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[paraslash.git] / 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 /** Canonical representation of a complex number. */
33 struct fft_complex {
34 /** Real part. */
35 fftsample_t re;
36 /** Imaginary part. */
37 fftsample_t im;
38 };
39
40 /** FFT Lookup table. */
41 struct fft_context {
42 /** Number of bits of this instance of the FFT. */
43 int nbits;
44 /** The lookup table for cosine values. */
45 uint16_t *revtab;
46 };
47
48 struct mdct_context {
49 /** Size of MDCT (number of input data * 2). */
50 int n;
51 /** n = 2^n bits. */
52 int nbits;
53 /** Cosine table for pre/post rotation. */
54 fftsample_t *tcos;
55 /** Sine table for pre/post rotation. */
56 fftsample_t *tsin;
57 /** The context for the underlying fast Fourier transform. */
58 struct fft_context fft;
59 };
60
61 /** \cond cosine_tabs */
62
63 /* cos(2 * pi * x / n) for 0 <= x <= n / 4, followed by its reverse */
64 #define COSINE_TAB(n) static fftsample_t cos_ ## n[n / 2] __a_aligned(16)
65
66 COSINE_TAB(16);
67 COSINE_TAB(32);
68 COSINE_TAB(64);
69 COSINE_TAB(128);
70 COSINE_TAB(256);
71 COSINE_TAB(512);
72 COSINE_TAB(1024);
73 COSINE_TAB(2048);
74 COSINE_TAB(4096);
75 COSINE_TAB(8192);
76 COSINE_TAB(16384);
77 COSINE_TAB(32768);
78 COSINE_TAB(65536);
79
80 static fftsample_t *cos_tabs[] = {
81 cos_16, cos_32, cos_64, cos_128, cos_256, cos_512, cos_1024, cos_2048,
82 cos_4096, cos_8192, cos_16384, cos_32768, cos_65536,
83 };
84 /** \endcond cosine_tabs */
85
86 __a_const static int split_radix_permutation(int i, int n)
87 {
88 int m;
89 if (n <= 2)
90 return i & 1;
91 m = n >> 1;
92 if ((i & m) == 0)
93 return split_radix_permutation(i, m) * 2;
94 m >>= 1;
95 if ((i & m) == 0)
96 return split_radix_permutation(i, m) * 4 + 1;
97 else
98 return split_radix_permutation(i, m) * 4 - 1;
99 }
100
101 #define BF(x, y, a, b) {\
102 x = a - b;\
103 y = a + b;\
104 }
105
106 #define BUTTERFLIES(a0, a1, a2, a3) {\
107 BF(t3, t5, t5, t1);\
108 BF(a2.re, a0.re, a0.re, t5);\
109 BF(a3.im, a1.im, a1.im, t3);\
110 BF(t4, t6, t2, t6);\
111 BF(a3.re, a1.re, a1.re, t4);\
112 BF(a2.im, a0.im, a0.im, t6);\
113 }
114
115 /*
116 * Force loading all the inputs before storing any. This is slightly slower for
117 * small data, but avoids store->load aliasing for addresses separated by large
118 * powers of 2.
119 */
120 #define BUTTERFLIES_BIG(a0, a1, a2, a3) {\
121 fftsample_t r0 = a0.re, i0 = a0.im, r1 = a1.re, i1 = a1.im;\
122 BF(t3, t5, t5, t1);\
123 BF(a2.re, a0.re, r0, t5);\
124 BF(a3.im, a1.im, i1, t3);\
125 BF(t4, t6, t2, t6);\
126 BF(a3.re, a1.re, r1, t4);\
127 BF(a2.im, a0.im, i0, t6);\
128 }
129
130 #define TRANSFORM(a0, a1, a2, a3, wre,wim) {\
131 t1 = a2.re * wre + a2.im * wim;\
132 t2 = a2.im * wre - a2.re * wim;\
133 t5 = a3.re * wre - a3.im * wim;\
134 t6 = a3.im * wre + a3.re * wim;\
135 BUTTERFLIES(a0, a1, a2, a3)\
136 }
137
138 #define TRANSFORM_ZERO(a0, a1, a2, a3) {\
139 t1 = a2.re;\
140 t2 = a2.im;\
141 t5 = a3.re;\
142 t6 = a3.im;\
143 BUTTERFLIES(a0, a1, a2, a3)\
144 }
145
146 /* z[0...8n - 1], w[1...2n - 1] */
147 #define PASS(name)\
148 static void name(struct fft_complex *z, const fftsample_t *wre, unsigned int n)\
149 {\
150 fftsample_t t1, t2, t3, t4, t5, t6;\
151 int o1 = 2 * n;\
152 int o2 = 4 * n;\
153 int o3 = 6 * n;\
154 const fftsample_t *wim = wre + o1;\
155 n--;\
156 \
157 TRANSFORM_ZERO(z[0], z[o1], z[o2], z[o3]);\
158 TRANSFORM(z[1], z[o1 + 1], z[o2 + 1], z[o3 + 1], wre[1], wim[-1]);\
159 do {\
160 z += 2;\
161 wre += 2;\
162 wim -= 2;\
163 TRANSFORM(z[0], z[o1], z[o2], z[o3], wre[0], wim[0]);\
164 TRANSFORM(z[1], z[o1 + 1], z[o2 + 1], z[o3 + 1], wre[1], wim[-1]);\
165 } while (--n);\
166 }
167
168 PASS(pass)
169 #undef BUTTERFLIES
170 #define BUTTERFLIES BUTTERFLIES_BIG
171
172 #define DECL_FFT(n, n2, n4)\
173 static void fft##n(struct fft_complex *z)\
174 {\
175 fft ## n2(z);\
176 fft ## n4(z + n4 * 2);\
177 fft ## n4(z + n4 * 3);\
178 pass(z, cos_ ## n, n4 / 2);\
179 }
180
181 static void fft4(struct fft_complex *z)
182 {
183 fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
184
185 BF(t3, t1, z[0].re, z[1].re);
186 BF(t8, t6, z[3].re, z[2].re);
187 BF(z[2].re, z[0].re, t1, t6);
188 BF(t4, t2, z[0].im, z[1].im);
189 BF(t7, t5, z[2].im, z[3].im);
190 BF(z[3].im, z[1].im, t4, t8);
191 BF(z[3].re, z[1].re, t3, t7);
192 BF(z[2].im, z[0].im, t2, t5);
193 }
194
195 static void fft8(struct fft_complex *z)
196 {
197 fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
198
199 fft4(z);
200
201 BF(t1, z[5].re, z[4].re, -z[5].re);
202 BF(t2, z[5].im, z[4].im, -z[5].im);
203 BF(t3, z[7].re, z[6].re, -z[7].re);
204 BF(t4, z[7].im, z[6].im, -z[7].im);
205 BF(t8, t1, t3, t1);
206 BF(t7, t2, t2, t4);
207 BF(z[4].re, z[0].re, z[0].re, t1);
208 BF(z[4].im, z[0].im, z[0].im, t2);
209 BF(z[6].re, z[2].re, z[2].re, t7);
210 BF(z[6].im, z[2].im, z[2].im, t8);
211
212 TRANSFORM(z[1], z[3], z[5], z[7], M_SQRT1_2, M_SQRT1_2);
213 }
214
215 static void fft16(struct fft_complex *z)
216 {
217 fftsample_t t1, t2, t3, t4, t5, t6;
218
219 fft8(z);
220 fft4(z + 8);
221 fft4(z + 12);
222
223 TRANSFORM_ZERO(z[0], z[4], z[8], z[12]);
224 TRANSFORM(z[2], z[6], z[10], z[14], M_SQRT1_2, M_SQRT1_2);
225 TRANSFORM(z[1], z[5], z[9], z[13], cos_16[1], cos_16[3]);
226 TRANSFORM(z[3], z[7], z[11], z[15], cos_16[3], cos_16[1]);
227 }
228
229 DECL_FFT(32, 16, 8)
230 DECL_FFT(64, 32, 16)
231 DECL_FFT(128, 64, 32)
232 DECL_FFT(256, 128, 64)
233 DECL_FFT(512, 256, 128)
234
235 DECL_FFT(1024, 512, 256)
236 DECL_FFT(2048, 1024, 512)
237 DECL_FFT(4096, 2048, 1024)
238 DECL_FFT(8192, 4096, 2048)
239 DECL_FFT(16384, 8192, 4096)
240 DECL_FFT(32768, 16384, 8192)
241 DECL_FFT(65536, 32768, 16384)
242
243 static void (*fft_dispatch[]) (struct fft_complex *) = {
244 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
245 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
246 };
247
248 static void fft(struct fft_context *s, struct fft_complex *z)
249 {
250 fft_dispatch[s->nbits - 2] (z);
251 }
252
253 /* complex multiplication: p = a * b */
254 #define CMUL(pre, pim, are, aim, bre, bim) \
255 {\
256 fftsample_t _are = (are);\
257 fftsample_t _aim = (aim);\
258 fftsample_t _bre = (bre);\
259 fftsample_t _bim = (bim);\
260 (pre) = _are * _bre - _aim * _bim;\
261 (pim) = _are * _bim + _aim * _bre;\
262 }
263
264 /**
265 * Compute the middle half of the inverse MDCT of size N = 2^nbits
266 *
267 * Thus excluding the parts that can be derived by symmetry.
268 *
269 * \param output N/2 samples.
270 * \param input N/2 samples.
271 */
272 static void imdct_half(struct mdct_context *s, fftsample_t *output,
273 const fftsample_t *input)
274 {
275 int k, n8, n4, n2, n, j;
276 const uint16_t *revtab = s->fft.revtab;
277 const fftsample_t *tcos = s->tcos;
278 const fftsample_t *tsin = s->tsin;
279 const fftsample_t *in1, *in2;
280 struct fft_complex *z = (struct fft_complex *)output;
281
282 n = 1 << s->nbits;
283 n2 = n >> 1;
284 n4 = n >> 2;
285 n8 = n >> 3;
286
287 /* pre rotation */
288 in1 = input;
289 in2 = input + n2 - 1;
290 for (k = 0; k < n4; k++) {
291 j = revtab[k];
292 CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
293 in1 += 2;
294 in2 -= 2;
295 }
296 fft(&s->fft, z);
297
298 /* post rotation + reordering */
299 for (k = 0; k < n8; k++) {
300 fftsample_t r0, i0, r1, i1;
301 CMUL(r0, i1, z[n8 - k - 1].im, z[n8 - k - 1].re,
302 tsin[n8 - k - 1], tcos[n8 - k - 1]);
303 CMUL(r1, i0, z[n8 + k].im, z[n8 + k].re, tsin[n8 + k],
304 tcos[n8 + k]);
305 z[n8 - k - 1].re = r0;
306 z[n8 - k - 1].im = i0;
307 z[n8 + k].re = r1;
308 z[n8 + k].im = i1;
309 }
310 }
311
312 /**
313 * Compute the inverse MDCT.
314 *
315 * \param ctx The initialized context structure.
316 * \param output N samples.
317 * \param input N/2 samples.
318 *
319 * \sa \ref imdct_init().
320 */
321 void imdct(struct mdct_context *ctx, float *output, const float *input)
322 {
323 int k;
324 int n = 1 << ctx->nbits;
325 int n2 = n >> 1;
326 int n4 = n >> 2;
327
328 imdct_half(ctx, output + n4, input);
329
330 for (k = 0; k < n4; k++) {
331 output[k] = -output[n2 - k - 1];
332 output[n - k - 1] = output[n2 + k];
333 }
334 }
335
336 static int fft_init(struct fft_context *s, int nbits)
337 {
338 int i, j, n;
339
340 if (nbits < 2 || nbits > 16)
341 return -E_FFT_BAD_PARAMS;
342 s->nbits = nbits;
343 n = 1 << nbits;
344
345 s->revtab = para_malloc(n * sizeof(uint16_t));
346 for (j = 4; j <= nbits; j++) {
347 int k = 1 << j;
348 double freq = 2 * M_PI / k;
349 fftsample_t *tab = cos_tabs[j - 4];
350 for (i = 0; i <= k / 4; i++)
351 tab[i] = cos(i * freq);
352 for (i = 1; i < k / 4; i++)
353 tab[k / 2 - i] = tab[i];
354 }
355 for (i = 0; i < n; i++)
356 s->revtab[-split_radix_permutation(i, n) & (n - 1)] = i;
357 return 0;
358 }
359
360 /**
361 * Initialize the inverse modified cosine transform.
362 *
363 * \param nbits The number of bits to use (4 <= \a nbits <= 18).
364 *
365 * \param result Opaque structure that must be passed to \ref imdct().
366 *
367 * \return Standard.
368 */
369 int imdct_init(int nbits, struct mdct_context **result)
370 {
371 int ret, n, n4, i;
372 double alpha;
373 struct mdct_context *s;
374
375 s = para_calloc(sizeof(*s));
376 n = 1 << nbits;
377 s->nbits = nbits;
378 s->n = n;
379 n4 = n >> 2;
380 s->tcos = para_malloc(n4 * sizeof(fftsample_t));
381 s->tsin = para_malloc(n4 * sizeof(fftsample_t));
382
383 for (i = 0; i < n4; i++) {
384 alpha = 2 * M_PI * (i + 1.0 / 8.0) / n;
385 s->tcos[i] = -cos(alpha);
386 s->tsin[i] = -sin(alpha);
387 }
388 ret = fft_init(&s->fft, s->nbits - 2);
389 if (ret < 0)
390 goto fail;
391 *result = s;
392 return 0;
393 fail:
394 freep(&s->tcos);
395 freep(&s->tsin);
396 free(s);
397 return ret;
398 }
399
400 /**
401 * Deallocate imdct resources.
402 *
403 * \param ctx The pointer obtained by imdct_init().
404 */
405 void imdct_end(struct mdct_context *ctx)
406 {
407 free(ctx->tcos);
408 free(ctx->tsin);
409 free(ctx->fft.revtab);
410 free(ctx);
411 }