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
|
/*
Copyright (C) 2011, 2012 Sebastian Pancratz
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#ifndef PADIC_H
#define PADIC_H
#ifdef PADIC_INLINES_C
#define PADIC_INLINE
#else
#define PADIC_INLINE static inline
#endif
#include "fmpz.h"
#include "padic_types.h"
#ifdef __cplusplus
extern "C" {
#endif
#define PADIC_DEFAULT_PREC WORD(20)
#define PADIC_TEST_PREC_MIN WORD(-100)
#define PADIC_TEST_PREC_MAX WORD(100)
#define padic_val(x) ((x)->v)
#define padic_prec(x) ((x)->N)
PADIC_INLINE
fmpz * padic_unit(const padic_t x)
{
return (fmpz *)(&(x->u));
}
PADIC_INLINE
slong padic_get_val(const padic_t x)
{
return x->v;
}
PADIC_INLINE
slong padic_get_prec(const padic_t x)
{
return x->N;
}
/* Context *******************************************************************/
void padic_ctx_init(padic_ctx_t ctx, const fmpz_t p, slong min, slong max, enum padic_print_mode mode);
void padic_ctx_clear(padic_ctx_t ctx);
PADIC_INLINE
int _padic_ctx_pow_ui(fmpz_t rop, ulong e, const padic_ctx_t ctx)
{
if (ctx->min <= (slong) e && (slong) e < ctx->max)
{
*rop = *(ctx->pow + (e - ctx->min));
return 0;
}
else
{
slong l = (slong) e;
if (l < 0)
{
flint_throw(FLINT_ERROR, "Exception (_padic_ctx_pow_ui). Power too large.\ne = %wu\nl = %wd\n", e, l);
}
fmpz_init(rop);
fmpz_pow_ui(rop, ctx->p, e);
return 1;
}
}
PADIC_INLINE
void padic_ctx_pow_ui(fmpz_t rop, ulong e, const padic_ctx_t ctx)
{
if (ctx->min <= (slong) e && (slong) e < ctx->max)
fmpz_set(rop, ctx->pow + (e - ctx->min));
else
{
slong l = (slong) e;
if (l < 0)
{
flint_throw(FLINT_ERROR, "Exception (padic_ctx_pow_ui). Power too large.\ne = %wu\nl = %wd\n", e, l);
}
fmpz_pow_ui(rop, ctx->p, e);
}
}
/* Memory management *********************************************************/
void padic_init(padic_t rop);
void padic_init2(padic_t rop, slong N);
void padic_clear(padic_t rop);
PADIC_INLINE void _padic_canonicalise(padic_t rop, const padic_ctx_t ctx)
{
if (!fmpz_is_zero(padic_unit(rop)))
{
padic_val(rop) += _fmpz_remove(padic_unit(rop), ctx->p, ctx->pinv);
}
else
{
padic_val(rop) = 0;
}
}
void _padic_reduce(padic_t rop, const padic_ctx_t ctx);
void padic_reduce(padic_t rop, const padic_ctx_t ctx);
/* Randomisation *************************************************************/
void padic_randtest(padic_t rop, flint_rand_t state, const padic_ctx_t ctx);
void padic_randtest_not_zero(padic_t rop, flint_rand_t state, const padic_ctx_t ctx);
void padic_randtest_int(padic_t rop, flint_rand_t state, const padic_ctx_t ctx);
/* Assignments and conversions ***********************************************/
void padic_set_si(padic_t rop, slong op, const padic_ctx_t ctx);
void padic_set_ui(padic_t rop, ulong op, const padic_ctx_t ctx);
void padic_set_fmpz(padic_t rop, const fmpz_t op, const padic_ctx_t ctx);
void padic_set_fmpq(padic_t rop, const fmpq_t op, const padic_ctx_t ctx);
#ifdef __GMP_H__
void padic_set_mpz(padic_t rop, const mpz_t op, const padic_ctx_t ctx);
void padic_set_mpq(padic_t rop, const mpq_t op, const padic_ctx_t ctx);
#endif
void padic_set(padic_t rop, const padic_t op, const padic_ctx_t ctx);
void padic_get_fmpz(fmpz_t rop, const padic_t op, const padic_ctx_t ctx);
void padic_get_fmpq(fmpq_t rop, const padic_t op, const padic_ctx_t ctx);
#ifdef __GMP_H__
void padic_get_mpz(mpz_t rop, const padic_t op, const padic_ctx_t ctx);
void padic_get_mpq(mpq_t rop, const padic_t op, const padic_ctx_t ctx);
#endif
PADIC_INLINE void padic_swap(padic_t op1, padic_t op2)
{
FLINT_SWAP(padic_struct, *op1, *op2);
}
PADIC_INLINE void padic_zero(padic_t rop)
{
fmpz_zero(padic_unit(rop));
padic_val(rop) = 0;
}
PADIC_INLINE void padic_one(padic_t rop)
{
if (padic_prec(rop) > 0)
{
fmpz_one(padic_unit(rop));
padic_val(rop) = 0;
}
else
padic_zero(rop);
}
/* Comparison ****************************************************************/
PADIC_INLINE int padic_is_zero(const padic_t op)
{
return fmpz_is_zero(padic_unit(op));
}
PADIC_INLINE int padic_is_one(const padic_t op)
{
return fmpz_is_one(padic_unit(op)) && (padic_val(op) == 0);
}
PADIC_INLINE int padic_equal(const padic_t op1, const padic_t op2)
{
return (padic_val(op1) == padic_val(op2)) &&
(fmpz_equal(padic_unit(op1), padic_unit(op2)));
}
/* Arithmetic operations *****************************************************/
slong * _padic_lifts_exps(slong *n, slong N);
void _padic_lifts_pows(fmpz *pow, const slong *a, slong n, const fmpz_t p);
void padic_add(padic_t rop, const padic_t op1, const padic_t op2, const padic_ctx_t ctx);
void padic_sub(padic_t rop, const padic_t op1, const padic_t op2, const padic_ctx_t ctx);
void padic_neg(padic_t rop, const padic_t op, const padic_ctx_t ctx);
void padic_mul(padic_t rop, const padic_t op1, const padic_t op2, const padic_ctx_t ctx);
void padic_shift(padic_t rop, const padic_t op, slong v, const padic_ctx_t ctx);
void padic_div(padic_t rop, const padic_t op1, const padic_t op2, const padic_ctx_t ctx);
void _padic_inv_precompute(padic_inv_t S, const fmpz_t p, slong N);
void _padic_inv_clear(padic_inv_t S);
void _padic_inv_precomp(fmpz_t rop, const fmpz_t op, const padic_inv_t S);
void _padic_inv(fmpz_t rop, const fmpz_t op, const fmpz_t p, slong N);
void padic_inv(padic_t rop, const padic_t op, const padic_ctx_t ctx);
int _padic_sqrt(fmpz_t rop, const fmpz_t op, const fmpz_t p, slong N);
int padic_sqrt(padic_t rop, const padic_t op, const padic_ctx_t ctx);
void padic_pow_si(padic_t rop, const padic_t op, slong e, const padic_ctx_t ctx);
/* Exponential ***************************************************************/
slong _padic_exp_bound(slong v, slong N, const fmpz_t p);
void _padic_exp(fmpz_t rop, const fmpz_t u, slong v, const fmpz_t p, slong N);
void _padic_exp_rectangular(fmpz_t rop, const fmpz_t u, slong v, const fmpz_t p, slong N);
void _padic_exp_balanced(fmpz_t rop, const fmpz_t u, slong v, const fmpz_t p, slong N);
int padic_exp(padic_t rop, const padic_t op, const padic_ctx_t ctx);
int padic_exp_rectangular(padic_t rop, const padic_t op, const padic_ctx_t ctx);
int padic_exp_balanced(padic_t rop, const padic_t op, const padic_ctx_t ctx);
/* Logarithm *****************************************************************/
slong _padic_log_bound(slong v, slong N, const fmpz_t p);
void _padic_log(fmpz_t z, const fmpz_t y, slong v, const fmpz_t p, slong N);
void _padic_log_rectangular(fmpz_t z, const fmpz_t y, slong v, const fmpz_t p, slong N);
void _padic_log_satoh(fmpz_t z, const fmpz_t y, slong v, const fmpz_t p, slong N);
void _padic_log_balanced(fmpz_t z, const fmpz_t y, slong FLINT_UNUSED(v), const fmpz_t p, slong N);
int padic_log(padic_t rop, const padic_t op, const padic_ctx_t ctx);
int padic_log_rectangular(padic_t rop, const padic_t op, const padic_ctx_t ctx);
int padic_log_satoh(padic_t rop, const padic_t op, const padic_ctx_t ctx);
int padic_log_balanced(padic_t rop, const padic_t op, const padic_ctx_t ctx);
/* Special functions *********************************************************/
void _padic_teichmuller(fmpz_t rop, const fmpz_t op, const fmpz_t p, slong N);
void padic_teichmuller(padic_t rop, const padic_t op, const padic_ctx_t ctx);
ulong padic_val_fac_ui_2(ulong N);
ulong padic_val_fac_ui(ulong N, const fmpz_t p);
void padic_val_fac(fmpz_t rop, const fmpz_t op, const fmpz_t p);
/* Input and output **********************************************************/
char * _padic_get_str(char * str, const padic_t op, const fmpz_t p, enum padic_print_mode mode);
char * padic_get_str(char * str, const padic_t op, const padic_ctx_t ctx);
#ifdef FLINT_HAVE_FILE
int _padic_fprint(FILE * file, const fmpz_t u, slong v, const padic_ctx_t ctx);
int padic_fprint(FILE * file, const padic_t op, const padic_ctx_t ctx);
#endif
int _padic_print(const fmpz_t u, slong v, const padic_ctx_t ctx);
int padic_print(const padic_t op, const padic_ctx_t ctx);
void padic_debug(const padic_t op);
#ifdef __cplusplus
}
#endif
#endif
|
