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
);