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