Botan: src/math/numbertheory/jacobi.cpp Source File

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jacobi.cpp
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1 /*
2 * Jacobi Function
3 * (C) 1999-2007 Jack Lloyd
4 *
5 * Distributed under the terms of the Botan license
6 */
7
8 #include <botan/numthry.h>
9
10 namespace Botan {
11
12 /*
13 * Calculate the Jacobi symbol
14 */
15 s32bit jacobi(const BigInt& a, const BigInt& n)
16 {
17 if(a.is_negative())
18 throw Invalid_Argument("jacobi: first argument must be non-negative");
19 if(n.is_even() || n < 2)
20 throw Invalid_Argument("jacobi: second argument must be odd and > 1");
21
22 BigInt x = a, y = n;
23 s32bit J = 1;
24
25 while(y > 1)
26 {
27 x %= y;
28 if(x > y / 2)
29 {
30 x = y - x;
31 if(y % 4 == 3)
32 J = -J;
33 }
34 if(x.is_zero())
35 return 0;
36
37 size_t shifts = low_zero_bits(x);
38 x >>= shifts;
39 if(shifts % 2)
40 {
41 word y_mod_8 = y % 8;
42 if(y_mod_8 == 3 || y_mod_8 == 5)
43 J = -J;
44 }
45
46 if(x % 4 == 3 && y % 4 == 3)
47 J = -J;
48 std::swap(x, y);
49 }
50 return J;
51 }
52
53 }
Botan::BigInt::is_even
bool is_even() const
Definition: bigint.h:158
Botan::BigInt
Definition: bigint.h:22
Botan::BigInt::is_negative
bool is_negative() const
Definition: bigint.h:245
Botan::Invalid_Argument
std::invalid_argument Invalid_Argument
Definition: exceptn.h:20
Botan::s32bit
signed int s32bit
Definition: types.h:37
Botan::jacobi
s32bit jacobi(const BigInt &a, const BigInt &n)
Definition: jacobi.cpp:15
Botan
Definition: algo_base.h:14
Botan::low_zero_bits
size_t low_zero_bits(const BigInt &n)
Definition: numthry.cpp:141
std::swap
void swap(Botan::MemoryRegion< T > &x, Botan::MemoryRegion< T > &y)
Definition: secmem.h:425
Botan::BigInt::is_zero
bool is_zero() const
Definition: bigint.h:176