1 // modifications made for aubio:
2 // - replace all 'double' with 'smpl_t'
3 // - include "aubio_priv.h" (for config.h and types.h)
4 // - add missing prototypes
5 // - use COS, SIN, and ATAN macros
6 // - add cast to (smpl_t) to avoid float conversion warnings
7 // - declare initialization as static
8 // - prefix public function with aubio_ooura_
10 #include "aubio_priv.h"
12 void aubio_ooura_cdft(int n, int isgn, smpl_t *a, int *ip, smpl_t *w);
13 void aubio_ooura_rdft(int n, int isgn, smpl_t *a, int *ip, smpl_t *w);
14 void aubio_ooura_ddct(int n, int isgn, smpl_t *a, int *ip, smpl_t *w);
15 void aubio_ooura_ddst(int n, int isgn, smpl_t *a, int *ip, smpl_t *w);
16 void aubio_ooura_dfct(int n, smpl_t *a, smpl_t *t, int *ip, smpl_t *w);
17 void aubio_ooura_dfst(int n, smpl_t *a, smpl_t *t, int *ip, smpl_t *w);
18 static void makewt(int nw, int *ip, smpl_t *w);
19 static void makect(int nc, int *ip, smpl_t *c);
20 static void bitrv2(int n, int *ip, smpl_t *a);
21 static void bitrv2conj(int n, int *ip, smpl_t *a);
22 static void cftfsub(int n, smpl_t *a, smpl_t *w);
23 static void cftbsub(int n, smpl_t *a, smpl_t *w);
24 static void cft1st(int n, smpl_t *a, smpl_t *w);
25 static void cftmdl(int n, int l, smpl_t *a, smpl_t *w);
26 static void rftfsub(int n, smpl_t *a, int nc, smpl_t *c);
27 static void rftbsub(int n, smpl_t *a, int nc, smpl_t *c);
28 static void dctsub(int n, smpl_t *a, int nc, smpl_t *c);
29 static void dstsub(int n, smpl_t *a, int nc, smpl_t *c);
32 Fast Fourier/Cosine/Sine Transform
34 data length :power of 2
40 cdft: Complex Discrete Fourier Transform
41 rdft: Real Discrete Fourier Transform
42 ddct: Discrete Cosine Transform
43 ddst: Discrete Sine Transform
44 dfct: Cosine Transform of RDFT (Real Symmetric DFT)
45 dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
47 void cdft(int, int, smpl_t *, int *, smpl_t *);
48 void rdft(int, int, smpl_t *, int *, smpl_t *);
49 void ddct(int, int, smpl_t *, int *, smpl_t *);
50 void ddst(int, int, smpl_t *, int *, smpl_t *);
51 void dfct(int, smpl_t *, smpl_t *, int *, smpl_t *);
52 void dfst(int, smpl_t *, smpl_t *, int *, smpl_t *);
55 -------- Complex DFT (Discrete Fourier Transform) --------
58 X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
60 X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
61 (notes: sum_j=0^n-1 is a summation from j=0 to n-1)
64 ip[0] = 0; // first time only
65 cdft(2*n, 1, a, ip, w);
67 ip[0] = 0; // first time only
68 cdft(2*n, -1, a, ip, w);
70 2*n :data length (int)
71 n >= 1, n = power of 2
72 a[0...2*n-1] :input/output data (smpl_t *)
75 a[2*j+1] = Im(x[j]), 0<=j<n
78 a[2*k+1] = Im(X[k]), 0<=k<n
79 ip[0...*] :work area for bit reversal (int *)
80 length of ip >= 2+sqrt(n)
83 2+(1<<(int)(log(n+0.5)/log(2))/2).
84 ip[0],ip[1] are pointers of the cos/sin table.
85 w[0...n/2-1] :cos/sin table (smpl_t *)
86 w[],ip[] are initialized if ip[0] == 0.
89 cdft(2*n, -1, a, ip, w);
91 cdft(2*n, 1, a, ip, w);
92 for (j = 0; j <= 2 * n - 1; j++) {
98 -------- Real DFT / Inverse of Real DFT --------
101 R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
102 I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
103 <case2> IRDFT (excluding scale)
104 a[k] = (R[0] + R[n/2]*cos(pi*k))/2 +
105 sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) +
106 sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
109 ip[0] = 0; // first time only
110 rdft(n, 1, a, ip, w);
112 ip[0] = 0; // first time only
113 rdft(n, -1, a, ip, w);
116 n >= 2, n = power of 2
117 a[0...n-1] :input/output data (smpl_t *)
120 a[2*k] = R[k], 0<=k<n/2
121 a[2*k+1] = I[k], 0<k<n/2
125 a[2*j] = R[j], 0<=j<n/2
126 a[2*j+1] = I[j], 0<j<n/2
128 ip[0...*] :work area for bit reversal (int *)
129 length of ip >= 2+sqrt(n/2)
132 2+(1<<(int)(log(n/2+0.5)/log(2))/2).
133 ip[0],ip[1] are pointers of the cos/sin table.
134 w[0...n/2-1] :cos/sin table (smpl_t *)
135 w[],ip[] are initialized if ip[0] == 0.
138 rdft(n, 1, a, ip, w);
140 rdft(n, -1, a, ip, w);
141 for (j = 0; j <= n - 1; j++) {
147 -------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
149 <case1> IDCT (excluding scale)
150 C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
152 C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
155 ip[0] = 0; // first time only
156 ddct(n, 1, a, ip, w);
158 ip[0] = 0; // first time only
159 ddct(n, -1, a, ip, w);
162 n >= 2, n = power of 2
163 a[0...n-1] :input/output data (smpl_t *)
166 ip[0...*] :work area for bit reversal (int *)
167 length of ip >= 2+sqrt(n/2)
170 2+(1<<(int)(log(n/2+0.5)/log(2))/2).
171 ip[0],ip[1] are pointers of the cos/sin table.
172 w[0...n*5/4-1] :cos/sin table (smpl_t *)
173 w[],ip[] are initialized if ip[0] == 0.
176 ddct(n, -1, a, ip, w);
179 ddct(n, 1, a, ip, w);
180 for (j = 0; j <= n - 1; j++) {
186 -------- DST (Discrete Sine Transform) / Inverse of DST --------
188 <case1> IDST (excluding scale)
189 S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
191 S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
194 ip[0] = 0; // first time only
195 ddst(n, 1, a, ip, w);
197 ip[0] = 0; // first time only
198 ddst(n, -1, a, ip, w);
201 n >= 2, n = power of 2
202 a[0...n-1] :input/output data (smpl_t *)
213 ip[0...*] :work area for bit reversal (int *)
214 length of ip >= 2+sqrt(n/2)
217 2+(1<<(int)(log(n/2+0.5)/log(2))/2).
218 ip[0],ip[1] are pointers of the cos/sin table.
219 w[0...n*5/4-1] :cos/sin table (smpl_t *)
220 w[],ip[] are initialized if ip[0] == 0.
223 ddst(n, -1, a, ip, w);
226 ddst(n, 1, a, ip, w);
227 for (j = 0; j <= n - 1; j++) {
233 -------- Cosine Transform of RDFT (Real Symmetric DFT) --------
235 C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
237 ip[0] = 0; // first time only
238 dfct(n, a, t, ip, w);
240 n :data length - 1 (int)
241 n >= 2, n = power of 2
242 a[0...n] :input/output data (smpl_t *)
245 t[0...n/2] :work area (smpl_t *)
246 ip[0...*] :work area for bit reversal (int *)
247 length of ip >= 2+sqrt(n/4)
250 2+(1<<(int)(log(n/4+0.5)/log(2))/2).
251 ip[0],ip[1] are pointers of the cos/sin table.
252 w[0...n*5/8-1] :cos/sin table (smpl_t *)
253 w[],ip[] are initialized if ip[0] == 0.
258 dfct(n, a, t, ip, w);
262 dfct(n, a, t, ip, w);
263 for (j = 0; j <= n; j++) {
269 -------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
271 S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
273 ip[0] = 0; // first time only
274 dfst(n, a, t, ip, w);
276 n :data length + 1 (int)
277 n >= 2, n = power of 2
278 a[0...n-1] :input/output data (smpl_t *)
281 (a[0] is used for work area)
282 t[0...n/2-1] :work area (smpl_t *)
283 ip[0...*] :work area for bit reversal (int *)
284 length of ip >= 2+sqrt(n/4)
287 2+(1<<(int)(log(n/4+0.5)/log(2))/2).
288 ip[0],ip[1] are pointers of the cos/sin table.
289 w[0...n*5/8-1] :cos/sin table (smpl_t *)
290 w[],ip[] are initialized if ip[0] == 0.
293 dfst(n, a, t, ip, w);
295 dfst(n, a, t, ip, w);
296 for (j = 1; j <= n - 1; j++) {
303 The cos/sin table is recalculated when the larger table required.
304 w[] and ip[] are compatible with all routines.
308 void aubio_ooura_cdft(int n, int isgn, smpl_t *a, int *ip, smpl_t *w)
310 void makewt(int nw, int *ip, smpl_t *w);
311 void bitrv2(int n, int *ip, smpl_t *a);
312 void bitrv2conj(int n, int *ip, smpl_t *a);
313 void cftfsub(int n, smpl_t *a, smpl_t *w);
314 void cftbsub(int n, smpl_t *a, smpl_t *w);
316 if (n > (ip[0] << 2)) {
317 makewt(n >> 2, ip, w);
321 bitrv2(n, ip + 2, a);
324 bitrv2conj(n, ip + 2, a);
333 void aubio_ooura_rdft(int n, int isgn, smpl_t *a, int *ip, smpl_t *w)
335 void makewt(int nw, int *ip, smpl_t *w);
336 void makect(int nc, int *ip, smpl_t *c);
337 void bitrv2(int n, int *ip, smpl_t *a);
338 void cftfsub(int n, smpl_t *a, smpl_t *w);
339 void cftbsub(int n, smpl_t *a, smpl_t *w);
340 void rftfsub(int n, smpl_t *a, int nc, smpl_t *c);
341 void rftbsub(int n, smpl_t *a, int nc, smpl_t *c);
353 makect(nc, ip, w + nw);
357 bitrv2(n, ip + 2, a);
359 rftfsub(n, a, nc, w + nw);
367 a[1] = (smpl_t)0.5 * (a[0] - a[1]);
370 rftbsub(n, a, nc, w + nw);
371 bitrv2(n, ip + 2, a);
380 void aubio_ooura_ddct(int n, int isgn, smpl_t *a, int *ip, smpl_t *w)
382 void makewt(int nw, int *ip, smpl_t *w);
383 void makect(int nc, int *ip, smpl_t *c);
384 void bitrv2(int n, int *ip, smpl_t *a);
385 void cftfsub(int n, smpl_t *a, smpl_t *w);
386 void cftbsub(int n, smpl_t *a, smpl_t *w);
387 void rftfsub(int n, smpl_t *a, int nc, smpl_t *c);
388 void rftbsub(int n, smpl_t *a, int nc, smpl_t *c);
389 void dctsub(int n, smpl_t *a, int nc, smpl_t *c);
401 makect(nc, ip, w + nw);
405 for (j = n - 2; j >= 2; j -= 2) {
406 a[j + 1] = a[j] - a[j - 1];
412 rftbsub(n, a, nc, w + nw);
413 bitrv2(n, ip + 2, a);
419 dctsub(n, a, nc, w + nw);
422 bitrv2(n, ip + 2, a);
424 rftfsub(n, a, nc, w + nw);
430 for (j = 2; j < n; j += 2) {
431 a[j - 1] = a[j] - a[j + 1];
439 void aubio_ooura_ddst(int n, int isgn, smpl_t *a, int *ip, smpl_t *w)
441 void makewt(int nw, int *ip, smpl_t *w);
442 void makect(int nc, int *ip, smpl_t *c);
443 void bitrv2(int n, int *ip, smpl_t *a);
444 void cftfsub(int n, smpl_t *a, smpl_t *w);
445 void cftbsub(int n, smpl_t *a, smpl_t *w);
446 void rftfsub(int n, smpl_t *a, int nc, smpl_t *c);
447 void rftbsub(int n, smpl_t *a, int nc, smpl_t *c);
448 void dstsub(int n, smpl_t *a, int nc, smpl_t *c);
460 makect(nc, ip, w + nw);
464 for (j = n - 2; j >= 2; j -= 2) {
465 a[j + 1] = -a[j] - a[j - 1];
471 rftbsub(n, a, nc, w + nw);
472 bitrv2(n, ip + 2, a);
478 dstsub(n, a, nc, w + nw);
481 bitrv2(n, ip + 2, a);
483 rftfsub(n, a, nc, w + nw);
489 for (j = 2; j < n; j += 2) {
490 a[j - 1] = -a[j] - a[j + 1];
498 void aubio_ooura_dfct(int n, smpl_t *a, smpl_t *t, int *ip, smpl_t *w)
500 void makewt(int nw, int *ip, smpl_t *w);
501 void makect(int nc, int *ip, smpl_t *c);
502 void bitrv2(int n, int *ip, smpl_t *a);
503 void cftfsub(int n, smpl_t *a, smpl_t *w);
504 void rftfsub(int n, smpl_t *a, int nc, smpl_t *c);
505 void dctsub(int n, smpl_t *a, int nc, smpl_t *c);
506 int j, k, l, m, mh, nw, nc;
507 smpl_t xr, xi, yr, yi;
517 makect(nc, ip, w + nw);
527 for (j = 1; j < mh; j++) {
529 xr = a[j] - a[n - j];
530 xi = a[j] + a[n - j];
531 yr = a[k] - a[n - k];
532 yi = a[k] + a[n - k];
538 t[mh] = a[mh] + a[n - mh];
540 dctsub(m, a, nc, w + nw);
542 bitrv2(m, ip + 2, a);
544 rftfsub(m, a, nc, w + nw);
548 a[n - 1] = a[0] - a[1];
550 for (j = m - 2; j >= 2; j -= 2) {
551 a[2 * j + 1] = a[j] + a[j + 1];
552 a[2 * j - 1] = a[j] - a[j + 1];
557 dctsub(m, t, nc, w + nw);
559 bitrv2(m, ip + 2, t);
561 rftfsub(m, t, nc, w + nw);
565 a[n - l] = t[0] - t[1];
568 for (j = 2; j < m; j += 2) {
570 a[k - l] = t[j] - t[j + 1];
571 a[k + l] = t[j] + t[j + 1];
575 for (j = 0; j < mh; j++) {
577 t[j] = t[m + k] - t[m + j];
578 t[k] = t[m + k] + t[m + j];
594 void aubio_ooura_dfst(int n, smpl_t *a, smpl_t *t, int *ip, smpl_t *w)
596 void makewt(int nw, int *ip, smpl_t *w);
597 void makect(int nc, int *ip, smpl_t *c);
598 void bitrv2(int n, int *ip, smpl_t *a);
599 void cftfsub(int n, smpl_t *a, smpl_t *w);
600 void rftfsub(int n, smpl_t *a, int nc, smpl_t *c);
601 void dstsub(int n, smpl_t *a, int nc, smpl_t *c);
602 int j, k, l, m, mh, nw, nc;
603 smpl_t xr, xi, yr, yi;
613 makect(nc, ip, w + nw);
618 for (j = 1; j < mh; j++) {
620 xr = a[j] + a[n - j];
621 xi = a[j] - a[n - j];
622 yr = a[k] + a[n - k];
623 yi = a[k] - a[n - k];
629 t[0] = a[mh] - a[n - mh];
632 dstsub(m, a, nc, w + nw);
634 bitrv2(m, ip + 2, a);
636 rftfsub(m, a, nc, w + nw);
640 a[n - 1] = a[1] - a[0];
642 for (j = m - 2; j >= 2; j -= 2) {
643 a[2 * j + 1] = a[j] - a[j + 1];
644 a[2 * j - 1] = -a[j] - a[j + 1];
649 dstsub(m, t, nc, w + nw);
651 bitrv2(m, ip + 2, t);
653 rftfsub(m, t, nc, w + nw);
657 a[n - l] = t[1] - t[0];
660 for (j = 2; j < m; j += 2) {
662 a[k - l] = -t[j] - t[j + 1];
663 a[k + l] = t[j] - t[j + 1];
667 for (j = 1; j < mh; j++) {
669 t[j] = t[m + k] + t[m + j];
670 t[k] = t[m + k] - t[m + j];
681 /* -------- initializing routines -------- */
686 void makewt(int nw, int *ip, smpl_t *w)
688 void bitrv2(int n, int *ip, smpl_t *a);
696 delta = ATAN(1.0) / nwh;
699 w[nwh] = COS(delta * nwh);
702 for (j = 2; j < nwh; j += 2) {
710 for (j = nwh - 2; j >= 2; j -= 2) {
716 bitrv2(nw, ip + 2, w);
722 void makect(int nc, int *ip, smpl_t *c)
730 delta = ATAN(1.0) / nch;
731 c[0] = COS(delta * nch);
732 c[nch] = (smpl_t)0.5 * c[0];
733 for (j = 1; j < nch; j++) {
734 c[j] = (smpl_t)0.5 * COS(delta * j);
735 c[nc - j] = (smpl_t)0.5 * SIN(delta * j);
741 /* -------- child routines -------- */
744 void bitrv2(int n, int *ip, smpl_t *a)
746 int j, j1, k, k1, l, m, m2;
747 smpl_t xr, xi, yr, yi;
752 while ((m << 3) < l) {
754 for (j = 0; j < m; j++) {
755 ip[m + j] = ip[j] + l;
761 for (k = 0; k < m; k++) {
762 for (j = 0; j < k; j++) {
804 j1 = 2 * k + m2 + ip[k];
816 for (k = 1; k < m; k++) {
817 for (j = 0; j < k; j++) {
844 void bitrv2conj(int n, int *ip, smpl_t *a)
846 int j, j1, k, k1, l, m, m2;
847 smpl_t xr, xi, yr, yi;
852 while ((m << 3) < l) {
854 for (j = 0; j < m; j++) {
855 ip[m + j] = ip[j] + l;
861 for (k = 0; k < m; k++) {
862 for (j = 0; j < k; j++) {
905 a[k1 + 1] = -a[k1 + 1];
917 a[k1 + 1] = -a[k1 + 1];
921 a[m2 + 1] = -a[m2 + 1];
922 for (k = 1; k < m; k++) {
923 for (j = 0; j < k; j++) {
946 a[k1 + 1] = -a[k1 + 1];
947 a[k1 + m2 + 1] = -a[k1 + m2 + 1];
953 void cftfsub(int n, smpl_t *a, smpl_t *w)
955 void cft1st(int n, smpl_t *a, smpl_t *w);
956 void cftmdl(int n, int l, smpl_t *a, smpl_t *w);
957 int j, j1, j2, j3, l;
958 smpl_t x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
964 while ((l << 3) <= n) {
970 for (j = 0; j < l; j += 2) {
975 x0i = a[j + 1] + a[j1 + 1];
977 x1i = a[j + 1] - a[j1 + 1];
979 x2i = a[j2 + 1] + a[j3 + 1];
981 x3i = a[j2 + 1] - a[j3 + 1];
983 a[j + 1] = x0i + x2i;
985 a[j2 + 1] = x0i - x2i;
987 a[j1 + 1] = x1i + x3r;
989 a[j3 + 1] = x1i - x3r;
991 } else if ((l << 1) == n) {
992 for (j = 0; j < l; j += 2) {
995 x0i = a[j + 1] - a[j1 + 1];
997 a[j + 1] += a[j1 + 1];
1005 void cftbsub(int n, smpl_t *a, smpl_t *w)
1007 void cft1st(int n, smpl_t *a, smpl_t *w);
1008 void cftmdl(int n, int l, smpl_t *a, smpl_t *w);
1009 int j, j1, j2, j3, j4, j5, j6, j7, l;
1010 smpl_t wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
1011 y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
1012 y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
1018 while ((l << 3) < n) {
1025 for (j = 0; j < l; j += 2) {
1034 x0i = -a[j + 1] - a[j1 + 1];
1036 x1i = -a[j + 1] + a[j1 + 1];
1037 x2r = a[j2] + a[j3];
1038 x2i = a[j2 + 1] + a[j3 + 1];
1039 x3r = a[j2] - a[j3];
1040 x3i = a[j2 + 1] - a[j3 + 1];
1049 x0r = a[j4] + a[j5];
1050 x0i = a[j4 + 1] + a[j5 + 1];
1051 x1r = a[j4] - a[j5];
1052 x1i = a[j4 + 1] - a[j5 + 1];
1053 x2r = a[j6] + a[j7];
1054 x2i = a[j6 + 1] + a[j7 + 1];
1055 x3r = a[j6] - a[j7];
1056 x3i = a[j6 + 1] - a[j7 + 1];
1065 y5r = wn4r * (x0r - x0i);
1066 y5i = wn4r * (x0r + x0i);
1067 y7r = wn4r * (x2r - x2i);
1068 y7i = wn4r * (x2r + x2i);
1070 a[j1 + 1] = y1i - y5i;
1072 a[j5 + 1] = y1i + y5i;
1074 a[j3 + 1] = y3i - y7r;
1076 a[j7 + 1] = y3i + y7r;
1078 a[j + 1] = y0i - y4i;
1080 a[j4 + 1] = y0i + y4i;
1082 a[j2 + 1] = y2i - y6r;
1084 a[j6 + 1] = y2i + y6r;
1086 } else if ((l << 2) == n) {
1087 for (j = 0; j < l; j += 2) {
1092 x0i = -a[j + 1] - a[j1 + 1];
1094 x1i = -a[j + 1] + a[j1 + 1];
1095 x2r = a[j2] + a[j3];
1096 x2i = a[j2 + 1] + a[j3 + 1];
1097 x3r = a[j2] - a[j3];
1098 x3i = a[j2 + 1] - a[j3 + 1];
1100 a[j + 1] = x0i - x2i;
1102 a[j2 + 1] = x0i + x2i;
1104 a[j1 + 1] = x1i - x3r;
1106 a[j3 + 1] = x1i + x3r;
1109 for (j = 0; j < l; j += 2) {
1112 x0i = -a[j + 1] + a[j1 + 1];
1114 a[j + 1] = -a[j + 1] - a[j1 + 1];
1122 void cft1st(int n, smpl_t *a, smpl_t *w)
1125 smpl_t wn4r, wtmp, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i,
1126 wk4r, wk4i, wk5r, wk5i, wk6r, wk6i, wk7r, wk7i;
1127 smpl_t x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
1128 y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
1129 y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
1152 x2r = a[12] + a[14];
1153 x2i = a[13] + a[15];
1154 x3r = a[12] - a[14];
1155 x3i = a[13] - a[15];
1164 y5r = wn4r * (x0r - x0i);
1165 y5i = wn4r * (x0r + x0i);
1166 y7r = wn4r * (x2r - x2i);
1167 y7i = wn4r * (x2r + x2i);
1187 x0r = a[16] + a[18];
1188 x0i = a[17] + a[19];
1189 x1r = a[16] - a[18];
1190 x1i = a[17] - a[19];
1191 x2r = a[20] + a[22];
1192 x2i = a[21] + a[23];
1193 x3r = a[20] - a[22];
1194 x3i = a[21] - a[23];
1203 x0r = a[24] + a[26];
1204 x0i = a[25] + a[27];
1205 x1r = a[24] - a[26];
1206 x1i = a[25] - a[27];
1207 x2r = a[28] + a[30];
1208 x2i = a[29] + a[31];
1209 x3r = a[28] - a[30];
1210 x3i = a[29] - a[31];
1219 y5r = wk1i * x0r - wk1r * x0i;
1220 y5i = wk1i * x0i + wk1r * x0r;
1221 y7r = wk1r * x2r + wk1i * x2i;
1222 y7i = wk1r * x2i - wk1i * x2r;
1223 x0r = wk1r * y1r - wk1i * y1i;
1224 x0i = wk1r * y1i + wk1i * y1r;
1229 x0r = wk1i * y3r - wk1r * y3i;
1230 x0i = wk1i * y3i + wk1r * y3r;
1241 a[20] = wn4r * (x0r - x0i);
1242 a[21] = wn4r * (x0i + x0r);
1245 a[28] = wn4r * (x0r - x0i);
1246 a[29] = wn4r * (x0i + x0r);
1248 for (j = 32; j < n; j += 16) {
1255 wk3r = wk1r - wtmp * wk1i;
1256 wk3i = wtmp * wk1r - wk1i;
1257 wk4r = 1 - wtmp * wk2i;
1260 wk5r = wk3r - wtmp * wk1i;
1261 wk5i = wtmp * wk1r - wk3i;
1262 wk6r = wk2r - wtmp * wk2i;
1263 wk6i = wtmp * wk2r - wk2i;
1264 wk7r = wk1r - wtmp * wk3i;
1265 wk7i = wtmp * wk3r - wk1i;
1266 x0r = a[j] + a[j + 2];
1267 x0i = a[j + 1] + a[j + 3];
1268 x1r = a[j] - a[j + 2];
1269 x1i = a[j + 1] - a[j + 3];
1270 x2r = a[j + 4] + a[j + 6];
1271 x2i = a[j + 5] + a[j + 7];
1272 x3r = a[j + 4] - a[j + 6];
1273 x3i = a[j + 5] - a[j + 7];
1282 x0r = a[j + 8] + a[j + 10];
1283 x0i = a[j + 9] + a[j + 11];
1284 x1r = a[j + 8] - a[j + 10];
1285 x1i = a[j + 9] - a[j + 11];
1286 x2r = a[j + 12] + a[j + 14];
1287 x2i = a[j + 13] + a[j + 15];
1288 x3r = a[j + 12] - a[j + 14];
1289 x3i = a[j + 13] - a[j + 15];
1298 y5r = wn4r * (x0r - x0i);
1299 y5i = wn4r * (x0r + x0i);
1300 y7r = wn4r * (x2r - x2i);
1301 y7i = wn4r * (x2r + x2i);
1304 a[j + 2] = wk1r * x0r - wk1i * x0i;
1305 a[j + 3] = wk1r * x0i + wk1i * x0r;
1308 a[j + 10] = wk5r * x0r - wk5i * x0i;
1309 a[j + 11] = wk5r * x0i + wk5i * x0r;
1312 a[j + 6] = wk3r * x0r - wk3i * x0i;
1313 a[j + 7] = wk3r * x0i + wk3i * x0r;
1316 a[j + 14] = wk7r * x0r - wk7i * x0i;
1317 a[j + 15] = wk7r * x0i + wk7i * x0r;
1319 a[j + 1] = y0i + y4i;
1322 a[j + 8] = wk4r * x0r - wk4i * x0i;
1323 a[j + 9] = wk4r * x0i + wk4i * x0r;
1326 a[j + 4] = wk2r * x0r - wk2i * x0i;
1327 a[j + 5] = wk2r * x0i + wk2i * x0r;
1330 a[j + 12] = wk6r * x0r - wk6i * x0i;
1331 a[j + 13] = wk6r * x0i + wk6i * x0r;
1337 void cftmdl(int n, int l, smpl_t *a, smpl_t *w)
1339 int j, j1, j2, j3, j4, j5, j6, j7, k, k1, m;
1340 smpl_t wn4r, wtmp, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i,
1341 wk4r, wk4i, wk5r, wk5i, wk6r, wk6i, wk7r, wk7i;
1342 smpl_t x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
1343 y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
1344 y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
1348 for (j = 0; j < l; j += 2) {
1357 x0i = a[j + 1] + a[j1 + 1];
1359 x1i = a[j + 1] - a[j1 + 1];
1360 x2r = a[j2] + a[j3];
1361 x2i = a[j2 + 1] + a[j3 + 1];
1362 x3r = a[j2] - a[j3];
1363 x3i = a[j2 + 1] - a[j3 + 1];
1372 x0r = a[j4] + a[j5];
1373 x0i = a[j4 + 1] + a[j5 + 1];
1374 x1r = a[j4] - a[j5];
1375 x1i = a[j4 + 1] - a[j5 + 1];
1376 x2r = a[j6] + a[j7];
1377 x2i = a[j6 + 1] + a[j7 + 1];
1378 x3r = a[j6] - a[j7];
1379 x3i = a[j6 + 1] - a[j7 + 1];
1388 y5r = wn4r * (x0r - x0i);
1389 y5i = wn4r * (x0r + x0i);
1390 y7r = wn4r * (x2r - x2i);
1391 y7i = wn4r * (x2r + x2i);
1393 a[j1 + 1] = y1i + y5i;
1395 a[j5 + 1] = y1i - y5i;
1397 a[j3 + 1] = y3i + y7r;
1399 a[j7 + 1] = y3i - y7r;
1401 a[j + 1] = y0i + y4i;
1403 a[j4 + 1] = y0i - y4i;
1405 a[j2 + 1] = y2i + y6r;
1407 a[j6 + 1] = y2i - y6r;
1412 for (j = m; j < l + m; j += 2) {
1421 x0i = a[j + 1] + a[j1 + 1];
1423 x1i = a[j + 1] - a[j1 + 1];
1424 x2r = a[j2] + a[j3];
1425 x2i = a[j2 + 1] + a[j3 + 1];
1426 x3r = a[j2] - a[j3];
1427 x3i = a[j2 + 1] - a[j3 + 1];
1436 x0r = a[j4] + a[j5];
1437 x0i = a[j4 + 1] + a[j5 + 1];
1438 x1r = a[j4] - a[j5];
1439 x1i = a[j4 + 1] - a[j5 + 1];
1440 x2r = a[j6] + a[j7];
1441 x2i = a[j6 + 1] + a[j7 + 1];
1442 x3r = a[j6] - a[j7];
1443 x3i = a[j6 + 1] - a[j7 + 1];
1452 y5r = wk1i * x0r - wk1r * x0i;
1453 y5i = wk1i * x0i + wk1r * x0r;
1454 y7r = wk1r * x2r + wk1i * x2i;
1455 y7i = wk1r * x2i - wk1i * x2r;
1456 x0r = wk1r * y1r - wk1i * y1i;
1457 x0i = wk1r * y1i + wk1i * y1r;
1459 a[j1 + 1] = x0i + y5i;
1461 a[j5 + 1] = x0r - y5r;
1462 x0r = wk1i * y3r - wk1r * y3i;
1463 x0i = wk1i * y3i + wk1r * y3r;
1465 a[j3 + 1] = x0i + y7i;
1467 a[j7 + 1] = x0r + y7r;
1469 a[j + 1] = y0i + y4i;
1471 a[j4 + 1] = y0r - y4r;
1474 a[j2] = wn4r * (x0r - x0i);
1475 a[j2 + 1] = wn4r * (x0i + x0r);
1478 a[j6] = wn4r * (x0r - x0i);
1479 a[j6 + 1] = wn4r * (x0i + x0r);
1482 for (k = 2 * m; k < n; k += m) {
1489 wk3r = wk1r - wtmp * wk1i;
1490 wk3i = wtmp * wk1r - wk1i;
1491 wk4r = 1 - wtmp * wk2i;
1494 wk5r = wk3r - wtmp * wk1i;
1495 wk5i = wtmp * wk1r - wk3i;
1496 wk6r = wk2r - wtmp * wk2i;
1497 wk6i = wtmp * wk2r - wk2i;
1498 wk7r = wk1r - wtmp * wk3i;
1499 wk7i = wtmp * wk3r - wk1i;
1500 for (j = k; j < l + k; j += 2) {
1509 x0i = a[j + 1] + a[j1 + 1];
1511 x1i = a[j + 1] - a[j1 + 1];
1512 x2r = a[j2] + a[j3];
1513 x2i = a[j2 + 1] + a[j3 + 1];
1514 x3r = a[j2] - a[j3];
1515 x3i = a[j2 + 1] - a[j3 + 1];
1524 x0r = a[j4] + a[j5];
1525 x0i = a[j4 + 1] + a[j5 + 1];
1526 x1r = a[j4] - a[j5];
1527 x1i = a[j4 + 1] - a[j5 + 1];
1528 x2r = a[j6] + a[j7];
1529 x2i = a[j6 + 1] + a[j7 + 1];
1530 x3r = a[j6] - a[j7];
1531 x3i = a[j6 + 1] - a[j7 + 1];
1540 y5r = wn4r * (x0r - x0i);
1541 y5i = wn4r * (x0r + x0i);
1542 y7r = wn4r * (x2r - x2i);
1543 y7i = wn4r * (x2r + x2i);
1546 a[j1] = wk1r * x0r - wk1i * x0i;
1547 a[j1 + 1] = wk1r * x0i + wk1i * x0r;
1550 a[j5] = wk5r * x0r - wk5i * x0i;
1551 a[j5 + 1] = wk5r * x0i + wk5i * x0r;
1554 a[j3] = wk3r * x0r - wk3i * x0i;
1555 a[j3 + 1] = wk3r * x0i + wk3i * x0r;
1558 a[j7] = wk7r * x0r - wk7i * x0i;
1559 a[j7 + 1] = wk7r * x0i + wk7i * x0r;
1561 a[j + 1] = y0i + y4i;
1564 a[j4] = wk4r * x0r - wk4i * x0i;
1565 a[j4 + 1] = wk4r * x0i + wk4i * x0r;
1568 a[j2] = wk2r * x0r - wk2i * x0i;
1569 a[j2 + 1] = wk2r * x0i + wk2i * x0r;
1572 a[j6] = wk6r * x0r - wk6i * x0i;
1573 a[j6 + 1] = wk6r * x0i + wk6i * x0r;
1580 void rftfsub(int n, smpl_t *a, int nc, smpl_t *c)
1582 int j, k, kk, ks, m;
1583 smpl_t wkr, wki, xr, xi, yr, yi;
1588 for (j = 2; j < m; j += 2) {
1591 wkr = (smpl_t)0.5 - c[nc - kk];
1594 xi = a[j + 1] + a[k + 1];
1595 yr = wkr * xr - wki * xi;
1596 yi = wkr * xi + wki * xr;
1605 void rftbsub(int n, smpl_t *a, int nc, smpl_t *c)
1607 int j, k, kk, ks, m;
1608 smpl_t wkr, wki, xr, xi, yr, yi;
1614 for (j = 2; j < m; j += 2) {
1617 wkr = (smpl_t)0.5 - c[nc - kk];
1620 xi = a[j + 1] + a[k + 1];
1621 yr = wkr * xr + wki * xi;
1622 yi = wkr * xi - wki * xr;
1624 a[j + 1] = yi - a[j + 1];
1626 a[k + 1] = yi - a[k + 1];
1628 a[m + 1] = -a[m + 1];
1632 void dctsub(int n, smpl_t *a, int nc, smpl_t *c)
1634 int j, k, kk, ks, m;
1635 smpl_t wkr, wki, xr;
1640 for (j = 1; j < m; j++) {
1643 wkr = c[kk] - c[nc - kk];
1644 wki = c[kk] + c[nc - kk];
1645 xr = wki * a[j] - wkr * a[k];
1646 a[j] = wkr * a[j] + wki * a[k];
1653 void dstsub(int n, smpl_t *a, int nc, smpl_t *c)
1655 int j, k, kk, ks, m;
1656 smpl_t wkr, wki, xr;
1661 for (j = 1; j < m; j++) {
1664 wkr = c[kk] - c[nc - kk];
1665 wki = c[kk] + c[nc - kk];
1666 xr = wki * a[k] - wkr * a[j];
1667 a[k] = wkr * a[k] + wki * a[j];