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
;
32 #define DECLARE_ALIGNED(n,t,v) t v __attribute__ ((aligned (n)))
33 #define DECLARE_ALIGNED_16(t, v) DECLARE_ALIGNED(16, t, v)
34 #define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
44 struct fft_complex
*exptab
;
45 struct fft_complex
*exptab1
; /* only used by SSE code */
46 struct fft_complex
*tmp_buf
;
50 /** Size of MDCT (i.e. number of input data * 2). */
54 /** pre/post rotation tables */
57 struct fft_context fft
;
60 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
61 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_16
[8]);
62 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_32
[16]);
63 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_64
[32]);
64 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_128
[64]);
65 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_256
[128]);
66 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_512
[256]);
67 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_1024
[512]);
68 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_2048
[1024]);
69 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_4096
[2048]);
70 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_8192
[4096]);
71 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_16384
[8192]);
72 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_32768
[16384]);
73 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_65536
[32768]);
75 static fftsample_t
*ff_cos_tabs
[] = {
76 ff_cos_16
, ff_cos_32
, ff_cos_64
, ff_cos_128
, ff_cos_256
,
77 ff_cos_512
, ff_cos_1024
, ff_cos_2048
, ff_cos_4096
, ff_cos_8192
,
78 ff_cos_16384
, ff_cos_32768
, ff_cos_65536
,
81 static int split_radix_permutation(int i
, int n
, int inverse
)
88 return split_radix_permutation(i
, m
, inverse
) * 2;
90 if (inverse
== !(i
& m
))
91 return split_radix_permutation(i
, m
, inverse
) * 4 + 1;
93 return split_radix_permutation(i
, m
, inverse
) * 4 - 1;
96 #define sqrthalf (float)M_SQRT1_2
98 #define BF(x,y,a,b) {\
103 #define BUTTERFLIES(a0,a1,a2,a3) {\
105 BF(a2.re, a0.re, a0.re, t5);\
106 BF(a3.im, a1.im, a1.im, t3);\
108 BF(a3.re, a1.re, a1.re, t4);\
109 BF(a2.im, a0.im, a0.im, t6);\
112 // force loading all the inputs before storing any.
113 // this is slightly slower for small data, but avoids store->load aliasing
114 // for addresses separated by large powers of 2.
115 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
116 fftsample_t r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
118 BF(a2.re, a0.re, r0, t5);\
119 BF(a3.im, a1.im, i1, t3);\
121 BF(a3.re, a1.re, r1, t4);\
122 BF(a2.im, a0.im, i0, t6);\
125 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
126 t1 = a2.re * wre + a2.im * wim;\
127 t2 = a2.im * wre - a2.re * wim;\
128 t5 = a3.re * wre - a3.im * wim;\
129 t6 = a3.im * wre + a3.re * wim;\
130 BUTTERFLIES(a0,a1,a2,a3)\
133 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
138 BUTTERFLIES(a0,a1,a2,a3)\
141 /* z[0...8n-1], w[1...2n-1] */
143 static void name(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]);\
165 #define BUTTERFLIES BUTTERFLIES_BIG
167 #define DECL_FFT(n,n2,n4)\
168 static void fft##n(struct fft_complex *z)\
173 pass(z,ff_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], sqrthalf
, sqrthalf
);
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], sqrthalf
, sqrthalf
);
219 TRANSFORM(z
[1], z
[5], z
[9], z
[13], ff_cos_16
[1], ff_cos_16
[3]);
220 TRANSFORM(z
[3], z
[7], z
[11], z
[15], ff_cos_16
[3], ff_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 */
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
],
300 z
[n8
- k
- 1].re
= r0
;
301 z
[n8
- k
- 1].im
= i0
;
308 * Compute the inverse MDCT of size N = 2^nbits.
310 * \param output N samples.
311 * \param input N/2 samples.
313 void imdct(struct mdct_context
*s
, float *output
, const float *input
)
316 int n
= 1 << s
->nbits
;
320 imdct_half(s
, 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
, int inverse
)
331 float alpha
, c1
, s1
, s2
;
334 if (nbits
< 2 || nbits
> 16)
335 return -E_FFT_BAD_PARAMS
;
340 s
->exptab
= para_malloc((n
/ 2) * sizeof(struct fft_complex
));
341 s
->revtab
= para_malloc(n
* sizeof(uint16_t));
342 s
->inverse
= inverse
;
344 s2
= inverse
? 1.0 : -1.0;
349 for (j
= 4; j
<= nbits
; j
++) {
351 double freq
= 2 * M_PI
/ k
;
352 fftsample_t
*tab
= ff_cos_tabs
[j
- 4];
353 for (i
= 0; i
<= k
/ 4; i
++)
354 tab
[i
] = cos(i
* freq
);
355 for (i
= 1; i
< k
/ 4; i
++)
356 tab
[k
/ 2 - i
] = tab
[i
];
358 for (i
= 0; i
< n
; i
++)
359 s
->revtab
[-split_radix_permutation(
360 i
, n
, s
->inverse
) & (n
- 1)] = i
;
361 s
->tmp_buf
= para_malloc(n
* sizeof(struct fft_complex
));
363 int np
, nblocks
, np2
, l
;
364 struct fft_complex
*q
;
366 for (i
= 0; i
< (n
/ 2); i
++) {
367 alpha
= 2 * M_PI
* (float) i
/ (float) n
;
369 s1
= sin(alpha
) * s2
;
370 s
->exptab
[i
].re
= c1
;
371 s
->exptab
[i
].im
= s1
;
377 s
->exptab1
= para_malloc(np
* 2 * sizeof(struct fft_complex
));
380 for (l
= 0; l
< np2
; l
+= 2 * nblocks
) {
382 *q
++ = s
->exptab
[l
+ nblocks
];
384 q
->re
= -s
->exptab
[l
].im
;
385 q
->im
= s
->exptab
[l
].re
;
387 q
->re
= -s
->exptab
[l
+ nblocks
].im
;
388 q
->im
= s
->exptab
[l
+ nblocks
].re
;
391 nblocks
= nblocks
>> 1;
392 } while (nblocks
!= 0);
394 /* compute bit reverse table */
395 for (i
= 0; i
< n
; i
++) {
397 for (j
= 0; j
< nbits
; j
++)
398 m
|= ((i
>> j
) & 1) << (nbits
- j
- 1);
405 static void fft_end(struct fft_context
*ctx
)
409 freep(&ctx
->exptab1
);
410 freep(&ctx
->tmp_buf
);
413 DECLARE_ALIGNED(16, float, ff_sine_128
[128]);
414 DECLARE_ALIGNED(16, float, ff_sine_256
[256]);
415 DECLARE_ALIGNED(16, float, ff_sine_512
[512]);
416 DECLARE_ALIGNED(16, float, ff_sine_1024
[1024]);
417 DECLARE_ALIGNED(16, float, ff_sine_2048
[2048]);
418 DECLARE_ALIGNED(16, float, ff_sine_4096
[4096]);
420 float *ff_sine_windows
[6] = {
421 ff_sine_128
, ff_sine_256
, ff_sine_512
, ff_sine_1024
,
422 ff_sine_2048
, ff_sine_4096
425 // Generate a sine window.
426 void sine_window_init(float *window
, int n
)
430 for (i
= 0; i
< n
; i
++)
431 window
[i
] = sinf((i
+ 0.5) * (M_PI
/ (2.0 * n
)));
435 * Init MDCT or IMDCT computation.
437 int imdct_init(int nbits
, int inverse
, struct mdct_context
**result
)
441 struct mdct_context
*s
;
443 s
= para_calloc(sizeof(*s
));
448 s
->tcos
= para_malloc(n4
* sizeof(fftsample_t
));
449 s
->tsin
= para_malloc(n4
* sizeof(fftsample_t
));
451 for (i
= 0; i
< n4
; i
++) {
452 alpha
= 2 * M_PI
* (i
+ 1.0 / 8.0) / n
;
453 s
->tcos
[i
] = -cos(alpha
);
454 s
->tsin
[i
] = -sin(alpha
);
456 ret
= fft_init(&s
->fft
, s
->nbits
- 2, inverse
);
468 void imdct_end(struct mdct_context
*ctx
)