Merge branch 'maint'
[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 <math.h>
19 #include <regex.h>
20
21 #include "para.h"
22 #include "error.h"
23 #include "string.h"
24 #include "imdct.h"
25 #include "wma.h"
26
27 typedef float fftsample_t;
28
29 /** Canonical representation of a complex number. */
30 struct fft_complex {
31 /** Real part. */
32 fftsample_t re;
33 /** Imaginary part. */
34 fftsample_t im;
35 };
36
37 /** FFT Lookup table. */
38 struct fft_context {
39 /** Number of bits of this instance of the FFT. */
40 int nbits;
41 /** The lookup table for cosine values. */
42 uint16_t *revtab;
43 };
44
45 struct mdct_context {
46 /** Size of MDCT (number of input data * 2). */
47 int n;
48 /** n = 2^n bits. */
49 int nbits;
50 /** Cosine table for pre/post rotation. */
51 fftsample_t *tcos;
52 /** Sine table for pre/post rotation. */
53 fftsample_t *tsin;
54 /** The context for the underlying fast Fourier transform. */
55 struct fft_context fft;
56 };
57
58 /** \cond cosine_tabs */
59
60 /* cos(2 * pi * x / n) for 0 <= x <= n / 4, followed by its reverse */
61 #define COSINE_TAB(n) static fftsample_t cos_ ## n[n / 2] __a_aligned(16)
62
63 COSINE_TAB(16);
64 COSINE_TAB(32);
65 COSINE_TAB(64);
66 COSINE_TAB(128);
67 COSINE_TAB(256);
68 COSINE_TAB(512);
69 COSINE_TAB(1024);
70 COSINE_TAB(2048);
71 COSINE_TAB(4096);
72 COSINE_TAB(8192);
73 COSINE_TAB(16384);
74 COSINE_TAB(32768);
75 COSINE_TAB(65536);
76
77 static fftsample_t *cos_tabs[] = {
78 cos_16, cos_32, cos_64, cos_128, cos_256, cos_512, cos_1024, cos_2048,
79 cos_4096, cos_8192, cos_16384, cos_32768, cos_65536,
80 };
81 /** \endcond cosine_tabs */
82
83 __a_const static int split_radix_permutation(int i, int n)
84 {
85 int m;
86 if (n <= 2)
87 return i & 1;
88 m = n >> 1;
89 if ((i & m) == 0)
90 return split_radix_permutation(i, m) * 2;
91 m >>= 1;
92 if ((i & m) == 0)
93 return split_radix_permutation(i, m) * 4 + 1;
94 else
95 return split_radix_permutation(i, m) * 4 - 1;
96 }
97
98 #define BF(x, y, a, b) {\
99 x = a - b;\
100 y = a + b;\
101 }
102
103 #define BUTTERFLIES(a0, a1, a2, a3) {\
104 BF(t3, t5, t5, t1);\
105 BF(a2.re, a0.re, a0.re, t5);\
106 BF(a3.im, a1.im, a1.im, t3);\
107 BF(t4, t6, t2, t6);\
108 BF(a3.re, a1.re, a1.re, t4);\
109 BF(a2.im, a0.im, a0.im, t6);\
110 }
111
112 /*
113 * Force loading all the inputs before storing any. This is slightly slower for
114 * small data, but avoids store->load aliasing for addresses separated by large
115 * powers of 2.
116 */
117 #define BUTTERFLIES_BIG(a0, a1, a2, a3) {\
118 fftsample_t r0 = a0.re, i0 = a0.im, r1 = a1.re, i1 = a1.im;\
119 BF(t3, t5, t5, t1);\
120 BF(a2.re, a0.re, r0, t5);\
121 BF(a3.im, a1.im, i1, t3);\
122 BF(t4, t6, t2, t6);\
123 BF(a3.re, a1.re, r1, t4);\
124 BF(a2.im, a0.im, i0, t6);\
125 }
126
127 #define TRANSFORM(a0, a1, a2, a3, wre,wim) {\
128 t1 = a2.re * wre + a2.im * wim;\
129 t2 = a2.im * wre - a2.re * wim;\
130 t5 = a3.re * wre - a3.im * wim;\
131 t6 = a3.im * wre + a3.re * wim;\
132 BUTTERFLIES(a0, a1, a2, a3)\
133 }
134
135 #define TRANSFORM_ZERO(a0, a1, a2, a3) {\
136 t1 = a2.re;\
137 t2 = a2.im;\
138 t5 = a3.re;\
139 t6 = a3.im;\
140 BUTTERFLIES(a0, a1, a2, a3)\
141 }
142
143 /* z[0...8n - 1], w[1...2n - 1] */
144 static void pass(struct fft_complex *z, const fftsample_t *wre, unsigned int n)
145 {
146 fftsample_t t1, t2, t3, t4, t5, t6;
147 int o1 = 2 * n;
148 int o2 = 4 * n;
149 int o3 = 6 * n;
150 const fftsample_t *wim = wre + o1;
151
152 n--;
153 TRANSFORM_ZERO(z[0], z[o1], z[o2], z[o3]);
154 TRANSFORM(z[1], z[o1 + 1], z[o2 + 1], z[o3 + 1], wre[1], wim[-1]);
155 do {
156 z += 2;
157 wre += 2;
158 wim -= 2;
159 TRANSFORM(z[0], z[o1], z[o2], z[o3], wre[0], wim[0]);
160 TRANSFORM(z[1], z[o1 + 1], z[o2 + 1], z[o3 + 1], wre[1], wim[-1]);
161 } while (--n);
162 }
163
164 #undef BUTTERFLIES
165 #define BUTTERFLIES BUTTERFLIES_BIG
166
167 #define DECL_FFT(n, n2, n4)\
168 static void fft##n(struct fft_complex *z)\
169 {\
170 fft ## n2(z);\
171 fft ## n4(z + n4 * 2);\
172 fft ## n4(z + n4 * 3);\
173 pass(z, cos_ ## n, n4 / 2);\
174 }
175
176 static void fft4(struct fft_complex *z)
177 {
178 fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
179
180 BF(t3, t1, z[0].re, z[1].re);
181 BF(t8, t6, z[3].re, z[2].re);
182 BF(z[2].re, z[0].re, t1, t6);
183 BF(t4, t2, z[0].im, z[1].im);
184 BF(t7, t5, z[2].im, z[3].im);
185 BF(z[3].im, z[1].im, t4, t8);
186 BF(z[3].re, z[1].re, t3, t7);
187 BF(z[2].im, z[0].im, t2, t5);
188 }
189
190 static void fft8(struct fft_complex *z)
191 {
192 fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
193
194 fft4(z);
195
196 BF(t1, z[5].re, z[4].re, -z[5].re);
197 BF(t2, z[5].im, z[4].im, -z[5].im);
198 BF(t3, z[7].re, z[6].re, -z[7].re);
199 BF(t4, z[7].im, z[6].im, -z[7].im);
200 BF(t8, t1, t3, t1);
201 BF(t7, t2, t2, t4);
202 BF(z[4].re, z[0].re, z[0].re, t1);
203 BF(z[4].im, z[0].im, z[0].im, t2);
204 BF(z[6].re, z[2].re, z[2].re, t7);
205 BF(z[6].im, z[2].im, z[2].im, t8);
206
207 TRANSFORM(z[1], z[3], z[5], z[7], M_SQRT1_2, M_SQRT1_2);
208 }
209
210 static void fft16(struct fft_complex *z)
211 {
212 fftsample_t t1, t2, t3, t4, t5, t6;
213
214 fft8(z);
215 fft4(z + 8);
216 fft4(z + 12);
217
218 TRANSFORM_ZERO(z[0], z[4], z[8], z[12]);
219 TRANSFORM(z[2], z[6], z[10], z[14], M_SQRT1_2, M_SQRT1_2);
220 TRANSFORM(z[1], z[5], z[9], z[13], cos_16[1], cos_16[3]);
221 TRANSFORM(z[3], z[7], z[11], z[15], cos_16[3], cos_16[1]);
222 }
223
224 DECL_FFT(32, 16, 8)
225 DECL_FFT(64, 32, 16)
226 DECL_FFT(128, 64, 32)
227 DECL_FFT(256, 128, 64)
228 DECL_FFT(512, 256, 128)
229
230 DECL_FFT(1024, 512, 256)
231 DECL_FFT(2048, 1024, 512)
232 DECL_FFT(4096, 2048, 1024)
233 DECL_FFT(8192, 4096, 2048)
234 DECL_FFT(16384, 8192, 4096)
235 DECL_FFT(32768, 16384, 8192)
236 DECL_FFT(65536, 32768, 16384)
237
238 static void (*fft_dispatch[]) (struct fft_complex *) = {
239 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
240 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
241 };
242
243 static void fft(struct fft_context *s, struct fft_complex *z)
244 {
245 fft_dispatch[s->nbits - 2] (z);
246 }
247
248 /* complex multiplication: p = a * b */
249 #define CMUL(pre, pim, are, aim, bre, bim) \
250 {\
251 fftsample_t _are = (are);\
252 fftsample_t _aim = (aim);\
253 fftsample_t _bre = (bre);\
254 fftsample_t _bim = (bim);\
255 (pre) = _are * _bre - _aim * _bim;\
256 (pim) = _are * _bim + _aim * _bre;\
257 }
258
259 /**
260 * Compute the middle half of the inverse MDCT of size N = 2^nbits
261 *
262 * Thus excluding the parts that can be derived by symmetry.
263 *
264 * \param output N/2 samples.
265 * \param input N/2 samples.
266 */
267 static void imdct_half(struct mdct_context *s, fftsample_t *output,
268 const fftsample_t *input)
269 {
270 int k, n8, n4, n2, n, j;
271 const uint16_t *revtab = s->fft.revtab;
272 const fftsample_t *tcos = s->tcos;
273 const fftsample_t *tsin = s->tsin;
274 const fftsample_t *in1, *in2;
275 struct fft_complex *z = (struct fft_complex *)output;
276
277 n = 1 << s->nbits;
278 n2 = n >> 1;
279 n4 = n >> 2;
280 n8 = n >> 3;
281
282 /* pre rotation */
283 in1 = input;
284 in2 = input + n2 - 1;
285 for (k = 0; k < n4; k++) {
286 j = revtab[k];
287 CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
288 in1 += 2;
289 in2 -= 2;
290 }
291 fft(&s->fft, z);
292
293 /* post rotation + reordering */
294 for (k = 0; k < n8; k++) {
295 fftsample_t r0, i0, r1, i1;
296 CMUL(r0, i1, z[n8 - k - 1].im, z[n8 - k - 1].re,
297 tsin[n8 - k - 1], tcos[n8 - k - 1]);
298 CMUL(r1, i0, z[n8 + k].im, z[n8 + k].re, tsin[n8 + k],
299 tcos[n8 + k]);
300 z[n8 - k - 1].re = r0;
301 z[n8 - k - 1].im = i0;
302 z[n8 + k].re = r1;
303 z[n8 + k].im = i1;
304 }
305 }
306
307 /**
308 * Compute the inverse MDCT.
309 *
310 * \param ctx The initialized context structure.
311 * \param output N samples.
312 * \param input N/2 samples.
313 *
314 * \sa \ref imdct_init().
315 */
316 void imdct(struct mdct_context *ctx, float *output, const float *input)
317 {
318 int k;
319 int n = 1 << ctx->nbits;
320 int n2 = n >> 1;
321 int n4 = n >> 2;
322
323 imdct_half(ctx, output + n4, input);
324
325 for (k = 0; k < n4; k++) {
326 output[k] = -output[n2 - k - 1];
327 output[n - k - 1] = output[n2 + k];
328 }
329 }
330
331 static int fft_init(struct fft_context *s, int nbits)
332 {
333 int i, j, n;
334
335 if (nbits < 2 || nbits > 16)
336 return -E_FFT_BAD_PARAMS;
337 s->nbits = nbits;
338 n = 1 << nbits;
339
340 s->revtab = para_malloc(n * sizeof(uint16_t));
341 for (j = 4; j <= nbits; j++) {
342 int k = 1 << j;
343 double freq = 2 * M_PI / k;
344 fftsample_t *tab = cos_tabs[j - 4];
345 for (i = 0; i <= k / 4; i++)
346 tab[i] = cos(i * freq);
347 for (i = 1; i < k / 4; i++)
348 tab[k / 2 - i] = tab[i];
349 }
350 for (i = 0; i < n; i++)
351 s->revtab[-split_radix_permutation(i, n) & (n - 1)] = i;
352 return 0;
353 }
354
355 /**
356 * Initialize the inverse modified cosine transform.
357 *
358 * \param nbits The number of bits to use (4 <= \a nbits <= 18).
359 *
360 * \param result Opaque structure that must be passed to \ref imdct().
361 *
362 * \return Standard.
363 */
364 int imdct_init(int nbits, struct mdct_context **result)
365 {
366 int ret, n, n4, i;
367 double alpha;
368 struct mdct_context *s;
369
370 s = para_calloc(sizeof(*s));
371 n = 1 << nbits;
372 s->nbits = nbits;
373 s->n = n;
374 n4 = n >> 2;
375 s->tcos = para_malloc(n4 * sizeof(fftsample_t));
376 s->tsin = para_malloc(n4 * sizeof(fftsample_t));
377
378 for (i = 0; i < n4; i++) {
379 alpha = 2 * M_PI * (i + 1.0 / 8.0) / n;
380 s->tcos[i] = -cos(alpha);
381 s->tsin[i] = -sin(alpha);
382 }
383 ret = fft_init(&s->fft, s->nbits - 2);
384 if (ret < 0)
385 goto fail;
386 *result = s;
387 return 0;
388 fail:
389 freep(&s->tcos);
390 freep(&s->tsin);
391 free(s);
392 return ret;
393 }
394
395 /**
396 * Deallocate imdct resources.
397 *
398 * \param ctx The pointer obtained by imdct_init().
399 */
400 void imdct_end(struct mdct_context *ctx)
401 {
402 free(ctx->tcos);
403 free(ctx->tsin);
404 free(ctx->fft.revtab);
405 free(ctx);
406 }