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 /** Canonical representation of a complex number. */
36 /** Imaginary part. */
40 /** FFT Lookup table. */
42 /** Number of bits of this instance of the FFT. */
44 /** The lookup table for cosine values. */
49 /** Size of MDCT (number of input data * 2). */
53 /** Cosine table for pre/post rotation. */
55 /** Sine table for pre/post rotation. */
57 /** The context for the underlying fast Fourier transform. */
58 struct fft_context fft
;
61 /** cos(2 * pi * x / n) for 0 <= x <= n / 4, followed by its reverse */
62 #define COSINE_TAB(n) fftsample_t cos_ ## n[n / 2] __aligned(16)
78 static fftsample_t
*cos_tabs
[] = {
79 cos_16
, cos_32
, cos_64
, cos_128
, cos_256
, cos_512
, cos_1024
, cos_2048
,
80 cos_4096
, cos_8192
, cos_16384
, cos_32768
, cos_65536
,
83 static int split_radix_permutation(int i
, int n
)
90 return split_radix_permutation(i
, m
) * 2;
93 return split_radix_permutation(i
, m
) * 4 + 1;
95 return split_radix_permutation(i
, m
) * 4 - 1;
99 #define SQRTHALF (float)0.70710678118654752440
101 #define BF(x, y, a, b) {\
106 #define BUTTERFLIES(a0, a1, a2, a3) {\
108 BF(a2.re, a0.re, a0.re, t5);\
109 BF(a3.im, a1.im, a1.im, t3);\
111 BF(a3.re, a1.re, a1.re, t4);\
112 BF(a2.im, a0.im, a0.im, t6);\
116 * Force loading all the inputs before storing any. This is slightly slower for
117 * small data, but avoids store->load aliasing for addresses separated by large
120 #define BUTTERFLIES_BIG(a0, a1, a2, a3) {\
121 fftsample_t r0 = a0.re, i0 = a0.im, r1 = a1.re, i1 = a1.im;\
123 BF(a2.re, a0.re, r0, t5);\
124 BF(a3.im, a1.im, i1, t3);\
126 BF(a3.re, a1.re, r1, t4);\
127 BF(a2.im, a0.im, i0, t6);\
130 #define TRANSFORM(a0, a1, a2, a3, wre,wim) {\
131 t1 = a2.re * wre + a2.im * wim;\
132 t2 = a2.im * wre - a2.re * wim;\
133 t5 = a3.re * wre - a3.im * wim;\
134 t6 = a3.im * wre + a3.re * wim;\
135 BUTTERFLIES(a0, a1, a2, a3)\
138 #define TRANSFORM_ZERO(a0, a1, a2, a3) {\
143 BUTTERFLIES(a0, a1, a2, a3)\
146 /* z[0...8n - 1], w[1...2n - 1] */
148 static void name(struct fft_complex *z, const fftsample_t *wre, unsigned int n)\
150 fftsample_t t1, t2, t3, t4, t5, t6;\
154 const fftsample_t *wim = wre + o1;\
157 TRANSFORM_ZERO(z[0], z[o1], z[o2], z[o3]);\
158 TRANSFORM(z[1], z[o1 + 1], z[o2 + 1], z[o3 + 1], wre[1], wim[-1]);\
163 TRANSFORM(z[0], z[o1], z[o2], z[o3], wre[0], wim[0]);\
164 TRANSFORM(z[1], z[o1 + 1], z[o2 + 1], z[o3 + 1], wre[1], wim[-1]);\
170 #define BUTTERFLIES BUTTERFLIES_BIG
172 #define DECL_FFT(n, n2, n4)\
173 static void fft##n(struct fft_complex *z)\
176 fft ## n4(z + n4 * 2);\
177 fft ## n4(z + n4 * 3);\
178 pass(z, cos_ ## n, n4 / 2);\
181 static void fft4(struct fft_complex
*z
)
183 fftsample_t t1
, t2
, t3
, t4
, t5
, t6
, t7
, t8
;
185 BF(t3
, t1
, z
[0].re
, z
[1].re
);
186 BF(t8
, t6
, z
[3].re
, z
[2].re
);
187 BF(z
[2].re
, z
[0].re
, t1
, t6
);
188 BF(t4
, t2
, z
[0].im
, z
[1].im
);
189 BF(t7
, t5
, z
[2].im
, z
[3].im
);
190 BF(z
[3].im
, z
[1].im
, t4
, t8
);
191 BF(z
[3].re
, z
[1].re
, t3
, t7
);
192 BF(z
[2].im
, z
[0].im
, t2
, t5
);
195 static void fft8(struct fft_complex
*z
)
197 fftsample_t t1
, t2
, t3
, t4
, t5
, t6
, t7
, t8
;
201 BF(t1
, z
[5].re
, z
[4].re
, -z
[5].re
);
202 BF(t2
, z
[5].im
, z
[4].im
, -z
[5].im
);
203 BF(t3
, z
[7].re
, z
[6].re
, -z
[7].re
);
204 BF(t4
, z
[7].im
, z
[6].im
, -z
[7].im
);
207 BF(z
[4].re
, z
[0].re
, z
[0].re
, t1
);
208 BF(z
[4].im
, z
[0].im
, z
[0].im
, t2
);
209 BF(z
[6].re
, z
[2].re
, z
[2].re
, t7
);
210 BF(z
[6].im
, z
[2].im
, z
[2].im
, t8
);
212 TRANSFORM(z
[1], z
[3], z
[5], z
[7], SQRTHALF
, SQRTHALF
);
215 static void fft16(struct fft_complex
*z
)
217 fftsample_t t1
, t2
, t3
, t4
, t5
, t6
;
223 TRANSFORM_ZERO(z
[0], z
[4], z
[8], z
[12]);
224 TRANSFORM(z
[2], z
[6], z
[10], z
[14], SQRTHALF
, SQRTHALF
);
225 TRANSFORM(z
[1], z
[5], z
[9], z
[13], cos_16
[1], cos_16
[3]);
226 TRANSFORM(z
[3], z
[7], z
[11], z
[15], cos_16
[3], cos_16
[1]);
231 DECL_FFT(128, 64, 32)
232 DECL_FFT(256, 128, 64)
233 DECL_FFT(512, 256, 128)
235 DECL_FFT(1024, 512, 256)
236 DECL_FFT(2048, 1024, 512)
237 DECL_FFT(4096, 2048, 1024)
238 DECL_FFT(8192, 4096, 2048)
239 DECL_FFT(16384, 8192, 4096)
240 DECL_FFT(32768, 16384, 8192)
241 DECL_FFT(65536, 32768, 16384)
243 static void (*fft_dispatch
[]) (struct fft_complex
*) = {
244 fft4
, fft8
, fft16
, fft32
, fft64
, fft128
, fft256
, fft512
, fft1024
,
245 fft2048
, fft4096
, fft8192
, fft16384
, fft32768
, fft65536
,
248 static void fft(struct fft_context
*s
, struct fft_complex
*z
)
250 fft_dispatch
[s
->nbits
- 2] (z
);
253 /* complex multiplication: p = a * b */
254 #define CMUL(pre, pim, are, aim, bre, bim) \
256 fftsample_t _are = (are);\
257 fftsample_t _aim = (aim);\
258 fftsample_t _bre = (bre);\
259 fftsample_t _bim = (bim);\
260 (pre) = _are * _bre - _aim * _bim;\
261 (pim) = _are * _bim + _aim * _bre;\
265 * Compute the middle half of the inverse MDCT of size N = 2^nbits
267 * Thus excluding the parts that can be derived by symmetry.
269 * \param output N/2 samples.
270 * \param input N/2 samples.
272 static void imdct_half(struct mdct_context
*s
, fftsample_t
*output
,
273 const fftsample_t
*input
)
275 int k
, n8
, n4
, n2
, n
, j
;
276 const uint16_t *revtab
= s
->fft
.revtab
;
277 const fftsample_t
*tcos
= s
->tcos
;
278 const fftsample_t
*tsin
= s
->tsin
;
279 const fftsample_t
*in1
, *in2
;
280 struct fft_complex
*z
= (struct fft_complex
*)output
;
289 in2
= input
+ n2
- 1;
290 for (k
= 0; k
< n4
; k
++) {
292 CMUL(z
[j
].re
, z
[j
].im
, *in2
, *in1
, tcos
[k
], tsin
[k
]);
298 /* post rotation + reordering */
300 for (k
= 0; k
< n8
; k
++) {
301 fftsample_t r0
, i0
, r1
, i1
;
302 CMUL(r0
, i1
, z
[n8
- k
- 1].im
, z
[n8
- k
- 1].re
,
303 tsin
[n8
- k
- 1], tcos
[n8
- k
- 1]);
304 CMUL(r1
, i0
, z
[n8
+ k
].im
, z
[n8
+ k
].re
, tsin
[n8
+ k
],
306 z
[n8
- k
- 1].re
= r0
;
307 z
[n8
- k
- 1].im
= i0
;
314 * Compute the inverse MDCT.
316 * \param ctx The initialized context structure.
317 * \param output N samples.
318 * \param input N/2 samples.
320 * \sa \ref imdct_init().
322 void imdct(struct mdct_context
*ctx
, float *output
, const float *input
)
325 int n
= 1 << ctx
->nbits
;
329 imdct_half(ctx
, output
+ n4
, input
);
331 for (k
= 0; k
< n4
; k
++) {
332 output
[k
] = -output
[n2
- k
- 1];
333 output
[n
- k
- 1] = output
[n2
+ k
];
337 static int fft_init(struct fft_context
*s
, int nbits
)
341 if (nbits
< 2 || nbits
> 16)
342 return -E_FFT_BAD_PARAMS
;
346 s
->revtab
= para_malloc(n
* sizeof(uint16_t));
347 for (j
= 4; j
<= nbits
; j
++) {
349 double freq
= 2 * M_PI
/ k
;
350 fftsample_t
*tab
= cos_tabs
[j
- 4];
351 for (i
= 0; i
<= k
/ 4; i
++)
352 tab
[i
] = cos(i
* freq
);
353 for (i
= 1; i
< k
/ 4; i
++)
354 tab
[k
/ 2 - i
] = tab
[i
];
356 for (i
= 0; i
< n
; i
++)
357 s
->revtab
[-split_radix_permutation(i
, n
) & (n
- 1)] = i
;
362 * Initialize the inverse modified cosine transform.
364 * \param nbits The number of bits to use (4 <= \a nbits <= 18).
366 * \param result Opaque structure that must be passed to \ref imdct().
370 int imdct_init(int nbits
, struct mdct_context
**result
)
374 struct mdct_context
*s
;
376 s
= para_calloc(sizeof(*s
));
381 s
->tcos
= para_malloc(n4
* sizeof(fftsample_t
));
382 s
->tsin
= para_malloc(n4
* sizeof(fftsample_t
));
384 for (i
= 0; i
< n4
; i
++) {
385 alpha
= 2 * M_PI
* (i
+ 1.0 / 8.0) / n
;
386 s
->tcos
[i
] = -cos(alpha
);
387 s
->tsin
[i
] = -sin(alpha
);
389 ret
= fft_init(&s
->fft
, s
->nbits
- 2);
402 * Deallocate imdct resources.
404 * \param ctx The pointer obtained by imdct_init().
406 void imdct_end(struct mdct_context
*ctx
)
410 free(ctx
->fft
.revtab
);