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 M_SQRT1_2      0.70710678118654752440   /* 1/sqrt(2) */
  33
  34 struct fft_complex {
  35         fftsample_t re, im;
  36 };
  37
  38 struct fft_context {
  39         int nbits;
  40         int inverse;
  41         uint16_t *revtab;
  42         struct fft_complex *exptab;
  43 };
  44
  45 struct mdct_context {
  46         /** Size of MDCT (i.e. number of input data * 2). */
  47         int n;
  48         /** n = 2^n bits. */
  49         int nbits;
  50         /** pre/post rotation tables */
  51         fftsample_t *tcos;
  52         fftsample_t *tsin;
  53         struct fft_context fft;
  54 };
  55
  56 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
  57 DECLARE_ALIGNED_16(fftsample_t, ff_cos_16[8]);
  58 DECLARE_ALIGNED_16(fftsample_t, ff_cos_32[16]);
  59 DECLARE_ALIGNED_16(fftsample_t, ff_cos_64[32]);
  60 DECLARE_ALIGNED_16(fftsample_t, ff_cos_128[64]);
  61 DECLARE_ALIGNED_16(fftsample_t, ff_cos_256[128]);
  62 DECLARE_ALIGNED_16(fftsample_t, ff_cos_512[256]);
  63 DECLARE_ALIGNED_16(fftsample_t, ff_cos_1024[512]);
  64 DECLARE_ALIGNED_16(fftsample_t, ff_cos_2048[1024]);
  65 DECLARE_ALIGNED_16(fftsample_t, ff_cos_4096[2048]);
  66 DECLARE_ALIGNED_16(fftsample_t, ff_cos_8192[4096]);
  67 DECLARE_ALIGNED_16(fftsample_t, ff_cos_16384[8192]);
  68 DECLARE_ALIGNED_16(fftsample_t, ff_cos_32768[16384]);
  69 DECLARE_ALIGNED_16(fftsample_t, ff_cos_65536[32768]);
  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, int inverse)
  78 {
  79         int m;
  80         if (n <= 2)
  81                 return i & 1;
  82         m = n >> 1;
  83         if (!(i & m))
  84                 return split_radix_permutation(i, m, inverse) * 2;
  85         m >>= 1;
  86         if (inverse == !(i & m))
  87                 return split_radix_permutation(i, m, inverse) * 4 + 1;
  88         else
  89                 return split_radix_permutation(i, m, inverse) * 4 - 1;
  90 }
  91
  92 #define sqrthalf (float)M_SQRT1_2
  93
  94 #define BF(x,y,a,b) {\
  95     x = a - b;\
  96     y = a + b;\
  97 }
  98
  99 #define BUTTERFLIES(a0,a1,a2,a3) {\
 100     BF(t3, t5, t5, t1);\
 101     BF(a2.re, a0.re, a0.re, t5);\
 102     BF(a3.im, a1.im, a1.im, t3);\
 103     BF(t4, t6, t2, t6);\
 104     BF(a3.re, a1.re, a1.re, t4);\
 105     BF(a2.im, a0.im, a0.im, t6);\
 106 }
 107
 108 // force loading all the inputs before storing any.
 109 // this is slightly slower for small data, but avoids store->load aliasing
 110 // for addresses separated by large powers of 2.
 111 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
 112     fftsample_t r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
 113     BF(t3, t5, t5, t1);\
 114     BF(a2.re, a0.re, r0, t5);\
 115     BF(a3.im, a1.im, i1, t3);\
 116     BF(t4, t6, t2, t6);\
 117     BF(a3.re, a1.re, r1, t4);\
 118     BF(a2.im, a0.im, i0, t6);\
 119 }
 120
 121 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
 122     t1 = a2.re * wre + a2.im * wim;\
 123     t2 = a2.im * wre - a2.re * wim;\
 124     t5 = a3.re * wre - a3.im * wim;\
 125     t6 = a3.im * wre + a3.re * wim;\
 126     BUTTERFLIES(a0,a1,a2,a3)\
 127 }
 128
 129 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
 130     t1 = a2.re;\
 131     t2 = a2.im;\
 132     t5 = a3.re;\
 133     t6 = a3.im;\
 134     BUTTERFLIES(a0,a1,a2,a3)\
 135 }
 136
 137 /* z[0...8n-1], w[1...2n-1] */
 138 #define PASS(name)\
 139 static void name(struct fft_complex *z, const fftsample_t *wre, unsigned int n)\
 140 {\
 141     fftsample_t t1, t2, t3, t4, t5, t6;\
 142     int o1 = 2*n;\
 143     int o2 = 4*n;\
 144     int o3 = 6*n;\
 145     const fftsample_t *wim = wre+o1;\
 146     n--;\
 147 \
 148     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
 149     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 150     do {\
 151         z += 2;\
 152         wre += 2;\
 153         wim -= 2;\
 154         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
 155         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 156     } while(--n);\
 157 }
 158
 159 PASS(pass)
 160 #undef BUTTERFLIES
 161 #define BUTTERFLIES BUTTERFLIES_BIG
 162
 163 #define DECL_FFT(n,n2,n4)\
 164 static void fft##n(struct fft_complex *z)\
 165 {\
 166     fft##n2(z);\
 167     fft##n4(z+n4*2);\
 168     fft##n4(z+n4*3);\
 169     pass(z,ff_cos_##n,n4/2);\
 170 }
 171 static void fft4(struct fft_complex *z)
 172 {
 173         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 174
 175         BF(t3, t1, z[0].re, z[1].re);
 176         BF(t8, t6, z[3].re, z[2].re);
 177         BF(z[2].re, z[0].re, t1, t6);
 178         BF(t4, t2, z[0].im, z[1].im);
 179         BF(t7, t5, z[2].im, z[3].im);
 180         BF(z[3].im, z[1].im, t4, t8);
 181         BF(z[3].re, z[1].re, t3, t7);
 182         BF(z[2].im, z[0].im, t2, t5);
 183 }
 184
 185 static void fft8(struct fft_complex *z)
 186 {
 187         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 188
 189         fft4(z);
 190
 191         BF(t1, z[5].re, z[4].re, -z[5].re);
 192         BF(t2, z[5].im, z[4].im, -z[5].im);
 193         BF(t3, z[7].re, z[6].re, -z[7].re);
 194         BF(t4, z[7].im, z[6].im, -z[7].im);
 195         BF(t8, t1, t3, t1);
 196         BF(t7, t2, t2, t4);
 197         BF(z[4].re, z[0].re, z[0].re, t1);
 198         BF(z[4].im, z[0].im, z[0].im, t2);
 199         BF(z[6].re, z[2].re, z[2].re, t7);
 200         BF(z[6].im, z[2].im, z[2].im, t8);
 201
 202         TRANSFORM(z[1], z[3], z[5], z[7], sqrthalf, sqrthalf);
 203 }
 204
 205 static void fft16(struct fft_complex *z)
 206 {
 207         fftsample_t t1, t2, t3, t4, t5, t6;
 208
 209         fft8(z);
 210         fft4(z + 8);
 211         fft4(z + 12);
 212
 213         TRANSFORM_ZERO(z[0], z[4], z[8], z[12]);
 214         TRANSFORM(z[2], z[6], z[10], z[14], sqrthalf, sqrthalf);
 215         TRANSFORM(z[1], z[5], z[9], z[13], ff_cos_16[1], ff_cos_16[3]);
 216         TRANSFORM(z[3], z[7], z[11], z[15], ff_cos_16[3], ff_cos_16[1]);
 217 }
 218
 219 DECL_FFT(32, 16, 8)
 220 DECL_FFT(64, 32, 16)
 221 DECL_FFT(128, 64, 32)
 222 DECL_FFT(256, 128, 64)
 223 DECL_FFT(512, 256, 128)
 224
 225 DECL_FFT(1024, 512, 256)
 226 DECL_FFT(2048, 1024, 512)
 227 DECL_FFT(4096, 2048, 1024)
 228 DECL_FFT(8192, 4096, 2048)
 229 DECL_FFT(16384, 8192, 4096)
 230 DECL_FFT(32768, 16384, 8192)
 231 DECL_FFT(65536, 32768, 16384)
 232
 233 static void (*fft_dispatch[]) (struct fft_complex *) = {
 234         fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
 235         fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
 236 };
 237
 238 static void fft(struct fft_context *s, struct fft_complex *z)
 239 {
 240         fft_dispatch[s->nbits - 2] (z);
 241 }
 242
 243 /* complex multiplication: p = a * b */
 244 #define CMUL(pre, pim, are, aim, bre, bim) \
 245 {\
 246         fftsample_t _are = (are);\
 247         fftsample_t _aim = (aim);\
 248         fftsample_t _bre = (bre);\
 249         fftsample_t _bim = (bim);\
 250         (pre) = _are * _bre - _aim * _bim;\
 251         (pim) = _are * _bim + _aim * _bre;\
 252 }
 253
 254 /**
 255  * Compute the middle half of the inverse MDCT of size N = 2^nbits
 256  *
 257  * Thus excluding the parts that can be derived by symmetry.
 258  *
 259  * \param output N/2 samples.
 260  * \param input N/2 samples.
 261  */
 262 static void imdct_half(struct mdct_context *s, fftsample_t *output,
 263                 const fftsample_t *input)
 264 {
 265         int k, n8, n4, n2, n, j;
 266         const uint16_t *revtab = s->fft.revtab;
 267         const fftsample_t *tcos = s->tcos;
 268         const fftsample_t *tsin = s->tsin;
 269         const fftsample_t *in1, *in2;
 270         struct fft_complex *z = (struct fft_complex *)output;
 271
 272         n = 1 << s->nbits;
 273         n2 = n >> 1;
 274         n4 = n >> 2;
 275         n8 = n >> 3;
 276
 277         /* pre rotation */
 278         in1 = input;
 279         in2 = input + n2 - 1;
 280         for (k = 0; k < n4; k++) {
 281                 j = revtab[k];
 282                 CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
 283                 in1 += 2;
 284                 in2 -= 2;
 285         }
 286         fft(&s->fft, z);
 287
 288         /* post rotation + reordering */
 289         output += n4;
 290         for (k = 0; k < n8; k++) {
 291                 fftsample_t r0, i0, r1, i1;
 292                 CMUL(r0, i1, z[n8 - k - 1].im, z[n8 - k - 1].re,
 293                         tsin[n8 - k - 1], tcos[n8 - k - 1]);
 294                 CMUL(r1, i0, z[n8 + k].im, z[n8 + k].re, tsin[n8 + k],
 295                         tcos[n8 + k]);
 296                 z[n8 - k - 1].re = r0;
 297                 z[n8 - k - 1].im = i0;
 298                 z[n8 + k].re = r1;
 299                 z[n8 + k].im = i1;
 300         }
 301 }
 302
 303 /**
 304  * Compute the inverse MDCT of size N = 2^nbits.
 305  *
 306  * \param output N samples.
 307  * \param input N/2 samples.
 308  */
 309 void imdct(struct mdct_context *s, float *output, const float *input)
 310 {
 311         int k;
 312         int n = 1 << s->nbits;
 313         int n2 = n >> 1;
 314         int n4 = n >> 2;
 315
 316         imdct_half(s, output + n4, input);
 317
 318         for (k = 0; k < n4; k++) {
 319                 output[k] = -output[n2 - k - 1];
 320                 output[n - k - 1] = output[n2 + k];
 321         }
 322 }
 323
 324 static int fft_init(struct fft_context *s, int nbits, int inverse)
 325 {
 326         int i, j, n;
 327
 328         if (nbits < 2 || nbits > 16)
 329                 return -E_FFT_BAD_PARAMS;
 330         s->nbits = nbits;
 331         n = 1 << nbits;
 332
 333         s->exptab = para_malloc((n / 2) * sizeof(struct fft_complex));
 334         s->revtab = para_malloc(n * sizeof(uint16_t));
 335         s->inverse = inverse;
 336
 337         for (j = 4; j <= nbits; j++) {
 338                 int k = 1 << j;
 339                 double freq = 2 * M_PI / k;
 340                 fftsample_t *tab = ff_cos_tabs[j - 4];
 341                 for (i = 0; i <= k / 4; i++)
 342                         tab[i] = cos(i * freq);
 343                 for (i = 1; i < k / 4; i++)
 344                         tab[k / 2 - i] = tab[i];
 345         }
 346         for (i = 0; i < n; i++)
 347                 s->revtab[-split_radix_permutation(
 348                         i, n, s->inverse) & (n - 1)] = i;
 349         return 0;
 350 }
 351
 352 static void fft_end(struct fft_context *ctx)
 353 {
 354         freep(&ctx->revtab);
 355         freep(&ctx->exptab);
 356 }
 357
 358 /**
 359  * Init MDCT or IMDCT computation.
 360  */
 361 int imdct_init(int nbits, int inverse, 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, inverse);
 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 void imdct_end(struct mdct_context *ctx)
 393 {
 394         freep(&ctx->tcos);
 395         freep(&ctx->tsin);
 396         fft_end(&ctx->fft);
 397         free(ctx);
 398 }