File: reodft010e-r2hc.c

package info (click to toggle)
fftw3 3.3.8-2
  • links: PTS, VCS
  • area: main
  • in suites: buster
  • size: 28,428 kB
  • sloc: ansic: 259,592; ml: 5,474; sh: 4,442; perl: 1,648; makefile: 1,156; fortran: 110
file content (410 lines) | stat: -rw-r--r-- 11,439 bytes parent folder | download | duplicates (2)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
/*
 * Copyright (c) 2003, 2007-14 Matteo Frigo
 * Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 *
 */


/* Do an R{E,O}DFT{01,10} problem via an R2HC problem, with some
   pre/post-processing ala FFTPACK. */

#include "reodft/reodft.h"

typedef struct {
     solver super;
} S;

typedef struct {
     plan_rdft super;
     plan *cld;
     twid *td;
     INT is, os;
     INT n;
     INT vl;
     INT ivs, ovs;
     rdft_kind kind;
} P;

/* A real-even-01 DFT operates logically on a size-4N array:
                   I 0 -r(I*) -I 0 r(I*),
   where r denotes reversal and * denotes deletion of the 0th element.
   To compute the transform of this, we imagine performing a radix-4
   (real-input) DIF step, which turns the size-4N DFT into 4 size-N
   (contiguous) DFTs, two of which are zero and two of which are
   conjugates.  The non-redundant size-N DFT has halfcomplex input, so
   we can do it with a size-N hc2r transform.  (In order to share
   plans with the re10 (inverse) transform, however, we use the DHT
   trick to re-express the hc2r problem as r2hc.  This has little cost
   since we are already pre- and post-processing the data in {i,n-i}
   order.)  Finally, we have to write out the data in the correct
   order...the two size-N redundant (conjugate) hc2r DFTs correspond
   to the even and odd outputs in O (i.e. the usual interleaved output
   of DIF transforms); since this data has even symmetry, we only
   write the first half of it.

   The real-even-10 DFT is just the reverse of these steps, i.e. a
   radix-4 DIT transform.  There, however, we just use the r2hc
   transform naturally without resorting to the DHT trick.

   A real-odd-01 DFT is very similar, except that the input is
   0 I (rI)* 0 -I -(rI)*.  This format, however, can be transformed
   into precisely the real-even-01 format above by sending I -> rI
   and shifting the array by N.  The former swap is just another
   transformation on the input during preprocessing; the latter
   multiplies the even/odd outputs by i/-i, which combines with
   the factor of -i (to take the imaginary part) to simply flip
   the sign of the odd outputs.  Vice-versa for real-odd-10.

   The FFTPACK source code was very helpful in working this out.
   (They do unnecessary passes over the array, though.)  The same
   algorithm is also described in:

      John Makhoul, "A fast cosine transform in one and two dimensions,"
      IEEE Trans. on Acoust. Speech and Sig. Proc., ASSP-28 (1), 27--34 (1980).

   Note that Numerical Recipes suggests a different algorithm that
   requires more operations and uses trig. functions for both the pre-
   and post-processing passes.
*/

static void apply_re01(const plan *ego_, R *I, R *O)
{
     const P *ego = (const P *) ego_;
     INT is = ego->is, os = ego->os;
     INT i, n = ego->n;
     INT iv, vl = ego->vl;
     INT ivs = ego->ivs, ovs = ego->ovs;
     R *W = ego->td->W;
     R *buf;

     buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);

     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
	  buf[0] = I[0];
	  for (i = 1; i < n - i; ++i) {
	       E a, b, apb, amb, wa, wb;
	       a = I[is * i];
	       b = I[is * (n - i)];
	       apb = a + b;
	       amb = a - b;
	       wa = W[2*i];
	       wb = W[2*i + 1];
	       buf[i] = wa * amb + wb * apb; 
	       buf[n - i] = wa * apb - wb * amb; 
	  }
	  if (i == n - i) {
	       buf[i] = K(2.0) * I[is * i] * W[2*i];
	  }
	  
	  {
	       plan_rdft *cld = (plan_rdft *) ego->cld;
	       cld->apply((plan *) cld, buf, buf);
	  }
	  
	  O[0] = buf[0];
	  for (i = 1; i < n - i; ++i) {
	       E a, b;
	       INT k;
	       a = buf[i];
	       b = buf[n - i];
	       k = i + i;
	       O[os * (k - 1)] = a - b;
	       O[os * k] = a + b;
	  }
	  if (i == n - i) {
	       O[os * (n - 1)] = buf[i];
	  }
     }

     X(ifree)(buf);
}

/* ro01 is same as re01, but with i <-> n - 1 - i in the input and
   the sign of the odd output elements flipped. */
static void apply_ro01(const plan *ego_, R *I, R *O)
{
     const P *ego = (const P *) ego_;
     INT is = ego->is, os = ego->os;
     INT i, n = ego->n;
     INT iv, vl = ego->vl;
     INT ivs = ego->ivs, ovs = ego->ovs;
     R *W = ego->td->W;
     R *buf;

     buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);

     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
	  buf[0] = I[is * (n - 1)];
	  for (i = 1; i < n - i; ++i) {
	       E a, b, apb, amb, wa, wb;
	       a = I[is * (n - 1 - i)];
	       b = I[is * (i - 1)];
	       apb = a + b;
	       amb = a - b;
	       wa = W[2*i];
	       wb = W[2*i+1];
	       buf[i] = wa * amb + wb * apb; 
	       buf[n - i] = wa * apb - wb * amb; 
	  }
	  if (i == n - i) {
	       buf[i] = K(2.0) * I[is * (i - 1)] * W[2*i];
	  }
	  
	  {
	       plan_rdft *cld = (plan_rdft *) ego->cld;
	       cld->apply((plan *) cld, buf, buf);
	  }
	  
	  O[0] = buf[0];
	  for (i = 1; i < n - i; ++i) {
	       E a, b;
	       INT k;
	       a = buf[i];
	       b = buf[n - i];
	       k = i + i;
	       O[os * (k - 1)] = b - a;
	       O[os * k] = a + b;
	  }
	  if (i == n - i) {
	       O[os * (n - 1)] = -buf[i];
	  }
     }

     X(ifree)(buf);
}

static void apply_re10(const plan *ego_, R *I, R *O)
{
     const P *ego = (const P *) ego_;
     INT is = ego->is, os = ego->os;
     INT i, n = ego->n;
     INT iv, vl = ego->vl;
     INT ivs = ego->ivs, ovs = ego->ovs;
     R *W = ego->td->W;
     R *buf;

     buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);

     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
	  buf[0] = I[0];
	  for (i = 1; i < n - i; ++i) {
	       E u, v;
	       INT k = i + i;
	       u = I[is * (k - 1)];
	       v = I[is * k];
	       buf[n - i] = u;
	       buf[i] = v;
	  }
	  if (i == n - i) {
	       buf[i] = I[is * (n - 1)];
	  }
	  
	  {
	       plan_rdft *cld = (plan_rdft *) ego->cld;
	       cld->apply((plan *) cld, buf, buf);
	  }
	  
	  O[0] = K(2.0) * buf[0];
	  for (i = 1; i < n - i; ++i) {
	       E a, b, wa, wb;
	       a = K(2.0) * buf[i];
	       b = K(2.0) * buf[n - i];
	       wa = W[2*i];
	       wb = W[2*i + 1];
	       O[os * i] = wa * a + wb * b;
	       O[os * (n - i)] = wb * a - wa * b;
	  }
	  if (i == n - i) {
	       O[os * i] = K(2.0) * buf[i] * W[2*i];
	  }
     }

     X(ifree)(buf);
}

/* ro10 is same as re10, but with i <-> n - 1 - i in the output and
   the sign of the odd input elements flipped. */
static void apply_ro10(const plan *ego_, R *I, R *O)
{
     const P *ego = (const P *) ego_;
     INT is = ego->is, os = ego->os;
     INT i, n = ego->n;
     INT iv, vl = ego->vl;
     INT ivs = ego->ivs, ovs = ego->ovs;
     R *W = ego->td->W;
     R *buf;

     buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);

     for (iv = 0; iv < vl; ++iv, I += ivs, O += ovs) {
	  buf[0] = I[0];
	  for (i = 1; i < n - i; ++i) {
	       E u, v;
	       INT k = i + i;
	       u = -I[is * (k - 1)];
	       v = I[is * k];
	       buf[n - i] = u;
	       buf[i] = v;
	  }
	  if (i == n - i) {
	       buf[i] = -I[is * (n - 1)];
	  }
	  
	  {
	       plan_rdft *cld = (plan_rdft *) ego->cld;
	       cld->apply((plan *) cld, buf, buf);
	  }
	  
	  O[os * (n - 1)] = K(2.0) * buf[0];
	  for (i = 1; i < n - i; ++i) {
	       E a, b, wa, wb;
	       a = K(2.0) * buf[i];
	       b = K(2.0) * buf[n - i];
	       wa = W[2*i];
	       wb = W[2*i + 1];
	       O[os * (n - 1 - i)] = wa * a + wb * b;
	       O[os * (i - 1)] = wb * a - wa * b;
	  }
	  if (i == n - i) {
	       O[os * (i - 1)] = K(2.0) * buf[i] * W[2*i];
	  }
     }

     X(ifree)(buf);
}

static void awake(plan *ego_, enum wakefulness wakefulness)
{
     P *ego = (P *) ego_;
     static const tw_instr reodft010e_tw[] = {
          { TW_COS, 0, 1 },
          { TW_SIN, 0, 1 },
          { TW_NEXT, 1, 0 }
     };

     X(plan_awake)(ego->cld, wakefulness);

     X(twiddle_awake)(wakefulness, &ego->td, reodft010e_tw, 
		      4*ego->n, 1, ego->n/2+1);
}

static void destroy(plan *ego_)
{
     P *ego = (P *) ego_;
     X(plan_destroy_internal)(ego->cld);
}

static void print(const plan *ego_, printer *p)
{
     const P *ego = (const P *) ego_;
     p->print(p, "(%se-r2hc-%D%v%(%p%))",
	      X(rdft_kind_str)(ego->kind), ego->n, ego->vl, ego->cld);
}

static int applicable0(const solver *ego_, const problem *p_)
{
     const problem_rdft *p = (const problem_rdft *) p_;
     UNUSED(ego_);

     return (1
	     && p->sz->rnk == 1
	     && p->vecsz->rnk <= 1
	     && (p->kind[0] == REDFT01 || p->kind[0] == REDFT10
		 || p->kind[0] == RODFT01 || p->kind[0] == RODFT10)
	  );
}

static int applicable(const solver *ego, const problem *p, const planner *plnr)
{
     return (!NO_SLOWP(plnr) && applicable0(ego, p));
}

static plan *mkplan(const solver *ego_, const problem *p_, planner *plnr)
{
     P *pln;
     const problem_rdft *p;
     plan *cld;
     R *buf;
     INT n;
     opcnt ops;

     static const plan_adt padt = {
	  X(rdft_solve), awake, print, destroy
     };

     if (!applicable(ego_, p_, plnr))
          return (plan *)0;

     p = (const problem_rdft *) p_;

     n = p->sz->dims[0].n;
     buf = (R *) MALLOC(sizeof(R) * n, BUFFERS);

     cld = X(mkplan_d)(plnr, X(mkproblem_rdft_1_d)(X(mktensor_1d)(n, 1, 1),
                                                   X(mktensor_0d)(),
                                                   buf, buf, R2HC));
     X(ifree)(buf);
     if (!cld)
          return (plan *)0;

     switch (p->kind[0]) {
	 case REDFT01: pln = MKPLAN_RDFT(P, &padt, apply_re01); break;
	 case REDFT10: pln = MKPLAN_RDFT(P, &padt, apply_re10); break;
	 case RODFT01: pln = MKPLAN_RDFT(P, &padt, apply_ro01); break;
	 case RODFT10: pln = MKPLAN_RDFT(P, &padt, apply_ro10); break;
	 default: A(0); return (plan*)0;
     }

     pln->n = n;
     pln->is = p->sz->dims[0].is;
     pln->os = p->sz->dims[0].os;
     pln->cld = cld;
     pln->td = 0;
     pln->kind = p->kind[0];
     
     X(tensor_tornk1)(p->vecsz, &pln->vl, &pln->ivs, &pln->ovs);
     
     X(ops_zero)(&ops);
     ops.other = 4 + (n-1)/2 * 10 + (1 - n % 2) * 5;
     if (p->kind[0] == REDFT01 || p->kind[0] == RODFT01) {
	  ops.add = (n-1)/2 * 6;
	  ops.mul = (n-1)/2 * 4 + (1 - n % 2) * 2;
     }
     else { /* 10 transforms */
	  ops.add = (n-1)/2 * 2;
	  ops.mul = 1 + (n-1)/2 * 6 + (1 - n % 2) * 2;
     }
     
     X(ops_zero)(&pln->super.super.ops);
     X(ops_madd2)(pln->vl, &ops, &pln->super.super.ops);
     X(ops_madd2)(pln->vl, &cld->ops, &pln->super.super.ops);

     return &(pln->super.super);
}

/* constructor */
static solver *mksolver(void)
{
     static const solver_adt sadt = { PROBLEM_RDFT, mkplan, 0 };
     S *slv = MKSOLVER(S, &sadt);
     return &(slv->super);
}

void X(reodft010e_r2hc_register)(planner *p)
{
     REGISTER_SOLVER(p, mksolver());
}