File: ulong_extras.h

package info (click to toggle)
flint 2.5.2-19
  • links: PTS, VCS
  • area: main
  • in suites: buster
  • size: 30,308 kB
  • sloc: ansic: 289,367; cpp: 11,210; python: 1,280; sh: 649; makefile: 283
file content (400 lines) | stat: -rw-r--r-- 11,874 bytes parent folder | download | duplicates (5)
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
/*=============================================================================

    This file is part of FLINT.

    FLINT 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.

    FLINT 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 FLINT; if not, write to the Free Software
    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301 USA

=============================================================================*/
/******************************************************************************

    Copyright (C) 2006, 2007, 2008, 2009 William Hart
    Copyright (C) 2008, Peter Shrimpton
    Copyright (C) 2009, Tom Boothby
    Copyright (C) 2010, Fredrik Johansson

******************************************************************************/

#ifndef ULONG_EXTRAS_H
#define ULONG_EXTRAS_H

#ifdef ULONG_EXTRAS_INLINES_C
#define ULONG_EXTRAS_INLINE FLINT_DLL
#else
#define ULONG_EXTRAS_INLINE static __inline__
#endif

#include <gmp.h>
#include "flint.h"

#ifdef __cplusplus
 extern "C" {
#endif

typedef struct pair_s
{
    mp_limb_t x, y;
} n_pair_t;

#define FLINT_MAX_FACTORS_IN_LIMB 15

typedef struct {
   int num;
   int exp[FLINT_MAX_FACTORS_IN_LIMB];
   mp_limb_t p[FLINT_MAX_FACTORS_IN_LIMB];
} n_factor_t;

#define FLINT_ODDPRIME_SMALL_CUTOFF 4096
#define FLINT_NUM_PRIMES_SMALL 172
#define FLINT_PRIMES_SMALL_CUTOFF 1030
#define FLINT_PSEUDOSQUARES_CUTOFF 1000

#define FLINT_FACTOR_TRIAL_PRIMES 3000
/* nth_prime(FLINT_FACTOR_TRIAL_PRIMES) */
#define FLINT_FACTOR_TRIAL_PRIMES_PRIME UWORD(27449)
#define FLINT_FACTOR_TRIAL_CUTOFF (UWORD(27449) * UWORD(27449))

#define FLINT_PRIMES_TAB_DEFAULT_CUTOFF 1000000

#define FLINT_FACTOR_SQUFOF_ITERS 50000
#define FLINT_FACTOR_ONE_LINE_MAX (UWORD(1)<<39)
#define FLINT_FACTOR_ONE_LINE_ITERS 40000

#define FLINT_PRIME_PI_ODD_LOOKUP_CUTOFF 311

#define FLINT_SIEVE_SIZE 65536

#if FLINT64
#define UWORD_MAX_PRIME UWORD(18446744073709551557)
#else
#define UWORD_MAX_PRIME UWORD(4294967291)
#endif

typedef struct
{
    slong small_i;
    slong small_num;
    unsigned int * small_primes;

    mp_limb_t sieve_a;
    mp_limb_t sieve_b;
    slong sieve_i;
    slong sieve_num;
    char * sieve;
}
n_primes_struct;

typedef n_primes_struct n_primes_t[1];

FLINT_DLL void n_primes_init(n_primes_t iter);

FLINT_DLL void n_primes_clear(n_primes_t iter);

FLINT_DLL void n_primes_extend_small(n_primes_t iter, mp_limb_t bound);

FLINT_DLL void n_primes_sieve_range(n_primes_t iter, mp_limb_t a, mp_limb_t b);

FLINT_DLL void n_primes_jump_after(n_primes_t iter, mp_limb_t n);

ULONG_EXTRAS_INLINE mp_limb_t
n_primes_next(n_primes_t iter)
{
    if (iter->small_i < iter->small_num)
        return iter->small_primes[(iter->small_i)++];

    for (;;)
    {
        while (iter->sieve_i < iter->sieve_num)
            if (iter->sieve[iter->sieve_i++] != 0)
                return iter->sieve_a + 2 * (iter->sieve_i - 1);

        if (iter->sieve_b == 0)
            n_primes_jump_after(iter, iter->small_primes[iter->small_num-1]);
        else
            n_primes_jump_after(iter, iter->sieve_b);
    }
}

extern const unsigned int flint_primes_small[];

extern FLINT_TLS_PREFIX mp_limb_t * _flint_primes[FLINT_BITS];
extern FLINT_TLS_PREFIX double * _flint_prime_inverses[FLINT_BITS];
extern FLINT_TLS_PREFIX int _flint_primes_used;

FLINT_DLL void n_compute_primes(ulong num_primes);

FLINT_DLL void n_cleanup_primes(void);

FLINT_DLL const mp_limb_t * n_primes_arr_readonly(ulong n);
FLINT_DLL const double * n_prime_inverses_arr_readonly(ulong n);

FLINT_DLL mp_limb_t n_randlimb(flint_rand_t state);

FLINT_DLL mp_limb_t n_randint(flint_rand_t state, mp_limb_t limit);

FLINT_DLL mp_limb_t n_randbits(flint_rand_t state, unsigned int bits);

FLINT_DLL mp_limb_t n_randtest_bits(flint_rand_t state, int bits);

FLINT_DLL mp_limb_t n_randtest(flint_rand_t state);

FLINT_DLL mp_limb_t n_randtest_not_zero(flint_rand_t state);

FLINT_DLL mp_limb_t n_randprime(flint_rand_t state, ulong bits, int proved);

FLINT_DLL mp_limb_t n_randtest_prime(flint_rand_t state, int proved);

FLINT_DLL mp_limb_t n_pow(mp_limb_t n, ulong exp);

FLINT_DLL mp_limb_t n_flog(mp_limb_t n, mp_limb_t b);

FLINT_DLL mp_limb_t n_clog(mp_limb_t n, mp_limb_t b);

ULONG_EXTRAS_INLINE 
double n_precompute_inverse(mp_limb_t n)
{
   return (double) 1 / (double) n;
}

ULONG_EXTRAS_INLINE
mp_limb_t n_preinvert_limb(mp_limb_t n)
{
   mp_limb_t norm, ninv;

   count_leading_zeros(norm, n);
   invert_limb(ninv, n<<norm);

   return ninv;
}

FLINT_DLL mp_limb_t n_mod_precomp(mp_limb_t a, mp_limb_t n, double ninv);

FLINT_DLL mp_limb_t n_mod2_precomp(mp_limb_t a, mp_limb_t n, double ninv);

FLINT_DLL mp_limb_t n_divrem2_precomp(mp_limb_t * q, mp_limb_t a, 
                                           mp_limb_t n, double npre);

FLINT_DLL mp_limb_t n_mod2_preinv(mp_limb_t a, mp_limb_t n, mp_limb_t ninv);

FLINT_DLL mp_limb_t n_ll_mod_preinv(mp_limb_t a_hi, mp_limb_t a_lo, 
                                        mp_limb_t n, mp_limb_t ninv);

FLINT_DLL mp_limb_t n_lll_mod_preinv(mp_limb_t a_hi, mp_limb_t a_mi, 
                        mp_limb_t a_lo, mp_limb_t n, mp_limb_t ninv);

FLINT_DLL mp_limb_t n_mulmod_precomp(mp_limb_t a, mp_limb_t b, 
                                           mp_limb_t n, double ninv);

FLINT_DLL mp_limb_t n_mulmod2_preinv(mp_limb_t a, mp_limb_t b, 
                                        mp_limb_t n, mp_limb_t ninv);

FLINT_DLL mp_limb_t n_mulmod_preinv(mp_limb_t a, mp_limb_t b, 
                            mp_limb_t n, mp_limb_t ninv, ulong norm);

FLINT_DLL mp_limb_t n_powmod_ui_precomp(mp_limb_t a, mp_limb_t exp, mp_limb_t n, double npre);

FLINT_DLL mp_limb_t n_powmod_precomp(mp_limb_t a, 
                     mp_limb_signed_t exp, mp_limb_t n, double npre);

ULONG_EXTRAS_INLINE
mp_limb_t n_powmod(mp_limb_t a, mp_limb_signed_t exp, mp_limb_t n)
{
   double npre = n_precompute_inverse(n);

   return n_powmod_precomp(a, exp, n, npre);
}

FLINT_DLL mp_limb_t n_powmod2_preinv(mp_limb_t a, 
                  mp_limb_signed_t exp, mp_limb_t n, mp_limb_t ninv);

FLINT_DLL mp_limb_t n_powmod2_ui_preinv(mp_limb_t a, mp_limb_t exp,
                                            mp_limb_t n, mp_limb_t ninv);

FLINT_DLL mp_limb_t n_powmod_ui_preinv(mp_limb_t a, mp_limb_t exp, mp_limb_t n, 
                                             mp_limb_t ninv, ulong norm);

ULONG_EXTRAS_INLINE
mp_limb_t n_powmod2(mp_limb_t a, mp_limb_signed_t exp, mp_limb_t n)
{
   mp_limb_t ninv = n_preinvert_limb(n);

   return n_powmod2_preinv(a, exp, n, ninv);
}

ULONG_EXTRAS_INLINE
mp_limb_t n_addmod(mp_limb_t x, mp_limb_t y, mp_limb_t n)
{
    return (n - y > x ? x + y : x + y - n);
}

ULONG_EXTRAS_INLINE
mp_limb_t n_submod(mp_limb_t x, mp_limb_t y, mp_limb_t n)
{
    return (y > x ? x - y + n : x - y);
}

ULONG_EXTRAS_INLINE
mp_limb_t n_negmod(mp_limb_t x, mp_limb_t n)
{
    return n_submod(0, x, n);
}

FLINT_DLL mp_limb_t n_sqrtmod(mp_limb_t a, mp_limb_t p);

FLINT_DLL slong n_sqrtmod_2pow(mp_limb_t ** sqrt, mp_limb_t a, slong exp); 

FLINT_DLL slong n_sqrtmod_primepow(mp_limb_t ** sqrt, mp_limb_t a, 
                                              mp_limb_t p, slong exp);

FLINT_DLL slong n_sqrtmodn(mp_limb_t ** sqrt, mp_limb_t a, n_factor_t * fac);

FLINT_DLL mp_limb_t n_gcd(mp_limb_t x, mp_limb_t y);

#define n_gcd_full n_gcd

FLINT_DLL mp_limb_t n_xgcd(mp_limb_t * a, mp_limb_t * b, mp_limb_t x, mp_limb_t y);

FLINT_DLL mp_limb_t n_invmod(mp_limb_t x, mp_limb_t y);

FLINT_DLL mp_limb_t n_gcdinv(mp_limb_t * a, mp_limb_t x, mp_limb_t y);

FLINT_DLL ulong n_revbin(ulong in, ulong bits);

FLINT_DLL int n_jacobi(mp_limb_signed_t x, mp_limb_t y);

FLINT_DLL int n_jacobi_unsigned(mp_limb_t x, mp_limb_t y);

FLINT_DLL mp_limb_t n_sqrt(mp_limb_t a);

FLINT_DLL mp_limb_t n_sqrtrem(mp_limb_t * r, mp_limb_t a);

FLINT_DLL int n_is_square(mp_limb_t x);

FLINT_DLL double n_cbrt_estimate(double a);

FLINT_DLL mp_limb_t n_cbrt(mp_limb_t a);

FLINT_DLL mp_limb_t n_cbrt_binary_search(mp_limb_t x);

FLINT_DLL mp_limb_t n_cbrt_newton_iteration(mp_limb_t n);

FLINT_DLL mp_limb_t n_cbrt_chebyshev_approx(mp_limb_t n);

FLINT_DLL mp_limb_t n_cbrtrem(mp_limb_t* remainder, mp_limb_t n);

FLINT_DLL int n_is_perfect_power235(mp_limb_t n);

FLINT_DLL int n_is_oddprime_small(mp_limb_t n);

FLINT_DLL int n_is_oddprime_binary(mp_limb_t n);

FLINT_DLL int n_is_probabprime_fermat(mp_limb_t n, mp_limb_t i);

FLINT_DLL int n_is_probabprime_fibonacci(mp_limb_t n);

FLINT_DLL int n_is_probabprime_lucas(mp_limb_t n);

FLINT_DLL int n_is_probabprime_BPSW(mp_limb_t n);

FLINT_DLL int n_is_strong_probabprime_precomp(mp_limb_t n, 
                              double npre, mp_limb_t a, mp_limb_t d);

FLINT_DLL int n_is_strong_probabprime2_preinv(mp_limb_t n, 
                           mp_limb_t ninv, mp_limb_t a, mp_limb_t d);

FLINT_DLL int n_is_probabprime(mp_limb_t n);

FLINT_DLL int n_is_prime_pseudosquare(mp_limb_t n);

FLINT_DLL int n_is_prime_pocklington(mp_limb_t n, ulong iterations);

FLINT_DLL int n_is_prime(mp_limb_t n);

FLINT_DLL mp_limb_t n_nth_prime(ulong n);

FLINT_DLL void n_nth_prime_bounds(mp_limb_t *lo, mp_limb_t *hi, ulong n);

FLINT_DLL ulong n_prime_pi(mp_limb_t n);

FLINT_DLL void n_prime_pi_bounds(ulong *lo, ulong *hi, mp_limb_t n);

FLINT_DLL int n_remove(mp_limb_t * n, mp_limb_t p);

FLINT_DLL int n_remove2_precomp(mp_limb_t * n, mp_limb_t p, double ppre);

ULONG_EXTRAS_INLINE
void n_factor_init(n_factor_t * factors)
{
    factors->num = UWORD(0);
}

FLINT_DLL void n_factor_insert(n_factor_t * factors, mp_limb_t p, ulong exp);

FLINT_DLL mp_limb_t n_factor_trial_range(n_factor_t * factors, 
                         mp_limb_t n, ulong start, ulong num_primes);

FLINT_DLL mp_limb_t n_factor_trial_partial(n_factor_t * factors, mp_limb_t n, 
                mp_limb_t * prod, ulong num_primes, mp_limb_t limit);

FLINT_DLL mp_limb_t n_factor_trial(n_factor_t * factors, 
                                  mp_limb_t n, ulong num_primes);

FLINT_DLL mp_limb_t n_factor_partial(n_factor_t * factors, 
                           mp_limb_t n, mp_limb_t limit, int proved);

FLINT_DLL mp_limb_t n_factor_power235(ulong *exp, mp_limb_t n);

FLINT_DLL mp_limb_t n_factor_one_line(mp_limb_t n, ulong iters);

FLINT_DLL mp_limb_t n_factor_lehman(mp_limb_t n);

FLINT_DLL mp_limb_t n_factor_SQUFOF(mp_limb_t n, ulong iters);

FLINT_DLL void n_factor(n_factor_t * factors, mp_limb_t n, int proved);

FLINT_DLL mp_limb_t n_factor_pp1(mp_limb_t n, ulong B1, ulong c);

FLINT_DLL int n_is_squarefree(mp_limb_t n);

FLINT_DLL int n_moebius_mu(mp_limb_t n);

FLINT_DLL void n_moebius_mu_vec(int * mu, ulong len);

FLINT_DLL mp_limb_t n_euler_phi(mp_limb_t n);

FLINT_DLL int n_sizeinbase(mp_limb_t n, int base);

FLINT_DLL mp_limb_t n_nextprime(mp_limb_t n, int proved);

FLINT_DLL mp_limb_t n_factorial_mod2_preinv(ulong n, mp_limb_t p, mp_limb_t pinv);

FLINT_DLL mp_limb_t n_factorial_fast_mod2_preinv(ulong n, mp_limb_t p, mp_limb_t pinv);

FLINT_DLL mp_limb_t n_primitive_root_prime_prefactor(mp_limb_t p, n_factor_t * factors);

FLINT_DLL mp_limb_t n_primitive_root_prime(mp_limb_t p);

FLINT_DLL mp_limb_t n_discrete_log_bsgs(mp_limb_t b, mp_limb_t a, mp_limb_t n);

FLINT_DLL mp_limb_t n_root_estimate(double a, int n);

FLINT_DLL mp_limb_t n_rootrem(mp_limb_t* remainder, mp_limb_t n, mp_limb_t root);

FLINT_DLL mp_limb_t n_root(mp_limb_t n, mp_limb_t root);

#ifdef __cplusplus
}
#endif

#endif