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 struct fft_complex {
  33         fftsample_t re, im;
  34 };
  35
  36 struct fft_context {
  37         int nbits;
  38         int inverse;
  39         uint16_t *revtab;
  40         struct fft_complex *exptab;
  41 };
  42
  43 struct mdct_context {
  44         /** Size of MDCT (i.e. number of input data * 2). */
  45         int n;
  46         /** n = 2^n bits. */
  47         int nbits;
  48         /** pre/post rotation tables */
  49         fftsample_t *tcos;
  50         fftsample_t *tsin;
  51         struct fft_context fft;
  52 };
  53
  54 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
  55 DECLARE_ALIGNED_16(fftsample_t, ff_cos_16[8]);
  56 DECLARE_ALIGNED_16(fftsample_t, ff_cos_32[16]);
  57 DECLARE_ALIGNED_16(fftsample_t, ff_cos_64[32]);
  58 DECLARE_ALIGNED_16(fftsample_t, ff_cos_128[64]);
  59 DECLARE_ALIGNED_16(fftsample_t, ff_cos_256[128]);
  60 DECLARE_ALIGNED_16(fftsample_t, ff_cos_512[256]);
  61 DECLARE_ALIGNED_16(fftsample_t, ff_cos_1024[512]);
  62 DECLARE_ALIGNED_16(fftsample_t, ff_cos_2048[1024]);
  63 DECLARE_ALIGNED_16(fftsample_t, ff_cos_4096[2048]);
  64 DECLARE_ALIGNED_16(fftsample_t, ff_cos_8192[4096]);
  65 DECLARE_ALIGNED_16(fftsample_t, ff_cos_16384[8192]);
  66 DECLARE_ALIGNED_16(fftsample_t, ff_cos_32768[16384]);
  67 DECLARE_ALIGNED_16(fftsample_t, ff_cos_65536[32768]);
  68
  69 static fftsample_t *ff_cos_tabs[] = {
  70         ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256,
  71         ff_cos_512, ff_cos_1024, ff_cos_2048, ff_cos_4096, ff_cos_8192,
  72         ff_cos_16384, ff_cos_32768, ff_cos_65536,
  73 };
  74
  75 static int split_radix_permutation(int i, int n, int inverse)
  76 {
  77         int m;
  78         if (n <= 2)
  79                 return i & 1;
  80         m = n >> 1;
  81         if (!(i & m))
  82                 return split_radix_permutation(i, m, inverse) * 2;
  83         m >>= 1;
  84         if (inverse == !(i & m))
  85                 return split_radix_permutation(i, m, inverse) * 4 + 1;
  86         else
  87                 return split_radix_permutation(i, m, inverse) * 4 - 1;
  88 }
  89
  90 #define SQRTHALF (float)0.70710678118654752440  /* 1/sqrt(2) */
  91
  92 #define BF(x,y,a,b) {\
  93     x = a - b;\
  94     y = a + b;\
  95 }
  96
  97 #define BUTTERFLIES(a0,a1,a2,a3) {\
  98     BF(t3, t5, t5, t1);\
  99     BF(a2.re, a0.re, a0.re, t5);\
 100     BF(a3.im, a1.im, a1.im, t3);\
 101     BF(t4, t6, t2, t6);\
 102     BF(a3.re, a1.re, a1.re, t4);\
 103     BF(a2.im, a0.im, a0.im, t6);\
 104 }
 105
 106 // force loading all the inputs before storing any.
 107 // this is slightly slower for small data, but avoids store->load aliasing
 108 // for addresses separated by large powers of 2.
 109 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
 110     fftsample_t r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
 111     BF(t3, t5, t5, t1);\
 112     BF(a2.re, a0.re, r0, t5);\
 113     BF(a3.im, a1.im, i1, t3);\
 114     BF(t4, t6, t2, t6);\
 115     BF(a3.re, a1.re, r1, t4);\
 116     BF(a2.im, a0.im, i0, t6);\
 117 }
 118
 119 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
 120     t1 = a2.re * wre + a2.im * wim;\
 121     t2 = a2.im * wre - a2.re * wim;\
 122     t5 = a3.re * wre - a3.im * wim;\
 123     t6 = a3.im * wre + a3.re * wim;\
 124     BUTTERFLIES(a0,a1,a2,a3)\
 125 }
 126
 127 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
 128     t1 = a2.re;\
 129     t2 = a2.im;\
 130     t5 = a3.re;\
 131     t6 = a3.im;\
 132     BUTTERFLIES(a0,a1,a2,a3)\
 133 }
 134
 135 /* z[0...8n-1], w[1...2n-1] */
 136 #define PASS(name)\
 137 static void name(struct fft_complex *z, const fftsample_t *wre, unsigned int n)\
 138 {\
 139     fftsample_t t1, t2, t3, t4, t5, t6;\
 140     int o1 = 2*n;\
 141     int o2 = 4*n;\
 142     int o3 = 6*n;\
 143     const fftsample_t *wim = wre+o1;\
 144     n--;\
 145 \
 146     TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
 147     TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 148     do {\
 149         z += 2;\
 150         wre += 2;\
 151         wim -= 2;\
 152         TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
 153         TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
 154     } while(--n);\
 155 }
 156
 157 PASS(pass)
 158 #undef BUTTERFLIES
 159 #define BUTTERFLIES BUTTERFLIES_BIG
 160
 161 #define DECL_FFT(n,n2,n4)\
 162 static void fft##n(struct fft_complex *z)\
 163 {\
 164     fft##n2(z);\
 165     fft##n4(z+n4*2);\
 166     fft##n4(z+n4*3);\
 167     pass(z,ff_cos_##n,n4/2);\
 168 }
 169 static void fft4(struct fft_complex *z)
 170 {
 171         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 172
 173         BF(t3, t1, z[0].re, z[1].re);
 174         BF(t8, t6, z[3].re, z[2].re);
 175         BF(z[2].re, z[0].re, t1, t6);
 176         BF(t4, t2, z[0].im, z[1].im);
 177         BF(t7, t5, z[2].im, z[3].im);
 178         BF(z[3].im, z[1].im, t4, t8);
 179         BF(z[3].re, z[1].re, t3, t7);
 180         BF(z[2].im, z[0].im, t2, t5);
 181 }
 182
 183 static void fft8(struct fft_complex *z)
 184 {
 185         fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
 186
 187         fft4(z);
 188
 189         BF(t1, z[5].re, z[4].re, -z[5].re);
 190         BF(t2, z[5].im, z[4].im, -z[5].im);
 191         BF(t3, z[7].re, z[6].re, -z[7].re);
 192         BF(t4, z[7].im, z[6].im, -z[7].im);
 193         BF(t8, t1, t3, t1);
 194         BF(t7, t2, t2, t4);
 195         BF(z[4].re, z[0].re, z[0].re, t1);
 196         BF(z[4].im, z[0].im, z[0].im, t2);
 197         BF(z[6].re, z[2].re, z[2].re, t7);
 198         BF(z[6].im, z[2].im, z[2].im, t8);
 199
 200         TRANSFORM(z[1], z[3], z[5], z[7], SQRTHALF, SQRTHALF);
 201 }
 202
 203 static void fft16(struct fft_complex *z)
 204 {
 205         fftsample_t t1, t2, t3, t4, t5, t6;
 206
 207         fft8(z);
 208         fft4(z + 8);
 209         fft4(z + 12);
 210
 211         TRANSFORM_ZERO(z[0], z[4], z[8], z[12]);
 212         TRANSFORM(z[2], z[6], z[10], z[14], SQRTHALF, SQRTHALF);
 213         TRANSFORM(z[1], z[5], z[9], z[13], ff_cos_16[1], ff_cos_16[3]);
 214         TRANSFORM(z[3], z[7], z[11], z[15], ff_cos_16[3], ff_cos_16[1]);
 215 }
 216
 217 DECL_FFT(32, 16, 8)
 218 DECL_FFT(64, 32, 16)
 219 DECL_FFT(128, 64, 32)
 220 DECL_FFT(256, 128, 64)
 221 DECL_FFT(512, 256, 128)
 222
 223 DECL_FFT(1024, 512, 256)
 224 DECL_FFT(2048, 1024, 512)
 225 DECL_FFT(4096, 2048, 1024)
 226 DECL_FFT(8192, 4096, 2048)
 227 DECL_FFT(16384, 8192, 4096)
 228 DECL_FFT(32768, 16384, 8192)
 229 DECL_FFT(65536, 32768, 16384)
 230
 231 static void (*fft_dispatch[]) (struct fft_complex *) = {
 232         fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
 233         fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
 234 };
 235
 236 static void fft(struct fft_context *s, struct fft_complex *z)
 237 {
 238         fft_dispatch[s->nbits - 2] (z);
 239 }
 240
 241 /* complex multiplication: p = a * b */
 242 #define CMUL(pre, pim, are, aim, bre, bim) \
 243 {\
 244         fftsample_t _are = (are);\
 245         fftsample_t _aim = (aim);\
 246         fftsample_t _bre = (bre);\
 247         fftsample_t _bim = (bim);\
 248         (pre) = _are * _bre - _aim * _bim;\
 249         (pim) = _are * _bim + _aim * _bre;\
 250 }
 251
 252 /**
 253  * Compute the middle half of the inverse MDCT of size N = 2^nbits
 254  *
 255  * Thus excluding the parts that can be derived by symmetry.
 256  *
 257  * \param output N/2 samples.
 258  * \param input N/2 samples.
 259  */
 260 static void imdct_half(struct mdct_context *s, fftsample_t *output,
 261                 const fftsample_t *input)
 262 {
 263         int k, n8, n4, n2, n, j;
 264         const uint16_t *revtab = s->fft.revtab;
 265         const fftsample_t *tcos = s->tcos;
 266         const fftsample_t *tsin = s->tsin;
 267         const fftsample_t *in1, *in2;
 268         struct fft_complex *z = (struct fft_complex *)output;
 269
 270         n = 1 << s->nbits;
 271         n2 = n >> 1;
 272         n4 = n >> 2;
 273         n8 = n >> 3;
 274
 275         /* pre rotation */
 276         in1 = input;
 277         in2 = input + n2 - 1;
 278         for (k = 0; k < n4; k++) {
 279                 j = revtab[k];
 280                 CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
 281                 in1 += 2;
 282                 in2 -= 2;
 283         }
 284         fft(&s->fft, z);
 285
 286         /* post rotation + reordering */
 287         output += n4;
 288         for (k = 0; k < n8; k++) {
 289                 fftsample_t r0, i0, r1, i1;
 290                 CMUL(r0, i1, z[n8 - k - 1].im, z[n8 - k - 1].re,
 291                         tsin[n8 - k - 1], tcos[n8 - k - 1]);
 292                 CMUL(r1, i0, z[n8 + k].im, z[n8 + k].re, tsin[n8 + k],
 293                         tcos[n8 + k]);
 294                 z[n8 - k - 1].re = r0;
 295                 z[n8 - k - 1].im = i0;
 296                 z[n8 + k].re = r1;
 297                 z[n8 + k].im = i1;
 298         }
 299 }
 300
 301 /**
 302  * Compute the inverse MDCT of size N = 2^nbits.
 303  *
 304  * \param output N samples.
 305  * \param input N/2 samples.
 306  */
 307 void imdct(struct mdct_context *s, float *output, const float *input)
 308 {
 309         int k;
 310         int n = 1 << s->nbits;
 311         int n2 = n >> 1;
 312         int n4 = n >> 2;
 313
 314         imdct_half(s, output + n4, input);
 315
 316         for (k = 0; k < n4; k++) {
 317                 output[k] = -output[n2 - k - 1];
 318                 output[n - k - 1] = output[n2 + k];
 319         }
 320 }
 321
 322 static int fft_init(struct fft_context *s, int nbits, int inverse)
 323 {
 324         int i, j, n;
 325
 326         if (nbits < 2 || nbits > 16)
 327                 return -E_FFT_BAD_PARAMS;
 328         s->nbits = nbits;
 329         n = 1 << nbits;
 330
 331         s->exptab = para_malloc((n / 2) * sizeof(struct fft_complex));
 332         s->revtab = para_malloc(n * sizeof(uint16_t));
 333         s->inverse = inverse;
 334         for (j = 4; j <= nbits; j++) {
 335                 int k = 1 << j;
 336                 double freq = 2 * M_PI / k;
 337                 fftsample_t *tab = ff_cos_tabs[j - 4];
 338                 for (i = 0; i <= k / 4; i++)
 339                         tab[i] = cos(i * freq);
 340                 for (i = 1; i < k / 4; i++)
 341                         tab[k / 2 - i] = tab[i];
 342         }
 343         for (i = 0; i < n; i++)
 344                 s->revtab[-split_radix_permutation(
 345                         i, n, s->inverse) & (n - 1)] = i;
 346         return 0;
 347 }
 348
 349 static void fft_end(struct fft_context *ctx)
 350 {
 351         freep(&ctx->revtab);
 352         freep(&ctx->exptab);
 353 }
 354
 355 /**
 356  * Init MDCT or IMDCT computation.
 357  */
 358 int imdct_init(int nbits, int inverse, struct mdct_context **result)
 359 {
 360         int ret, n, n4, i;
 361         double alpha;
 362         struct mdct_context *s;
 363
 364         s = para_calloc(sizeof(*s));
 365         n = 1 << nbits;
 366         s->nbits = nbits;
 367         s->n = n;
 368         n4 = n >> 2;
 369         s->tcos = para_malloc(n4 * sizeof(fftsample_t));
 370         s->tsin = para_malloc(n4 * sizeof(fftsample_t));
 371
 372         for (i = 0; i < n4; i++) {
 373                 alpha = 2 * M_PI * (i + 1.0 / 8.0) / n;
 374                 s->tcos[i] = -cos(alpha);
 375                 s->tsin[i] = -sin(alpha);
 376         }
 377         ret = fft_init(&s->fft, s->nbits - 2, inverse);
 378         if (ret < 0)
 379                 goto fail;
 380         *result = s;
 381         return 0;
 382 fail:
 383         freep(&s->tcos);
 384         freep(&s->tsin);
 385         free(s);
 386         return ret;
 387 }
 388
 389 void imdct_end(struct mdct_context *ctx)
 390 {
 391         freep(&ctx->tcos);
 392         freep(&ctx->tsin);
 393         fft_end(&ctx->fft);
 394         free(ctx);
 395 }