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
|
/*
* Division Algorithm
* (C) 1999-2007,2012 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/divide.h>
#include <botan/internal/mp_core.h>
#include <botan/internal/mp_madd.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();
}
bool division_check(word q, word y2, word y1,
word x3, word x2, word x1)
{
// Compute (y3,y2,y1) = (y2,y1) * q
word y3 = 0;
y1 = word_madd2(q, y1, &y3);
y2 = word_madd2(q, y2, &y3);
// Return (y3,y2,y1) >? (x3,x2,x1)
if(y3 > x3) return true;
if(y3 < x3) return false;
if(y2 > x2) return true;
if(y2 < x2) return false;
if(y1 > x1) return true;
if(y1 < x1) return false;
return false;
}
}
/*
* 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 size_t y_words = y.sig_words();
r = x;
q = 0;
r.set_sign(BigInt::Positive);
y.set_sign(BigInt::Positive);
int32_t compare = r.cmp(y);
if(compare == 0)
{
q = 1;
r = 0;
}
else if(compare > 0)
{
size_t shifts = 0;
word y_top = y.word_at(y.sig_words()-1);
while(y_top < MP_WORD_TOP_BIT) { y_top <<= 1; ++shifts; }
y <<= shifts;
r <<= shifts;
const size_t n = r.sig_words() - 1, t = y_words - 1;
if(n < t)
throw Internal_Error("BigInt division word sizes");
q.grow_to(n - t + 1);
word* q_words = q.mutable_data();
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_words[n-t] += 1; }
for(size_t 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_words[j-t-1] = MP_WORD_MAX;
else
q_words[j-t-1] = bigint_divop(x_j0, x_j1, y_t);
while(division_check(q_words[j-t-1],
y_t, y.word_at(t-1),
x_j0, x_j1, r.word_at(j-2)))
{
q_words[j-t-1] -= 1;
}
r -= (q_words[j-t-1] * y) << (MP_WORD_BITS * (j-t-1));
if(r.is_negative())
{
r += y << (MP_WORD_BITS * (j-t-1));
q_words[j-t-1] -= 1;
}
}
r >>= shifts;
}
sign_fixup(x, y_arg, q, r);
}
}
|
