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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 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 (number of input data * 2). */
43 int n;
44 /** n = 2^n bits. */
45 int nbits;
46 /** Cosine table for pre/post rotation. */
47 fftsample_t *tcos;
48 /** Sine table for pre/post rotation. */
49 fftsample_t *tsin;
50 /** The context for the underlying fast Fourier transform. */
51 struct fft_context fft;
52 };
53
54 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
55 DECLARE_ALIGNED_16(fftsample_t, ff_cos_16[8]);
56 DECLARE_ALIGNED_16(fftsample_t, ff_cos_32[16]);
57 DECLARE_ALIGNED_16(fftsample_t, ff_cos_64[32]);
58 DECLARE_ALIGNED_16(fftsample_t, ff_cos_128[64]);
59 DECLARE_ALIGNED_16(fftsample_t, ff_cos_256[128]);
60 DECLARE_ALIGNED_16(fftsample_t, ff_cos_512[256]);
61 DECLARE_ALIGNED_16(fftsample_t, ff_cos_1024[512]);
62 DECLARE_ALIGNED_16(fftsample_t, ff_cos_2048[1024]);
63 DECLARE_ALIGNED_16(fftsample_t, ff_cos_4096[2048]);
64 DECLARE_ALIGNED_16(fftsample_t, ff_cos_8192[4096]);
65 DECLARE_ALIGNED_16(fftsample_t, ff_cos_16384[8192]);
66 DECLARE_ALIGNED_16(fftsample_t, ff_cos_32768[16384]);
67 DECLARE_ALIGNED_16(fftsample_t, ff_cos_65536[32768]);
68
69 static fftsample_t *ff_cos_tabs[] = {
70 ff_cos_16, ff_cos_32, ff_cos_64, ff_cos_128, ff_cos_256,
71 ff_cos_512, ff_cos_1024, ff_cos_2048, ff_cos_4096, ff_cos_8192,
72 ff_cos_16384, ff_cos_32768, ff_cos_65536,
73 };
74
75 static int split_radix_permutation(int i, int n)
76 {
77 int m;
78 if (n <= 2)
79 return i & 1;
80 m = n >> 1;
81 if ((i & m) == 0)
82 return split_radix_permutation(i, m) * 2;
83 m >>= 1;
84 if ((i & m) == 0)
85 return split_radix_permutation(i, m) * 4 + 1;
86 else
87 return split_radix_permutation(i, m) * 4 - 1;
88 }
89
90 /** 1 / sqrt(2). */
91 #define SQRTHALF (float)0.70710678118654752440
92
93 #define BF(x,y,a,b) {\
94 x = a - b;\
95 y = a + b;\
96 }
97
98 #define BUTTERFLIES(a0,a1,a2,a3) {\
99 BF(t3, t5, t5, t1);\
100 BF(a2.re, a0.re, a0.re, t5);\
101 BF(a3.im, a1.im, a1.im, t3);\
102 BF(t4, t6, t2, t6);\
103 BF(a3.re, a1.re, a1.re, t4);\
104 BF(a2.im, a0.im, a0.im, t6);\
105 }
106
107 // force loading all the inputs before storing any.
108 // this is slightly slower for small data, but avoids store->load aliasing
109 // for addresses separated by large powers of 2.
110 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
111 fftsample_t r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
112 BF(t3, t5, t5, t1);\
113 BF(a2.re, a0.re, r0, t5);\
114 BF(a3.im, a1.im, i1, t3);\
115 BF(t4, t6, t2, t6);\
116 BF(a3.re, a1.re, r1, t4);\
117 BF(a2.im, a0.im, i0, t6);\
118 }
119
120 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
121 t1 = a2.re * wre + a2.im * wim;\
122 t2 = a2.im * wre - a2.re * wim;\
123 t5 = a3.re * wre - a3.im * wim;\
124 t6 = a3.im * wre + a3.re * wim;\
125 BUTTERFLIES(a0,a1,a2,a3)\
126 }
127
128 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
129 t1 = a2.re;\
130 t2 = a2.im;\
131 t5 = a3.re;\
132 t6 = a3.im;\
133 BUTTERFLIES(a0,a1,a2,a3)\
134 }
135
136 /* z[0...8n-1], w[1...2n-1] */
137 #define PASS(name)\
138 static void name(struct fft_complex *z, const fftsample_t *wre, unsigned int n)\
139 {\
140 fftsample_t t1, t2, t3, t4, t5, t6;\
141 int o1 = 2*n;\
142 int o2 = 4*n;\
143 int o3 = 6*n;\
144 const fftsample_t *wim = wre+o1;\
145 n--;\
146 \
147 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
148 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
149 do {\
150 z += 2;\
151 wre += 2;\
152 wim -= 2;\
153 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
154 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
155 } while(--n);\
156 }
157
158 PASS(pass)
159 #undef BUTTERFLIES
160 #define BUTTERFLIES BUTTERFLIES_BIG
161
162 #define DECL_FFT(n,n2,n4)\
163 static void fft##n(struct fft_complex *z)\
164 {\
165 fft##n2(z);\
166 fft##n4(z+n4*2);\
167 fft##n4(z+n4*3);\
168 pass(z,ff_cos_##n,n4/2);\
169 }
170 static void fft4(struct fft_complex *z)
171 {
172 fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
173
174 BF(t3, t1, z[0].re, z[1].re);
175 BF(t8, t6, z[3].re, z[2].re);
176 BF(z[2].re, z[0].re, t1, t6);
177 BF(t4, t2, z[0].im, z[1].im);
178 BF(t7, t5, z[2].im, z[3].im);
179 BF(z[3].im, z[1].im, t4, t8);
180 BF(z[3].re, z[1].re, t3, t7);
181 BF(z[2].im, z[0].im, t2, t5);
182 }
183
184 static void fft8(struct fft_complex *z)
185 {
186 fftsample_t t1, t2, t3, t4, t5, t6, t7, t8;
187
188 fft4(z);
189
190 BF(t1, z[5].re, z[4].re, -z[5].re);
191 BF(t2, z[5].im, z[4].im, -z[5].im);
192 BF(t3, z[7].re, z[6].re, -z[7].re);
193 BF(t4, z[7].im, z[6].im, -z[7].im);
194 BF(t8, t1, t3, t1);
195 BF(t7, t2, t2, t4);
196 BF(z[4].re, z[0].re, z[0].re, t1);
197 BF(z[4].im, z[0].im, z[0].im, t2);
198 BF(z[6].re, z[2].re, z[2].re, t7);
199 BF(z[6].im, z[2].im, z[2].im, t8);
200
201 TRANSFORM(z[1], z[3], z[5], z[7], SQRTHALF, SQRTHALF);
202 }
203
204 static void fft16(struct fft_complex *z)
205 {
206 fftsample_t t1, t2, t3, t4, t5, t6;
207
208 fft8(z);
209 fft4(z + 8);
210 fft4(z + 12);
211
212 TRANSFORM_ZERO(z[0], z[4], z[8], z[12]);
213 TRANSFORM(z[2], z[6], z[10], z[14], SQRTHALF, SQRTHALF);
214 TRANSFORM(z[1], z[5], z[9], z[13], ff_cos_16[1], ff_cos_16[3]);
215 TRANSFORM(z[3], z[7], z[11], z[15], ff_cos_16[3], ff_cos_16[1]);
216 }
217
218 DECL_FFT(32, 16, 8)
219 DECL_FFT(64, 32, 16)
220 DECL_FFT(128, 64, 32)
221 DECL_FFT(256, 128, 64)
222 DECL_FFT(512, 256, 128)
223
224 DECL_FFT(1024, 512, 256)
225 DECL_FFT(2048, 1024, 512)
226 DECL_FFT(4096, 2048, 1024)
227 DECL_FFT(8192, 4096, 2048)
228 DECL_FFT(16384, 8192, 4096)
229 DECL_FFT(32768, 16384, 8192)
230 DECL_FFT(65536, 32768, 16384)
231
232 static void (*fft_dispatch[]) (struct fft_complex *) = {
233 fft4, fft8, fft16, fft32, fft64, fft128, fft256, fft512, fft1024,
234 fft2048, fft4096, fft8192, fft16384, fft32768, fft65536,
235 };
236
237 static void fft(struct fft_context *s, struct fft_complex *z)
238 {
239 fft_dispatch[s->nbits - 2] (z);
240 }
241
242 /* complex multiplication: p = a * b */
243 #define CMUL(pre, pim, are, aim, bre, bim) \
244 {\
245 fftsample_t _are = (are);\
246 fftsample_t _aim = (aim);\
247 fftsample_t _bre = (bre);\
248 fftsample_t _bim = (bim);\
249 (pre) = _are * _bre - _aim * _bim;\
250 (pim) = _are * _bim + _aim * _bre;\
251 }
252
253 /**
254 * Compute the middle half of the inverse MDCT of size N = 2^nbits
255 *
256 * Thus excluding the parts that can be derived by symmetry.
257 *
258 * \param output N/2 samples.
259 * \param input N/2 samples.
260 */
261 static void imdct_half(struct mdct_context *s, fftsample_t *output,
262 const fftsample_t *input)
263 {
264 int k, n8, n4, n2, n, j;
265 const uint16_t *revtab = s->fft.revtab;
266 const fftsample_t *tcos = s->tcos;
267 const fftsample_t *tsin = s->tsin;
268 const fftsample_t *in1, *in2;
269 struct fft_complex *z = (struct fft_complex *)output;
270
271 n = 1 << s->nbits;
272 n2 = n >> 1;
273 n4 = n >> 2;
274 n8 = n >> 3;
275
276 /* pre rotation */
277 in1 = input;
278 in2 = input + n2 - 1;
279 for (k = 0; k < n4; k++) {
280 j = revtab[k];
281 CMUL(z[j].re, z[j].im, *in2, *in1, tcos[k], tsin[k]);
282 in1 += 2;
283 in2 -= 2;
284 }
285 fft(&s->fft, z);
286
287 /* post rotation + reordering */
288 output += n4;
289 for (k = 0; k < n8; k++) {
290 fftsample_t r0, i0, r1, i1;
291 CMUL(r0, i1, z[n8 - k - 1].im, z[n8 - k - 1].re,
292 tsin[n8 - k - 1], tcos[n8 - k - 1]);
293 CMUL(r1, i0, z[n8 + k].im, z[n8 + k].re, tsin[n8 + k],
294 tcos[n8 + k]);
295 z[n8 - k - 1].re = r0;
296 z[n8 - k - 1].im = i0;
297 z[n8 + k].re = r1;
298 z[n8 + k].im = i1;
299 }
300 }
301
302 /**
303 * Compute the inverse MDCT.
304 *
305 * \param ctx The initialized context structure.
306 * \param output N samples.
307 * \param input N/2 samples.
308 *
309 * \sa \ref imdct_init().
310 */
311 void imdct(struct mdct_context *ctx, float *output, const float *input)
312 {
313 int k;
314 int n = 1 << ctx->nbits;
315 int n2 = n >> 1;
316 int n4 = n >> 2;
317
318 imdct_half(ctx, output + n4, input);
319
320 for (k = 0; k < n4; k++) {
321 output[k] = -output[n2 - k - 1];
322 output[n - k - 1] = output[n2 + k];
323 }
324 }
325
326 static int fft_init(struct fft_context *s, int nbits)
327 {
328 int i, j, n;
329
330 if (nbits < 2 || nbits > 16)
331 return -E_FFT_BAD_PARAMS;
332 s->nbits = nbits;
333 n = 1 << nbits;
334
335 s->revtab = para_malloc(n * sizeof(uint16_t));
336 for (j = 4; j <= nbits; j++) {
337 int k = 1 << j;
338 double freq = 2 * M_PI / k;
339 fftsample_t *tab = ff_cos_tabs[j - 4];
340 for (i = 0; i <= k / 4; i++)
341 tab[i] = cos(i * freq);
342 for (i = 1; i < k / 4; i++)
343 tab[k / 2 - i] = tab[i];
344 }
345 for (i = 0; i < n; i++)
346 s->revtab[-split_radix_permutation(i, n) & (n - 1)] = i;
347 return 0;
348 }
349
350 /**
351 * Initialize the inverse modified cosine transform.
352 *
353 * \param nbits The number of bits to use (4 <= \a nbits <= 18).
354 *
355 * \param result Opaque structure that must be passed to \ref imdct().
356 *
357 * \return Standard.
358 */
359 int imdct_init(int nbits, struct mdct_context **result)
360 {
361 int ret, n, n4, i;
362 double alpha;
363 struct mdct_context *s;
364
365 s = para_calloc(sizeof(*s));
366 n = 1 << nbits;
367 s->nbits = nbits;
368 s->n = n;
369 n4 = n >> 2;
370 s->tcos = para_malloc(n4 * sizeof(fftsample_t));
371 s->tsin = para_malloc(n4 * sizeof(fftsample_t));
372
373 for (i = 0; i < n4; i++) {
374 alpha = 2 * M_PI * (i + 1.0 / 8.0) / n;
375 s->tcos[i] = -cos(alpha);
376 s->tsin[i] = -sin(alpha);
377 }
378 ret = fft_init(&s->fft, s->nbits - 2);
379 if (ret < 0)
380 goto fail;
381 *result = s;
382 return 0;
383 fail:
384 freep(&s->tcos);
385 freep(&s->tsin);
386 free(s);
387 return ret;
388 }
389
390 /**
391 * Deallocate imdct resources.
392 *
393 * \param ctx The pointer obtained by imdct_init().
394 */
395 void imdct_end(struct mdct_context *ctx)
396 {
397 free(ctx->tcos);
398 free(ctx->tsin);
399 free(ctx->fft.revtab);
400 free(ctx);
401 }