 DECL_FFT(128, 64, 32)
 225 DECL_FFT(256, 128, 64)
 226 DECL_FFT(512, 256, 128)
 227
 228 DECL_FFT(1024, 512, 256)
 229 DECL_FFT(2048, 1024, 512)
 230 DECL_FFT(4096, 2048, 1024)
 231 DECL_FFT(8192, 4096, 2048)
 232 DECL_FFT(16384, 8192, 4096)
 233 DECL_FFT(32768, 16384, 8192)
 234 DECL_FFT(65536, 32768, 16384)
 235
 236 static void (*fft_dispatch[]) (struct fft_complex *) = {
 237         fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
 238         fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
 239 };
 240
 241 static void fft(struct fft_context *s, struct fft_complex *z)
 242 {
 243         fft_dispatch[s->nbits - 2] (z);
 244 }
 245
 246 /* complex multiplication: p = a * b */
 247 #define CMUL(pre, pim, are, aim, bre, bim) \
 248 {\
 249         fftsample_t _are = (are);\
 250         fftsample_t _aim = (aim);\
 251         fftsample_t _bre = (bre);\
 252         fftsample_t _bim = (bim);\
 253         (pre) = _are * _bre - _aim * _bim;\
 254         (pim) = _are * _bim + _aim * _bre;\
 255 }
 256
 257 /**
 258  * Compute the middle half of the inverse MDCT of size N = 2^nbits
 259  *
 260  * Thus excluding the parts that can be derived by symmetry.
 261  *
 262  * \param output N/2 samples.
 263  * \param input N/2 samples.
 264  */
 265 static void imdct_half(struct mdct_context *s, fftsample_t *output,
 266                 const fftsample_t *input)
 267 {
 268         int k, n8, n4, n2, n, j;
 269         const uint16_t *revtab = s->fft.revtab;
 270         const fftsample_t *tcos = s->tcos;
 271         const fftsample_t *tsin = s->tsin;
 272         const fftsample_t *in1, *in2;
 273         struct fft_complex *z = (struct fft_complex *)output;
 274
 275         n = 1 << s->nbits;
 276         n2 = n >> 1;
 277         n4 = n >> 2;
 278         n8 = n >> 3;
 279
 280         /* pre rotation */
 281         in1 = input;
 282         in2 = input + n2 - 1;
 283         for (k = 0; k < n4; k++) {
 284                 j = revtab[k];
 285                 CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
 286                 in1 += 2;
 287                 in2 -= 2;
 288         }
 289         fft(&s->fft, z);
 290
 291         /* post rotation + reordering */
 292         output += n4;
 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 of size N = 2^nbits.
 308  *
 309  * \param output N samples.
 310  * \param input N/2 samples.
 311  */
 312 void imdct(struct mdct_context *s, float *output, const float *input)
 313 {
 314         int k;
 315         int n = 1 << s->nbits;
 316         int n2 = n >> 1;
 317         int n4 = n >> 2;
 318
 319         imdct_half(s, output + n4, input);
 320
 321         for (k = 0; k < n4; k++) {
 322                 output[k] = -output[n2 - k - 1];
 323                 output[n - k - 1] = output[n2 + k];
 324         }
 325 }
 326
 327 static int fft_init(struct fft_context *s, int nbits, int inverse)
 328 {
 329         int i, j, n;
 330
 331         if (nbits < 2 || nbits > 16)
 332                 return -E_FFT_BAD_PARAMS;
 333         s->nbits = nbits;
 334         n = 1 << nbits;
 335
 336         s->tmp_buf = NULL;
 337         s->exptab = para_malloc((n / 2) * sizeof(struct fft_complex));
 338         s->revtab = para_malloc(n * sizeof(uint16_t));
 339         s->inverse = inverse;
 340
 341         for (j = 4; j <= nbits; j++) {
 342                 int k = 1 << j;
 343                 double freq = 2 * M_PI / k;
 344                 fftsample_t *tab = ff_cos_tabs[j - 4];
 345                 for (i = 0; i <= k / 4; i++)
 346                         tab[i] = cos(i * freq);
 347                 for (i = 1; i < k / 4; i++)
 348                         tab[k / 2 - i] = tab[i];
 349         }
 350         for (i = 0; i < n; i++)
 351                 s->revtab[-split_radix_permutation(
 352                         i, n, s->inverse) & (n - 1)] = i;
 353         s->tmp_buf = para_malloc(n * sizeof(struct fft_complex));
 354         return 0;
 355 }
 356
 357 static void fft_end(struct fft_context *ctx)
 358 {
 359         freep(&ctx->revtab);
 360         freep(&ctx->exptab);
 361         freep(&ctx->tmp_buf);
 362 }
 363
 364 DECLARE_ALIGNED(16, float, ff_sine_128[128]);
 365 DECLARE_ALIGNED(16, float, ff_sine_256[256]);
 366 DECLARE_ALIGNED(16, float, ff_sine_512[512]);
 367 DECLARE_ALIGNED(16, float, ff_sine_1024[1024]);
 368 DECLARE_ALIGNED(16, float, ff_sine_2048[2048]);
 369 DECLARE_ALIGNED(16, float, ff_sine_4096[4096]);
 370
 371 float *ff_sine_windows[6] = {
 372         ff_sine_128, ff_sine_256, ff_sine_512, ff_sine_1024,
 373         ff_sine_2048, ff_sine_4096
 374 };
 375
 376 // Generate a sine window.
 377 void sine_window_init(float *window, int n)
 378 {
 379         int i;
 380
 381         for (i = 0; i < n; i++)
 382                 window[i] = sinf((i + 0.5) * (M_PI / (2.0 * n)));
 383 }
 384
 385 /**
 386  * Init MDCT or IMDCT computation.
 387  */
 388 int imdct_init(int nbits, int inverse, struct mdct_context **result)
 389 {
 390         int ret, n, n4, i;
 391         double alpha;
 392         struct mdct_context *s;
 393
 394         s = para_calloc(sizeof(*s));
 395         n = 1 << nbits;
 396         s->nbits = nbits;
 397         s->n = n;
 398         n4 = n >> 2;
 399         s->tcos = para_malloc(n4 * sizeof(fftsample_t));
 400         s->tsin = para_malloc(n4 * sizeof(fftsample_t));
 401
 402         for (i = 0; i < n4; i++) {
 403                 alpha = 2 * M_PI * (i + 1.0 / 8.0) / n;
 404                 s->tcos[i] = -cos(alpha);
 405                 s->tsin[i] = -sin(alpha);
 406         }
 407         ret = fft_init(&s->fft, s->nbits - 2, inverse);
 408         if (ret < 0)
 409                 goto fail;
 410         *result = s;
 411         return 0;
 412 fail:
 413         freep(&s->tcos);
 414         freep(&s->tsin);
 415         free(s);
 416         return ret;
 417 }
 418
 419 void imdct_end(struct mdct_context *ctx)
 420 {
 421         freep(&ctx->tcos);
 422         freep(&ctx->tsin);
 423         fft_end(&ctx->fft);
 424         free(ctx);
 425 }