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Merge pull request #1123 from Kelimion/bigint

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big: Add Extended Euclidean algorithm.
This commit is contained in:
Jeroen van Rijn
2021-09-05 14:07:14 +02:00
committed by GitHub
parent b45842c33f f33d0725db
commit b2fa4ec675
2 changed files with 85 additions and 2 deletions
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4
core/math/big/example.odin
View File

@@ -86,13 +86,13 @@ print :: proc(name: string, a: ^Int, base := i8(10), print_name := true, newline
}
}
printf :: fmt.printf;
// printf :: fmt.printf;
demo :: proc() {
a, b, c, d, e, f, res := &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{};
defer destroy(a, b, c, d, e, f, res);
bits := 111;
bits := 64;
trials := -1;
flags := Primality_Flags{};

83
core/math/big/prime.odin
View File

@@ -1280,6 +1280,89 @@ internal_random_prime :: proc(a: ^Int, size_in_bits: int, trials: int, flags :=
return;
}
/*
Extended Euclidean algorithm of (a, b) produces `a * u1` + `b * u2` = `u3`.
*/
internal_int_extended_euclidean :: proc(a, b, U1, U2, U3: ^Int, allocator := context.allocator) -> (err: Error) {
context.allocator = allocator;
u1, u2, u3, v1, v2, v3, t1, t2, t3, q, tmp := &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{}, &Int{};
defer internal_destroy(u1, u2, u3, v1, v2, v3, t1, t2, t3, q, tmp);
internal_init_multi(u1, u2, u3, v1, v2, v3, t1, t2, t3, q, tmp) or_return;
/*
Initialize, (u1, u2, u3) = (1, 0, a).
*/
internal_set(u1, 1) or_return;
internal_set(u3, a) or_return;
/*
Initialize, (v1, v2, v3) = (0, 1, b).
*/
internal_set(v2, 1) or_return;
internal_set(v3, b) or_return;
/*
Loop while v3 != 0
*/
for !internal_is_zero(v3) {
/*
q = u3 / v3
*/
internal_div(q, u3, v3) or_return;
/*
(t1, t2, t3) = (u1, u2, u3) - (v1, v2, v3)q
*/
internal_mul(tmp, v1, q) or_return;
internal_sub( t1, u1, tmp) or_return;
internal_mul(tmp, v2, q) or_return;
internal_sub( t2, u2, tmp) or_return;
internal_mul(tmp, v3, q) or_return;
internal_sub( t3, u3, tmp) or_return;
/*
(u1, u2, u3) = (v1, v2, v3)
*/
internal_set(u1, v1) or_return;
internal_set(u2, v2) or_return;
internal_set(u3, v3) or_return;
/*
(v1, v2, v3) = (t1, t2, t3)
*/
internal_set(v1, t1) or_return;
internal_set(v2, t2) or_return;
internal_set(v3, t3) or_return;
}
/*
Make sure U3 >= 0.
*/
if internal_is_negative(u3) {
internal_neg(u1, u1) or_return;
internal_neg(u2, u2) or_return;
internal_neg(u3, u3) or_return;
}
/*
Copy result out.
*/
if U1 != nil {
internal_swap(u1, U1);
}
if U2 != nil {
internal_swap(u2, U2);
}
if U3 != nil {
internal_swap(u3, U3);
}
return;
}
/*
Returns the number of Rabin-Miller trials needed for a given bit size.
*/