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
/*
Copyright (C) 2010 Sebastian Pancratz
Copyright (C) 2014, 2021 Fredrik Johansson
Copyright (C) 2019 William Hart
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/>.
*/
#include "longlong.h"
#include "fmpz.h"
#include "fmpz_vec.h"
#include "fmpz_poly.h"
static void
fmpz_divexact_checked(fmpz_t Q, const fmpz_t A, const fmpz_t B)
{
fmpz_t r;
fmpz_init(r);
fmpz_fdiv_qr(Q, r, A, B);
if (!fmpz_is_zero(r))
{
fmpz_clear(r); /* flint_throw */
flint_throw(FLINT_ERROR, "Not an exact division\n");
}
/* no need to clear r */
}
void
_fmpz_poly_div_series_basecase(fmpz * Q, const fmpz * A, slong Alen,
const fmpz * B, slong Blen, slong n)
{
Alen = FLINT_MIN(Alen, n);
Blen = FLINT_MIN(Blen, n);
if (Blen == 1)
{
if (fmpz_is_pm1(B + 0))
{
if (fmpz_is_one(B + 0))
_fmpz_vec_set(Q, A, Alen);
else
_fmpz_vec_neg(Q, A, Alen);
}
else
{
slong i;
for (i = 0; i < Alen; i++)
fmpz_divexact_checked(Q + i, A + i, B);
}
_fmpz_vec_zero(Q + Alen, n - Alen);
}
else if (Alen == 1 && fmpz_is_pm1(B + 0))
{
_fmpz_poly_inv_series_basecase(Q, B, Blen, n);
if (!fmpz_is_one(A + 0))
_fmpz_vec_scalar_mul_fmpz(Q, Q, n, A + 0);
}
else
{
slong i, j, nsmall;
char *Bbits;
slong b, bits, Qbits;
TMP_INIT;
TMP_START;
if (fmpz_is_pm1(B + 0))
{
if (fmpz_is_one(B + 0))
fmpz_set(Q + 0, A + 0);
else
fmpz_neg(Q + 0, A + 0);
}
else
{
fmpz_divexact_checked(Q + 0, A + 0, B + 0);
}
/* Bbits[i] = max(bits(B[0]), ..., bits(B[i])), as long as coeffs are small */
Bbits = TMP_ALLOC(Blen);
Bbits[0] = fmpz_bits(B + 0);
/* Maximum bits of all Q coefficients encountered so far */
Qbits = fmpz_bits(Q + 0);
/* We have small coefficients for i < nsmall */
for (nsmall = 0; nsmall < Blen; nsmall++)
{
b = B[nsmall];
if (COEFF_IS_MPZ(b))
break;
b = FLINT_ABS(b);
if (nsmall == 0 || (b >> Bbits[nsmall - 1]) != 0)
Bbits[nsmall] = FLINT_BIT_COUNT(b);
else
Bbits[nsmall] = Bbits[nsmall - 1];
}
for (i = 1; i < n; i++)
{
if (i >= nsmall || Qbits > SMALL_FMPZ_BITCOUNT_MAX || Bbits[i] > SMALL_FMPZ_BITCOUNT_MAX)
{
/* Can't use fast code. */
bits = WORD_MAX;
}
else
{
/* Can maybe use fast code; bound bits. */
b = FLINT_MIN(i, Blen - 1);
bits = FLINT_BIT_COUNT(b);
/* Bit size of product. */
bits += Bbits[i] + Qbits;
/* Sign. */
bits += 1;
}
if (bits <= 3 * FLINT_BITS - 1)
{
if (bits <= FLINT_BITS - 1)
{
slong s, x, y;
s = 0;
for (j = 1; j < FLINT_MIN(i + 1, Blen); j++)
{
x = B[j];
y = Q[i - j];
s += x * y;
}
fmpz_set_si(Q + i, s);
}
else if (bits <= 2 * FLINT_BITS - 1)
{
ulong hi, lo, shi, slo;
slong x, y;
shi = slo = 0;
for (j = 1; j < FLINT_MIN(i + 1, Blen); j++)
{
x = B[j];
y = Q[i - j];
smul_ppmm(hi, lo, x, y);
add_ssaaaa(shi, slo, shi, slo, hi, lo);
}
fmpz_set_signed_uiui(Q + i, shi, slo);
}
else
{
ulong hi, lo, cy, shh, shi, slo;
slong x, y;
shh = shi = slo = 0;
for (j = 1; j < FLINT_MIN(i + 1, Blen); j++)
{
x = B[j];
y = Q[i - j];
smul_ppmm(hi, lo, x, y);
add_sssaaaaaa(cy, shi, slo, 0, shi, slo, 0, hi, lo);
shh += (0 <= (slong) hi) ? cy : cy - 1;
}
fmpz_set_signed_uiuiui(Q + i, shh, shi, slo);
}
}
else
{
slong l = FLINT_MIN(i, Blen - 1);
/* todo: merge final subtraction */
_fmpz_vec_dot_general(Q + i, NULL, 0, B + 1, Q + i - l, 1, l);
}
if (i < Alen)
{
if (fmpz_is_pm1(B + 0))
{
if (fmpz_is_one(B + 0))
fmpz_sub(Q + i, A + i, Q + i);
else
fmpz_sub(Q + i, Q + i, A + i);
}
else
{
fmpz_sub(Q + i, A + i, Q + i);
fmpz_divexact_checked(Q + i, Q + i, B + 0);
}
}
else
{
if (fmpz_is_pm1(B + 0))
{
if (fmpz_is_one(B + 0))
fmpz_neg(Q + i, Q + i);
}
else
{
fmpz_neg(Q + i, Q + i);
fmpz_divexact_checked(Q + i, Q + i, B + 0);
}
}
if (COEFF_IS_MPZ(*(Q + i)))
{
/* Will no longer use fast code */
nsmall = i;
}
else
{
/* Update Qbits */
b = FLINT_ABS(*(Q + i));
b = FLINT_BIT_COUNT(b);
Qbits = FLINT_MAX(Qbits, b);
}
}
TMP_END;
}
}
void fmpz_poly_div_series_basecase(fmpz_poly_t Q, const fmpz_poly_t A,
const fmpz_poly_t B, slong n)
{
slong Alen = FLINT_MIN(A->length, n);
slong Blen = FLINT_MIN(B->length, n);
if (Blen == 0)
{
flint_throw(FLINT_DIVZERO, "Exception (fmpz_poly_div_series_basecase). Division by zero.\n");
}
if (Alen == 0)
{
fmpz_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
fmpz_poly_t t;
fmpz_poly_init2(t, n);
_fmpz_poly_div_series_basecase(t->coeffs, A->coeffs, Alen, B->coeffs, Blen, n);
fmpz_poly_swap(Q, t);
fmpz_poly_clear(t);
}
else
{
fmpz_poly_fit_length(Q, n);
_fmpz_poly_div_series_basecase(Q->coeffs, A->coeffs, Alen, B->coeffs, Blen, n);
}
_fmpz_poly_set_length(Q, n);
_fmpz_poly_normalise(Q);
}