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, see file COPYING.LIB.
14 * \file imdct.c Inverse modified discrete cosine transform.
26 typedef float fftsample_t;
28 /** Canonical representation of a complex number. */
32 /** Imaginary part. */
36 /** FFT Lookup table. */
38 /** Number of bits of this instance of the FFT. */
40 /** The lookup table for cosine values. */
45 /** Size of MDCT (number of input data * 2). */
49 /** Cosine table for pre/post rotation. */
51 /** Sine table for pre/post rotation. */
53 /** The context for the underlying fast Fourier transform. */
54 struct fft_context fft;
57 /** \cond cosine_tabs */
59 /* cos(2 * pi * x / n) for 0 <= x <= n / 4, followed by its reverse */
60 #define COSINE_TAB(n) static fftsample_t cos_ ## n[n / 2] __a_aligned(16)
76 static fftsample_t *cos_tabs[] = {
77 cos_16, cos_32, cos_64, cos_128, cos_256, cos_512, cos_1024, cos_2048,
78 cos_4096, cos_8192, cos_16384, cos_32768, cos_65536,
80 /** \endcond cosine_tabs */
82 __a_const static int split_radix_permutation(int i, int n)
89 return split_radix_permutation(i, m) * 2;
92 return split_radix_permutation(i, m) * 4 + 1;
94 return split_radix_permutation(i, m) * 4 - 1;
97 #define BF(x, y, a, b) {\
102 #define BUTTERFLIES(a0, a1, a2, a3) {\
104 BF(a2.re, a0.re, a0.re, t5);\
105 BF(a3.im, a1.im, a1.im, t3);\
107 BF(a3.re, a1.re, a1.re, t4);\
108 BF(a2.im, a0.im, a0.im, t6);\
112 * Force loading all the inputs before storing any. This is slightly slower for
113 * small data, but avoids store->load aliasing for addresses separated by large
116 #define BUTTERFLIES_BIG(a0, a1, a2, a3) {\
117 fftsample_t r0 = a0.re, i0 = a0.im, r1 = a1.re, i1 = a1.im;\
119 BF(a2.re, a0.re, r0, t5);\
120 BF(a3.im, a1.im, i1, t3);\
122 BF(a3.re, a1.re, r1, t4);\
123 BF(a2.im, a0.im, i0, t6);\
126 #define TRANSFORM(a0, a1, a2, a3, wre,wim) {\
127 t1 = a2.re * wre + a2.im * wim;\
128 t2 = a2.im * wre - a2.re * wim;\
129 t5 = a3.re * wre - a3.im * wim;\
130 t6 = a3.im * wre + a3.re * wim;\
131 BUTTERFLIES(a0, a1, a2, a3)\
134 #define TRANSFORM_ZERO(a0, a1, a2, a3) {\
139 BUTTERFLIES(a0, a1, a2, a3)\
142 /* z[0...8n - 1], w[1...2n - 1] */
143 static void pass(struct fft_complex *z, const fftsample_t *wre, unsigned int n)
145 fftsample_t t1, t2, t3, t4, t5, t6;
149 const fftsample_t *wim = wre + o1;
152 TRANSFORM_ZERO(z[0], z[o1], z[o2], z[o3]);
153 TRANSFORM(z[1], z[o1 + 1], z[o2 + 1], z[o3 + 1], wre[1], wim[-1]);
158 TRANSFORM(z[0], z[o1], z[o2], z[o3], wre[0], wim[0]);
159 TRANSFORM(z[1], z[o1 + 1], z[o2 + 1], z[o3 + 1], wre[1], wim[-1]);
164 #define BUTTERFLIES BUTTERFLIES_BIG
166 #define DECL_FFT(n, n2, n4)\
167 static void fft##n(struct fft_complex *z)\
170 fft ## n4(z + n4 * 2);\
171 fft ## n4(z + n4 * 3);\
172 pass(z, cos_ ## n, n4 / 2);\
175 static void fft4(struct fft_complex *z)
177 fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
179 BF(t3, t1, z[0].re, z[1].re);
180 BF(t8, t6, z[3].re, z[2].re);
181 BF(z[2].re, z[0].re, t1, t6);
182 BF(t4, t2, z[0].im, z[1].im);
183 BF(t7, t5, z[2].im, z[3].im);
184 BF(z[3].im, z[1].im, t4, t8);
185 BF(z[3].re, z[1].re, t3, t7);
186 BF(z[2].im, z[0].im, t2, t5);
189 static void fft8(struct fft_complex *z)
191 fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
195 BF(t1, z[5].re, z[4].re, -z[5].re);
196 BF(t2, z[5].im, z[4].im, -z[5].im);
197 BF(t3, z[7].re, z[6].re, -z[7].re);
198 BF(t4, z[7].im, z[6].im, -z[7].im);
201 BF(z[4].re, z[0].re, z[0].re, t1);
202 BF(z[4].im, z[0].im, z[0].im, t2);
203 BF(z[6].re, z[2].re, z[2].re, t7);
204 BF(z[6].im, z[2].im, z[2].im, t8);
206 TRANSFORM(z[1], z[3], z[5], z[7], M_SQRT1_2, M_SQRT1_2);
209 static void fft16(struct fft_complex *z)
211 fftsample_t t1, t2, t3, t4, t5, t6;
217 TRANSFORM_ZERO(z[0], z[4], z[8], z[12]);
218 TRANSFORM(z[2], z[6], z[10], z[14], M_SQRT1_2, M_SQRT1_2);
219 TRANSFORM(z[1], z[5], z[9], z[13], cos_16[1], cos_16[3]);
220 TRANSFORM(z[3], z[7], z[11], z[15], cos_16[3], cos_16[1]);
225 DECL_FFT(128, 64, 32)
226 DECL_FFT(256, 128, 64)
227 DECL_FFT(512, 256, 128)
229 DECL_FFT(1024, 512, 256)
230 DECL_FFT(2048, 1024, 512)
231 DECL_FFT(4096, 2048, 1024)
232 DECL_FFT(8192, 4096, 2048)
233 DECL_FFT(16384, 8192, 4096)
234 DECL_FFT(32768, 16384, 8192)
235 DECL_FFT(65536, 32768, 16384)
237 static void (*fft_dispatch[]) (struct fft_complex *) = {
238 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
239 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
242 static void fft(struct fft_context *s, struct fft_complex *z)
244 fft_dispatch[s->nbits - 2] (z);
247 /* complex multiplication: p = a * b */
248 #define CMUL(pre, pim, are, aim, bre, bim) \
250 fftsample_t _are = (are);\
251 fftsample_t _aim = (aim);\
252 fftsample_t _bre = (bre);\
253 fftsample_t _bim = (bim);\
254 (pre) = _are * _bre - _aim * _bim;\
255 (pim) = _are * _bim + _aim * _bre;\
259 * Compute the middle half of the inverse MDCT of size N = 2^nbits
261 * Thus excluding the parts that can be derived by symmetry.
263 * \param output N/2 samples.
264 * \param input N/2 samples.
266 static void imdct_half(struct mdct_context *s, fftsample_t *output,
267 const fftsample_t *input)
269 int k, n8, n4, n2, n, j;
270 const uint16_t *revtab = s->fft.revtab;
271 const fftsample_t *tcos = s->tcos;
272 const fftsample_t *tsin = s->tsin;
273 const fftsample_t *in1, *in2;
274 struct fft_complex *z = (struct fft_complex *)output;
283 in2 = input + n2 - 1;
284 for (k = 0; k < n4; k++) {
286 CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
292 /* post rotation + reordering */
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],
299 z[n8 - k - 1].re = r0;
300 z[n8 - k - 1].im = i0;
307 * Compute the inverse MDCT.
309 * \param ctx The initialized context structure.
310 * \param output N samples.
311 * \param input N/2 samples.
313 * \sa \ref imdct_init().
315 void imdct(struct mdct_context *ctx, float *output, const float *input)
318 int n = 1 << ctx->nbits;
322 imdct_half(ctx, output + n4, input);
324 for (k = 0; k < n4; k++) {
325 output[k] = -output[n2 - k - 1];
326 output[n - k - 1] = output[n2 + k];
330 static int fft_init(struct fft_context *s, int nbits)
334 if (nbits < 2 || nbits > 16)
335 return -E_FFT_BAD_PARAMS;
339 s->revtab = para_malloc(n * sizeof(uint16_t));
340 for (j = 4; j <= nbits; j++) {
342 double freq = 2 * M_PI / k;
343 fftsample_t *tab = cos_tabs[j - 4];
344 for (i = 0; i <= k / 4; i++)
345 tab[i] = cos(i * freq);
346 for (i = 1; i < k / 4; i++)
347 tab[k / 2 - i] = tab[i];
349 for (i = 0; i < n; i++)
350 s->revtab[-split_radix_permutation(i, n) & (n - 1)] = i;
355 * Initialize the inverse modified cosine transform.
357 * \param nbits The number of bits to use (4 <= \a nbits <= 18).
359 * \param result Opaque structure that must be passed to \ref imdct().
363 int imdct_init(int nbits, struct mdct_context **result)
367 struct mdct_context *s;
369 s = para_calloc(sizeof(*s));
374 s->tcos = para_malloc(n4 * sizeof(fftsample_t));
375 s->tsin = para_malloc(n4 * sizeof(fftsample_t));
377 for (i = 0; i < n4; i++) {
378 alpha = 2 * M_PI * (i + 1.0 / 8.0) / n;
379 s->tcos[i] = -cos(alpha);
380 s->tsin[i] = -sin(alpha);
382 ret = fft_init(&s->fft, s->nbits - 2);
395 * Deallocate imdct resources.
397 * \param ctx The pointer obtained by imdct_init().
399 void imdct_end(struct mdct_context *ctx)
403 free(ctx->fft.revtab);