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
;
42 /** Size of MDCT (number of input data * 2). */
46 /** Cosine table for pre/post rotation. */
48 /** Sine table for pre/post rotation. */
50 /** The context for the underlying fast Fourier transform. */
51 struct fft_context fft
;
54 /** cos(2 * pi * x / n) for 0 <= x <= n / 4, followed by its reverse */
55 #define COSINE_TAB(n) fftsample_t ff_cos_ ## n[n / 2] __aligned(16)
71 static fftsample_t
*ff_cos_tabs
[] = {
72 ff_cos_16
, ff_cos_32
, ff_cos_64
, ff_cos_128
, ff_cos_256
,
73 ff_cos_512
, ff_cos_1024
, ff_cos_2048
, ff_cos_4096
, ff_cos_8192
,
74 ff_cos_16384
, ff_cos_32768
, ff_cos_65536
,
77 static int split_radix_permutation(int i
, int n
)
84 return split_radix_permutation(i
, m
) * 2;
87 return split_radix_permutation(i
, m
) * 4 + 1;
89 return split_radix_permutation(i
, m
) * 4 - 1;
93 #define SQRTHALF (float)0.70710678118654752440
95 #define BF(x,y,a,b) {\
100 #define BUTTERFLIES(a0,a1,a2,a3) {\
102 BF(a2.re, a0.re, a0.re, t5);\
103 BF(a3.im, a1.im, a1.im, t3);\
105 BF(a3.re, a1.re, a1.re, t4);\
106 BF(a2.im, a0.im, a0.im, t6);\
109 // force loading all the inputs before storing any.
110 // this is slightly slower for small data, but avoids store->load aliasing
111 // for addresses separated by large powers of 2.
112 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
113 fftsample_t r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
115 BF(a2.re, a0.re, r0, t5);\
116 BF(a3.im, a1.im, i1, t3);\
118 BF(a3.re, a1.re, r1, t4);\
119 BF(a2.im, a0.im, i0, t6);\
122 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
123 t1 = a2.re * wre + a2.im * wim;\
124 t2 = a2.im * wre - a2.re * wim;\
125 t5 = a3.re * wre - a3.im * wim;\
126 t6 = a3.im * wre + a3.re * wim;\
127 BUTTERFLIES(a0,a1,a2,a3)\
130 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
135 BUTTERFLIES(a0,a1,a2,a3)\
138 /* z[0...8n-1], w[1...2n-1] */
140 static void name(struct fft_complex *z, const fftsample_t *wre, unsigned int n)\
142 fftsample_t t1, t2, t3, t4, t5, t6;\
146 const fftsample_t *wim = wre+o1;\
149 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
150 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
155 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
156 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
162 #define BUTTERFLIES BUTTERFLIES_BIG
164 #define DECL_FFT(n,n2,n4)\
165 static void fft##n(struct fft_complex *z)\
170 pass(z,ff_cos_##n,n4/2);\
172 static void fft4(struct fft_complex
*z
)
174 fftsample_t t1
, t2
, t3
, t4
, t5
, t6
, t7
, t8
;
176 BF(t3
, t1
, z
[0].re
, z
[1].re
);
177 BF(t8
, t6
, z
[3].re
, z
[2].re
);
178 BF(z
[2].re
, z
[0].re
, t1
, t6
);
179 BF(t4
, t2
, z
[0].im
, z
[1].im
);
180 BF(t7
, t5
, z
[2].im
, z
[3].im
);
181 BF(z
[3].im
, z
[1].im
, t4
, t8
);
182 BF(z
[3].re
, z
[1].re
, t3
, t7
);
183 BF(z
[2].im
, z
[0].im
, t2
, t5
);
186 static void fft8(struct fft_complex
*z
)
188 fftsample_t t1
, t2
, t3
, t4
, t5
, t6
, t7
, t8
;
192 BF(t1
, z
[5].re
, z
[4].re
, -z
[5].re
);
193 BF(t2
, z
[5].im
, z
[4].im
, -z
[5].im
);
194 BF(t3
, z
[7].re
, z
[6].re
, -z
[7].re
);
195 BF(t4
, z
[7].im
, z
[6].im
, -z
[7].im
);
198 BF(z
[4].re
, z
[0].re
, z
[0].re
, t1
);
199 BF(z
[4].im
, z
[0].im
, z
[0].im
, t2
);
200 BF(z
[6].re
, z
[2].re
, z
[2].re
, t7
);
201 BF(z
[6].im
, z
[2].im
, z
[2].im
, t8
);
203 TRANSFORM(z
[1], z
[3], z
[5], z
[7], SQRTHALF
, SQRTHALF
);
206 static void fft16(struct fft_complex
*z
)
208 fftsample_t t1
, t2
, t3
, t4
, t5
, t6
;
214 TRANSFORM_ZERO(z
[0], z
[4], z
[8], z
[12]);
215 TRANSFORM(z
[2], z
[6], z
[10], z
[14], SQRTHALF
, SQRTHALF
);
216 TRANSFORM(z
[1], z
[5], z
[9], z
[13], ff_cos_16
[1], ff_cos_16
[3]);
217 TRANSFORM(z
[3], z
[7], z
[11], z
[15], ff_cos_16
[3], ff_cos_16
[1]);
222 DECL_FFT(128, 64, 32)
223 DECL_FFT(256, 128, 64)
224 DECL_FFT(512, 256, 128)
226 DECL_FFT(1024, 512, 256)
227 DECL_FFT(2048, 1024, 512)
228 DECL_FFT(4096, 2048, 1024)
229 DECL_FFT(8192, 4096, 2048)
230 DECL_FFT(16384, 8192, 4096)
231 DECL_FFT(32768, 16384, 8192)
232 DECL_FFT(65536, 32768, 16384)
234 static void (*fft_dispatch
[]) (struct fft_complex
*) = {
235 fft4
, fft8
, fft16
, fft32
, fft64
, fft128
, fft256
, fft512
, fft1024
,
236 fft2048
, fft4096
, fft8192
, fft16384
, fft32768
, fft65536
,
239 static void fft(struct fft_context
*s
, struct fft_complex
*z
)
241 fft_dispatch
[s
->nbits
- 2] (z
);
244 /* complex multiplication: p = a * b */
245 #define CMUL(pre, pim, are, aim, bre, bim) \
247 fftsample_t _are = (are);\
248 fftsample_t _aim = (aim);\
249 fftsample_t _bre = (bre);\
250 fftsample_t _bim = (bim);\
251 (pre) = _are * _bre - _aim * _bim;\
252 (pim) = _are * _bim + _aim * _bre;\
256 * Compute the middle half of the inverse MDCT of size N = 2^nbits
258 * Thus excluding the parts that can be derived by symmetry.
260 * \param output N/2 samples.
261 * \param input N/2 samples.
263 static void imdct_half(struct mdct_context
*s
, fftsample_t
*output
,
264 const fftsample_t
*input
)
266 int k
, n8
, n4
, n2
, n
, j
;
267 const uint16_t *revtab
= s
->fft
.revtab
;
268 const fftsample_t
*tcos
= s
->tcos
;
269 const fftsample_t
*tsin
= s
->tsin
;
270 const fftsample_t
*in1
, *in2
;
271 struct fft_complex
*z
= (struct fft_complex
*)output
;
280 in2
= input
+ n2
- 1;
281 for (k
= 0; k
< n4
; k
++) {
283 CMUL(z
[j
].re
, z
[j
].im
, *in2
, *in1
, tcos
[k
], tsin
[k
]);
289 /* post rotation + reordering */
291 for (k
= 0; k
< n8
; k
++) {
292 fftsample_t r0
, i0
, r1
, i1
;
293 CMUL(r0
, i1
, z
[n8
- k
- 1].im
, z
[n8
- k
- 1].re
,
294 tsin
[n8
- k
- 1], tcos
[n8
- k
- 1]);
295 CMUL(r1
, i0
, z
[n8
+ k
].im
, z
[n8
+ k
].re
, tsin
[n8
+ k
],
297 z
[n8
- k
- 1].re
= r0
;
298 z
[n8
- k
- 1].im
= i0
;
305 * Compute the inverse MDCT.
307 * \param ctx The initialized context structure.
308 * \param output N samples.
309 * \param input N/2 samples.
311 * \sa \ref imdct_init().
313 void imdct(struct mdct_context
*ctx
, float *output
, const float *input
)
316 int n
= 1 << ctx
->nbits
;
320 imdct_half(ctx
, 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
)
332 if (nbits
< 2 || nbits
> 16)
333 return -E_FFT_BAD_PARAMS
;
337 s
->revtab
= para_malloc(n
* sizeof(uint16_t));
338 for (j
= 4; j
<= nbits
; j
++) {
340 double freq
= 2 * M_PI
/ k
;
341 fftsample_t
*tab
= ff_cos_tabs
[j
- 4];
342 for (i
= 0; i
<= k
/ 4; i
++)
343 tab
[i
] = cos(i
* freq
);
344 for (i
= 1; i
< k
/ 4; i
++)
345 tab
[k
/ 2 - i
] = tab
[i
];
347 for (i
= 0; i
< n
; i
++)
348 s
->revtab
[-split_radix_permutation(i
, n
) & (n
- 1)] = i
;
353 * Initialize the inverse modified cosine transform.
355 * \param nbits The number of bits to use (4 <= \a nbits <= 18).
357 * \param result Opaque structure that must be passed to \ref imdct().
361 int imdct_init(int nbits
, struct mdct_context
**result
)
365 struct mdct_context
*s
;
367 s
= para_calloc(sizeof(*s
));
372 s
->tcos
= para_malloc(n4
* sizeof(fftsample_t
));
373 s
->tsin
= para_malloc(n4
* sizeof(fftsample_t
));
375 for (i
= 0; i
< n4
; i
++) {
376 alpha
= 2 * M_PI
* (i
+ 1.0 / 8.0) / n
;
377 s
->tcos
[i
] = -cos(alpha
);
378 s
->tsin
[i
] = -sin(alpha
);
380 ret
= fft_init(&s
->fft
, s
->nbits
- 2);
393 * Deallocate imdct resources.
395 * \param ctx The pointer obtained by imdct_init().
397 void imdct_end(struct mdct_context
*ctx
)
401 free(ctx
->fft
.revtab
);