4 * Extracted 2009 from mplayer 2009-02-10 libavcodec/fft.c and libavcodec/mdct.c
6 * Copyright (c) 2008 Loren Merritt
7 * Copyright (c) 2002 Fabrice Bellard
8 * Partly based on libdjbfft by D. J. Bernstein
10 * Licensed under the GNU Lesser General Public License.
11 * For licencing details see COPYING.LIB.
15 * \file imdct.c Inverse modified discrete cosine transform.
30 typedef float fftsample_t;
42 /** Size of MDCT (number of input data * 2). */
46 /** Cosine table for pre/post rotation. */
48 /** Sine table for pre/post rotation. */
50 /** The context for the underlying fast Fourier transform. */
51 struct fft_context fft;
54 /** cos(2 * pi * x / n) for 0 <= x <= n / 4, followed by its reverse */
55 #define COSINE_TAB(n) fftsample_t ff_cos_ ## n[n / 2] __aligned(16)
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,
77 static int split_radix_permutation(int i, int n)
84 return split_radix_permutation(i, m) * 2;
87 return split_radix_permutation(i, m) * 4 + 1;
89 return split_radix_permutation(i, m) * 4 - 1;
93 #define SQRTHALF (float)0.70710678118654752440
95 #define BF(x,y,a,b) {\
100 #define BUTTERFLIES(a0,a1,a2,a3) {\
102 BF(a2.re, a0.re, a0.re, t5);\
103 BF(a3.im, a1.im, a1.im, t3);\
105 BF(a3.re, a1.re, a1.re, t4);\
106 BF(a2.im, a0.im, a0.im, t6);\
109 // force loading all the inputs before storing any.
110 // this is slightly slower for small data, but avoids store->load aliasing
111 // for addresses separated by large powers of 2.
112 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
113 fftsample_t r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
115 BF(a2.re, a0.re, r0, t5);\
116 BF(a3.im, a1.im, i1, t3);\
118 BF(a3.re, a1.re, r1, t4);\
119 BF(a2.im, a0.im, i0, t6);\
122 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
123 t1 = a2.re * wre + a2.im * wim;\
124 t2 = a2.im * wre - a2.re * wim;\
125 t5 = a3.re * wre - a3.im * wim;\
126 t6 = a3.im * wre + a3.re * wim;\
127 BUTTERFLIES(a0,a1,a2,a3)\
130 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
135 BUTTERFLIES(a0,a1,a2,a3)\
138 /* z[0...8n-1], w[1...2n-1] */
140 static void name(struct fft_complex *z, const fftsample_t *wre, unsigned int n)\
142 fftsample_t t1, t2, t3, t4, t5, t6;\
146 const fftsample_t *wim = wre+o1;\
149 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
150 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
155 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
156 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
162 #define BUTTERFLIES BUTTERFLIES_BIG
164 #define DECL_FFT(n,n2,n4)\
165 static void fft##n(struct fft_complex *z)\
170 pass(z,ff_cos_##n,n4/2);\
172 static void fft4(struct fft_complex *z)
174 fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
176 BF(t3, t1, z[0].re, z[1].re);
177 BF(t8, t6, z[3].re, z[2].re);
178 BF(z[2].re, z[0].re, t1, t6);
179 BF(t4, t2, z[0].im, z[1].im);
180 BF(t7, t5, z[2].im, z[3].im);
181 BF(z[3].im, z[1].im, t4, t8);
182 BF(z[3].re, z[1].re, t3, t7);
183 BF(z[2].im, z[0].im, t2, t5);
186 static void fft8(struct fft_complex *z)
188 fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
192 BF(t1, z[5].re, z[4].re, -z[5].re);
193 BF(t2, z[5].im, z[4].im, -z[5].im);
194 BF(t3, z[7].re, z[6].re, -z[7].re);
195 BF(t4, z[7].im, z[6].im, -z[7].im);
198 BF(z[4].re, z[0].re, z[0].re, t1);
199 BF(z[4].im, z[0].im, z[0].im, t2);
200 BF(z[6].re, z[2].re, z[2].re, t7);
201 BF(z[6].im, z[2].im, z[2].im, t8);
203 TRANSFORM(z[1], z[3], z[5], z[7], SQRTHALF, SQRTHALF);
206 static void fft16(struct fft_complex *z)
208 fftsample_t t1, t2, t3, t4, t5, t6;
214 TRANSFORM_ZERO(z[0], z[4], z[8], z[12]);
215 TRANSFORM(z[2], z[6], z[10], z[14], SQRTHALF, SQRTHALF);
216 TRANSFORM(z[1], z[5], z[9], z[13], ff_cos_16[1], ff_cos_16[3]);
217 TRANSFORM(z[3], z[7], z[11], z[15], ff_cos_16[3], ff_cos_16[1]);
222 DECL_FFT(128, 64, 32)
223 DECL_FFT(256, 128, 64)
224 DECL_FFT(512, 256, 128)
226 DECL_FFT(1024, 512, 256)
227 DECL_FFT(2048, 1024, 512)
228 DECL_FFT(4096, 2048, 1024)
229 DECL_FFT(8192, 4096, 2048)
230 DECL_FFT(16384, 8192, 4096)
231 DECL_FFT(32768, 16384, 8192)
232 DECL_FFT(65536, 32768, 16384)
234 static void (*fft_dispatch[]) (struct fft_complex *) = {
235 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
236 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
239 static void fft(struct fft_context *s, struct fft_complex *z)
241 fft_dispatch[s->nbits - 2] (z);
244 /* complex multiplication: p = a * b */
245 #define CMUL(pre, pim, are, aim, bre, bim) \
247 fftsample_t _are = (are);\
248 fftsample_t _aim = (aim);\
249 fftsample_t _bre = (bre);\
250 fftsample_t _bim = (bim);\
251 (pre) = _are * _bre - _aim * _bim;\
252 (pim) = _are * _bim + _aim * _bre;\
256 * Compute the middle half of the inverse MDCT of size N = 2^nbits
258 * Thus excluding the parts that can be derived by symmetry.
260 * \param output N/2 samples.
261 * \param input N/2 samples.
263 static void imdct_half(struct mdct_context *s, fftsample_t *output,
264 const fftsample_t *input)
266 int k, n8, n4, n2, n, j;
267 const uint16_t *revtab = s->fft.revtab;
268 const fftsample_t *tcos = s->tcos;
269 const fftsample_t *tsin = s->tsin;
270 const fftsample_t *in1, *in2;
271 struct fft_complex *z = (struct fft_complex *)output;
280 in2 = input + n2 - 1;
281 for (k = 0; k < n4; k++) {
283 CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
289 /* post rotation + reordering */
291 for (k = 0; k < n8; k++) {
292 fftsample_t r0, i0, r1, i1;
293 CMUL(r0, i1, z[n8 - k - 1].im, z[n8 - k - 1].re,
294 tsin[n8 - k - 1], tcos[n8 - k - 1]);
295 CMUL(r1, i0, z[n8 + k].im, z[n8 + k].re, tsin[n8 + k],
297 z[n8 - k - 1].re = r0;
298 z[n8 - k - 1].im = i0;
305 * Compute the inverse MDCT.
307 * \param ctx The initialized context structure.
308 * \param output N samples.
309 * \param input N/2 samples.
311 * \sa \ref imdct_init().
313 void imdct(struct mdct_context *ctx, float *output, const float *input)
316 int n = 1 << ctx->nbits;
320 imdct_half(ctx, output + n4, input);
322 for (k = 0; k < n4; k++) {
323 output[k] = -output[n2 - k - 1];
324 output[n - k - 1] = output[n2 + k];
328 static int fft_init(struct fft_context *s, int nbits)
332 if (nbits < 2 || nbits > 16)
333 return -E_FFT_BAD_PARAMS;
337 s->revtab = para_malloc(n * sizeof(uint16_t));
338 for (j = 4; j <= nbits; j++) {
340 double freq = 2 * M_PI / k;
341 fftsample_t *tab = ff_cos_tabs[j - 4];
342 for (i = 0; i <= k / 4; i++)
343 tab[i] = cos(i * freq);
344 for (i = 1; i < k / 4; i++)
345 tab[k / 2 - i] = tab[i];
347 for (i = 0; i < n; i++)
348 s->revtab[-split_radix_permutation(i, n) & (n - 1)] = i;
353 * Initialize the inverse modified cosine transform.
355 * \param nbits The number of bits to use (4 <= \a nbits <= 18).
357 * \param result Opaque structure that must be passed to \ref imdct().
361 int imdct_init(int nbits, struct mdct_context **result)
365 struct mdct_context *s;
367 s = para_calloc(sizeof(*s));
372 s->tcos = para_malloc(n4 * sizeof(fftsample_t));
373 s->tsin = para_malloc(n4 * sizeof(fftsample_t));
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);
380 ret = fft_init(&s->fft, s->nbits - 2);
393 * Deallocate imdct resources.
395 * \param ctx The pointer obtained by imdct_init().
397 void imdct_end(struct mdct_context *ctx)
401 free(ctx->fft.revtab);