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 M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
42 struct fft_complex
*exptab
;
46 /** Size of MDCT (i.e. number of input data * 2). */
50 /** pre/post rotation tables */
53 struct fft_context fft
;
56 /* cos(2*pi*x/n) for 0<=x<=n/4, followed by its reverse */
57 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_16
[8]);
58 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_32
[16]);
59 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_64
[32]);
60 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_128
[64]);
61 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_256
[128]);
62 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_512
[256]);
63 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_1024
[512]);
64 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_2048
[1024]);
65 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_4096
[2048]);
66 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_8192
[4096]);
67 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_16384
[8192]);
68 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_32768
[16384]);
69 DECLARE_ALIGNED_16(fftsample_t
, ff_cos_65536
[32768]);
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
, int inverse
)
84 return split_radix_permutation(i
, m
, inverse
) * 2;
86 if (inverse
== !(i
& m
))
87 return split_radix_permutation(i
, m
, inverse
) * 4 + 1;
89 return split_radix_permutation(i
, m
, inverse
) * 4 - 1;
92 #define sqrthalf (float)M_SQRT1_2
94 #define BF(x,y,a,b) {\
99 #define BUTTERFLIES(a0,a1,a2,a3) {\
101 BF(a2.re, a0.re, a0.re, t5);\
102 BF(a3.im, a1.im, a1.im, t3);\
104 BF(a3.re, a1.re, a1.re, t4);\
105 BF(a2.im, a0.im, a0.im, t6);\
108 // force loading all the inputs before storing any.
109 // this is slightly slower for small data, but avoids store->load aliasing
110 // for addresses separated by large powers of 2.
111 #define BUTTERFLIES_BIG(a0,a1,a2,a3) {\
112 fftsample_t r0=a0.re, i0=a0.im, r1=a1.re, i1=a1.im;\
114 BF(a2.re, a0.re, r0, t5);\
115 BF(a3.im, a1.im, i1, t3);\
117 BF(a3.re, a1.re, r1, t4);\
118 BF(a2.im, a0.im, i0, t6);\
121 #define TRANSFORM(a0,a1,a2,a3,wre,wim) {\
122 t1 = a2.re * wre + a2.im * wim;\
123 t2 = a2.im * wre - a2.re * wim;\
124 t5 = a3.re * wre - a3.im * wim;\
125 t6 = a3.im * wre + a3.re * wim;\
126 BUTTERFLIES(a0,a1,a2,a3)\
129 #define TRANSFORM_ZERO(a0,a1,a2,a3) {\
134 BUTTERFLIES(a0,a1,a2,a3)\
137 /* z[0...8n-1], w[1...2n-1] */
139 static void name(struct fft_complex *z, const fftsample_t *wre, unsigned int n)\
141 fftsample_t t1, t2, t3, t4, t5, t6;\
145 const fftsample_t *wim = wre+o1;\
148 TRANSFORM_ZERO(z[0],z[o1],z[o2],z[o3]);\
149 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
154 TRANSFORM(z[0],z[o1],z[o2],z[o3],wre[0],wim[0]);\
155 TRANSFORM(z[1],z[o1+1],z[o2+1],z[o3+1],wre[1],wim[-1]);\
161 #define BUTTERFLIES BUTTERFLIES_BIG
163 #define DECL_FFT(n,n2,n4)\
164 static void fft##n(struct fft_complex *z)\
169 pass(z,ff_cos_##n,n4/2);\
171 static void fft4(struct fft_complex
*z
)
173 fftsample_t t1
, t2
, t3
, t4
, t5
, t6
, t7
, t8
;
175 BF(t3
, t1
, z
[0].re
, z
[1].re
);
176 BF(t8
, t6
, z
[3].re
, z
[2].re
);
177 BF(z
[2].re
, z
[0].re
, t1
, t6
);
178 BF(t4
, t2
, z
[0].im
, z
[1].im
);
179 BF(t7
, t5
, z
[2].im
, z
[3].im
);
180 BF(z
[3].im
, z
[1].im
, t4
, t8
);
181 BF(z
[3].re
, z
[1].re
, t3
, t7
);
182 BF(z
[2].im
, z
[0].im
, t2
, t5
);
185 static void fft8(struct fft_complex
*z
)
187 fftsample_t t1
, t2
, t3
, t4
, t5
, t6
, t7
, t8
;
191 BF(t1
, z
[5].re
, z
[4].re
, -z
[5].re
);
192 BF(t2
, z
[5].im
, z
[4].im
, -z
[5].im
);
193 BF(t3
, z
[7].re
, z
[6].re
, -z
[7].re
);
194 BF(t4
, z
[7].im
, z
[6].im
, -z
[7].im
);
197 BF(z
[4].re
, z
[0].re
, z
[0].re
, t1
);
198 BF(z
[4].im
, z
[0].im
, z
[0].im
, t2
);
199 BF(z
[6].re
, z
[2].re
, z
[2].re
, t7
);
200 BF(z
[6].im
, z
[2].im
, z
[2].im
, t8
);
202 TRANSFORM(z
[1], z
[3], z
[5], z
[7], sqrthalf
, sqrthalf
);
205 static void fft16(struct fft_complex
*z
)
207 fftsample_t t1
, t2
, t3
, t4
, t5
, t6
;
213 TRANSFORM_ZERO(z
[0], z
[4], z
[8], z
[12]);
214 TRANSFORM(z
[2], z
[6], z
[10], z
[14], sqrthalf
, sqrthalf
);
215 TRANSFORM(z
[1], z
[5], z
[9], z
[13], ff_cos_16
[1], ff_cos_16
[3]);
216 TRANSFORM(z
[3], z
[7], z
[11], z
[15], ff_cos_16
[3], ff_cos_16
[1]);
221 DECL_FFT(128, 64, 32)
222 DECL_FFT(256, 128, 64)
223 DECL_FFT(512, 256, 128)
225 DECL_FFT(1024, 512, 256)
226 DECL_FFT(2048, 1024, 512)
227 DECL_FFT(4096, 2048, 1024)
228 DECL_FFT(8192, 4096, 2048)
229 DECL_FFT(16384, 8192, 4096)
230 DECL_FFT(32768, 16384, 8192)
231 DECL_FFT(65536, 32768, 16384)
233 static void (*fft_dispatch
[]) (struct fft_complex
*) = {
234 fft4
, fft8
, fft16
, fft32
, fft64
, fft128
, fft256
, fft512
, fft1024
,
235 fft2048
, fft4096
, fft8192
, fft16384
, fft32768
, fft65536
,
238 static void fft(struct fft_context
*s
, struct fft_complex
*z
)
240 fft_dispatch
[s
->nbits
- 2] (z
);
243 /* complex multiplication: p = a * b */
244 #define CMUL(pre, pim, are, aim, bre, bim) \
246 fftsample_t _are = (are);\
247 fftsample_t _aim = (aim);\
248 fftsample_t _bre = (bre);\
249 fftsample_t _bim = (bim);\
250 (pre) = _are * _bre - _aim * _bim;\
251 (pim) = _are * _bim + _aim * _bre;\
255 * Compute the middle half of the inverse MDCT of size N = 2^nbits
257 * Thus excluding the parts that can be derived by symmetry.
259 * \param output N/2 samples.
260 * \param input N/2 samples.
262 static void imdct_half(struct mdct_context
*s
, fftsample_t
*output
,
263 const fftsample_t
*input
)
265 int k
, n8
, n4
, n2
, n
, j
;
266 const uint16_t *revtab
= s
->fft
.revtab
;
267 const fftsample_t
*tcos
= s
->tcos
;
268 const fftsample_t
*tsin
= s
->tsin
;
269 const fftsample_t
*in1
, *in2
;
270 struct fft_complex
*z
= (struct fft_complex
*)output
;
279 in2
= input
+ n2
- 1;
280 for (k
= 0; k
< n4
; k
++) {
282 CMUL(z
[j
].re
, z
[j
].im
, *in2
, *in1
, tcos
[k
], tsin
[k
]);
288 /* post rotation + reordering */
290 for (k
= 0; k
< n8
; k
++) {
291 fftsample_t r0
, i0
, r1
, i1
;
292 CMUL(r0
, i1
, z
[n8
- k
- 1].im
, z
[n8
- k
- 1].re
,
293 tsin
[n8
- k
- 1], tcos
[n8
- k
- 1]);
294 CMUL(r1
, i0
, z
[n8
+ k
].im
, z
[n8
+ k
].re
, tsin
[n8
+ k
],
296 z
[n8
- k
- 1].re
= r0
;
297 z
[n8
- k
- 1].im
= i0
;
304 * Compute the inverse MDCT of size N = 2^nbits.
306 * \param output N samples.
307 * \param input N/2 samples.
309 void imdct(struct mdct_context
*s
, float *output
, const float *input
)
312 int n
= 1 << s
->nbits
;
316 imdct_half(s
, output
+ n4
, input
);
318 for (k
= 0; k
< n4
; k
++) {
319 output
[k
] = -output
[n2
- k
- 1];
320 output
[n
- k
- 1] = output
[n2
+ k
];
324 static int fft_init(struct fft_context
*s
, int nbits
, int inverse
)
328 if (nbits
< 2 || nbits
> 16)
329 return -E_FFT_BAD_PARAMS
;
333 s
->exptab
= para_malloc((n
/ 2) * sizeof(struct fft_complex
));
334 s
->revtab
= para_malloc(n
* sizeof(uint16_t));
335 s
->inverse
= inverse
;
337 for (j
= 4; j
<= nbits
; j
++) {
339 double freq
= 2 * M_PI
/ k
;
340 fftsample_t
*tab
= ff_cos_tabs
[j
- 4];
341 for (i
= 0; i
<= k
/ 4; i
++)
342 tab
[i
] = cos(i
* freq
);
343 for (i
= 1; i
< k
/ 4; i
++)
344 tab
[k
/ 2 - i
] = tab
[i
];
346 for (i
= 0; i
< n
; i
++)
347 s
->revtab
[-split_radix_permutation(
348 i
, n
, s
->inverse
) & (n
- 1)] = i
;
352 static void fft_end(struct fft_context
*ctx
)
359 * Init MDCT or IMDCT computation.
361 int imdct_init(int nbits
, int inverse
, 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, inverse
);
392 void imdct_end(struct mdct_context
*ctx
)