Added Cairo extended GCD function

[yuvalsw]

This change is 

[orizi]

Reviewable status: 0 of 3 files reviewed, 2 unresolved discussions (waiting on @yuvalsw)

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corelib/src/integer.cairo line 1540 at r2 (raw file):

// TODO(yuval): use signed integers once supported.
/// Extended GCD: finds numbers (g, s, t, sign_s, sign_t) such that
/// g = gcd(x, y) = sign_s*s*a + sign_t*t*b

extract to another module.
(maybe even a submodule of an algorithm module)

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corelib/src/test/integer_test.cairo line 7 at r1 (raw file):

use integer::
{ u16_sqrt , u32_sqrt , u64_sqrt , u8_sqrt , BoundedInt , u128_wrapping_sub } ; #[test]
fn test_u8_operators() {

you probably need to update formatter.

Code quote:

use option::OptionTrait;
use integer::
{ u16_sqrt , u32_sqrt , u64_sqrt , u8_sqrt , BoundedInt , u128_wrapping_sub } ; #[test]

fn test_u8_operators() {

[orizi]

Reviewed 2 of 5 files at r3.
Reviewable status: 2 of 8 files reviewed, 3 unresolved discussions (waiting on @yuvalsw)

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corelib/src/math.cairo line 26 at r4 (raw file):

>(
    a: NonZero<T>, b: NonZero<T>
) -> (T, T, bool, T, bool) {

is there a a real need for both bools?

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corelib/src/math.cairo line 49 at r4 (raw file):

    fn is_one(self: T) -> bool;
    /// Returns whether self is not equal to 1, the multiplicative identity element.
    fn is_non_one(self: T) -> bool;

i think we don't need these:

• not used here.
• as efficient if you -1 and use is_zero.

Code quote:

    /// Returns whether self is equal to 1, the multiplicative identity element.
    fn is_one(self: T) -> bool;
    /// Returns whether self is not equal to 1, the multiplicative identity element.
    fn is_non_one(self: T) -> bool;

[yuvalsw]

corelib/src/math.cairo line 49 at r4 (raw file):

Previously, orizi wrote…

i think we don't need these:

• not used here.
• as efficient if you -1 and use is_zero.

This is orthogonal to this PR (I moved it from integer.cairo).
Anyway, I agree, but I added these to look like zeroable. We can make a future PR to change both.

[yuvalsw]

Reviewable status: 2 of 8 files reviewed, 3 unresolved discussions (waiting on @orizi)

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corelib/src/integer.cairo line 1540 at r2 (raw file):

Previously, orizi wrote…

extract to another module.
(maybe even a submodule of an algorithm module)

Done.

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corelib/src/math.cairo line 26 at r4 (raw file):

Previously, orizi wrote…

is there a a real need for both bools?

Done.

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corelib/src/test/integer_test.cairo line 7 at r1 (raw file):

Previously, orizi wrote…

you probably need to update formatter.

Done.

[orizi]

Reviewed 2 of 6 files at r4, 2 of 2 files at r5.
Reviewable status: 6 of 8 files reviewed, all discussions resolved

[orizi]

Reviewed 1 of 6 files at r4, 2 of 2 files at r6, all commit messages.
Reviewable status: complete! all files reviewed, all discussions resolved (waiting on @yuvalsw)

[orizi]

Reviewed 1 of 1 files at r7, all commit messages.
Reviewable status: complete! all files reviewed, all discussions resolved (waiting on @yuvalsw)

[orizi]

Reviewed 2 of 2 files at r8, all commit messages.
Reviewable status: complete! all files reviewed, all discussions resolved (waiting on @yuvalsw)