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)