rs_tfhe 0.1.1

A high-performance Rust implementation of TFHE (Torus Fully Homomorphic Encryption) with advanced programmable bootstrapping capabilities
Documentation 
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
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641

#include <stdint.h>
#include <cmath>

#include <string>
#include <cassert>
#include <vector>
#include <iostream>
#include <cstdlib>

#ifdef DEBUG_ALL
#include <complex>
#endif

#include "spqlios-fft.h"

using namespace std;

namespace {
#ifdef DEBUG_ALL
    //reverse the bits of i (mod n)
    int32_t rev(int32_t i, int32_t n) {
        int32_t reps=0;
        for (int32_t j=1; j<n; j*=2) {
        reps = 2*reps + (i%2);
        i/=2;
        }
        return reps;
    }

    bool very_close(const complex<double>& a,const complex<double>& b) {
        bool reps = (abs(a-b)<1e-5);
        if (!reps) {
        cerr << "not close: " << a << " vs. " << b << endl;
        }
        return reps;
    }

    bool very_close(const double& a,const double& b) {
        bool reps = (abs(a-b)<1e-5);
        if (!reps) {
        cerr << "not close: " << a << " vs. " << b << endl;
        }
        return reps;
    }
#endif


    typedef struct {
        uint64_t n;
        double *aligned_trig_tables;
        double *aligned_data;
        void *buf;
    } FFT_PRECOMP;

    typedef struct {
        uint64_t n;
        double *aligned_trig_tables;
        double *aligned_data;
        void *buf;
    } IFFT_PRECOMP;

//trig_tables:
//|cos0,cos1,cos2,cos3|sin0,sin1,sin2,sin3|cos4,cos5,cos6,cos7|.... -> n/4
//|cos0,cos2,cos4,cos6|sin0,sin2,sin4,sin6|cos8,cos10,cos12,cos14|.... -> n/4
//...
//|cos0,cos2,cos4,cos6|sin0,sin2,sin4,sin6|cos8,cos10,cos12,cos14|.... -> n/4


//trig_tables:
//|cos0,cos1,cos2,cos3|sin0,sin1,sin2,sin3|cos4,cos5,cos6,cos7|.... -> n/4
//|cos0,cos2,cos4,cos6|sin0,sin2,sin4,sin6|cos8,cos10,cos12,cos14|.... -> n/4
//...
//|cos0,cos2,cos4,cos6|sin0,sin2,sin4,sin6|cos8,cos10,cos12,cos14|.... -> n/4

    inline void dotp4(double * res, const double * a, const double * b) {
        for (int32_t i = 0; i < 4; i++) res[i] = a[i] * b[i];
    }

    inline void add4(double * res, const double * a, const double * b) {
        for (int32_t i = 0; i < 4; i++) res[i] = a[i] + b[i];
    }

    inline void sub4(double * res, const double * a, const double * b) {
        for (int32_t i = 0; i < 4; i++) res[i] = a[i] - b[i];
    }

    inline void copy4(double * res, const double * a) {
        for (int32_t i = 0; i < 4; i++) res[i] = a[i];
    }


    void require(bool condition, const string &message = "[condition]") {
        if (!condition) {
            cerr << "unmet condition: " << condition << endl;
            abort();
        }
    }

    double accurate_cos(int32_t i, int32_t n) { //cos(2pi*i/n)
        i = ((i % n) + n) % n;
        if (i >= 3 * n / 4) return cos(2. * M_PI * (n - i) / double(n));
        if (i >= 2 * n / 4) return -cos(2. * M_PI * (i - n / 2) / double(n));
        if (i >= 1 * n / 4) return -cos(2. * M_PI * (n / 2 - i) / double(n));
        return cos(2. * M_PI * (i) / double(n));
    }

    double accurate_sin(int32_t i, int32_t n) { //sin(2pi*i/n)
        i = ((i % n) + n) % n;
        if (i >= 3 * n / 4) return -sin(2. * M_PI * (n - i) / double(n));
        if (i >= 2 * n / 4) return -sin(2. * M_PI * (i - n / 2) / double(n));
        if (i >= 1 * n / 4) return sin(2. * M_PI * (n / 2 - i) / double(n));
        return sin(2. * M_PI * (i) / double(n));
    }


#ifdef DEBUG_ALL
    //at the beginning of iteration halfnn:
    //   m=n/halfnn
    //   P_{j%m}(omb^i)
    //   for j in [rev(1,m) to rev(3,m)[
    //   and i in [0,halfnn[
    void fft_check(
        int32_t n, int32_t halfnn, int32_t table_offset,
            const double* pre, const double* pim,
        const vector<complex<double> >& p,
        const vector<complex<double> >& powombar
        ) {
            int32_t ns4=n/4;
        cerr << "Checking iteration " << halfnn  << " (offset: "<< (table_offset) << ")" << endl;
        for (int32_t i=0; i<ns4; i++) {
            cout << "i: " << i << "   " << pre[i] << " : " << pim[i] << endl;
        }
        int32_t m = n/halfnn;
        int32_t rev1m = rev(1,m);
        int32_t rev3m = rev(3,m);
        int32_t idex = 0;
        for (int32_t revj=rev1m; revj<rev3m; revj++) {
            int32_t j = rev(revj,m);
            cerr << "check-- j: " << j << "(mod " << m << ")" << endl;
            for (int32_t i=0; i<halfnn; i++) {
            cerr << "check--- i: " << i << endl;
            complex<double> test_cur(pre[idex],pim[idex]);
            //P_sum_[k=j%m] p_k omb^ik-j
            complex<double> pij = 0;
            for (int32_t k=j; k<n; k+=m) {
                if (halfnn==8 && j==1 && i==1) cerr << "pij(" << pij << ")" << "+= p_"<<k<<"("<<p[k]<<") * omb["<<i*(k-j)<<"]("<< powombar[(i*(k-j)) % n] <<")" << endl;
                pij += p[k] * powombar[(i*(k-j)) % n];
            }
            assert(very_close(test_cur,pij));
            idex++;
            }
        }
    }
#endif

}

extern "C" void *new_fft_table(int32_t nn) {
    require(nn >= 16, "n must be >=16");
    require((nn & (nn - 1)) == 0, "n must be a power of 2");
    int32_t n = 2 * nn;
    int32_t ns4 = n / 4;
    FFT_PRECOMP *reps = new FFT_PRECOMP;
    void *buf = malloc(32 + n * 8 + nn * 8);
    uint64_t aligned_addr = (uint64_t(buf) + 31) & 0xFFFFFFFFFFFFFFE0l;
    //assert(((uint64_t)reps)%32==0); //verify alignment
    reps->n = n;
    reps->aligned_trig_tables = (double *) aligned_addr;
    reps->aligned_data = (double *) (aligned_addr + n * 8);
    reps->buf = buf;
    double *ptr = reps->aligned_trig_tables;
    //subsequent iterations
    for (int32_t halfnn = 4; halfnn < ns4; halfnn *= 2) {
        int32_t nn = 2 * halfnn;
        int32_t j = n / nn;
        //cerr << "- b: " << halfnn  << "(offset: " << (ptr-reps->trig_tables) << ", mult: " << j << ")" << endl;
        for (int32_t i = 0; i < halfnn; i += 4) {
            //cerr << "--- i: " << i << endl;
            for (int32_t k = 0; k < 4; k++)
                *(ptr++) = accurate_cos(-j * (i + k), n);
            for (int32_t k = 0; k < 4; k++)
                *(ptr++) = accurate_sin(-j * (i + k), n);
        }
    }
    //last iteration
    for (int32_t i = 0; i < ns4; i += 4) {
        for (int32_t k = 0; k < 4; k++)
            *(ptr++) = accurate_cos(-(i + k), n);
        for (int32_t k = 0; k < 4; k++)
            *(ptr++) = accurate_sin(-(i + k), n);
    }
    return reps;
}
extern "C" double *fft_table_get_buffer(const void *tables) {
    FFT_PRECOMP *reps = (FFT_PRECOMP *) tables;
    return reps->aligned_data;
}
extern "C" double *ifft_table_get_buffer(const void *tables) {
    IFFT_PRECOMP *reps = (IFFT_PRECOMP *) tables;
    return reps->aligned_data;
}

//c has size n/2
extern "C" void fft_model(const void *tables) {
    double tmp0[4];
    double tmp1[4];
    double tmp2[4];
    double tmp3[4];
    FFT_PRECOMP *fft_tables = (FFT_PRECOMP *) tables;
    const int32_t n = fft_tables->n;
    const double *trig_tables = fft_tables->aligned_trig_tables;
    double *c = fft_tables->aligned_data;

    int32_t ns4 = n / 4;
    double *pre = c;     //size n/4
    double *pim = c + ns4; //size n/4

#ifdef DEBUG_ALL
    vector<complex<double> > p; p.resize(n);
    vector<complex<double> > powombar; powombar.resize(n);
    for (int32_t i=0; i<n; i++)
    powombar[i]=complex<double>(accurate_cos(-i,n),accurate_sin(-i,n));
    for (int32_t i=0; i<n; i+=2)
    p[i]=0;
    int32_t rev1n = rev(1,n);
    int32_t rev3n = rev(3,n);
    for (int32_t revi=rev1n; revi<rev3n; revi++) {
    int32_t i = rev(revi,n);
    p[i]=complex<double>(pre[revi-rev1n],pim[revi-rev1n]);
    p[n-i]=conj(p[i]);
    cerr << "p_" << i << " = " << p[i] << endl;
    }
#endif

    //general loop
    //size 2
    {
#ifdef DEBUG_ALL
        int32_t halfnn = 1;
        //int32_t nn = 2;
        int32_t table_offset = 0;
        fft_check(n, halfnn, table_offset, pre, pim, p, powombar);
#endif
        //[1  1]
        //[1 -1]
        //     [1  1]
        //     [1 -1]
        for (int32_t block = 0; block < ns4; block += 4) {
            double *d0 = pre + block;
            double *d1 = pim + block;
            tmp0[0] = d0[0];
            tmp0[1] = d0[0];
            tmp0[2] = d0[2];
            tmp0[3] = d0[2];
            tmp1[0] = d0[1];
            tmp1[1] = -d0[1];
            tmp1[2] = d0[3];
            tmp1[3] = -d0[3];
            add4(d0, tmp0, tmp1);
            tmp0[0] = d1[0];
            tmp0[1] = d1[0];
            tmp0[2] = d1[2];
            tmp0[3] = d1[2];
            tmp1[0] = d1[1];
            tmp1[1] = -d1[1];
            tmp1[2] = d1[3];
            tmp1[3] = -d1[3];
            add4(d1, tmp0, tmp1);
        }
    }


    //size 4
    //[1  0  1  0]
    //[0  1  0 -i]
    //[1  0 -1  0]
    //[0  1  0  i]
    // r0 + r2    i0 + i2
    // r1 + i3    i1 - r3
    // r0 - r2    i0 - i2
    // r1 - i3    i1 + r3
    {
#ifdef DEBUG_ALL
        int32_t halfnn = 2;
        //int32_t nn = 4;
        int32_t table_offset = 0;
        fft_check(n, halfnn, table_offset, pre, pim, p, powombar);
#endif
        for (int32_t block = 0; block < ns4; block += 4) {
            double *re = pre + block;
            double *im = pim + block;
            tmp0[0] = re[0];
            tmp0[1] = re[1];
            tmp0[2] = re[0];
            tmp0[3] = re[1];
            tmp1[0] = re[2];
            tmp1[1] = im[3];
            tmp1[2] = -re[2];
            tmp1[3] = -im[3];
            tmp2[0] = im[0];
            tmp2[1] = im[1];
            tmp2[2] = im[0];
            tmp2[3] = im[1];
            tmp3[0] = im[2];
            tmp3[1] = -re[3];
            tmp3[2] = -im[2];
            tmp3[3] = re[3];
            add4(re, tmp0, tmp1);
            add4(im, tmp2, tmp3);
        }
    }

    //general loop
    const double *cur_tt = trig_tables;
    for (int32_t halfnn = 4; halfnn < ns4; halfnn *= 2) {
        int32_t nn = 2 * halfnn;
#ifdef DEBUG_ALL
        int32_t m = n/halfnn;
        fft_check(n, halfnn, cur_tt-trig_tables, pre, pim, p, powombar);
#endif
        for (int32_t block = 0; block < ns4; block += nn) {
#ifdef DEBUG_ALL
            int32_t j = rev(rev(1,m)+block,m);
            cerr << "-- j: " << j  << "(mod: " << m << ")" << endl;
#endif
            for (int32_t off = 0; off < halfnn; off += 4) {
#ifdef DEBUG_ALL
                cerr << "--- i: " << off << endl;
#endif
                double *re0 = pre + block + off;
                double *im0 = pim + block + off;
                double *re1 = pre + block + halfnn + off;
                double *im1 = pim + block + halfnn + off;
                const double *tcs = cur_tt + 2 * off;
                const double *tsn = tcs + 4;
#ifdef DEBUG_ALL
                assert(very_close(tcs[0],accurate_cos(-(n/nn)*off,n)));
                assert(very_close(tcs[1],accurate_cos(-(n/nn)*(off+1),n)));
                assert(very_close(tcs[2],accurate_cos(-(n/nn)*(off+2),n)));
                assert(very_close(tcs[3],accurate_cos(-(n/nn)*(off+3),n)));
                assert(very_close(tsn[0],accurate_sin(-(n/nn)*off,n)));
                assert(very_close(tsn[1],accurate_sin(-(n/nn)*(off+1),n)));
                assert(very_close(tsn[2],accurate_sin(-(n/nn)*(off+2),n)));
                assert(very_close(tsn[3],accurate_sin(-(n/nn)*(off+3),n)));
#endif
                dotp4(tmp0, re1, tcs); // re*cos
                dotp4(tmp1, re1, tsn); // re*sin
                dotp4(tmp2, im1, tcs); // im*cos
                dotp4(tmp3, im1, tsn); // im*sin
                sub4(tmp0, tmp0, tmp3); // re2
                add4(tmp1, tmp1, tmp2); // im2
                add4(tmp2, re0, tmp0); // re + re
                add4(tmp3, im0, tmp1); // im + im
                sub4(tmp0, re0, tmp0); // re - re
                sub4(tmp1, im0, tmp1); // im - im
                copy4(re0, tmp2);
                copy4(im0, tmp3);
                copy4(re1, tmp0);
                copy4(im1, tmp1);
            }
        }
        cur_tt += nn;
    }

    {
#ifdef DEBUG_ALL
        int32_t halfnn = ns4;
        //int32_t nn = n/2;
        fft_check(n, halfnn, cur_tt-trig_tables, pre, pim, p, powombar);
#endif
    }

    //multiply by omb^j
    for (int32_t j = 0; j < ns4; j += 4) {
        const double *r0 = cur_tt + 2 * j;
        const double *r1 = r0 + 4;
#ifdef DEBUG_ALL
        assert(very_close(r0[0],accurate_cos(-j,n)));
        assert(very_close(r0[1],accurate_cos(-(j+1),n)));
        assert(very_close(r0[2],accurate_cos(-(j+2),n)));
        assert(very_close(r0[3],accurate_cos(-(j+3),n)));
        assert(very_close(r1[0],accurate_sin(-j,n)));
        assert(very_close(r1[1],accurate_sin(-(j+1),n)));
        assert(very_close(r1[2],accurate_sin(-(j+2),n)));
        assert(very_close(r1[3],accurate_sin(-(j+3),n)));
#endif
        //(re*cos-im*sin) + i (im*cos+re*sin)
        double *d0 = pre + j;
        double *d1 = pim + j;
        dotp4(tmp0, d0, r0); //re*cos
        dotp4(tmp1, d1, r0); //im*cos
        dotp4(tmp2, d0, r1); //re*sin
        dotp4(tmp3, d1, r1); //im*sin
        sub4(d0, tmp0, tmp3);
        add4(d1, tmp1, tmp2);
    }
}


extern "C" void *new_ifft_table(int32_t nn) {
    require(nn >= 16, "n must be >=16");
    require((nn & (nn - 1)) == 0, "n must be a power of 2");
    int32_t n = 2 * nn;
    int32_t ns4 = n / 4;
    IFFT_PRECOMP *reps = new IFFT_PRECOMP;
    //assert(((uint64_t)reps)%32==0); //verify alignment
    void *buf = malloc(32 + n * 8 + nn * 8);
    uint64_t aligned_addr = (uint64_t(buf) + 31) & 0xFFFFFFFFFFFFFFE0l;
    //assert(((uint64_t)reps)%32==0); //verify alignment
    reps->n = n;
    reps->aligned_trig_tables = (double *) aligned_addr;
    reps->aligned_data = (double *) (aligned_addr + n * 8);
    reps->buf = buf;
    reps->n = n;
    double *ptr = reps->aligned_trig_tables;
    //first iteration
    for (int32_t j = 0; j < ns4; j += 4) {
        for (int32_t k = 0; k < 4; k++)
            *(ptr++) = accurate_cos(j + k, n);
        for (int32_t k = 0; k < 4; k++)
            *(ptr++) = accurate_sin(j + k, n);
    }
    //subsequent iterations
    for (int32_t nn = ns4; nn >= 8; nn /= 2) {
        int32_t halfnn = nn / 2;
        int32_t j = n / nn;
        //cerr << "- b: " << nn  << "(offset: " << (ptr-reps->trig_tables) << ", mult: " << j << ")" << endl;
        for (int32_t i = 0; i < halfnn; i += 4) {
            //cerr << "--- i: " << i << endl;
            for (int32_t k = 0; k < 4; k++)
                *(ptr++) = accurate_cos(j * (i + k), n);
            for (int32_t k = 0; k < 4; k++)
                *(ptr++) = accurate_sin(j * (i + k), n);
        }
    }
    return reps;
}

namespace {
#ifdef DEBUG_ALL
    void ifft_check(int32_t n, int32_t nn, int32_t table_offset, const double* are, const double* aim, const vector<complex<double> >& a, const vector<complex<double> >& powomega) {
        int32_t ns4=n/4;
        cerr << "Checking iteration " << nn  << " (offset: "<< (table_offset) << ")" << endl;
        for (int32_t i=0; i<ns4; i++) {
        cout << "i: " << i << "   " << are[i] << " : " << aim[i] << endl;
        }
        int32_t m = n/nn;
        int32_t rev1m = rev(1,m);
        int32_t rev3m = rev(3,m);
        int32_t idex = 0;
        for (int32_t revj=rev1m; revj<rev3m; revj++) {
        int32_t j = rev(revj,m);
        cerr << "check-- j: " << j << endl;
        for (int32_t i=0; i<nn; i++) {
            cerr << "check--- i: " << i << "(mod " << nn << ")" << endl;
            complex<double> test_cur(are[idex],aim[idex]);
            //sum_[t=i%nn] a_t omega^jt
            complex<double> pij = 0;
            for (int32_t k=i; k<n; k+=nn)
            pij += a[k] * powomega[(k*j) % n];
            assert(very_close(test_cur,pij));
            idex++;
        }
        }
    }
#endif
}
//c has size n/2
extern "C" void ifft_model(void *tables) {
    double tmp0[4];
    double tmp1[4];
    double tmp2[4];
    double tmp3[4];
    IFFT_PRECOMP *fft_tables = (IFFT_PRECOMP *) tables;
    const int32_t n = fft_tables->n;
    const double *trig_tables = fft_tables->aligned_trig_tables;
    double *c = fft_tables->aligned_data;

#ifdef DEBUG_ALL
    vector<complex<double> > a; a.resize(n);
    vector<complex<double> > powomega; powomega.resize(n);
    for (int32_t i=0; i<n; i++)
    powomega[i]=complex<double>(accurate_cos(i,n),accurate_sin(i,n));
    for (int32_t i=0; i<n/2; i++)
    a[i]=c[i]/2.;
    for (int32_t i=0; i<n/2; i++)
    a[n/2+i]=-c[i]/2.;
#endif


    int32_t ns4 = n / 4;
    double *are = c;    //size n/4
    double *aim = c + ns4; //size n/4

    //multiply by omega^j
    for (int32_t j = 0; j < ns4; j += 4) {
        const double *r0 = trig_tables + 2 * j;
        const double *r1 = r0 + 4;
#ifdef DEBUG_ALL
        assert(very_close(r0[0],accurate_cos(j,n)));
        assert(very_close(r0[1],accurate_cos(j+1,n)));
        assert(very_close(r0[2],accurate_cos(j+2,n)));
        assert(very_close(r0[3],accurate_cos(j+3,n)));
        assert(very_close(r1[0],accurate_sin(j,n)));
        assert(very_close(r1[1],accurate_sin(j+1,n)));
        assert(very_close(r1[2],accurate_sin(j+2,n)));
        assert(very_close(r1[3],accurate_sin(j+3,n)));
#endif
        //(re*cos-im*sin) + i (im*cos+re*sin)
        double *d0 = are + j;
        double *d1 = aim + j;
        dotp4(tmp0, d0, r0); //re*cos
        dotp4(tmp1, d1, r0); //im*cos
        dotp4(tmp2, d0, r1); //re*sin
        dotp4(tmp3, d1, r1); //im*sin
        sub4(d0, tmp0, tmp3);
        add4(d1, tmp1, tmp2);
    }


    //at the beginning of iteration nn
    // a_{j,i} has P_{i%nn}(omega^j) 
    // where j between [rev(1) and rev(3)[
    // and i between [0 and nn[
    const double *cur_tt = trig_tables;
    for (int32_t nn = ns4; nn >= 8; nn /= 2) {
        int32_t halfnn = nn / 2;
        cur_tt += 2 * nn;
#ifdef DEBUG_ALL
        int32_t m = n/nn;
        ifft_check(n, nn, cur_tt-trig_tables, are, aim, a, powomega);
#endif
        for (int32_t block = 0; block < ns4; block += nn) {
#ifdef DEBUG_ALL
            int32_t j = rev(rev(1,m)+block,m);
            cerr << "-- j: " << j  << "(offset: " << (cur_tt-trig_tables) << ")" << endl;
#endif
            for (int32_t off = 0; off < halfnn; off += 4) {
#ifdef DEBUG_ALL
                cerr << "--- i: " << off << endl;
#endif
                double *d00 = are + block + off;
                double *d01 = aim + block + off;
                double *d10 = are + block + halfnn + off;
                double *d11 = aim + block + halfnn + off;
                add4(tmp0, d00, d10); // re + re
                add4(tmp1, d01, d11); // im + im
                sub4(tmp2, d00, d10); // re - re
                sub4(tmp3, d01, d11); // im - im
                copy4(d00, tmp0);
                copy4(d01, tmp1);
                const double *r0 = cur_tt + 2 * off;
                const double *r1 = r0 + 4;
#ifdef NDEBUG
                assert(very_close(r0[0],accurate_cos((ns4/halfnn)*off,n)));
                assert(very_close(r0[1],accurate_cos((ns4/halfnn)*(off+1),n)));
                assert(very_close(r0[2],accurate_cos((ns4/halfnn)*(off+2),n)));
                assert(very_close(r0[3],accurate_cos((ns4/halfnn)*(off+3),n)));
                assert(very_close(r1[0],accurate_sin((ns4/halfnn)*off,n)));
                assert(very_close(r1[1],accurate_sin((ns4/halfnn)*(off+1),n)));
                assert(very_close(r1[2],accurate_sin((ns4/halfnn)*(off+2),n)));
                assert(very_close(r1[3],accurate_sin((ns4/halfnn)*(off+3),n)));
#endif
                dotp4(tmp0, tmp2, r0); //re*cos
                dotp4(tmp1, tmp3, r1); //im*sin
                sub4(d10, tmp0, tmp1);
                dotp4(tmp0, tmp2, r1); //re*sin
                dotp4(tmp1, tmp3, r0); //im*cos
                add4(d11, tmp0, tmp1);
            }
        }
    }

    //size 4
    {
#ifdef DEBUG_ALL
        int32_t nn = 4;
        //int32_t halfnn = 2;
        ifft_check(n, nn, cur_tt-trig_tables, are, aim, a, powomega);
#endif
        for (int32_t block = 0; block < ns4; block += 4) {
            double *d0 = are + block;
            double *d1 = aim + block;
            tmp0[0] = d0[0];
            tmp0[1] = d0[1];
            tmp0[2] = d0[0];
            tmp0[3] = -d1[1];
            tmp1[0] = d0[2];
            tmp1[1] = d0[3];
            tmp1[2] = -d0[2];
            tmp1[3] = d1[3];
            tmp2[0] = d1[0];
            tmp2[1] = d1[1];
            tmp2[2] = d1[0];
            tmp2[3] = d0[1];
            tmp3[0] = d1[2];
            tmp3[1] = d1[3];
            tmp3[2] = -d1[2];
            tmp3[3] = -d0[3];
            add4(d0, tmp0, tmp1);
            add4(d1, tmp2, tmp3);
        }
    }

    //size 2
    {
#ifdef DEBUG_ALL
        int32_t nn = 2;
        //int32_t halfnn = 1;
        ifft_check(n, nn, cur_tt-trig_tables, are, aim, a, powomega);
#endif
        for (int32_t block = 0; block < ns4; block += 4) {
            double *d0 = are + block;
            double *d1 = aim + block;
            tmp0[0] = d0[0];
            tmp0[1] = d0[0];
            tmp0[2] = d0[2];
            tmp0[3] = d0[2];
            tmp1[0] = d0[1];
            tmp1[1] = -d0[1];
            tmp1[2] = d0[3];
            tmp1[3] = -d0[3];
            add4(d0, tmp0, tmp1);
            tmp0[0] = d1[0];
            tmp0[1] = d1[0];
            tmp0[2] = d1[2];
            tmp0[3] = d1[2];
            tmp1[0] = d1[1];
            tmp1[1] = -d1[1];
            tmp1[2] = d1[3];
            tmp1[3] = -d1[3];
            add4(d1, tmp0, tmp1);
        }
    }
    {
#ifdef DEBUG_ALL
        int32_t nn = 1;
        ifft_check(n, nn, cur_tt-trig_tables, are, aim, a, powomega);
#endif
    }
}