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
|
/*
Copyright (C) 2012 Fredrik Johansson
This file is part of Arb.
Arb 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "fmpr.h"
/* like mpn_scan0b, but takes an upper size */
static __inline__ flint_bitcnt_t
mpn_scan0b(mp_srcptr up, mp_size_t size, flint_bitcnt_t from_bit)
{
mp_limb_t t;
slong i, c;
i = from_bit / GMP_NUMB_BITS;
c = from_bit % FLINT_BITS;
t = ((~up[i]) >> c) << c;
while (t == 0)
{
i++;
if (i == size)
return size * FLINT_BITS;
else
t = ~up[i];
}
count_trailing_zeros(c, t);
return (i * FLINT_BITS) + c;
}
slong
_fmpr_set_round(fmpz_t rman, fmpz_t rexp,
const fmpz_t man, const fmpz_t exp, slong prec, fmpr_rnd_t rnd)
{
if (!COEFF_IS_MPZ(*man))
{
slong lead, trail, bc, v, w, shift, ret;
int negative;
v = *man;
count_trailing_zeros(trail, v);
v >>= trail;
shift = trail;
ret = FMPR_RESULT_EXACT;
/* may need to round */
if (prec < FLINT_BITS - 2 - trail)
{
if (v < 0)
{
negative = 1;
w = -v;
}
else
{
negative = 0;
w = v;
}
count_leading_zeros(lead, w);
bc = FLINT_BITS - lead;
/* round */
if (prec < bc)
{
w = (w >> (bc - prec)) + rounds_up(rnd, negative);
shift += bc - prec;
count_trailing_zeros(trail, w);
w >>= trail;
shift += trail;
v = negative ? -w : w;
ret = trail;
/* special case: if w overflowed to the next power of two,
the error bound must be multiplied by 2 */
ret -= (trail == prec);
}
}
/* the input is small, so the output must be small too */
_fmpz_demote(rman);
*rman = v;
fmpz_add_ui_inline(rexp, exp, shift);
return ret;
}
else
{
slong size, bc, val, val_bits, val_limbs, ret;
int negative, increment;
mp_ptr d;
__mpz_struct * z = COEFF_TO_PTR(*man);
size = z->_mp_size;
negative = size < 0;
size = FLINT_ABS(size);
d = z->_mp_d;
/* bit size */
count_leading_zeros(bc, d[size - 1]);
bc = FLINT_BITS - bc;
bc += (size - 1) * FLINT_BITS;
/* quick exit */
if (bc <= prec && (d[0] & 1))
{
if (rman != man) fmpz_set(rman, man);
if (rexp != exp) fmpz_set(rexp, exp);
return FMPR_RESULT_EXACT;
}
/* trailing zeros */
val_limbs = 0;
while (d[val_limbs] == 0)
val_limbs++;
count_trailing_zeros(val_bits, d[val_limbs]);
val = val_bits + (val_limbs * FLINT_BITS);
/* no rounding necessary; just copy or shift to destination */
if (bc - val <= prec)
{
ret = FMPR_RESULT_EXACT;
increment = 0;
}
else
{
/* truncation */
if (!rounds_up(rnd, negative))
{
val = mpn_scan1(d, bc - prec);
increment = 0;
}
/* round to next higher odd mantissa */
else
{
val = mpn_scan0b(d, size, bc - prec);
/* can overflow to next power of 2 */
if (val == bc)
{
fmpz_set_si(rman, negative ? -1 : 1);
fmpz_add_ui_inline(rexp, exp, bc);
return prec - 1;
}
/* otherwise, incrementing will not cause overflow below */
increment = 1;
}
val_limbs = val / FLINT_BITS;
val_bits = val % FLINT_BITS;
ret = prec - (bc - val);
}
/* the output mantissa is a small fmpz */
if (bc - val <= FLINT_BITS - 2)
{
mp_limb_t h;
if (val_limbs + 1 == size || val_bits == 0)
h = d[val_limbs] >> val_bits;
else
h = (d[val_limbs] >> val_bits)
| (d[val_limbs + 1] << (FLINT_BITS - val_bits));
h += increment;
_fmpz_demote(rman);
*rman = negative ? -h : h;
}
/* the output mantissa is an mpz */
else
{
if (rman == man)
{
mpz_tdiv_q_2exp(z, z, val);
if (increment) z->_mp_d[0]++;
}
else
{
__mpz_struct * w = _fmpz_promote(rman);
/* must reload pointer, as promoting rman could change it */
z = COEFF_TO_PTR(*man);
mpz_tdiv_q_2exp(w, z, val);
if (increment)
w->_mp_d[0]++;
}
}
fmpz_add_ui_inline(rexp, exp, val);
return ret;
}
}
|
