2 Copyright (c) 2003-2004, Mark Borgerding
6 Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
8 * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
9 * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
10 * Neither the author nor the names of any contributors may be used to endorse or promote products derived from this software without specific prior written permission.
12 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
16 #include "_kiss_fft_guts.h"
17 /* The guts header contains all the multiplication and addition macros that are defined for
18 fixed or floating point complex numbers. It also delares the kf_ internal functions.
21 static kiss_fft_cpx *scratchbuf = NULL;
22 static size_t nscratchbuf = 0;
23 static kiss_fft_cpx *tmpbuf = NULL;
24 static size_t ntmpbuf = 0;
26 #define CHECKBUF(buf,nbuf,n) \
28 if ( nbuf < (size_t)(n) ) {\
30 buf = (kiss_fft_cpx*)KISS_FFT_MALLOC(sizeof(kiss_fft_cpx)*(n)); \
37 kf_bfly2 (kiss_fft_cpx * Fout,
38 const size_t fstride, const kiss_fft_cfg st, int m)
41 kiss_fft_cpx *tw1 = st->twiddles;
49 C_MUL (t, *Fout2, *tw1);
51 C_SUB (*Fout2, *Fout, t);
59 kf_bfly4 (kiss_fft_cpx * Fout,
60 const size_t fstride, const kiss_fft_cfg st, const size_t m)
62 kiss_fft_cpx *tw1, *tw2, *tw3;
63 kiss_fft_cpx scratch[6];
65 const size_t m2 = 2 * m;
66 const size_t m3 = 3 * m;
68 tw3 = tw2 = tw1 = st->twiddles;
72 C_FIXDIV (Fout[m], 4);
73 C_FIXDIV (Fout[m2], 4);
74 C_FIXDIV (Fout[m3], 4);
76 C_MUL (scratch[0], Fout[m], *tw1);
77 C_MUL (scratch[1], Fout[m2], *tw2);
78 C_MUL (scratch[2], Fout[m3], *tw3);
80 C_SUB (scratch[5], *Fout, scratch[1]);
81 C_ADDTO (*Fout, scratch[1]);
82 C_ADD (scratch[3], scratch[0], scratch[2]);
83 C_SUB (scratch[4], scratch[0], scratch[2]);
84 C_SUB (Fout[m2], *Fout, scratch[3]);
88 C_ADDTO (*Fout, scratch[3]);
91 Fout[m].r = scratch[5].r - scratch[4].i;
92 Fout[m].i = scratch[5].i + scratch[4].r;
93 Fout[m3].r = scratch[5].r + scratch[4].i;
94 Fout[m3].i = scratch[5].i - scratch[4].r;
96 Fout[m].r = scratch[5].r + scratch[4].i;
97 Fout[m].i = scratch[5].i - scratch[4].r;
98 Fout[m3].r = scratch[5].r - scratch[4].i;
99 Fout[m3].i = scratch[5].i + scratch[4].r;
106 kf_bfly3 (kiss_fft_cpx * Fout,
107 const size_t fstride, const kiss_fft_cfg st, size_t m)
110 const size_t m2 = 2 * m;
111 kiss_fft_cpx *tw1, *tw2;
112 kiss_fft_cpx scratch[5];
115 epi3 = st->twiddles[fstride * m];
117 tw1 = tw2 = st->twiddles;
121 C_FIXDIV (Fout[m], 3);
122 C_FIXDIV (Fout[m2], 3);
124 C_MUL (scratch[1], Fout[m], *tw1);
125 C_MUL (scratch[2], Fout[m2], *tw2);
127 C_ADD (scratch[3], scratch[1], scratch[2]);
128 C_SUB (scratch[0], scratch[1], scratch[2]);
132 Fout[m].r = Fout->r - HALF_OF (scratch[3].r);
133 Fout[m].i = Fout->i - HALF_OF (scratch[3].i);
135 C_MULBYSCALAR (scratch[0], epi3.i);
137 C_ADDTO (*Fout, scratch[3]);
139 Fout[m2].r = Fout[m].r + scratch[0].i;
140 Fout[m2].i = Fout[m].i - scratch[0].r;
142 Fout[m].r -= scratch[0].i;
143 Fout[m].i += scratch[0].r;
150 kf_bfly5 (kiss_fft_cpx * Fout,
151 const size_t fstride, const kiss_fft_cfg st, int m)
153 kiss_fft_cpx *Fout0, *Fout1, *Fout2, *Fout3, *Fout4;
155 kiss_fft_cpx scratch[13];
156 kiss_fft_cpx *twiddles = st->twiddles;
160 ya = twiddles[fstride * m];
161 yb = twiddles[fstride * 2 * m];
165 Fout2 = Fout0 + 2 * m;
166 Fout3 = Fout0 + 3 * m;
167 Fout4 = Fout0 + 4 * m;
170 for (u = 0; u < m; ++u) {
171 C_FIXDIV (*Fout0, 5);
172 C_FIXDIV (*Fout1, 5);
173 C_FIXDIV (*Fout2, 5);
174 C_FIXDIV (*Fout3, 5);
175 C_FIXDIV (*Fout4, 5);
178 C_MUL (scratch[1], *Fout1, tw[u * fstride]);
179 C_MUL (scratch[2], *Fout2, tw[2 * u * fstride]);
180 C_MUL (scratch[3], *Fout3, tw[3 * u * fstride]);
181 C_MUL (scratch[4], *Fout4, tw[4 * u * fstride]);
183 C_ADD (scratch[7], scratch[1], scratch[4]);
184 C_SUB (scratch[10], scratch[1], scratch[4]);
185 C_ADD (scratch[8], scratch[2], scratch[3]);
186 C_SUB (scratch[9], scratch[2], scratch[3]);
188 Fout0->r += scratch[7].r + scratch[8].r;
189 Fout0->i += scratch[7].i + scratch[8].i;
192 scratch[0].r + S_MUL (scratch[7].r, ya.r) + S_MUL (scratch[8].r, yb.r);
194 scratch[0].i + S_MUL (scratch[7].i, ya.r) + S_MUL (scratch[8].i, yb.r);
196 scratch[6].r = S_MUL (scratch[10].i, ya.i) + S_MUL (scratch[9].i, yb.i);
197 scratch[6].i = -S_MUL (scratch[10].r, ya.i) - S_MUL (scratch[9].r, yb.i);
199 C_SUB (*Fout1, scratch[5], scratch[6]);
200 C_ADD (*Fout4, scratch[5], scratch[6]);
203 scratch[0].r + S_MUL (scratch[7].r, yb.r) + S_MUL (scratch[8].r, ya.r);
205 scratch[0].i + S_MUL (scratch[7].i, yb.r) + S_MUL (scratch[8].i, ya.r);
206 scratch[12].r = -S_MUL (scratch[10].i, yb.i) + S_MUL (scratch[9].i, ya.i);
207 scratch[12].i = S_MUL (scratch[10].r, yb.i) - S_MUL (scratch[9].r, ya.i);
209 C_ADD (*Fout2, scratch[11], scratch[12]);
210 C_SUB (*Fout3, scratch[11], scratch[12]);
220 /* perform the butterfly for one stage of a mixed radix FFT */
222 kf_bfly_generic (kiss_fft_cpx * Fout,
223 const size_t fstride, const kiss_fft_cfg st, int m, int p)
226 kiss_fft_cpx *twiddles = st->twiddles;
228 int Norig = st->nfft;
230 CHECKBUF (scratchbuf, nscratchbuf, p);
232 for (u = 0; u < m; ++u) {
234 for (q1 = 0; q1 < p; ++q1) {
235 scratchbuf[q1] = Fout[k];
236 C_FIXDIV (scratchbuf[q1], p);
241 for (q1 = 0; q1 < p; ++q1) {
244 Fout[k] = scratchbuf[0];
245 for (q = 1; q < p; ++q) {
246 twidx += fstride * k;
249 C_MUL (t, scratchbuf[q], twiddles[twidx]);
250 C_ADDTO (Fout[k], t);
258 kf_work (kiss_fft_cpx * Fout,
259 const kiss_fft_cpx * f,
260 const size_t fstride, int in_stride, int *factors, const kiss_fft_cfg st)
262 kiss_fft_cpx *Fout_beg = Fout;
263 const int p = *factors++; /* the radix */
264 const int m = *factors++; /* stage's fft length/p */
265 const kiss_fft_cpx *Fout_end = Fout + p * m;
270 f += fstride * in_stride;
271 } while (++Fout != Fout_end);
274 kf_work (Fout, f, fstride * p, in_stride, factors, st);
275 f += fstride * in_stride;
276 } while ((Fout += m) != Fout_end);
283 kf_bfly2 (Fout, fstride, st, m);
286 kf_bfly3 (Fout, fstride, st, m);
289 kf_bfly4 (Fout, fstride, st, m);
292 kf_bfly5 (Fout, fstride, st, m);
295 kf_bfly_generic (Fout, fstride, st, m, p);
300 /* facbuf is populated by p1,m1,p2,m2, ...
305 kf_factor (int n, int *facbuf)
310 floor_sqrt = floor (sqrt ((double) n));
312 /*factor out powers of 4, powers of 2, then any remaining primes */
327 p = n; /* no more factors, skip to end */
337 * User-callable function to allocate all necessary storage space for the fft.
339 * The return value is a contiguous block of memory, allocated with malloc. As such,
340 * It can be freed with free(), rather than a kiss_fft-specific function.
343 kiss_fft_alloc (int nfft, int inverse_fft, void *mem, size_t * lenmem)
345 kiss_fft_cfg st = NULL;
346 size_t memneeded = sizeof (struct kiss_fft_state)
347 + sizeof (kiss_fft_cpx) * (nfft - 1); /* twiddle factors */
349 if (lenmem == NULL) {
350 st = (kiss_fft_cfg) KISS_FFT_MALLOC (memneeded);
352 if (mem != NULL && *lenmem >= memneeded)
353 st = (kiss_fft_cfg) mem;
360 st->inverse = inverse_fft;
362 for (i = 0; i < nfft; ++i) {
364 3.141592653589793238462643383279502884197169399375105820974944;
365 double phase = -2 * pi * i / nfft;
369 kf_cexp (st->twiddles + i, phase);
372 kf_factor (nfft, st->factors);
381 kiss_fft_stride (kiss_fft_cfg st, const kiss_fft_cpx * fin, kiss_fft_cpx * fout,
385 CHECKBUF (tmpbuf, ntmpbuf, st->nfft);
386 kf_work (tmpbuf, fin, 1, in_stride, st->factors, st);
387 memcpy (fout, tmpbuf, sizeof (kiss_fft_cpx) * st->nfft);
389 kf_work (fout, fin, 1, in_stride, st->factors, st);
394 kiss_fft (kiss_fft_cfg cfg, const kiss_fft_cpx * fin, kiss_fft_cpx * fout)
396 kiss_fft_stride (cfg, fin, fout, 1);
400 /* not really necessary to call, but if someone is doing in-place ffts, they may want to free the
401 buffers from CHECKBUF
404 kiss_fft_cleanup (void)
415 kiss_fft_next_fast_size (int n)
427 break; /* n is completely factorable by twos, threes, and fives */