16 | * dimension :one 17 | * data length :power of 2 18 | * decimation :frequency 19 | * radix :split-radix 20 | * data :inplace 21 | * table :use 22 | *23 | *
25 | * The cos/sin table is recalculated when the larger table required. 26 | * w[] and ip[] are compatible with all routines. 27 | *
28 | * @author Takuya OOURA 29 | * @author Naohide Sano (nsano) 30 | * @version 0.00 060127 nsano port to java version
40 | * [definition]
41 | * <case1>
42 | * X[k] = sum_j=0ˆn-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
43 | * <case2>
44 | * X[k] = sum_j=0ˆn-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
45 | * (notes: sum_j=0ˆn-1 is a summation from j=0 to n-1)
46 | * [usage]
47 | * <case1>
48 | * ip[0] = 0; // first time only
49 | * cdft(2*n, 1, a, ip, w);
50 | * <case2>
51 | * ip[0] = 0; // first time only
52 | * cdft(2*n, -1, a, ip, w);
53 | * [remark]
54 | * Inverse of
55 | * cdft(2*n, -1, a, ip, w);
56 | * is
57 | * cdft(2*n, 1, a, ip, w);
58 | * for (j = 0; j <= 2 * n - 1; j++) {
59 | * a[j] *= 1.0 / n;
60 | * }
61 | * .
62 | *
63 | * @param n 2*n data length (int)
64 | * n >= 1, n = power of 2
65 | * @param isgn
66 | * @param a a[0...2*n-1] input/output data (REAL *)
67 | * input data
68 | * a[2*j] = Re(x[j]),
69 | * a[2*j+1] = Im(x[j]), 0<=j<n
70 | * output data
71 | * a[2*k] = Re(X[k]),
72 | * a[2*k+1] = Im(X[k]), 0<=k<n
73 | * @param ip ip[0...*] work area for bit reversal (int *)
74 | * length of ip >= 2+sqrt(n)
75 | * strictly,
76 | * length of ip >=
77 | * 2+(1<<(int)(log(n+0.5)/log(2))/2).
78 | * ip[0],ip[1] are pointers of the cos/sin table.
79 | * @param w w[0...n/2-1] cos/sin table (REAL *)
80 | * w[],ip[] are initialized if ip[0] == 0.
81 | */
82 | public void cdft(int n, int isgn, double[] a, int[] ip, double[] w) {
83 | int nw;
84 |
85 | nw = ip[0];
86 | if (n > (nw << 2)) {
87 | nw = n >> 2;
88 | makewt(nw, ip, w);
89 | }
90 | if (isgn >= 0) {
91 | cftfsub(n, a, ip, 2, nw, w);
92 | } else {
93 | cftbsub(n, a, ip, 2, nw, w);
94 | }
95 | }
96 |
97 | /**
98 | * Real Discrete Fourier Transform.
99 | *
100 | * [definition]
101 | * <case1> RDFT
102 | * R[k] = sum_j = 0 & ˆ (n - 1) a[j] * cos(2 * pi * j * k / n), 0 <= k <= n / 2
103 | * I[k] = sum_j = 0 & ˆ (n - 1) a[j] * sin(2 * pi * j * k / n), 0 < k < n / 2
104 | * <case2> IRDFT (excluding scale)
105 | * a[k] = (R[0] + R[n / 2] * cos(pi * k)) / 2 +
106 | * sum_j = 1 & ˆ (n / 2 - 1) R[j] * cos(2 * pi * j * k / n) +
107 | * sum_j = 1 & ˆ (n / 2 - 1) I[j] * sin(2 * pi * j * k / n), 0 <= k < n
108 | * [usage]
109 | * <case1>
110 | * ip[0] = 0; // first time only
111 | * rdft(n, 1, a, ip, w);
112 | * <case2>
113 | * ip[0] = 0; // first time only
114 | * rdft(n, -1, a, ip, w);
115 | * [remark]
116 | * Inverse of
117 | * rdft(n, 1, a, ip, w);
118 | * is
119 | * rdft(n, -1, a, ip, w);
120 | * for (j = 0; j <= n - 1; j++) {
121 | * a[j] *= 2.0 / n;
122 | * }
123 | * .
124 | *
125 | * @param n data length 130 | * <case1> 131 | * output data 132 | * a[2 * k] = R[k], 0 <= k < n / 2 133 | * a[2 * k + 1] = I[k], 0 < k < n / 2 134 | * a[1] = R[n/2] 135 | * <case2> 136 | * input data 137 | * a[2 * j] = R[j], 0 <= j < n / 2 138 | * a[2 * j + 1] = I[j], 0 < j < n / 2 139 | * a[1] = R[n / 2] 140 | *141 | * @param ip [0...*] work area for bit reversal 142 | *
143 | * length of ip >= 2 + sqrt(n / 2) 144 | * strictly, 145 | * length of ip >= 146 | * 2 + (1 << (int) (log(n / 2 + 0.5) / log(2)) / 2). 147 | *148 | * ip[0],ip[1] are pointers of the cos/sin table. 149 | * @param w [0...n/2-1] cos/sin table
191 | * [definition]
192 | * <case1> IDCT (excluding scale)
193 | * C[k] = sum_j=0ˆn-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
194 | * <case2> DCT
195 | * C[k] = sum_j=0ˆn-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
196 | * [usage]
197 | * <case1>
198 | * ip[0] = 0; // first time only
199 | * ddct(n, 1, a, ip, w);
200 | * <case2>
201 | * ip[0] = 0; // first time only
202 | * ddct(n, -1, a, ip, w);
203 | * [remark]
204 | * Inverse of
205 | * ddct(n, -1, a, ip, w);
206 | * is
207 | * a[0] *= 0.5;
208 | * ddct(n, 1, a, ip, w);
209 | * for (j = 0; j <= n - 1; j++) {
210 | * a[j] *= 2.0 / n;
211 | * }
212 | * .
213 | *
214 | * @param n data length (int)
215 | * 216 | * n >= 2, n = power of 2 217 | *218 | * @param isgn 219 | * @param a [0...n-1] input/output data (REAL *) 220 | *
221 | * output data 222 | * a[k] = C[k], 0<=k<n 223 | *224 | * @param ip [0...*] work area for bit reversal (int *) 225 | *
226 | * length of ip >= 2+sqrt(n/2) 227 | * strictly, 228 | * length of ip >= 229 | * 2+(1<<(int)(log(n/2+0.5)/log(2))/2). 230 | * ip[0],ip[1] are pointers of the cos/sin table. 231 | *232 | * @param w [0...n*5/4-1] cos/sin table (REAL *) 233 | *
234 | * w[],ip[] are initialized if ip[0] == 0. 235 | *236 | */ 237 | public void ddct(int n, int isgn, double[] a, int[] ip, double[] w) { 238 | int j, nw, nc; 239 | double xr; 240 | 241 | nw = ip[0]; 242 | if (n > (nw << 2)) { 243 | nw = n >> 2; 244 | makewt(nw, ip, w); 245 | } 246 | nc = ip[1]; 247 | if (n > nc) { 248 | nc = n; 249 | makect(nc, ip, w, nw); 250 | } 251 | if (isgn < 0) { 252 | xr = a[n - 1]; 253 | for (j = n - 2; j >= 2; j -= 2) { 254 | a[j + 1] = a[j] - a[j - 1]; 255 | a[j] += a[j - 1]; 256 | } 257 | a[1] = a[0] - xr; 258 | a[0] += xr; 259 | if (n > 4) { 260 | rftbsub(n, a, nc, w, nw); 261 | cftbsub(n, a, ip, 2, nw, w); 262 | } else if (n == 4) { 263 | cftbsub(n, a, ip, 2, nw, w); 264 | } 265 | } 266 | dctsub(n, a, nc, w, nw); 267 | if (isgn >= 0) { 268 | if (n > 4) { 269 | cftfsub(n, a, ip, 2, nw, w); 270 | rftfsub(n, a, nc, w, nw); 271 | } else if (n == 4) { 272 | cftfsub(n, a, ip, 2, nw, w); 273 | } 274 | xr = a[0] - a[1]; 275 | a[0] += a[1]; 276 | for (j = 2; j < n; j += 2) { 277 | a[j - 1] = a[j] - a[j + 1]; 278 | a[j] += a[j + 1]; 279 | } 280 | a[n - 1] = xr; 281 | } 282 | } 283 | 284 | /** 285 | * Discrete Sine Transform. 286 | *
287 | * [definition]
288 | * <case1> IDST (excluding scale)
289 | * S[k] = sum_j=1ˆn A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
290 | * <case2> DST
291 | * S[k] = sum_j=0ˆn-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
292 | * [usage]
293 | * <case1>
294 | * ip[0] = 0; // first time only
295 | * ddst(n, 1, a, ip, w);
296 | * <case2>
297 | * ip[0] = 0; // first time only
298 | * ddst(n, -1, a, ip, w);
299 | * [remark]
300 | * Inverse of
301 | * ddst(n, -1, a, ip, w);
302 | * is
303 | * a[0] *= 0.5;
304 | * ddst(n, 1, a, ip, w);
305 | * for (j = 0; j <= n - 1; j++) {
306 | * a[j] *= 2.0 / n;
307 | * }
308 | * .
309 | *
310 | * @param n data length (int)
311 | * n >= 2, n = power of 2
312 | * @param isgn
313 | * @param a [0...n-1] input/output data (REAL *)
314 | * <case1>
315 | * input data
316 | * a[j] = A[j], 0<j<n
317 | * a[0] = A[n]
318 | * output data
319 | * a[k] = S[k], 0<=k<n
320 | * <case2>
321 | * output data
322 | * a[k] = S[k], 0<k<n
323 | * a[0] = S[n]
324 | * @param ip [0...*] work area for bit reversal (int *)
325 | * length of ip >= 2+sqrt(n/2)
326 | * strictly,
327 | * length of ip >=
328 | * 2+(1<<(int)(log(n/2+0.5)/log(2))/2).
329 | * ip[0],ip[1] are pointers of the cos/sin table.
330 | * @param w [0...n*5/4-1] cos/sin table (REAL *)
331 | * w[],ip[] are initialized if ip[0] == 0.
332 | */
333 | public void ddst(int n, int isgn, double[] a, int[] ip, double[] w) {
334 | int j, nw, nc;
335 | double xr;
336 |
337 | nw = ip[0];
338 | if (n > (nw << 2)) {
339 | nw = n >> 2;
340 | makewt(nw, ip, w);
341 | }
342 | nc = ip[1];
343 | if (n > nc) {
344 | nc = n;
345 | makect(nc, ip, w, nw);
346 | }
347 | if (isgn < 0) {
348 | xr = a[n - 1];
349 | for (j = n - 2; j >= 2; j -= 2) {
350 | a[j + 1] = -a[j] - a[j - 1];
351 | a[j] -= a[j - 1];
352 | }
353 | a[1] = a[0] + xr;
354 | a[0] -= xr;
355 | if (n > 4) {
356 | rftbsub(n, a, nc, w, nw);
357 | cftbsub(n, a, ip, 2, nw, w);
358 | } else if (n == 4) {
359 | cftbsub(n, a, ip, 2, nw, w);
360 | }
361 | }
362 | dstsub(n, a, nc, w, nw);
363 | if (isgn >= 0) {
364 | if (n > 4) {
365 | cftfsub(n, a, ip, 2, nw, w);
366 | rftfsub(n, a, nc, w, nw);
367 | } else if (n == 4) {
368 | cftfsub(n, a, ip, 2, nw, w);
369 | }
370 | xr = a[0] - a[1];
371 | a[0] += a[1];
372 | for (j = 2; j < n; j += 2) {
373 | a[j - 1] = -a[j] - a[j + 1];
374 | a[j] -= a[j + 1];
375 | }
376 | a[n - 1] = -xr;
377 | }
378 | }
379 |
380 | /**
381 | * Cosine Transform of RDFT (Real Symmetric DFT).
382 | *
383 | * [definition]
384 | * C[k] = sum_j=0ˆn a[j]*cos(pi*j*k/n), 0<=k<=n
385 | * [usage]
386 | * ip[0] = 0; // first time only
387 | * dfct(n, a, t, ip, w);
388 | * [parameters]
389 | * [remark]
390 | * Inverse of
391 | * a[0] *= 0.5;
392 | * a[n] *= 0.5;
393 | * dfct(n, a, t, ip, w);
394 | * is
395 | * a[0] *= 0.5;
396 | * a[n] *= 0.5;
397 | * dfct(n, a, t, ip, w);
398 | * for (j = 0; j <= n; j++) {
399 | * a[j] *= 2.0 / n;
400 | * }
401 | * .
402 | *
403 | * @param n data length - 1 (int)
404 | * 405 | * n >= 2, n = power of 2 406 | *407 | * @param a [0...n] input/output data (REAL *) 408 | *
409 | * output data 410 | * a[k] = C[k], 0<=k<=n 411 | *412 | * @param t [0...n/2] work area (REAL *) 413 | * @param ip [0...*] work area for bit reversal (int *) 414 | *
415 | * length of ip >= 2+sqrt(n/4) 416 | * strictly, 417 | * length of ip >= 418 | * 2+(1<<(int)(log(n/4+0.5)/log(2))/2). 419 | * ip[0],ip[1] are pointers of the cos/sin table. 420 | *421 | * @param w [0...n*5/8-1] cos/sin table (REAL *) 422 | *
423 | * w[],ip[] are initialized if ip[0] == 0. 424 | *425 | */ 426 | public void dfct(int n, double[] a, double[] t, int[] ip, double[] w) { 427 | int j, k, l, m, mh, nw, nc; 428 | double xr, xi, yr, yi; 429 | 430 | nw = ip[0]; 431 | if (n > (nw << 3)) { 432 | nw = n >> 3; 433 | makewt(nw, ip, w); 434 | } 435 | nc = ip[1]; 436 | if (n > (nc << 1)) { 437 | nc = n >> 1; 438 | makect(nc, ip, w, nw); 439 | } 440 | m = n >> 1; 441 | yi = a[m]; 442 | xi = a[0] + a[n]; 443 | a[0] -= a[n]; 444 | t[0] = xi - yi; 445 | t[m] = xi + yi; 446 | if (n > 2) { 447 | mh = m >> 1; 448 | for (j = 1; j < mh; j++) { 449 | k = m - j; 450 | xr = a[j] - a[n - j]; 451 | xi = a[j] + a[n - j]; 452 | yr = a[k] - a[n - k]; 453 | yi = a[k] + a[n - k]; 454 | a[j] = xr; 455 | a[k] = yr; 456 | t[j] = xi - yi; 457 | t[k] = xi + yi; 458 | } 459 | t[mh] = a[mh] + a[n - mh]; 460 | a[mh] -= a[n - mh]; 461 | dctsub(m, a, nc, w, nw); 462 | if (m > 4) { 463 | cftfsub(m, a, ip, 2, nw, w); 464 | rftfsub(m, a, nc, w, nw); 465 | } else if (m == 4) { 466 | cftfsub(m, a, ip, 2, nw, w); 467 | } 468 | a[n - 1] = a[0] - a[1]; 469 | a[1] = a[0] + a[1]; 470 | for (j = m - 2; j >= 2; j -= 2) { 471 | a[2 * j + 1] = a[j] + a[j + 1]; 472 | a[2 * j - 1] = a[j] - a[j + 1]; 473 | } 474 | l = 2; 475 | m = mh; 476 | while (m >= 2) { 477 | dctsub(m, t, nc, w, nw); 478 | if (m > 4) { 479 | cftfsub(m, t, ip, 2, nw, w); 480 | rftfsub(m, t, nc, w, nw); 481 | } else if (m == 4) { 482 | cftfsub(m, t, ip, 2, nw, w); 483 | } 484 | a[n - l] = t[0] - t[1]; 485 | a[l] = t[0] + t[1]; 486 | k = 0; 487 | for (j = 2; j < m; j += 2) { 488 | k += l << 2; 489 | a[k - l] = t[j] - t[j + 1]; 490 | a[k + l] = t[j] + t[j + 1]; 491 | } 492 | l <<= 1; 493 | mh = m >> 1; 494 | for (j = 0; j < mh; j++) { 495 | k = m - j; 496 | t[j] = t[m + k] - t[m + j]; 497 | t[k] = t[m + k] + t[m + j]; 498 | } 499 | t[mh] = t[m + mh]; 500 | m = mh; 501 | } 502 | a[l] = t[0]; 503 | a[n] = t[2] - t[1]; 504 | a[0] = t[2] + t[1]; 505 | } else { 506 | a[1] = a[0]; 507 | a[2] = t[0]; 508 | a[0] = t[1]; 509 | } 510 | } 511 | 512 | /** 513 | * Sine Transform of RDFT (Real Anti-symmetric DFT). 514 | *
515 | * [definition]
516 | * S[k] = sum_j=1ˆn-1 a[j]*sin(pi*j*k/n), 0<k<n
517 | * [usage]
518 | * ip[0] = 0; // first time only
519 | * dfst(n, a, t, ip, w);
520 | * [remark]
521 | * Inverse of
522 | * dfst(n, a, t, ip, w);
523 | * is
524 | * dfst(n, a, t, ip, w);
525 | * for (j = 1; j <= n - 1; j++) {
526 | * a[j] *= 2.0 / n;
527 | * }
528 | * .
529 | *
530 | * @param n data length + 1 (int)
531 | * 532 | * n >= 2, n = power of 2 533 | *534 | * @param a [0...n-1] input/output data (REAL *) 535 | *
536 | * output data 537 | * a[k] = S[k], 0<k<n 538 | * (a[0] is used for work area) 539 | *540 | * @param t [0...n/2-1] work area (REAL *) 541 | * @param ip [0...*] work area for bit reversal (int *) 542 | *
543 | * length of ip >= 2+sqrt(n/4) 544 | * strictly, 545 | * length of ip >= 546 | * 2+(1<<(int)(log(n/4+0.5)/log(2))/2). 547 | * ip[0],ip[1] are pointers of the cos/sin table. 548 | *549 | * @param w [0...n*5/8-1] cos/sin table (REAL *) 550 | *
551 | * w[],ip[] are initialized if ip[0] == 0. 552 | *553 | */ 554 | public void dfst(int n, double[] a, double[] t, int[] ip, double[] w) { 555 | int j, k, l, m, mh, nw, nc; 556 | double xr, xi, yr, yi; 557 | 558 | nw = ip[0]; 559 | if (n > (nw << 3)) { 560 | nw = n >> 3; 561 | makewt(nw, ip, w); 562 | } 563 | nc = ip[1]; 564 | if (n > (nc << 1)) { 565 | nc = n >> 1; 566 | makect(nc, ip, w, nw); 567 | } 568 | if (n > 2) { 569 | m = n >> 1; 570 | mh = m >> 1; 571 | for (j = 1; j < mh; j++) { 572 | k = m - j; 573 | xr = a[j] + a[n - j]; 574 | xi = a[j] - a[n - j]; 575 | yr = a[k] + a[n - k]; 576 | yi = a[k] - a[n - k]; 577 | a[j] = xr; 578 | a[k] = yr; 579 | t[j] = xi + yi; 580 | t[k] = xi - yi; 581 | } 582 | t[0] = a[mh] - a[n - mh]; 583 | a[mh] += a[n - mh]; 584 | a[0] = a[m]; 585 | dstsub(m, a, nc, w, nw); 586 | if (m > 4) { 587 | cftfsub(m, a, ip, 2, nw, w); 588 | rftfsub(m, a, nc, w, nw); 589 | } else if (m == 4) { 590 | cftfsub(m, a, ip, 2, nw, w); 591 | } 592 | a[n - 1] = a[1] - a[0]; 593 | a[1] = a[0] + a[1]; 594 | for (j = m - 2; j >= 2; j -= 2) { 595 | a[2 * j + 1] = a[j] - a[j + 1]; 596 | a[2 * j - 1] = -a[j] - a[j + 1]; 597 | } 598 | l = 2; 599 | m = mh; 600 | while (m >= 2) { 601 | dstsub(m, t, nc, w, nw); 602 | if (m > 4) { 603 | cftfsub(m, t, ip, 2, nw, w); 604 | rftfsub(m, t, nc, w, nw); 605 | } else if (m == 4) { 606 | cftfsub(m, t, ip, 2, nw, w); 607 | } 608 | a[n - l] = t[1] - t[0]; 609 | a[l] = t[0] + t[1]; 610 | k = 0; 611 | for (j = 2; j < m; j += 2) { 612 | k += l << 2; 613 | a[k - l] = -t[j] - t[j + 1]; 614 | a[k + l] = t[j] - t[j + 1]; 615 | } 616 | l <<= 1; 617 | mh = m >> 1; 618 | for (j = 1; j < mh; j++) { 619 | k = m - j; 620 | t[j] = t[m + k] + t[m + j]; 621 | t[k] = t[m + k] - t[m + j]; 622 | } 623 | t[0] = t[m + mh]; 624 | m = mh; 625 | } 626 | a[l] = t[0]; 627 | } 628 | a[0] = 0; 629 | } 630 | 631 | // -------- initializing routines -------- 632 | 633 | /** */ 634 | private void makewt(int nw, int[] ip, double[] w) { 635 | int j, nwh, nw0, nw1; 636 | double delta, wn4r, wk1r, wk1i, wk3r, wk3i; 637 | 638 | ip[0] = nw; 639 | ip[1] = 1; 640 | if (nw > 2) { 641 | nwh = nw >> 1; 642 | // delta = Math.atan(1.0) / nwh; 643 | delta = Math.PI / 4 / nwh; 644 | wn4r = Math.cos(delta * nwh); 645 | w[0] = 1; 646 | w[1] = wn4r; 647 | if (nwh >= 4) { 648 | w[2] = 0.5 / Math.cos(delta * 2); 649 | w[3] = 0.5 / Math.cos(delta * 6); 650 | } 651 | for (j = 4; j < nwh; j += 4) { 652 | w[j] = Math.cos(delta * j); 653 | w[j + 1] = Math.sin(delta * j); 654 | w[j + 2] = Math.cos(3 * delta * j); 655 | w[j + 3] = Math.sin(3 * delta * j); 656 | } 657 | nw0 = 0; 658 | while (nwh > 2) { 659 | nw1 = nw0 + nwh; 660 | nwh >>= 1; 661 | w[nw1] = 1; 662 | w[nw1 + 1] = wn4r; 663 | if (nwh >= 4) { 664 | wk1r = w[nw0 + 4]; 665 | wk3r = w[nw0 + 6]; 666 | w[nw1 + 2] = 0.5 / wk1r; 667 | w[nw1 + 3] = 0.5 / wk3r; 668 | } 669 | for (j = 4; j < nwh; j += 4) { 670 | wk1r = w[nw0 + 2 * j]; 671 | wk1i = w[nw0 + 2 * j + 1]; 672 | wk3r = w[nw0 + 2 * j + 2]; 673 | wk3i = w[nw0 + 2 * j + 3]; 674 | w[nw1 + j] = wk1r; 675 | w[nw1 + j + 1] = wk1i; 676 | w[nw1 + j + 2] = wk3r; 677 | w[nw1 + j + 3] = wk3i; 678 | } 679 | nw0 = nw1; 680 | } 681 | } 682 | } 683 | 684 | /** */ 685 | private void makect(int nc, int[] ip, double[] c, int cP) { 686 | int j, nch; 687 | double delta; 688 | 689 | ip[1] = nc; 690 | if (nc > 1) { 691 | nch = nc >> 1; 692 | // delta = Math.atan(1.0) / nch; 693 | delta = Math.PI / 4 / nch; 694 | c[cP + 0] = Math.cos(delta * nch); 695 | c[cP + nch] = 0.5 * c[cP + 0]; 696 | for (j = 1; j < nch; j++) { 697 | c[cP + j] = 0.5 * Math.cos(delta * j); 698 | c[cP + nc - j] = 0.5 * Math.sin(delta * j); 699 | } 700 | } 701 | } 702 | 703 | // -------- child routines -------- 704 | 705 | /** 706 | * 2nd 707 | * @see #rdft(int, int, double[], int[], double[]) 708 | * @see #ddct(int, int, double[], int[], double[]) 709 | * @see #cdft(int, int, double[], int[], double[]) 710 | * @see #ddst(int, int, double[], int[], double[]) 711 | * @see #dfst(int, double[], double[], int[], double[]) 712 | * @see #dfct(int, double[], double[], int[], double[]) 713 | */ 714 | private void cftfsub(int n, double[] a, int[] ip, int ipP, int nw, double[] w) { 715 | int m; 716 | 717 | if (n > 32) { 718 | m = n >> 2; 719 | cftf1st(n, a, w, nw - m); 720 | if (n > CDFT_RECURSIVE_N) { 721 | cftrec1(m, a, 0, nw, w); 722 | cftrec2(m, a, m, nw, w); 723 | cftrec1(m, a, 2 * m, nw, w); 724 | cftrec1(m, a, 3 * m, nw, w); 725 | } else if (m > 32) { 726 | cftexp1(n, a, 0, nw, w); 727 | } else { 728 | cftfx41(n, a, 0, nw, w); 729 | } 730 | bitrv2(n, ip, ipP, a); 731 | } else if (n > 8) { 732 | if (n == 32) { 733 | cftf161(a, 0, w, nw - 8); 734 | bitrv216(a); 735 | } else { 736 | cftf081(a, 0, w, 0); 737 | bitrv208(a); 738 | } 739 | } else if (n == 8) { 740 | cftf040(a); 741 | } else if (n == 4) { 742 | cftx020(a); 743 | } 744 | } 745 | 746 | /** 747 | * 2nd 748 | * @see #rdft(int, int, double[], int[], double[]) 749 | * @see #ddct(int, int, double[], int[], double[]) 750 | * @see #cdft(int, int, double[], int[], double[]) 751 | * @see #ddst(int, int, double[], int[], double[]) 752 | */ 753 | private void cftbsub(int n, double[] a, int[] ip, int ipP, int nw, double[] w) { 754 | int m; 755 | 756 | if (n > 32) { 757 | m = n >> 2; 758 | cftb1st(n, a, w, nw - m); 759 | if (n > CDFT_RECURSIVE_N) { 760 | cftrec1(m, a, 0, nw, w); 761 | cftrec2(m, a, m, nw, w); 762 | cftrec1(m, a, 2 * m, nw, w); 763 | cftrec1(m, a, 3 * m, nw, w); 764 | } else if (m > 32) { 765 | cftexp1(n, a, 0, nw, w); 766 | } else { 767 | cftfx41(n, a, 0, nw, w); 768 | } 769 | bitrv2conj(n, ip, ipP, a); 770 | } else if (n > 8) { 771 | if (n == 32) { 772 | cftf161(a, 0, w, nw - 8); 773 | bitrv216neg(a); 774 | } else { 775 | cftf081(a, 0, w, 0); 776 | bitrv208neg(a); 777 | } 778 | } else if (n == 8) { 779 | cftb040(a); 780 | } else if (n == 4) { 781 | cftx020(a); 782 | } 783 | } 784 | 785 | /** 786 | * 3rd 787 | * @see #cftfsub(int, double[], int[], int, int, double[]) 788 | */ 789 | private final void bitrv2(int n, int[] ip, int ipP, double[] a) { 790 | int j, j1, k, k1, l, m, m2; 791 | double xr, xi, yr, yi; 792 | 793 | ip[ipP + 0] = 0; 794 | l = n; 795 | m = 1; 796 | while ((m << 3) < l) { 797 | l >>= 1; 798 | for (j = 0; j < m; j++) { 799 | ip[ipP + m + j] = ip[ipP + j] + l; 800 | } 801 | m <<= 1; 802 | } 803 | m2 = 2 * m; 804 | if ((m << 3) == l) { 805 | for (k = 0; k < m; k++) { 806 | for (j = 0; j < k; j++) { 807 | j1 = 2 * j + ip[ipP + k]; 808 | k1 = 2 * k + ip[ipP + j]; 809 | xr = a[j1]; 810 | xi = a[j1 + 1]; 811 | yr = a[k1]; 812 | yi = a[k1 + 1]; 813 | a[j1] = yr; 814 | a[j1 + 1] = yi; 815 | a[k1] = xr; 816 | a[k1 + 1] = xi; 817 | j1 += m2; 818 | k1 += 2 * m2; 819 | xr = a[j1]; 820 | xi = a[j1 + 1]; 821 | yr = a[k1]; 822 | yi = a[k1 + 1]; 823 | a[j1] = yr; 824 | a[j1 + 1] = yi; 825 | a[k1] = xr; 826 | a[k1 + 1] = xi; 827 | j1 += m2; 828 | k1 -= m2; 829 | xr = a[j1]; 830 | xi = a[j1 + 1]; 831 | yr = a[k1]; 832 | yi = a[k1 + 1]; 833 | a[j1] = yr; 834 | a[j1 + 1] = yi; 835 | a[k1] = xr; 836 | a[k1 + 1] = xi; 837 | j1 += m2; 838 | k1 += 2 * m2; 839 | xr = a[j1]; 840 | xi = a[j1 + 1]; 841 | yr = a[k1]; 842 | yi = a[k1 + 1]; 843 | a[j1] = yr; 844 | a[j1 + 1] = yi; 845 | a[k1] = xr; 846 | a[k1 + 1] = xi; 847 | } 848 | j1 = 2 * k + m2 + ip[ipP + k]; 849 | k1 = j1 + m2; 850 | xr = a[j1]; 851 | xi = a[j1 + 1]; 852 | yr = a[k1]; 853 | yi = a[k1 + 1]; 854 | a[j1] = yr; 855 | a[j1 + 1] = yi; 856 | a[k1] = xr; 857 | a[k1 + 1] = xi; 858 | } 859 | } else { 860 | for (k = 1; k < m; k++) { 861 | for (j = 0; j < k; j++) { 862 | j1 = 2 * j + ip[ipP + k]; 863 | k1 = 2 * k + ip[ipP + j]; 864 | xr = a[j1]; 865 | xi = a[j1 + 1]; 866 | yr = a[k1]; 867 | yi = a[k1 + 1]; 868 | a[j1] = yr; 869 | a[j1 + 1] = yi; 870 | a[k1] = xr; 871 | a[k1 + 1] = xi; 872 | j1 += m2; 873 | k1 += m2; 874 | xr = a[j1]; 875 | xi = a[j1 + 1]; 876 | yr = a[k1]; 877 | yi = a[k1 + 1]; 878 | a[j1] = yr; 879 | a[j1 + 1] = yi; 880 | a[k1] = xr; 881 | a[k1 + 1] = xi; 882 | } 883 | } 884 | } 885 | } 886 | 887 | /** 888 | * 3rd 889 | * @see #cftbsub(int, double[], int[], int, int, double[]) 890 | */ 891 | private final void bitrv2conj(int n, int[] ip, int ipP, double[] a) { 892 | int j, j1, k, k1, l, m, m2; 893 | double xr, xi, yr, yi; 894 | 895 | ip[ipP + 0] = 0; 896 | l = n; 897 | m = 1; 898 | while ((m << 3) < l) { 899 | l >>= 1; 900 | for (j = 0; j < m; j++) { 901 | ip[ipP + m + j] = ip[ipP + j] + l; 902 | } 903 | m <<= 1; 904 | } 905 | m2 = 2 * m; 906 | if ((m << 3) == l) { 907 | for (k = 0; k < m; k++) { 908 | for (j = 0; j < k; j++) { 909 | j1 = 2 * j + ip[ipP + k]; 910 | k1 = 2 * k + ip[ipP + j]; 911 | xr = a[j1]; 912 | xi = -a[j1 + 1]; 913 | yr = a[k1]; 914 | yi = -a[k1 + 1]; 915 | a[j1] = yr; 916 | a[j1 + 1] = yi; 917 | a[k1] = xr; 918 | a[k1 + 1] = xi; 919 | j1 += m2; 920 | k1 += 2 * m2; 921 | xr = a[j1]; 922 | xi = -a[j1 + 1]; 923 | yr = a[k1]; 924 | yi = -a[k1 + 1]; 925 | a[j1] = yr; 926 | a[j1 + 1] = yi; 927 | a[k1] = xr; 928 | a[k1 + 1] = xi; 929 | j1 += m2; 930 | k1 -= m2; 931 | xr = a[j1]; 932 | xi = -a[j1 + 1]; 933 | yr = a[k1]; 934 | yi = -a[k1 + 1]; 935 | a[j1] = yr; 936 | a[j1 + 1] = yi; 937 | a[k1] = xr; 938 | a[k1 + 1] = xi; 939 | j1 += m2; 940 | k1 += 2 * m2; 941 | xr = a[j1]; 942 | xi = -a[j1 + 1]; 943 | yr = a[k1]; 944 | yi = -a[k1 + 1]; 945 | a[j1] = yr; 946 | a[j1 + 1] = yi; 947 | a[k1] = xr; 948 | a[k1 + 1] = xi; 949 | } 950 | k1 = 2 * k + ip[ipP + k]; 951 | a[k1 + 1] = -a[k1 + 1]; 952 | j1 = k1 + m2; 953 | k1 = j1 + m2; 954 | xr = a[j1]; 955 | xi = -a[j1 + 1]; 956 | yr = a[k1]; 957 | yi = -a[k1 + 1]; 958 | a[j1] = yr; 959 | a[j1 + 1] = yi; 960 | a[k1] = xr; 961 | a[k1 + 1] = xi; 962 | k1 += m2; 963 | a[k1 + 1] = -a[k1 + 1]; 964 | } 965 | } else { 966 | a[1] = -a[1]; 967 | a[m2 + 1] = -a[m2 + 1]; 968 | for (k = 1; k < m; k++) { 969 | for (j = 0; j < k; j++) { 970 | j1 = 2 * j + ip[ipP + k]; 971 | k1 = 2 * k + ip[ipP + j]; 972 | xr = a[j1]; 973 | xi = -a[j1 + 1]; 974 | yr = a[k1]; 975 | yi = -a[k1 + 1]; 976 | a[j1] = yr; 977 | a[j1 + 1] = yi; 978 | a[k1] = xr; 979 | a[k1 + 1] = xi; 980 | j1 += m2; 981 | k1 += m2; 982 | xr = a[j1]; 983 | xi = -a[j1 + 1]; 984 | yr = a[k1]; 985 | yi = -a[k1 + 1]; 986 | a[j1] = yr; 987 | a[j1 + 1] = yi; 988 | a[k1] = xr; 989 | a[k1 + 1] = xi; 990 | } 991 | k1 = 2 * k + ip[ipP + k]; 992 | a[k1 + 1] = -a[k1 + 1]; 993 | a[k1 + m2 + 1] = -a[k1 + m2 + 1]; 994 | } 995 | } 996 | } 997 | 998 | /** 999 | * 3rd 1000 | * @see #cftfsub(int, double[], int[], int, int, double[]) 1001 | */ 1002 | private void bitrv216(double[] a) { 1003 | double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x7r, x7i, x8r, x8i, x10r, x10i, x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i; 1004 | 1005 | x1r = a[2]; 1006 | x1i = a[3]; 1007 | x2r = a[4]; 1008 | x2i = a[5]; 1009 | x3r = a[6]; 1010 | x3i = a[7]; 1011 | x4r = a[8]; 1012 | x4i = a[9]; 1013 | x5r = a[10]; 1014 | x5i = a[11]; 1015 | x7r = a[14]; 1016 | x7i = a[15]; 1017 | x8r = a[16]; 1018 | x8i = a[17]; 1019 | x10r = a[20]; 1020 | x10i = a[21]; 1021 | x11r = a[22]; 1022 | x11i = a[23]; 1023 | x12r = a[24]; 1024 | x12i = a[25]; 1025 | x13r = a[26]; 1026 | x13i = a[27]; 1027 | x14r = a[28]; 1028 | x14i = a[29]; 1029 | a[2] = x8r; 1030 | a[3] = x8i; 1031 | a[4] = x4r; 1032 | a[5] = x4i; 1033 | a[6] = x12r; 1034 | a[7] = x12i; 1035 | a[8] = x2r; 1036 | a[9] = x2i; 1037 | a[10] = x10r; 1038 | a[11] = x10i; 1039 | a[14] = x14r; 1040 | a[15] = x14i; 1041 | a[16] = x1r; 1042 | a[17] = x1i; 1043 | a[20] = x5r; 1044 | a[21] = x5i; 1045 | a[22] = x13r; 1046 | a[23] = x13i; 1047 | a[24] = x3r; 1048 | a[25] = x3i; 1049 | a[26] = x11r; 1050 | a[27] = x11i; 1051 | a[28] = x7r; 1052 | a[29] = x7i; 1053 | } 1054 | 1055 | /** 1056 | * 3rd 1057 | * @see #cftbsub(int, double[], int[], int, int, double[]) 1058 | */ 1059 | private void bitrv216neg(double[] a) { 1060 | double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x6r, x6i, x7r, x7i, x8r, x8i, x9r, x9i, x10r, x10i, x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i, x15r, x15i; 1061 | 1062 | x1r = a[2]; 1063 | x1i = a[3]; 1064 | x2r = a[4]; 1065 | x2i = a[5]; 1066 | x3r = a[6]; 1067 | x3i = a[7]; 1068 | x4r = a[8]; 1069 | x4i = a[9]; 1070 | x5r = a[10]; 1071 | x5i = a[11]; 1072 | x6r = a[12]; 1073 | x6i = a[13]; 1074 | x7r = a[14]; 1075 | x7i = a[15]; 1076 | x8r = a[16]; 1077 | x8i = a[17]; 1078 | x9r = a[18]; 1079 | x9i = a[19]; 1080 | x10r = a[20]; 1081 | x10i = a[21]; 1082 | x11r = a[22]; 1083 | x11i = a[23]; 1084 | x12r = a[24]; 1085 | x12i = a[25]; 1086 | x13r = a[26]; 1087 | x13i = a[27]; 1088 | x14r = a[28]; 1089 | x14i = a[29]; 1090 | x15r = a[30]; 1091 | x15i = a[31]; 1092 | a[2] = x15r; 1093 | a[3] = x15i; 1094 | a[4] = x7r; 1095 | a[5] = x7i; 1096 | a[6] = x11r; 1097 | a[7] = x11i; 1098 | a[8] = x3r; 1099 | a[9] = x3i; 1100 | a[10] = x13r; 1101 | a[11] = x13i; 1102 | a[12] = x5r; 1103 | a[13] = x5i; 1104 | a[14] = x9r; 1105 | a[15] = x9i; 1106 | a[16] = x1r; 1107 | a[17] = x1i; 1108 | a[18] = x14r; 1109 | a[19] = x14i; 1110 | a[20] = x6r; 1111 | a[21] = x6i; 1112 | a[22] = x10r; 1113 | a[23] = x10i; 1114 | a[24] = x2r; 1115 | a[25] = x2i; 1116 | a[26] = x12r; 1117 | a[27] = x12i; 1118 | a[28] = x4r; 1119 | a[29] = x4i; 1120 | a[30] = x8r; 1121 | a[31] = x8i; 1122 | } 1123 | 1124 | /** 1125 | * 3rd 1126 | * @see #cftfsub(int, double[], int[], int, int, double[]) 1127 | */ 1128 | private void bitrv208(double[] a) { 1129 | double x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i; 1130 | 1131 | x1r = a[2]; 1132 | x1i = a[3]; 1133 | x3r = a[6]; 1134 | x3i = a[7]; 1135 | x4r = a[8]; 1136 | x4i = a[9]; 1137 | x6r = a[12]; 1138 | x6i = a[13]; 1139 | a[2] = x4r; 1140 | a[3] = x4i; 1141 | a[6] = x6r; 1142 | a[7] = x6i; 1143 | a[8] = x1r; 1144 | a[9] = x1i; 1145 | a[12] = x3r; 1146 | a[13] = x3i; 1147 | } 1148 | 1149 | /** 1150 | * 3rd 1151 | * @see #cftbsub(int, double[], int[], int, int, double[]) 1152 | */ 1153 | private void bitrv208neg(double[] a) { 1154 | double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, x5r, x5i, x6r, x6i, x7r, x7i; 1155 | 1156 | x1r = a[2]; 1157 | x1i = a[3]; 1158 | x2r = a[4]; 1159 | x2i = a[5]; 1160 | x3r = a[6]; 1161 | x3i = a[7]; 1162 | x4r = a[8]; 1163 | x4i = a[9]; 1164 | x5r = a[10]; 1165 | x5i = a[11]; 1166 | x6r = a[12]; 1167 | x6i = a[13]; 1168 | x7r = a[14]; 1169 | x7i = a[15]; 1170 | a[2] = x7r; 1171 | a[3] = x7i; 1172 | a[4] = x3r; 1173 | a[5] = x3i; 1174 | a[6] = x5r; 1175 | a[7] = x5i; 1176 | a[8] = x1r; 1177 | a[9] = x1i; 1178 | a[10] = x6r; 1179 | a[11] = x6i; 1180 | a[12] = x2r; 1181 | a[13] = x2i; 1182 | a[14] = x4r; 1183 | a[15] = x4i; 1184 | } 1185 | 1186 | /** 1187 | * 3rd 1188 | * @see #cftfsub(int, double[], int[], int, int, double[]) 1189 | */ 1190 | private void cftf1st(int n, double[] a, double[] w, int wP) { 1191 | int j, j0, j1, j2, j3, k, m, mh; 1192 | double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i; 1193 | double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i; 1194 | 1195 | mh = n >> 3; 1196 | m = 2 * mh; 1197 | j1 = m; 1198 | j2 = j1 + m; 1199 | j3 = j2 + m; 1200 | x0r = a[0] + a[j2]; 1201 | x0i = a[1] + a[j2 + 1]; 1202 | x1r = a[0] - a[j2]; 1203 | x1i = a[1] - a[j2 + 1]; 1204 | x2r = a[j1] + a[j3]; 1205 | x2i = a[j1 + 1] + a[j3 + 1]; 1206 | x3r = a[j1] - a[j3]; 1207 | x3i = a[j1 + 1] - a[j3 + 1]; 1208 | a[0] = x0r + x2r; 1209 | a[1] = x0i + x2i; 1210 | a[j1] = x0r - x2r; 1211 | a[j1 + 1] = x0i - x2i; 1212 | a[j2] = x1r - x3i; 1213 | a[j2 + 1] = x1i + x3r; 1214 | a[j3] = x1r + x3i; 1215 | a[j3 + 1] = x1i - x3r; 1216 | wn4r = w[wP + 1]; 1217 | csc1 = w[wP + 2]; 1218 | csc3 = w[wP + 3]; 1219 | wd1r = 1; 1220 | wd1i = 0; 1221 | wd3r = 1; 1222 | wd3i = 0; 1223 | k = 0; 1224 | for (j = 2; j < mh - 2; j += 4) { 1225 | k += 4; 1226 | wk1r = csc1 * (wd1r + w[wP + k]); 1227 | wk1i = csc1 * (wd1i + w[wP + k + 1]); 1228 | wk3r = csc3 * (wd3r + w[wP + k + 2]); 1229 | wk3i = csc3 * (wd3i - w[wP + k + 3]); 1230 | wd1r = w[wP + k]; 1231 | wd1i = w[wP + k + 1]; 1232 | wd3r = w[wP + k + 2]; 1233 | wd3i = -w[wP + k + 3]; 1234 | j1 = j + m; 1235 | j2 = j1 + m; 1236 | j3 = j2 + m; 1237 | x0r = a[j] + a[j2]; 1238 | x0i = a[j + 1] + a[j2 + 1]; 1239 | x1r = a[j] - a[j2]; 1240 | x1i = a[j + 1] - a[j2 + 1]; 1241 | y0r = a[j + 2] + a[j2 + 2]; 1242 | y0i = a[j + 3] + a[j2 + 3]; 1243 | y1r = a[j + 2] - a[j2 + 2]; 1244 | y1i = a[j + 3] - a[j2 + 3]; 1245 | x2r = a[j1] + a[j3]; 1246 | x2i = a[j1 + 1] + a[j3 + 1]; 1247 | x3r = a[j1] - a[j3]; 1248 | x3i = a[j1 + 1] - a[j3 + 1]; 1249 | y2r = a[j1 + 2] + a[j3 + 2]; 1250 | y2i = a[j1 + 3] + a[j3 + 3]; 1251 | y3r = a[j1 + 2] - a[j3 + 2]; 1252 | y3i = a[j1 + 3] - a[j3 + 3]; 1253 | a[j] = x0r + x2r; 1254 | a[j + 1] = x0i + x2i; 1255 | a[j + 2] = y0r + y2r; 1256 | a[j + 3] = y0i + y2i; 1257 | a[j1] = x0r - x2r; 1258 | a[j1 + 1] = x0i - x2i; 1259 | a[j1 + 2] = y0r - y2r; 1260 | a[j1 + 3] = y0i - y2i; 1261 | x0r = x1r - x3i; 1262 | x0i = x1i + x3r; 1263 | a[j2] = wk1r * x0r - wk1i * x0i; 1264 | a[j2 + 1] = wk1r * x0i + wk1i * x0r; 1265 | x0r = y1r - y3i; 1266 | x0i = y1i + y3r; 1267 | a[j2 + 2] = wd1r * x0r - wd1i * x0i; 1268 | a[j2 + 3] = wd1r * x0i + wd1i * x0r; 1269 | x0r = x1r + x3i; 1270 | x0i = x1i - x3r; 1271 | a[j3] = wk3r * x0r + wk3i * x0i; 1272 | a[j3 + 1] = wk3r * x0i - wk3i * x0r; 1273 | x0r = y1r + y3i; 1274 | x0i = y1i - y3r; 1275 | a[j3 + 2] = wd3r * x0r + wd3i * x0i; 1276 | a[j3 + 3] = wd3r * x0i - wd3i * x0r; 1277 | j0 = m - j; 1278 | j1 = j0 + m; 1279 | j2 = j1 + m; 1280 | j3 = j2 + m; 1281 | x0r = a[j0] + a[j2]; 1282 | x0i = a[j0 + 1] + a[j2 + 1]; 1283 | x1r = a[j0] - a[j2]; 1284 | x1i = a[j0 + 1] - a[j2 + 1]; 1285 | y0r = a[j0 - 2] + a[j2 - 2]; 1286 | y0i = a[j0 - 1] + a[j2 - 1]; 1287 | y1r = a[j0 - 2] - a[j2 - 2]; 1288 | y1i = a[j0 - 1] - a[j2 - 1]; 1289 | x2r = a[j1] + a[j3]; 1290 | x2i = a[j1 + 1] + a[j3 + 1]; 1291 | x3r = a[j1] - a[j3]; 1292 | x3i = a[j1 + 1] - a[j3 + 1]; 1293 | y2r = a[j1 - 2] + a[j3 - 2]; 1294 | y2i = a[j1 - 1] + a[j3 - 1]; 1295 | y3r = a[j1 - 2] - a[j3 - 2]; 1296 | y3i = a[j1 - 1] - a[j3 - 1]; 1297 | a[j0] = x0r + x2r; 1298 | a[j0 + 1] = x0i + x2i; 1299 | a[j0 - 2] = y0r + y2r; 1300 | a[j0 - 1] = y0i + y2i; 1301 | a[j1] = x0r - x2r; 1302 | a[j1 + 1] = x0i - x2i; 1303 | a[j1 - 2] = y0r - y2r; 1304 | a[j1 - 1] = y0i - y2i; 1305 | x0r = x1r - x3i; 1306 | x0i = x1i + x3r; 1307 | a[j2] = wk1i * x0r - wk1r * x0i; 1308 | a[j2 + 1] = wk1i * x0i + wk1r * x0r; 1309 | x0r = y1r - y3i; 1310 | x0i = y1i + y3r; 1311 | a[j2 - 2] = wd1i * x0r - wd1r * x0i; 1312 | a[j2 - 1] = wd1i * x0i + wd1r * x0r; 1313 | x0r = x1r + x3i; 1314 | x0i = x1i - x3r; 1315 | a[j3] = wk3i * x0r + wk3r * x0i; 1316 | a[j3 + 1] = wk3i * x0i - wk3r * x0r; 1317 | x0r = y1r + y3i; 1318 | x0i = y1i - y3r; 1319 | a[j3 - 2] = wd3i * x0r + wd3r * x0i; 1320 | a[j3 - 1] = wd3i * x0i - wd3r * x0r; 1321 | } 1322 | wk1r = csc1 * (wd1r + wn4r); 1323 | wk1i = csc1 * (wd1i + wn4r); 1324 | wk3r = csc3 * (wd3r - wn4r); 1325 | wk3i = csc3 * (wd3i - wn4r); 1326 | j0 = mh; 1327 | j1 = j0 + m; 1328 | j2 = j1 + m; 1329 | j3 = j2 + m; 1330 | x0r = a[j0 - 2] + a[j2 - 2]; 1331 | x0i = a[j0 - 1] + a[j2 - 1]; 1332 | x1r = a[j0 - 2] - a[j2 - 2]; 1333 | x1i = a[j0 - 1] - a[j2 - 1]; 1334 | x2r = a[j1 - 2] + a[j3 - 2]; 1335 | x2i = a[j1 - 1] + a[j3 - 1]; 1336 | x3r = a[j1 - 2] - a[j3 - 2]; 1337 | x3i = a[j1 - 1] - a[j3 - 1]; 1338 | a[j0 - 2] = x0r + x2r; 1339 | a[j0 - 1] = x0i + x2i; 1340 | a[j1 - 2] = x0r - x2r; 1341 | a[j1 - 1] = x0i - x2i; 1342 | x0r = x1r - x3i; 1343 | x0i = x1i + x3r; 1344 | a[j2 - 2] = wk1r * x0r - wk1i * x0i; 1345 | a[j2 - 1] = wk1r * x0i + wk1i * x0r; 1346 | x0r = x1r + x3i; 1347 | x0i = x1i - x3r; 1348 | a[j3 - 2] = wk3r * x0r + wk3i * x0i; 1349 | a[j3 - 1] = wk3r * x0i - wk3i * x0r; 1350 | x0r = a[j0] + a[j2]; 1351 | x0i = a[j0 + 1] + a[j2 + 1]; 1352 | x1r = a[j0] - a[j2]; 1353 | x1i = a[j0 + 1] - a[j2 + 1]; 1354 | x2r = a[j1] + a[j3]; 1355 | x2i = a[j1 + 1] + a[j3 + 1]; 1356 | x3r = a[j1] - a[j3]; 1357 | x3i = a[j1 + 1] - a[j3 + 1]; 1358 | a[j0] = x0r + x2r; 1359 | a[j0 + 1] = x0i + x2i; 1360 | a[j1] = x0r - x2r; 1361 | a[j1 + 1] = x0i - x2i; 1362 | x0r = x1r - x3i; 1363 | x0i = x1i + x3r; 1364 | a[j2] = wn4r * (x0r - x0i); 1365 | a[j2 + 1] = wn4r * (x0i + x0r); 1366 | x0r = x1r + x3i; 1367 | x0i = x1i - x3r; 1368 | a[j3] = -wn4r * (x0r + x0i); 1369 | a[j3 + 1] = -wn4r * (x0i - x0r); 1370 | x0r = a[j0 + 2] + a[j2 + 2]; 1371 | x0i = a[j0 + 3] + a[j2 + 3]; 1372 | x1r = a[j0 + 2] - a[j2 + 2]; 1373 | x1i = a[j0 + 3] - a[j2 + 3]; 1374 | x2r = a[j1 + 2] + a[j3 + 2]; 1375 | x2i = a[j1 + 3] + a[j3 + 3]; 1376 | x3r = a[j1 + 2] - a[j3 + 2]; 1377 | x3i = a[j1 + 3] - a[j3 + 3]; 1378 | a[j0 + 2] = x0r + x2r; 1379 | a[j0 + 3] = x0i + x2i; 1380 | a[j1 + 2] = x0r - x2r; 1381 | a[j1 + 3] = x0i - x2i; 1382 | x0r = x1r - x3i; 1383 | x0i = x1i + x3r; 1384 | a[j2 + 2] = wk1i * x0r - wk1r * x0i; 1385 | a[j2 + 3] = wk1i * x0i + wk1r * x0r; 1386 | x0r = x1r + x3i; 1387 | x0i = x1i - x3r; 1388 | a[j3 + 2] = wk3i * x0r + wk3r * x0i; 1389 | a[j3 + 3] = wk3i * x0i - wk3r * x0r; 1390 | } 1391 | 1392 | /** 1393 | * 3rd 1394 | * @see #cftbsub(int, double[], int[], int, int, double[]) 1395 | */ 1396 | private final void cftb1st(int n, double[] a, double[] w, int wP) { 1397 | int j, j0, j1, j2, j3, k, m, mh; 1398 | double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i; 1399 | double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i; 1400 | 1401 | mh = n >> 3; 1402 | m = 2 * mh; 1403 | j1 = m; 1404 | j2 = j1 + m; 1405 | j3 = j2 + m; 1406 | x0r = a[0] + a[j2]; 1407 | x0i = -a[1] - a[j2 + 1]; 1408 | x1r = a[0] - a[j2]; 1409 | x1i = -a[1] + a[j2 + 1]; 1410 | x2r = a[j1] + a[j3]; 1411 | x2i = a[j1 + 1] + a[j3 + 1]; 1412 | x3r = a[j1] - a[j3]; 1413 | x3i = a[j1 + 1] - a[j3 + 1]; 1414 | a[0] = x0r + x2r; 1415 | a[1] = x0i - x2i; 1416 | a[j1] = x0r - x2r; 1417 | a[j1 + 1] = x0i + x2i; 1418 | a[j2] = x1r + x3i; 1419 | a[j2 + 1] = x1i + x3r; 1420 | a[j3] = x1r - x3i; 1421 | a[j3 + 1] = x1i - x3r; 1422 | wn4r = w[wP + 1]; 1423 | csc1 = w[wP + 2]; 1424 | csc3 = w[wP + 3]; 1425 | wd1r = 1; 1426 | wd1i = 0; 1427 | wd3r = 1; 1428 | wd3i = 0; 1429 | k = 0; 1430 | for (j = 2; j < mh - 2; j += 4) { 1431 | k += 4; 1432 | wk1r = csc1 * (wd1r + w[wP + k]); 1433 | wk1i = csc1 * (wd1i + w[wP + k + 1]); 1434 | wk3r = csc3 * (wd3r + w[wP + k + 2]); 1435 | wk3i = csc3 * (wd3i - w[wP + k + 3]); 1436 | wd1r = w[wP + k]; 1437 | wd1i = w[wP + k + 1]; 1438 | wd3r = w[wP + k + 2]; 1439 | wd3i = -w[wP + k + 3]; 1440 | j1 = j + m; 1441 | j2 = j1 + m; 1442 | j3 = j2 + m; 1443 | x0r = a[j] + a[j2]; 1444 | x0i = -a[j + 1] - a[j2 + 1]; 1445 | x1r = a[j] - a[j2]; 1446 | x1i = -a[j + 1] + a[j2 + 1]; 1447 | y0r = a[j + 2] + a[j2 + 2]; 1448 | y0i = -a[j + 3] - a[j2 + 3]; 1449 | y1r = a[j + 2] - a[j2 + 2]; 1450 | y1i = -a[j + 3] + a[j2 + 3]; 1451 | x2r = a[j1] + a[j3]; 1452 | x2i = a[j1 + 1] + a[j3 + 1]; 1453 | x3r = a[j1] - a[j3]; 1454 | x3i = a[j1 + 1] - a[j3 + 1]; 1455 | y2r = a[j1 + 2] + a[j3 + 2]; 1456 | y2i = a[j1 + 3] + a[j3 + 3]; 1457 | y3r = a[j1 + 2] - a[j3 + 2]; 1458 | y3i = a[j1 + 3] - a[j3 + 3]; 1459 | a[j] = x0r + x2r; 1460 | a[j + 1] = x0i - x2i; 1461 | a[j + 2] = y0r + y2r; 1462 | a[j + 3] = y0i - y2i; 1463 | a[j1] = x0r - x2r; 1464 | a[j1 + 1] = x0i + x2i; 1465 | a[j1 + 2] = y0r - y2r; 1466 | a[j1 + 3] = y0i + y2i; 1467 | x0r = x1r + x3i; 1468 | x0i = x1i + x3r; 1469 | a[j2] = wk1r * x0r - wk1i * x0i; 1470 | a[j2 + 1] = wk1r * x0i + wk1i * x0r; 1471 | x0r = y1r + y3i; 1472 | x0i = y1i + y3r; 1473 | a[j2 + 2] = wd1r * x0r - wd1i * x0i; 1474 | a[j2 + 3] = wd1r * x0i + wd1i * x0r; 1475 | x0r = x1r - x3i; 1476 | x0i = x1i - x3r; 1477 | a[j3] = wk3r * x0r + wk3i * x0i; 1478 | a[j3 + 1] = wk3r * x0i - wk3i * x0r; 1479 | x0r = y1r - y3i; 1480 | x0i = y1i - y3r; 1481 | a[j3 + 2] = wd3r * x0r + wd3i * x0i; 1482 | a[j3 + 3] = wd3r * x0i - wd3i * x0r; 1483 | j0 = m - j; 1484 | j1 = j0 + m; 1485 | j2 = j1 + m; 1486 | j3 = j2 + m; 1487 | x0r = a[j0] + a[j2]; 1488 | x0i = -a[j0 + 1] - a[j2 + 1]; 1489 | x1r = a[j0] - a[j2]; 1490 | x1i = -a[j0 + 1] + a[j2 + 1]; 1491 | y0r = a[j0 - 2] + a[j2 - 2]; 1492 | y0i = -a[j0 - 1] - a[j2 - 1]; 1493 | y1r = a[j0 - 2] - a[j2 - 2]; 1494 | y1i = -a[j0 - 1] + a[j2 - 1]; 1495 | x2r = a[j1] + a[j3]; 1496 | x2i = a[j1 + 1] + a[j3 + 1]; 1497 | x3r = a[j1] - a[j3]; 1498 | x3i = a[j1 + 1] - a[j3 + 1]; 1499 | y2r = a[j1 - 2] + a[j3 - 2]; 1500 | y2i = a[j1 - 1] + a[j3 - 1]; 1501 | y3r = a[j1 - 2] - a[j3 - 2]; 1502 | y3i = a[j1 - 1] - a[j3 - 1]; 1503 | a[j0] = x0r + x2r; 1504 | a[j0 + 1] = x0i - x2i; 1505 | a[j0 - 2] = y0r + y2r; 1506 | a[j0 - 1] = y0i - y2i; 1507 | a[j1] = x0r - x2r; 1508 | a[j1 + 1] = x0i + x2i; 1509 | a[j1 - 2] = y0r - y2r; 1510 | a[j1 - 1] = y0i + y2i; 1511 | x0r = x1r + x3i; 1512 | x0i = x1i + x3r; 1513 | a[j2] = wk1i * x0r - wk1r * x0i; 1514 | a[j2 + 1] = wk1i * x0i + wk1r * x0r; 1515 | x0r = y1r + y3i; 1516 | x0i = y1i + y3r; 1517 | a[j2 - 2] = wd1i * x0r - wd1r * x0i; 1518 | a[j2 - 1] = wd1i * x0i + wd1r * x0r; 1519 | x0r = x1r - x3i; 1520 | x0i = x1i - x3r; 1521 | a[j3] = wk3i * x0r + wk3r * x0i; 1522 | a[j3 + 1] = wk3i * x0i - wk3r * x0r; 1523 | x0r = y1r - y3i; 1524 | x0i = y1i - y3r; 1525 | a[j3 - 2] = wd3i * x0r + wd3r * x0i; 1526 | a[j3 - 1] = wd3i * x0i - wd3r * x0r; 1527 | } 1528 | wk1r = csc1 * (wd1r + wn4r); 1529 | wk1i = csc1 * (wd1i + wn4r); 1530 | wk3r = csc3 * (wd3r - wn4r); 1531 | wk3i = csc3 * (wd3i - wn4r); 1532 | j0 = mh; 1533 | j1 = j0 + m; 1534 | j2 = j1 + m; 1535 | j3 = j2 + m; 1536 | x0r = a[j0 - 2] + a[j2 - 2]; 1537 | x0i = -a[j0 - 1] - a[j2 - 1]; 1538 | x1r = a[j0 - 2] - a[j2 - 2]; 1539 | x1i = -a[j0 - 1] + a[j2 - 1]; 1540 | x2r = a[j1 - 2] + a[j3 - 2]; 1541 | x2i = a[j1 - 1] + a[j3 - 1]; 1542 | x3r = a[j1 - 2] - a[j3 - 2]; 1543 | x3i = a[j1 - 1] - a[j3 - 1]; 1544 | a[j0 - 2] = x0r + x2r; 1545 | a[j0 - 1] = x0i - x2i; 1546 | a[j1 - 2] = x0r - x2r; 1547 | a[j1 - 1] = x0i + x2i; 1548 | x0r = x1r + x3i; 1549 | x0i = x1i + x3r; 1550 | a[j2 - 2] = wk1r * x0r - wk1i * x0i; 1551 | a[j2 - 1] = wk1r * x0i + wk1i * x0r; 1552 | x0r = x1r - x3i; 1553 | x0i = x1i - x3r; 1554 | a[j3 - 2] = wk3r * x0r + wk3i * x0i; 1555 | a[j3 - 1] = wk3r * x0i - wk3i * x0r; 1556 | x0r = a[j0] + a[j2]; 1557 | x0i = -a[j0 + 1] - a[j2 + 1]; 1558 | x1r = a[j0] - a[j2]; 1559 | x1i = -a[j0 + 1] + a[j2 + 1]; 1560 | x2r = a[j1] + a[j3]; 1561 | x2i = a[j1 + 1] + a[j3 + 1]; 1562 | x3r = a[j1] - a[j3]; 1563 | x3i = a[j1 + 1] - a[j3 + 1]; 1564 | a[j0] = x0r + x2r; 1565 | a[j0 + 1] = x0i - x2i; 1566 | a[j1] = x0r - x2r; 1567 | a[j1 + 1] = x0i + x2i; 1568 | x0r = x1r + x3i; 1569 | x0i = x1i + x3r; 1570 | a[j2] = wn4r * (x0r - x0i); 1571 | a[j2 + 1] = wn4r * (x0i + x0r); 1572 | x0r = x1r - x3i; 1573 | x0i = x1i - x3r; 1574 | a[j3] = -wn4r * (x0r + x0i); 1575 | a[j3 + 1] = -wn4r * (x0i - x0r); 1576 | x0r = a[j0 + 2] + a[j2 + 2]; 1577 | x0i = -a[j0 + 3] - a[j2 + 3]; 1578 | x1r = a[j0 + 2] - a[j2 + 2]; 1579 | x1i = -a[j0 + 3] + a[j2 + 3]; 1580 | x2r = a[j1 + 2] + a[j3 + 2]; 1581 | x2i = a[j1 + 3] + a[j3 + 3]; 1582 | x3r = a[j1 + 2] - a[j3 + 2]; 1583 | x3i = a[j1 + 3] - a[j3 + 3]; 1584 | a[j0 + 2] = x0r + x2r; 1585 | a[j0 + 3] = x0i - x2i; 1586 | a[j1 + 2] = x0r - x2r; 1587 | a[j1 + 3] = x0i + x2i; 1588 | x0r = x1r + x3i; 1589 | x0i = x1i + x3r; 1590 | a[j2 + 2] = wk1i * x0r - wk1r * x0i; 1591 | a[j2 + 3] = wk1i * x0i + wk1r * x0r; 1592 | x0r = x1r - x3i; 1593 | x0i = x1i - x3r; 1594 | a[j3 + 2] = wk3i * x0r + wk3r * x0i; 1595 | a[j3 + 3] = wk3i * x0i - wk3r * x0r; 1596 | } 1597 | 1598 | /** */ 1599 | private void cftrec1(int n, double[] a, int aP, int nw, double[] w) { 1600 | int m; 1601 | 1602 | m = n >> 2; 1603 | cftmdl1(n, a, aP, w, nw - 2 * m); 1604 | if (n > CDFT_RECURSIVE_N) { 1605 | cftrec1(m, a, aP, nw, w); 1606 | cftrec2(m, a, aP + m, nw, w); 1607 | cftrec1(m, a, aP + 2 * m, nw, w); 1608 | cftrec1(m, a, aP + 3 * m, nw, w); 1609 | } else { 1610 | cftexp1(n, a, aP, nw, w); 1611 | } 1612 | } 1613 | 1614 | /** */ 1615 | private void cftrec2(int n, double[] a, int aP, int nw, double[] w) { 1616 | int m; 1617 | 1618 | m = n >> 2; 1619 | cftmdl2(n, a, aP, w, nw - n); 1620 | if (n > CDFT_RECURSIVE_N) { 1621 | cftrec1(m, a, aP, nw, w); 1622 | cftrec2(m, a, aP + m, nw, w); 1623 | cftrec1(m, a, aP + 2 * m, nw, w); 1624 | cftrec2(m, a, aP + 3 * m, nw, w); 1625 | } else { 1626 | cftexp2(n, a, aP, nw, w); 1627 | } 1628 | } 1629 | 1630 | /** */ 1631 | private void cftexp1(int n, double[] a, int aP, int nw, double[] w) { 1632 | int j, k, l; 1633 | 1634 | l = n >> 2; 1635 | while (l > 128) { 1636 | for (k = l; k < n; k <<= 2) { 1637 | for (j = k - l; j < n; j += 4 * k) { 1638 | cftmdl1(l, a, aP + j, w, nw - (l >> 1)); 1639 | cftmdl2(l, a, aP + k + j, w, nw - l); 1640 | cftmdl1(l, a, aP + 2 * k + j, w, nw - (l >> 1)); 1641 | } 1642 | } 1643 | cftmdl1(l, a, aP + n - l, w, nw - (l >> 1)); 1644 | l >>= 2; 1645 | } 1646 | for (k = l; k < n; k <<= 2) { 1647 | for (j = k - l; j < n; j += 4 * k) { 1648 | cftmdl1(l, a, aP + j, w, nw - (l >> 1)); 1649 | cftfx41(l, a, aP + j, nw, w); 1650 | cftmdl2(l, a, aP + k + j, w, nw - l); 1651 | cftfx42(l, a, aP + k + j, nw, w); 1652 | cftmdl1(l, a, aP + 2 * k + j, w, nw - (l >> 1)); 1653 | cftfx41(l, a, aP + 2 * k + j, nw, w); 1654 | } 1655 | } 1656 | cftmdl1(l, a, aP + n - l, w, nw - (l >> 1)); 1657 | cftfx41(l, a, aP + n - l, nw, w); 1658 | } 1659 | 1660 | /** */ 1661 | private void cftexp2(int n, double[] a, int aP, int nw, double[] w) { 1662 | int j, k, l, m; 1663 | 1664 | m = n >> 1; 1665 | l = n >> 2; 1666 | while (l > 128) { 1667 | for (k = l; k < m; k <<= 2) { 1668 | for (j = k - l; j < m; j += 2 * k) { 1669 | cftmdl1(l, a, aP + j, w, nw - (l >> 1)); 1670 | cftmdl1(l, a, aP + m + j, w, nw - (l >> 1)); 1671 | } 1672 | for (j = 2 * k - l; j < m; j += 4 * k) { 1673 | cftmdl2(l, a, aP + j, w, nw - l); 1674 | cftmdl2(l, a, aP + m + j, w, nw - l); 1675 | } 1676 | } 1677 | l >>= 2; 1678 | } 1679 | for (k = l; k < m; k <<= 2) { 1680 | for (j = k - l; j < m; j += 2 * k) { 1681 | cftmdl1(l, a, aP + j, w, nw - (l >> 1)); 1682 | cftfx41(l, a, aP + j, nw, w); 1683 | cftmdl1(l, a, aP + m + j, w, nw - (l >> 1)); 1684 | cftfx41(l, a, aP + m + j, nw, w); 1685 | } 1686 | for (j = 2 * k - l; j < m; j += 4 * k) { 1687 | cftmdl2(l, a, aP + j, w, nw - l); 1688 | cftfx42(l, a, aP + j, nw, w); 1689 | cftmdl2(l, a, aP + m + j, w, nw - l); 1690 | cftfx42(l, a, aP + m + j, nw, w); 1691 | } 1692 | } 1693 | } 1694 | 1695 | /** */ 1696 | private final void cftmdl1(int n, double[] a, int aP, double[] w, int wP) { 1697 | int j, j0, j1, j2, j3, k, m, mh; 1698 | double wn4r, wk1r, wk1i, wk3r, wk3i; 1699 | double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; 1700 | 1701 | mh = n >> 3; 1702 | m = 2 * mh; 1703 | j1 = m; 1704 | j2 = j1 + m; 1705 | j3 = j2 + m; 1706 | x0r = a[aP + 0] + a[aP + j2]; 1707 | x0i = a[aP + 1] + a[aP + j2 + 1]; 1708 | x1r = a[aP + 0] - a[aP + j2]; 1709 | x1i = a[aP + 1] - a[aP + j2 + 1]; 1710 | x2r = a[aP + j1] + a[aP + j3]; 1711 | x2i = a[aP + j1 + 1] + a[aP + j3 + 1]; 1712 | x3r = a[aP + j1] - a[aP + j3]; 1713 | x3i = a[aP + j1 + 1] - a[aP + j3 + 1]; 1714 | a[aP + 0] = x0r + x2r; 1715 | a[aP + 1] = x0i + x2i; 1716 | a[aP + j1] = x0r - x2r; 1717 | a[aP + j1 + 1] = x0i - x2i; 1718 | a[aP + j2] = x1r - x3i; 1719 | a[aP + j2 + 1] = x1i + x3r; 1720 | a[aP + j3] = x1r + x3i; 1721 | a[aP + j3 + 1] = x1i - x3r; 1722 | wn4r = w[wP + 1]; 1723 | k = 0; 1724 | for (j = 2; j < mh; j += 2) { 1725 | k += 4; 1726 | wk1r = w[wP + k]; 1727 | wk1i = w[wP + k + 1]; 1728 | wk3r = w[wP + k + 2]; 1729 | wk3i = -w[wP + k + 3]; 1730 | j1 = j + m; 1731 | j2 = j1 + m; 1732 | j3 = j2 + m; 1733 | x0r = a[aP + j] + a[aP + j2]; 1734 | x0i = a[aP + j + 1] + a[aP + j2 + 1]; 1735 | x1r = a[aP + j] - a[aP + j2]; 1736 | x1i = a[aP + j + 1] - a[aP + j2 + 1]; 1737 | x2r = a[aP + j1] + a[aP + j3]; 1738 | x2i = a[aP + j1 + 1] + a[aP + j3 + 1]; 1739 | x3r = a[aP + j1] - a[aP + j3]; 1740 | x3i = a[aP + j1 + 1] - a[aP + j3 + 1]; 1741 | a[aP + j] = x0r + x2r; 1742 | a[aP + j + 1] = x0i + x2i; 1743 | a[aP + j1] = x0r - x2r; 1744 | a[aP + j1 + 1] = x0i - x2i; 1745 | x0r = x1r - x3i; 1746 | x0i = x1i + x3r; 1747 | a[aP + j2] = wk1r * x0r - wk1i * x0i; 1748 | a[aP + j2 + 1] = wk1r * x0i + wk1i * x0r; 1749 | x0r = x1r + x3i; 1750 | x0i = x1i - x3r; 1751 | a[aP + j3] = wk3r * x0r + wk3i * x0i; 1752 | a[aP + j3 + 1] = wk3r * x0i - wk3i * x0r; 1753 | j0 = m - j; 1754 | j1 = j0 + m; 1755 | j2 = j1 + m; 1756 | j3 = j2 + m; 1757 | x0r = a[aP + j0] + a[aP + j2]; 1758 | x0i = a[aP + j0 + 1] + a[aP + j2 + 1]; 1759 | x1r = a[aP + j0] - a[aP + j2]; 1760 | x1i = a[aP + j0 + 1] - a[aP + j2 + 1]; 1761 | x2r = a[aP + j1] + a[aP + j3]; 1762 | x2i = a[aP + j1 + 1] + a[aP + j3 + 1]; 1763 | x3r = a[aP + j1] - a[aP + j3]; 1764 | x3i = a[aP + j1 + 1] - a[aP + j3 + 1]; 1765 | a[aP + j0] = x0r + x2r; 1766 | a[aP + j0 + 1] = x0i + x2i; 1767 | a[aP + j1] = x0r - x2r; 1768 | a[aP + j1 + 1] = x0i - x2i; 1769 | x0r = x1r - x3i; 1770 | x0i = x1i + x3r; 1771 | a[aP + j2] = wk1i * x0r - wk1r * x0i; 1772 | a[aP + j2 + 1] = wk1i * x0i + wk1r * x0r; 1773 | x0r = x1r + x3i; 1774 | x0i = x1i - x3r; 1775 | a[aP + j3] = wk3i * x0r + wk3r * x0i; 1776 | a[aP + j3 + 1] = wk3i * x0i - wk3r * x0r; 1777 | } 1778 | j0 = mh; 1779 | j1 = j0 + m; 1780 | j2 = j1 + m; 1781 | j3 = j2 + m; 1782 | x0r = a[aP + j0] + a[aP + j2]; 1783 | x0i = a[aP + j0 + 1] + a[aP + j2 + 1]; 1784 | x1r = a[aP + j0] - a[aP + j2]; 1785 | x1i = a[aP + j0 + 1] - a[aP + j2 + 1]; 1786 | x2r = a[aP + j1] + a[aP + j3]; 1787 | x2i = a[aP + j1 + 1] + a[aP + j3 + 1]; 1788 | x3r = a[aP + j1] - a[aP + j3]; 1789 | x3i = a[aP + j1 + 1] - a[aP + j3 + 1]; 1790 | a[aP + j0] = x0r + x2r; 1791 | a[aP + j0 + 1] = x0i + x2i; 1792 | a[aP + j1] = x0r - x2r; 1793 | a[aP + j1 + 1] = x0i - x2i; 1794 | x0r = x1r - x3i; 1795 | x0i = x1i + x3r; 1796 | a[aP + j2] = wn4r * (x0r - x0i); 1797 | a[aP + j2 + 1] = wn4r * (x0i + x0r); 1798 | x0r = x1r + x3i; 1799 | x0i = x1i - x3r; 1800 | a[aP + j3] = -wn4r * (x0r + x0i); 1801 | a[aP + j3 + 1] = -wn4r * (x0i - x0r); 1802 | } 1803 | 1804 | /** */ 1805 | private final void cftmdl2(int n, double[] a, int aP, double[] w, int wP) { 1806 | int j, j0, j1, j2, j3, k, kr, m, mh; 1807 | double wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i; 1808 | double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i; 1809 | 1810 | mh = n >> 3; 1811 | m = 2 * mh; 1812 | wn4r = w[wP + 1]; 1813 | j1 = m; 1814 | j2 = j1 + m; 1815 | j3 = j2 + m; 1816 | x0r = a[aP + 0] - a[aP + j2 + 1]; 1817 | x0i = a[aP + 1] + a[aP + j2]; 1818 | x1r = a[aP + 0] + a[aP + j2 + 1]; 1819 | x1i = a[aP + 1] - a[aP + j2]; 1820 | x2r = a[aP + j1] - a[aP + j3 + 1]; 1821 | x2i = a[aP + j1 + 1] + a[aP + j3]; 1822 | x3r = a[aP + j1] + a[aP + j3 + 1]; 1823 | x3i = a[aP + j1 + 1] - a[aP + j3]; 1824 | y0r = wn4r * (x2r - x2i); 1825 | y0i = wn4r * (x2i + x2r); 1826 | a[aP + 0] = x0r + y0r; 1827 | a[aP + 1] = x0i + y0i; 1828 | a[aP + j1] = x0r - y0r; 1829 | a[aP + j1 + 1] = x0i - y0i; 1830 | y0r = wn4r * (x3r - x3i); 1831 | y0i = wn4r * (x3i + x3r); 1832 | a[aP + j2] = x1r - y0i; 1833 | a[aP + j2 + 1] = x1i + y0r; 1834 | a[aP + j3] = x1r + y0i; 1835 | a[aP + j3 + 1] = x1i - y0r; 1836 | k = 0; 1837 | kr = 2 * m; 1838 | for (j = 2; j < mh; j += 2) { 1839 | k += 4; 1840 | wk1r = w[wP + k]; 1841 | wk1i = w[wP + k + 1]; 1842 | wk3r = w[wP + k + 2]; 1843 | wk3i = -w[wP + k + 3]; 1844 | kr -= 4; 1845 | wd1i = w[wP + kr]; 1846 | wd1r = w[wP + kr + 1]; 1847 | wd3i = w[wP + kr + 2]; 1848 | wd3r = -w[wP + kr + 3]; 1849 | j1 = j + m; 1850 | j2 = j1 + m; 1851 | j3 = j2 + m; 1852 | x0r = a[aP + j] - a[aP + j2 + 1]; 1853 | x0i = a[aP + j + 1] + a[aP + j2]; 1854 | x1r = a[aP + j] + a[aP + j2 + 1]; 1855 | x1i = a[aP + j + 1] - a[aP + j2]; 1856 | x2r = a[aP + j1] - a[aP + j3 + 1]; 1857 | x2i = a[aP + j1 + 1] + a[aP + j3]; 1858 | x3r = a[aP + j1] + a[aP + j3 + 1]; 1859 | x3i = a[aP + j1 + 1] - a[aP + j3]; 1860 | y0r = wk1r * x0r - wk1i * x0i; 1861 | y0i = wk1r * x0i + wk1i * x0r; 1862 | y2r = wd1r * x2r - wd1i * x2i; 1863 | y2i = wd1r * x2i + wd1i * x2r; 1864 | a[aP + j] = y0r + y2r; 1865 | a[aP + j + 1] = y0i + y2i; 1866 | a[aP + j1] = y0r - y2r; 1867 | a[aP + j1 + 1] = y0i - y2i; 1868 | y0r = wk3r * x1r + wk3i * x1i; 1869 | y0i = wk3r * x1i - wk3i * x1r; 1870 | y2r = wd3r * x3r + wd3i * x3i; 1871 | y2i = wd3r * x3i - wd3i * x3r; 1872 | a[aP + j2] = y0r + y2r; 1873 | a[aP + j2 + 1] = y0i + y2i; 1874 | a[aP + j3] = y0r - y2r; 1875 | a[aP + j3 + 1] = y0i - y2i; 1876 | j0 = m - j; 1877 | j1 = j0 + m; 1878 | j2 = j1 + m; 1879 | j3 = j2 + m; 1880 | x0r = a[aP + j0] - a[aP + j2 + 1]; 1881 | x0i = a[aP + j0 + 1] + a[aP + j2]; 1882 | x1r = a[aP + j0] + a[aP + j2 + 1]; 1883 | x1i = a[aP + j0 + 1] - a[aP + j2]; 1884 | x2r = a[aP + j1] - a[aP + j3 + 1]; 1885 | x2i = a[aP + j1 + 1] + a[aP + j3]; 1886 | x3r = a[aP + j1] + a[aP + j3 + 1]; 1887 | x3i = a[aP + j1 + 1] - a[aP + j3]; 1888 | y0r = wd1i * x0r - wd1r * x0i; 1889 | y0i = wd1i * x0i + wd1r * x0r; 1890 | y2r = wk1i * x2r - wk1r * x2i; 1891 | y2i = wk1i * x2i + wk1r * x2r; 1892 | a[aP + j0] = y0r + y2r; 1893 | a[aP + j0 + 1] = y0i + y2i; 1894 | a[aP + j1] = y0r - y2r; 1895 | a[aP + j1 + 1] = y0i - y2i; 1896 | y0r = wd3i * x1r + wd3r * x1i; 1897 | y0i = wd3i * x1i - wd3r * x1r; 1898 | y2r = wk3i * x3r + wk3r * x3i; 1899 | y2i = wk3i * x3i - wk3r * x3r; 1900 | a[aP + j2] = y0r + y2r; 1901 | a[aP + j2 + 1] = y0i + y2i; 1902 | a[aP + j3] = y0r - y2r; 1903 | a[aP + j3 + 1] = y0i - y2i; 1904 | } 1905 | wk1r = w[wP + m]; 1906 | wk1i = w[wP + m + 1]; 1907 | j0 = mh; 1908 | j1 = j0 + m; 1909 | j2 = j1 + m; 1910 | j3 = j2 + m; 1911 | x0r = a[aP + j0] - a[aP + j2 + 1]; 1912 | x0i = a[aP + j0 + 1] + a[aP + j2]; 1913 | x1r = a[aP + j0] + a[aP + j2 + 1]; 1914 | x1i = a[aP + j0 + 1] - a[aP + j2]; 1915 | x2r = a[aP + j1] - a[aP + j3 + 1]; 1916 | x2i = a[aP + j1 + 1] + a[aP + j3]; 1917 | x3r = a[aP + j1] + a[aP + j3 + 1]; 1918 | x3i = a[aP + j1 + 1] - a[aP + j3]; 1919 | y0r = wk1r * x0r - wk1i * x0i; 1920 | y0i = wk1r * x0i + wk1i * x0r; 1921 | y2r = wk1i * x2r - wk1r * x2i; 1922 | y2i = wk1i * x2i + wk1r * x2r; 1923 | a[aP + j0] = y0r + y2r; 1924 | a[aP + j0 + 1] = y0i + y2i; 1925 | a[aP + j1] = y0r - y2r; 1926 | a[aP + j1 + 1] = y0i - y2i; 1927 | y0r = wk1i * x1r - wk1r * x1i; 1928 | y0i = wk1i * x1i + wk1r * x1r; 1929 | y2r = wk1r * x3r - wk1i * x3i; 1930 | y2i = wk1r * x3i + wk1i * x3r; 1931 | a[aP + j2] = y0r - y2r; 1932 | a[aP + j2 + 1] = y0i - y2i; 1933 | a[aP + j3] = y0r + y2r; 1934 | a[aP + j3 + 1] = y0i + y2i; 1935 | } 1936 | 1937 | /** */ 1938 | private void cftfx41(int n, double[] a, int aP, int nw, double[] w) { 1939 | if (n == 128) { 1940 | cftf161(a, aP, w, nw - 8); 1941 | cftf162(a, aP + 32, w, nw - 32); 1942 | cftf161(a, aP + 64, w, nw - 8); 1943 | cftf161(a, aP + 96, w, nw - 8); 1944 | } else { 1945 | cftf081(a, aP, w, nw - 16); 1946 | cftf082(a, aP + 16, w, nw - 16); 1947 | cftf081(a, aP + 32, w, nw - 16); 1948 | cftf081(a, aP + 48, w, nw - 16); 1949 | } 1950 | } 1951 | 1952 | /** */ 1953 | private void cftfx42(int n, double[] a, int aP, int nw, double[] w) { 1954 | if (n == 128) { 1955 | cftf161(a, aP, w, nw - 8); 1956 | cftf162(a, aP + 32, w, nw - 32); 1957 | cftf161(a, aP + 64, w, nw - 8); 1958 | cftf162(a, aP + 96, w, nw - 32); 1959 | } else { 1960 | cftf081(a, aP, w, nw - 16); 1961 | cftf082(a, aP + 16, w, nw - 16); 1962 | cftf081(a, aP + 32, w, nw - 16); 1963 | cftf082(a, aP + 48, w, nw - 16); 1964 | } 1965 | } 1966 | 1967 | /** */ 1968 | private void cftf161(double[] a, int aP, double[] w, int wP) { 1969 | double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i, y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i; 1970 | 1971 | wn4r = w[wP + 1]; 1972 | wk1i = wn4r * w[wP + 2]; 1973 | wk1r = wk1i + w[wP + 2]; 1974 | x0r = a[aP + 0] + a[aP + 16]; 1975 | x0i = a[aP + 1] + a[aP + 17]; 1976 | x1r = a[aP + 0] - a[aP + 16]; 1977 | x1i = a[aP + 1] - a[aP + 17]; 1978 | x2r = a[aP + 8] + a[aP + 24]; 1979 | x2i = a[aP + 9] + a[aP + 25]; 1980 | x3r = a[aP + 8] - a[aP + 24]; 1981 | x3i = a[aP + 9] - a[aP + 25]; 1982 | y0r = x0r + x2r; 1983 | y0i = x0i + x2i; 1984 | y4r = x0r - x2r; 1985 | y4i = x0i - x2i; 1986 | y8r = x1r - x3i; 1987 | y8i = x1i + x3r; 1988 | y12r = x1r + x3i; 1989 | y12i = x1i - x3r; 1990 | x0r = a[aP + 2] + a[aP + 18]; 1991 | x0i = a[aP + 3] + a[aP + 19]; 1992 | x1r = a[aP + 2] - a[aP + 18]; 1993 | x1i = a[aP + 3] - a[aP + 19]; 1994 | x2r = a[aP + 10] + a[aP + 26]; 1995 | x2i = a[aP + 11] + a[aP + 27]; 1996 | x3r = a[aP + 10] - a[aP + 26]; 1997 | x3i = a[aP + 11] - a[aP + 27]; 1998 | y1r = x0r + x2r; 1999 | y1i = x0i + x2i; 2000 | y5r = x0r - x2r; 2001 | y5i = x0i - x2i; 2002 | x0r = x1r - x3i; 2003 | x0i = x1i + x3r; 2004 | y9r = wk1r * x0r - wk1i * x0i; 2005 | y9i = wk1r * x0i + wk1i * x0r; 2006 | x0r = x1r + x3i; 2007 | x0i = x1i - x3r; 2008 | y13r = wk1i * x0r - wk1r * x0i; 2009 | y13i = wk1i * x0i + wk1r * x0r; 2010 | x0r = a[aP + 4] + a[aP + 20]; 2011 | x0i = a[aP + 5] + a[aP + 21]; 2012 | x1r = a[aP + 4] - a[aP + 20]; 2013 | x1i = a[aP + 5] - a[aP + 21]; 2014 | x2r = a[aP + 12] + a[aP + 28]; 2015 | x2i = a[aP + 13] + a[aP + 29]; 2016 | x3r = a[aP + 12] - a[aP + 28]; 2017 | x3i = a[aP + 13] - a[aP + 29]; 2018 | y2r = x0r + x2r; 2019 | y2i = x0i + x2i; 2020 | y6r = x0r - x2r; 2021 | y6i = x0i - x2i; 2022 | x0r = x1r - x3i; 2023 | x0i = x1i + x3r; 2024 | y10r = wn4r * (x0r - x0i); 2025 | y10i = wn4r * (x0i + x0r); 2026 | x0r = x1r + x3i; 2027 | x0i = x1i - x3r; 2028 | y14r = wn4r * (x0r + x0i); 2029 | y14i = wn4r * (x0i - x0r); 2030 | x0r = a[aP + 6] + a[aP + 22]; 2031 | x0i = a[aP + 7] + a[aP + 23]; 2032 | x1r = a[aP + 6] - a[aP + 22]; 2033 | x1i = a[aP + 7] - a[aP + 23]; 2034 | x2r = a[aP + 14] + a[aP + 30]; 2035 | x2i = a[aP + 15] + a[aP + 31]; 2036 | x3r = a[aP + 14] - a[aP + 30]; 2037 | x3i = a[aP + 15] - a[aP + 31]; 2038 | y3r = x0r + x2r; 2039 | y3i = x0i + x2i; 2040 | y7r = x0r - x2r; 2041 | y7i = x0i - x2i; 2042 | x0r = x1r - x3i; 2043 | x0i = x1i + x3r; 2044 | y11r = wk1i * x0r - wk1r * x0i; 2045 | y11i = wk1i * x0i + wk1r * x0r; 2046 | x0r = x1r + x3i; 2047 | x0i = x1i - x3r; 2048 | y15r = wk1r * x0r - wk1i * x0i; 2049 | y15i = wk1r * x0i + wk1i * x0r; 2050 | x0r = y12r - y14r; 2051 | x0i = y12i - y14i; 2052 | x1r = y12r + y14r; 2053 | x1i = y12i + y14i; 2054 | x2r = y13r - y15r; 2055 | x2i = y13i - y15i; 2056 | x3r = y13r + y15r; 2057 | x3i = y13i + y15i; 2058 | a[aP + 24] = x0r + x2r; 2059 | a[aP + 25] = x0i + x2i; 2060 | a[aP + 26] = x0r - x2r; 2061 | a[aP + 27] = x0i - x2i; 2062 | a[aP + 28] = x1r - x3i; 2063 | a[aP + 29] = x1i + x3r; 2064 | a[aP + 30] = x1r + x3i; 2065 | a[aP + 31] = x1i - x3r; 2066 | x0r = y8r + y10r; 2067 | x0i = y8i + y10i; 2068 | x1r = y8r - y10r; 2069 | x1i = y8i - y10i; 2070 | x2r = y9r + y11r; 2071 | x2i = y9i + y11i; 2072 | x3r = y9r - y11r; 2073 | x3i = y9i - y11i; 2074 | a[aP + 16] = x0r + x2r; 2075 | a[aP + 17] = x0i + x2i; 2076 | a[aP + 18] = x0r - x2r; 2077 | a[aP + 19] = x0i - x2i; 2078 | a[aP + 20] = x1r - x3i; 2079 | a[aP + 21] = x1i + x3r; 2080 | a[aP + 22] = x1r + x3i; 2081 | a[aP + 23] = x1i - x3r; 2082 | x0r = y5r - y7i; 2083 | x0i = y5i + y7r; 2084 | x2r = wn4r * (x0r - x0i); 2085 | x2i = wn4r * (x0i + x0r); 2086 | x0r = y5r + y7i; 2087 | x0i = y5i - y7r; 2088 | x3r = wn4r * (x0r - x0i); 2089 | x3i = wn4r * (x0i + x0r); 2090 | x0r = y4r - y6i; 2091 | x0i = y4i + y6r; 2092 | x1r = y4r + y6i; 2093 | x1i = y4i - y6r; 2094 | a[aP + 8] = x0r + x2r; 2095 | a[aP + 9] = x0i + x2i; 2096 | a[aP + 10] = x0r - x2r; 2097 | a[aP + 11] = x0i - x2i; 2098 | a[aP + 12] = x1r - x3i; 2099 | a[aP + 13] = x1i + x3r; 2100 | a[aP + 14] = x1r + x3i; 2101 | a[aP + 15] = x1i - x3r; 2102 | x0r = y0r + y2r; 2103 | x0i = y0i + y2i; 2104 | x1r = y0r - y2r; 2105 | x1i = y0i - y2i; 2106 | x2r = y1r + y3r; 2107 | x2i = y1i + y3i; 2108 | x3r = y1r - y3r; 2109 | x3i = y1i - y3i; 2110 | a[aP + 0] = x0r + x2r; 2111 | a[aP + 1] = x0i + x2i; 2112 | a[aP + 2] = x0r - x2r; 2113 | a[aP + 3] = x0i - x2i; 2114 | a[aP + 4] = x1r - x3i; 2115 | a[aP + 5] = x1i + x3r; 2116 | a[aP + 6] = x1r + x3i; 2117 | a[aP + 7] = x1i - x3r; 2118 | } 2119 | 2120 | /** */ 2121 | private void cftf162(double[] a, int aP, double[] w, int wP) { 2122 | double wn4r, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i, x0r, x0i, x1r, x1i, x2r, x2i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i, y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i, y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i; 2123 | 2124 | wn4r = w[wP + 1]; 2125 | wk1r = w[wP + 4]; 2126 | wk1i = w[wP + 5]; 2127 | wk3r = w[wP + 6]; 2128 | wk3i = w[wP + 7]; 2129 | wk2r = w[wP + 8]; 2130 | wk2i = w[wP + 9]; 2131 | x1r = a[aP + 0] - a[aP + 17]; 2132 | x1i = a[aP + 1] + a[aP + 16]; 2133 | x0r = a[aP + 8] - a[aP + 25]; 2134 | x0i = a[aP + 9] + a[aP + 24]; 2135 | x2r = wn4r * (x0r - x0i); 2136 | x2i = wn4r * (x0i + x0r); 2137 | y0r = x1r + x2r; 2138 | y0i = x1i + x2i; 2139 | y4r = x1r - x2r; 2140 | y4i = x1i - x2i; 2141 | x1r = a[aP + 0] + a[aP + 17]; 2142 | x1i = a[aP + 1] - a[aP + 16]; 2143 | x0r = a[aP + 8] + a[aP + 25]; 2144 | x0i = a[aP + 9] - a[aP + 24]; 2145 | x2r = wn4r * (x0r - x0i); 2146 | x2i = wn4r * (x0i + x0r); 2147 | y8r = x1r - x2i; 2148 | y8i = x1i + x2r; 2149 | y12r = x1r + x2i; 2150 | y12i = x1i - x2r; 2151 | x0r = a[aP + 2] - a[aP + 19]; 2152 | x0i = a[aP + 3] + a[aP + 18]; 2153 | x1r = wk1r * x0r - wk1i * x0i; 2154 | x1i = wk1r * x0i + wk1i * x0r; 2155 | x0r = a[aP + 10] - a[aP + 27]; 2156 | x0i = a[aP + 11] + a[aP + 26]; 2157 | x2r = wk3i * x0r - wk3r * x0i; 2158 | x2i = wk3i * x0i + wk3r * x0r; 2159 | y1r = x1r + x2r; 2160 | y1i = x1i + x2i; 2161 | y5r = x1r - x2r; 2162 | y5i = x1i - x2i; 2163 | x0r = a[aP + 2] + a[aP + 19]; 2164 | x0i = a[aP + 3] - a[aP + 18]; 2165 | x1r = wk3r * x0r - wk3i * x0i; 2166 | x1i = wk3r * x0i + wk3i * x0r; 2167 | x0r = a[aP + 10] + a[aP + 27]; 2168 | x0i = a[aP + 11] - a[aP + 26]; 2169 | x2r = wk1r * x0r + wk1i * x0i; 2170 | x2i = wk1r * x0i - wk1i * x0r; 2171 | y9r = x1r - x2r; 2172 | y9i = x1i - x2i; 2173 | y13r = x1r + x2r; 2174 | y13i = x1i + x2i; 2175 | x0r = a[aP + 4] - a[aP + 21]; 2176 | x0i = a[aP + 5] + a[aP + 20]; 2177 | x1r = wk2r * x0r - wk2i * x0i; 2178 | x1i = wk2r * x0i + wk2i * x0r; 2179 | x0r = a[aP + 12] - a[aP + 29]; 2180 | x0i = a[aP + 13] + a[aP + 28]; 2181 | x2r = wk2i * x0r - wk2r * x0i; 2182 | x2i = wk2i * x0i + wk2r * x0r; 2183 | y2r = x1r + x2r; 2184 | y2i = x1i + x2i; 2185 | y6r = x1r - x2r; 2186 | y6i = x1i - x2i; 2187 | x0r = a[aP + 4] + a[aP + 21]; 2188 | x0i = a[aP + 5] - a[aP + 20]; 2189 | x1r = wk2i * x0r - wk2r * x0i; 2190 | x1i = wk2i * x0i + wk2r * x0r; 2191 | x0r = a[aP + 12] + a[aP + 29]; 2192 | x0i = a[aP + 13] - a[aP + 28]; 2193 | x2r = wk2r * x0r - wk2i * x0i; 2194 | x2i = wk2r * x0i + wk2i * x0r; 2195 | y10r = x1r - x2r; 2196 | y10i = x1i - x2i; 2197 | y14r = x1r + x2r; 2198 | y14i = x1i + x2i; 2199 | x0r = a[aP + 6] - a[aP + 23]; 2200 | x0i = a[aP + 7] + a[aP + 22]; 2201 | x1r = wk3r * x0r - wk3i * x0i; 2202 | x1i = wk3r * x0i + wk3i * x0r; 2203 | x0r = a[aP + 14] - a[aP + 31]; 2204 | x0i = a[aP + 15] + a[aP + 30]; 2205 | x2r = wk1i * x0r - wk1r * x0i; 2206 | x2i = wk1i * x0i + wk1r * x0r; 2207 | y3r = x1r + x2r; 2208 | y3i = x1i + x2i; 2209 | y7r = x1r - x2r; 2210 | y7i = x1i - x2i; 2211 | x0r = a[aP + 6] + a[aP + 23]; 2212 | x0i = a[aP + 7] - a[aP + 22]; 2213 | x1r = wk1i * x0r + wk1r * x0i; 2214 | x1i = wk1i * x0i - wk1r * x0r; 2215 | x0r = a[aP + 14] + a[aP + 31]; 2216 | x0i = a[aP + 15] - a[aP + 30]; 2217 | x2r = wk3i * x0r - wk3r * x0i; 2218 | x2i = wk3i * x0i + wk3r * x0r; 2219 | y11r = x1r + x2r; 2220 | y11i = x1i + x2i; 2221 | y15r = x1r - x2r; 2222 | y15i = x1i - x2i; 2223 | x1r = y0r + y2r; 2224 | x1i = y0i + y2i; 2225 | x2r = y1r + y3r; 2226 | x2i = y1i + y3i; 2227 | a[aP + 0] = x1r + x2r; 2228 | a[aP + 1] = x1i + x2i; 2229 | a[aP + 2] = x1r - x2r; 2230 | a[aP + 3] = x1i - x2i; 2231 | x1r = y0r - y2r; 2232 | x1i = y0i - y2i; 2233 | x2r = y1r - y3r; 2234 | x2i = y1i - y3i; 2235 | a[aP + 4] = x1r - x2i; 2236 | a[aP + 5] = x1i + x2r; 2237 | a[aP + 6] = x1r + x2i; 2238 | a[aP + 7] = x1i - x2r; 2239 | x1r = y4r - y6i; 2240 | x1i = y4i + y6r; 2241 | x0r = y5r - y7i; 2242 | x0i = y5i + y7r; 2243 | x2r = wn4r * (x0r - x0i); 2244 | x2i = wn4r * (x0i + x0r); 2245 | a[aP + 8] = x1r + x2r; 2246 | a[aP + 9] = x1i + x2i; 2247 | a[aP + 10] = x1r - x2r; 2248 | a[aP + 11] = x1i - x2i; 2249 | x1r = y4r + y6i; 2250 | x1i = y4i - y6r; 2251 | x0r = y5r + y7i; 2252 | x0i = y5i - y7r; 2253 | x2r = wn4r * (x0r - x0i); 2254 | x2i = wn4r * (x0i + x0r); 2255 | a[aP + 12] = x1r - x2i; 2256 | a[aP + 13] = x1i + x2r; 2257 | a[aP + 14] = x1r + x2i; 2258 | a[aP + 15] = x1i - x2r; 2259 | x1r = y8r + y10r; 2260 | x1i = y8i + y10i; 2261 | x2r = y9r - y11r; 2262 | x2i = y9i - y11i; 2263 | a[aP + 16] = x1r + x2r; 2264 | a[aP + 17] = x1i + x2i; 2265 | a[aP + 18] = x1r - x2r; 2266 | a[aP + 19] = x1i - x2i; 2267 | x1r = y8r - y10r; 2268 | x1i = y8i - y10i; 2269 | x2r = y9r + y11r; 2270 | x2i = y9i + y11i; 2271 | a[aP + 20] = x1r - x2i; 2272 | a[aP + 21] = x1i + x2r; 2273 | a[aP + 22] = x1r + x2i; 2274 | a[aP + 23] = x1i - x2r; 2275 | x1r = y12r - y14i; 2276 | x1i = y12i + y14r; 2277 | x0r = y13r + y15i; 2278 | x0i = y13i - y15r; 2279 | x2r = wn4r * (x0r - x0i); 2280 | x2i = wn4r * (x0i + x0r); 2281 | a[aP + 24] = x1r + x2r; 2282 | a[aP + 25] = x1i + x2i; 2283 | a[aP + 26] = x1r - x2r; 2284 | a[aP + 27] = x1i - x2i; 2285 | x1r = y12r + y14i; 2286 | x1i = y12i - y14r; 2287 | x0r = y13r - y15i; 2288 | x0i = y13i + y15r; 2289 | x2r = wn4r * (x0r - x0i); 2290 | x2i = wn4r * (x0i + x0r); 2291 | a[aP + 28] = x1r - x2i; 2292 | a[aP + 29] = x1i + x2r; 2293 | a[aP + 30] = x1r + x2i; 2294 | a[aP + 31] = x1i - x2r; 2295 | } 2296 | 2297 | /** */ 2298 | private void cftf081(double[] a, int aP, double[] w, int wP) { 2299 | double wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i; 2300 | 2301 | wn4r = w[wP + 1]; 2302 | x0r = a[aP + 0] + a[aP + 8]; 2303 | x0i = a[aP + 1] + a[aP + 9]; 2304 | x1r = a[aP + 0] - a[aP + 8]; 2305 | x1i = a[aP + 1] - a[aP + 9]; 2306 | x2r = a[aP + 4] + a[aP + 12]; 2307 | x2i = a[aP + 5] + a[aP + 13]; 2308 | x3r = a[aP + 4] - a[aP + 12]; 2309 | x3i = a[aP + 5] - a[aP + 13]; 2310 | y0r = x0r + x2r; 2311 | y0i = x0i + x2i; 2312 | y2r = x0r - x2r; 2313 | y2i = x0i - x2i; 2314 | y1r = x1r - x3i; 2315 | y1i = x1i + x3r; 2316 | y3r = x1r + x3i; 2317 | y3i = x1i - x3r; 2318 | x0r = a[aP + 2] + a[aP + 10]; 2319 | x0i = a[aP + 3] + a[aP + 11]; 2320 | x1r = a[aP + 2] - a[aP + 10]; 2321 | x1i = a[aP + 3] - a[aP + 11]; 2322 | x2r = a[aP + 6] + a[aP + 14]; 2323 | x2i = a[aP + 7] + a[aP + 15]; 2324 | x3r = a[aP + 6] - a[aP + 14]; 2325 | x3i = a[aP + 7] - a[aP + 15]; 2326 | y4r = x0r + x2r; 2327 | y4i = x0i + x2i; 2328 | y6r = x0r - x2r; 2329 | y6i = x0i - x2i; 2330 | x0r = x1r - x3i; 2331 | x0i = x1i + x3r; 2332 | x2r = x1r + x3i; 2333 | x2i = x1i - x3r; 2334 | y5r = wn4r * (x0r - x0i); 2335 | y5i = wn4r * (x0r + x0i); 2336 | y7r = wn4r * (x2r - x2i); 2337 | y7i = wn4r * (x2r + x2i); 2338 | a[aP + 8] = y1r + y5r; 2339 | a[aP + 9] = y1i + y5i; 2340 | a[aP + 10] = y1r - y5r; 2341 | a[aP + 11] = y1i - y5i; 2342 | a[aP + 12] = y3r - y7i; 2343 | a[aP + 13] = y3i + y7r; 2344 | a[aP + 14] = y3r + y7i; 2345 | a[aP + 15] = y3i - y7r; 2346 | a[aP + 0] = y0r + y4r; 2347 | a[aP + 1] = y0i + y4i; 2348 | a[aP + 2] = y0r - y4r; 2349 | a[aP + 3] = y0i - y4i; 2350 | a[aP + 4] = y2r - y6i; 2351 | a[aP + 5] = y2i + y6r; 2352 | a[aP + 6] = y2r + y6i; 2353 | a[aP + 7] = y2i - y6r; 2354 | } 2355 | 2356 | /** */ 2357 | private void cftf082(double[] a, int aP, double[] w, int wP) { 2358 | double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i, y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i; 2359 | 2360 | wn4r = w[wP + 1]; 2361 | wk1r = w[wP + 4]; 2362 | wk1i = w[wP + 5]; 2363 | y0r = a[aP + 0] - a[aP + 9]; 2364 | y0i = a[aP + 1] + a[aP + 8]; 2365 | y1r = a[aP + 0] + a[aP + 9]; 2366 | y1i = a[aP + 1] - a[aP + 8]; 2367 | x0r = a[aP + 4] - a[aP + 13]; 2368 | x0i = a[aP + 5] + a[aP + 12]; 2369 | y2r = wn4r * (x0r - x0i); 2370 | y2i = wn4r * (x0i + x0r); 2371 | x0r = a[aP + 4] + a[aP + 13]; 2372 | x0i = a[aP + 5] - a[aP + 12]; 2373 | y3r = wn4r * (x0r - x0i); 2374 | y3i = wn4r * (x0i + x0r); 2375 | x0r = a[aP + 2] - a[aP + 11]; 2376 | x0i = a[aP + 3] + a[aP + 10]; 2377 | y4r = wk1r * x0r - wk1i * x0i; 2378 | y4i = wk1r * x0i + wk1i * x0r; 2379 | x0r = a[aP + 2] + a[aP + 11]; 2380 | x0i = a[aP + 3] - a[aP + 10]; 2381 | y5r = wk1i * x0r - wk1r * x0i; 2382 | y5i = wk1i * x0i + wk1r * x0r; 2383 | x0r = a[aP + 6] - a[aP + 15]; 2384 | x0i = a[aP + 7] + a[aP + 14]; 2385 | y6r = wk1i * x0r - wk1r * x0i; 2386 | y6i = wk1i * x0i + wk1r * x0r; 2387 | x0r = a[aP + 6] + a[aP + 15]; 2388 | x0i = a[aP + 7] - a[aP + 14]; 2389 | y7r = wk1r * x0r - wk1i * x0i; 2390 | y7i = wk1r * x0i + wk1i * x0r; 2391 | x0r = y0r + y2r; 2392 | x0i = y0i + y2i; 2393 | x1r = y4r + y6r; 2394 | x1i = y4i + y6i; 2395 | a[aP + 0] = x0r + x1r; 2396 | a[aP + 1] = x0i + x1i; 2397 | a[aP + 2] = x0r - x1r; 2398 | a[aP + 3] = x0i - x1i; 2399 | x0r = y0r - y2r; 2400 | x0i = y0i - y2i; 2401 | x1r = y4r - y6r; 2402 | x1i = y4i - y6i; 2403 | a[aP + 4] = x0r - x1i; 2404 | a[aP + 5] = x0i + x1r; 2405 | a[aP + 6] = x0r + x1i; 2406 | a[aP + 7] = x0i - x1r; 2407 | x0r = y1r - y3i; 2408 | x0i = y1i + y3r; 2409 | x1r = y5r - y7r; 2410 | x1i = y5i - y7i; 2411 | a[aP + 8] = x0r + x1r; 2412 | a[aP + 9] = x0i + x1i; 2413 | a[aP + 10] = x0r - x1r; 2414 | a[aP + 11] = x0i - x1i; 2415 | x0r = y1r + y3i; 2416 | x0i = y1i - y3r; 2417 | x1r = y5r + y7r; 2418 | x1i = y5i + y7i; 2419 | a[aP + 12] = x0r - x1i; 2420 | a[aP + 13] = x0i + x1r; 2421 | a[aP + 14] = x0r + x1i; 2422 | a[aP + 15] = x0i - x1r; 2423 | } 2424 | 2425 | /** 2426 | * 3rd 2427 | * when n = 8. 2428 | * @see #cftfsub(int, double[], int[], int, int, double[]) 2429 | */ 2430 | private void cftf040(double[] a) { 2431 | double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; 2432 | 2433 | x0r = a[0] + a[4]; 2434 | x0i = a[1] + a[5]; 2435 | x1r = a[0] - a[4]; 2436 | x1i = a[1] - a[5]; 2437 | x2r = a[2] + a[6]; 2438 | x2i = a[3] + a[7]; 2439 | x3r = a[2] - a[6]; 2440 | x3i = a[3] - a[7]; 2441 | a[0] = x0r + x2r; 2442 | a[1] = x0i + x2i; 2443 | a[4] = x0r - x2r; 2444 | a[5] = x0i - x2i; 2445 | a[2] = x1r - x3i; 2446 | a[3] = x1i + x3r; 2447 | a[6] = x1r + x3i; 2448 | a[7] = x1i - x3r; 2449 | } 2450 | 2451 | /** 2452 | * 3rd 2453 | * when n = 8. 2454 | * @see #cftbsub(int, double[], int[], int, int, double[]) 2455 | */ 2456 | private void cftb040(double[] a) { 2457 | double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; 2458 | 2459 | x0r = a[0] + a[4]; 2460 | x0i = a[1] + a[5]; 2461 | x1r = a[0] - a[4]; 2462 | x1i = a[1] - a[5]; 2463 | x2r = a[2] + a[6]; 2464 | x2i = a[3] + a[7]; 2465 | x3r = a[2] - a[6]; 2466 | x3i = a[3] - a[7]; 2467 | a[0] = x0r + x2r; 2468 | a[1] = x0i + x2i; 2469 | a[4] = x0r - x2r; 2470 | a[5] = x0i - x2i; 2471 | a[2] = x1r + x3i; 2472 | a[3] = x1i - x3r; 2473 | a[6] = x1r - x3i; 2474 | a[7] = x1i + x3r; 2475 | } 2476 | 2477 | /** 2478 | * 3rd 2479 | * when n = 4. 2480 | * @see #cftbsub(int, double[], int[], int, int, double[]) 2481 | * @see #cftfsub(int, double[], int[], int, int, double[]) 2482 | */ 2483 | private void cftx020(double[] a) { 2484 | double x0r, x0i; 2485 | 2486 | x0r = a[0] - a[2]; 2487 | x0i = a[1] - a[3]; 2488 | a[0] += a[2]; 2489 | a[1] += a[3]; 2490 | a[2] = x0r; 2491 | a[3] = x0i; 2492 | } 2493 | 2494 | /** 2495 | * 2nd 2496 | * @see #rdft(int, int, double[], int[], double[]) 2497 | * @see #ddct(int, int, double[], int[], double[]) 2498 | * @see #ddst(int, int, double[], int[], double[]) 2499 | * @see #dfst(int, double[], double[], int[], double[]) 2500 | * @see #dfct(int, double[], double[], int[], double[]) 2501 | */ 2502 | private void rftfsub(int n, double[] a, int nc, double[] c, int cP) { 2503 | int j, k, kk, ks, m; 2504 | double wkr, wki, xr, xi, yr, yi; 2505 | 2506 | m = n >> 1; 2507 | ks = 2 * nc / m; 2508 | kk = 0; 2509 | for (j = 2; j < m; j += 2) { 2510 | k = n - j; 2511 | kk += ks; 2512 | wkr = 0.5 - c[cP + nc - kk]; 2513 | wki = c[cP + kk]; 2514 | xr = a[j] - a[k]; 2515 | xi = a[j + 1] + a[k + 1]; 2516 | yr = wkr * xr - wki * xi; 2517 | yi = wkr * xi + wki * xr; 2518 | a[j] -= yr; 2519 | a[j + 1] -= yi; 2520 | a[k] += yr; 2521 | a[k + 1] -= yi; 2522 | } 2523 | } 2524 | 2525 | /** 2526 | * 2nd 2527 | * @see #rdft(int, int, double[], int[], double[]) 2528 | * @see #ddct(int, int, double[], int[], double[]) 2529 | * @see #ddst(int, int, double[], int[], double[]) 2530 | */ 2531 | private void rftbsub(int n, double[] a, int nc, double[] c, int cP) { 2532 | int j, k, kk, ks, m; 2533 | double wkr, wki, xr, xi, yr, yi; 2534 | 2535 | m = n >> 1; 2536 | ks = 2 * nc / m; 2537 | kk = 0; 2538 | for (j = 2; j < m; j += 2) { 2539 | k = n - j; 2540 | kk += ks; 2541 | wkr = 0.5 - c[cP + nc - kk]; 2542 | wki = c[cP + kk]; 2543 | xr = a[j] - a[k]; 2544 | xi = a[j + 1] + a[k + 1]; 2545 | yr = wkr * xr + wki * xi; 2546 | yi = wkr * xi - wki * xr; 2547 | a[j] -= yr; 2548 | a[j + 1] -= yi; 2549 | a[k] += yr; 2550 | a[k + 1] -= yi; 2551 | } 2552 | } 2553 | 2554 | /** 2555 | * 2nd 2556 | * @see #ddct(int, int, double[], int[], double[]) 2557 | * @see #dfct(int, double[], double[], int[], double[]) 2558 | */ 2559 | private void dctsub(int n, double[] a, int nc, double[] c, int cP) { 2560 | int j, k, kk, ks, m; 2561 | double wkr, wki, xr; 2562 | 2563 | m = n >> 1; 2564 | ks = nc / n; 2565 | kk = 0; 2566 | for (j = 1; j < m; j++) { 2567 | k = n - j; 2568 | kk += ks; 2569 | wkr = c[cP + kk] - c[cP + nc - kk]; 2570 | wki = c[cP + kk] + c[cP + nc - kk]; 2571 | xr = wki * a[j] - wkr * a[k]; 2572 | a[j] = wkr * a[j] + wki * a[k]; 2573 | a[k] = xr; 2574 | } 2575 | a[m] *= c[cP + 0]; 2576 | } 2577 | 2578 | /** 2579 | * 2nd 2580 | * @see #ddst(int, int, double[], int[], double[]) 2581 | * @see #dfst(int, double[], double[], int[], double[]) 2582 | */ 2583 | private void dstsub(int n, double[] a, int nc, double[] c, int cP) { 2584 | int j, k, kk, ks, m; 2585 | double wkr, wki, xr; 2586 | 2587 | m = n >> 1; 2588 | ks = nc / n; 2589 | kk = 0; 2590 | for (j = 1; j < m; j++) { 2591 | k = n - j; 2592 | kk += ks; 2593 | wkr = c[cP + kk] - c[cP + nc - kk]; 2594 | wki = c[cP + kk] + c[cP + nc - kk]; 2595 | xr = wki * a[k] - wkr * a[j]; 2596 | a[k] = wkr * a[k] + wki * a[j]; 2597 | a[j] = xr; 2598 | } 2599 | a[m] *= c[cP + 0]; 2600 | } 2601 | } 2602 | 2603 | /* */ 2604 | --------------------------------------------------------------------------------