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
|
/*
* Division Algorithm
* (C) 1999-2007 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#include <botan/divide.h>
#include <botan/mp_core.h>
namespace Botan {
namespace {
/*
* Handle signed operands, if necessary
*/
void sign_fixup(const BigInt& x, const BigInt& y, BigInt& q, BigInt& r)
{
if(x.sign() == BigInt::Negative)
{
q.flip_sign();
if(r.is_nonzero()) { --q; r = y.abs() - r; }
}
if(y.sign() == BigInt::Negative)
q.flip_sign();
}
}
/*
* Solve x = q * y + r
*/
void divide(const BigInt& x, const BigInt& y_arg, BigInt& q, BigInt& r)
{
if(y_arg.is_zero())
throw BigInt::DivideByZero();
BigInt y = y_arg;
const u32bit y_words = y.sig_words();
r = x;
r.set_sign(BigInt::Positive);
y.set_sign(BigInt::Positive);
s32bit compare = r.cmp(y);
if(compare < 0)
q = 0;
else if(compare == 0)
{
q = 1;
r = 0;
}
else
{
u32bit shifts = 0;
word y_top = y[y.sig_words()-1];
while(y_top < MP_WORD_TOP_BIT) { y_top <<= 1; ++shifts; }
y <<= shifts;
r <<= shifts;
const u32bit n = r.sig_words() - 1, t = y_words - 1;
q.get_reg().create(n - t + 1);
if(n <= t)
{
while(r > y) { r -= y; ++q; }
r >>= shifts;
sign_fixup(x, y_arg, q, r);
return;
}
BigInt temp = y << (MP_WORD_BITS * (n-t));
while(r >= temp) { r -= temp; ++q[n-t]; }
for(u32bit j = n; j != t; --j)
{
const word x_j0 = r.word_at(j);
const word x_j1 = r.word_at(j-1);
const word y_t = y.word_at(t);
if(x_j0 == y_t)
q[j-t-1] = MP_WORD_MAX;
else
q[j-t-1] = bigint_divop(x_j0, x_j1, y_t);
while(bigint_divcore(q[j-t-1], y_t, y.word_at(t-1),
x_j0, x_j1, r.word_at(j-2)))
--q[j-t-1];
r -= (q[j-t-1] * y) << (MP_WORD_BITS * (j-t-1));
if(r.is_negative())
{
r += y << (MP_WORD_BITS * (j-t-1));
--q[j-t-1];
}
}
r >>= shifts;
}
sign_fixup(x, y_arg, q, r);
}
}
|
