Added libfunc for u256_inv_mod_n.

[orizi]

This change is 

[liorgold2]

Reviewable status: 0 of 10 files reviewed, 1 unresolved discussion (waiting on @orizi and @spapinistarkware)

a discussion (no related file):
Change PR title: div -> inv.

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[orizi]

Reviewable status: 0 of 10 files reviewed, 1 unresolved discussion (waiting on @liorgold2 and @spapinistarkware)

a discussion (no related file):

Previously, liorgold2 wrote…

Change PR title: div -> inv.

Done.

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[liorgold2]

Reviewable status: 0 of 10 files reviewed, 2 unresolved discussions (waiting on @orizi and @spapinistarkware)

a discussion (no related file):
Shouldn't the target branch be sierra-minor-update?

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[orizi]

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a discussion (no related file):

Previously, liorgold2 wrote…

Shouldn't the target branch be sierra-minor-update?

no - since not in the allowed list.

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[liorgold2]

Reviewable status: 0 of 10 files reviewed, 3 unresolved discussions (waiting on @orizi and @spapinistarkware)

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corelib/src/test/math_test.cairo line 98 at r2 (raw file):

        .unwrap();
    assert(q == 0, '0 / 3 != 0 (13)');
    assert(

Missing tests (e.g., random 256-bit numbers)

[orizi]

Reviewable status: 0 of 10 files reviewed, 3 unresolved discussions (waiting on @liorgold2 and @spapinistarkware)

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corelib/src/test/math_test.cairo line 98 at r2 (raw file):

Previously, liorgold2 wrote…

Missing tests (e.g., random 256-bit numbers)

Done.

[liorgold2]

Reviewed 2 of 10 files at r3.
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[liorgold2]

Reviewed 2 of 10 files at r3, all commit messages.
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corelib/src/test/math_test.cairo line 98 at r2 (raw file):

Previously, orizi wrote…

Done.

Still missing.

[orizi]

Reviewable status: 4 of 10 files reviewed, 3 unresolved discussions (waiting on @liorgold2 and @spapinistarkware)

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corelib/src/test/math_test.cairo line 98 at r2 (raw file):

Previously, liorgold2 wrote…

Still missing.

somehow got lost - readded.

[liorgold2]

Reviewed 1 of 6 files at r4, all commit messages.
Reviewable status: 3 of 10 files reviewed, 5 unresolved discussions (waiting on @orizi and @spapinistarkware)

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corelib/src/math.cairo line 81 at r4 (raw file):

/// Returns `1 / b (mod n)`, or None if `b` is not invertible modulo `n`.
/// Additionally returns several `U128MulGuarantee`s that are required for validating the calculation.

Line too long.

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corelib/src/math.cairo line 100 at r4 (raw file):

/// Returns `a / b (mod n)`, or None if `b` is not invertible modulo `n`.
fn u256_div_mod_n(a: u256, b: NonZero<u256>, n: NonZero<u256>) -> Option<u256> {

Can you split u256_inv_mod_n out of this function?

[liorgold2]

Reviewable status: 3 of 10 files reviewed, 6 unresolved discussions (waiting on @orizi and @spapinistarkware)

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corelib/src/test/math_test.cairo line 2 at r4 (raw file):

/// Helper for making a non-zero value.
fn nz<N, impl TryIntoNonZeroN: TryInto<N, NonZero<N>>>(n: N) -> NonZero<N> {

Use + syntax.

[liorgold2]

Reviewed 2 of 10 files at r3, 1 of 6 files at r4.
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[orizi]

Reviewable status: 6 of 10 files reviewed, 6 unresolved discussions (waiting on @liorgold2 and @spapinistarkware)

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corelib/src/math.cairo line 81 at r4 (raw file):

Previously, liorgold2 wrote…

Line too long.

Done.

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corelib/src/math.cairo line 100 at r4 (raw file):

Previously, liorgold2 wrote…

Can you split u256_inv_mod_n out of this function?

Done.

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corelib/src/test/math_test.cairo line 2 at r4 (raw file):

Previously, liorgold2 wrote…

Use + syntax.

Done.

[liorgold2]

Reviewed 1 of 6 files at r4, 2 of 2 files at r5, all commit messages.
Reviewable status: 8 of 10 files reviewed, 9 unresolved discussions (waiting on @orizi and @spapinistarkware)

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corelib/src/math.cairo line 100 at r5 (raw file):

> implicits(RangeCheck) nopanic;

/// Returns the inverse of `a` modulo `n`, or None if `b` is not invertible modulo `n`.

.

Suggestion:

/// Returns the inverse of `a` modulo `n`, or None if `a` is not invertible modulo `n`.

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corelib/src/test/math_test.cairo line 65 at r5 (raw file):

    assert(math::u256_div_mod_n(7, 2, nz(13)) == Option::Some(10), '7 / 2 != 10 (13)');
    assert(math::u256_div_mod_n(0, 3, nz(13)) == Option::Some(0), '0 / 3 != 0 (13)');
    assert(math::u256_div_mod_n(4, 3, nz(6)).is_none(), '4 / 3 == None (6)');

Add:

assert(math::u256_div_mod_n(5, 4, nz(6)).is_none(), '4 / 3 == None (6)');

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corelib/src/test/math_test.cairo line 101 at r5 (raw file):

        'Random large values 2'
    );
}

Add one with a large odd gcd (>2**128)

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crates/cairo-lang-casm/src/hints/mod.rs line 240 at r5 (raw file):

    /// `g * t = n`
    ///
    /// In all cases - `name`0 is the least significant limb.

Suggestion:

    /// Provides the inverse of b (represented by 2 128-bit limbs) modulo n (represented by 2 128-bit
    /// limbs), or a proof that b has no inverse.
    ///
    /// In case b has an inverse: Returns `r` and `k` such that:
    ///   * `r = 1 / b (mod n)`
    ///   * `k = (result * b - 1) / n`
    ///   * `g0_or_no_inv = 0`
    ///
    /// In case b has no inverse: Returns `g`, `s`, and `t`, such that:
    /// `g > 1`
    /// `g == 2 || g % 2 == 1` (in particular, `g0_or_no_inv = g0 != 0`)
    /// `g * s = b`
    /// `g * t = n`
    ///
    /// In all cases - `name`0 is the least significant limb.

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crates/cairo-lang-casm/src/hints/mod.rs line 728 at r5 (raw file):

                        from starkware.python.math_utils import igcdex
    

Remove spaces.

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crates/cairo-lang-casm/src/hints/mod.rs line 730 at r5 (raw file):

    
                        b = {b0} + {b1} * 2**128
                        n = {n0} + {n1} * 2**128

Suggestion:

                        b = {b0} + ({b1} << 128)
                        n = {n0} + ({n1} << 128)

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crates/cairo-lang-casm/src/hints/mod.rs line 746 at r5 (raw file):

                        else:
                            r %= n
                            if r < 0:

This can't happen after the %, right?

[liorgold2]

Reviewed 1 of 6 files at r4.
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crates/cairo-lang-runner/src/casm_run/mod.rs line 1952 at r5 (raw file):

            } else {
                r %= &n;
                if r.is_negative() {

I guess this one (unlike python) is necessary?

[liorgold2]

Reviewed 1 of 6 files at r4.
Reviewable status: all files reviewed, 10 unresolved discussions (waiting on @orizi and @spapinistarkware)

[orizi]

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corelib/src/math.cairo line 100 at r5 (raw file):

Previously, liorgold2 wrote…

.

Done.

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corelib/src/test/math_test.cairo line 65 at r5 (raw file):

Previously, liorgold2 wrote…

Add:

assert(math::u256_div_mod_n(5, 4, nz(6)).is_none(), '4 / 3 == None (6)');

Done.

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corelib/src/test/math_test.cairo line 101 at r5 (raw file):

Previously, liorgold2 wrote…

Add one with a large odd gcd (>2**128)

Done.

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crates/cairo-lang-casm/src/hints/mod.rs line 240 at r5 (raw file):

    /// `g * t = n`
    ///
    /// In all cases - `name`0 is the least significant limb.

Done.

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crates/cairo-lang-casm/src/hints/mod.rs line 728 at r5 (raw file):

Previously, liorgold2 wrote…

Remove spaces.

Done.

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crates/cairo-lang-casm/src/hints/mod.rs line 730 at r5 (raw file):

    
                        b = {b0} + {b1} * 2**128
                        n = {n0} + {n1} * 2**128

Done.

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crates/cairo-lang-casm/src/hints/mod.rs line 746 at r5 (raw file):

Previously, liorgold2 wrote…

This can't happen after the %, right?

correct - fixed as this is python.

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crates/cairo-lang-runner/src/casm_run/mod.rs line 1952 at r5 (raw file):

Previously, liorgold2 wrote…

I guess this one (unlike python) is necessary?

we have no promise from extended gcd to get a negative r - so this is required here (as rust is like c++ AFAIK)

[liorgold2]

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corelib/src/test/math_test.cairo line 101 at r5 (raw file):

Previously, orizi wrote…

Done.

Add another test with b==n==256-bit odd number. This will test the branch where g1 is large.

[liorgold2]

Reviewable status: complete! all files reviewed, all discussions resolved (waiting on @spapinistarkware)

[liorgold2]

Reviewable status: all files reviewed, 1 unresolved discussion (waiting on @orizi and @spapinistarkware)

[orizi]

Reviewable status: 9 of 10 files reviewed, 1 unresolved discussion (waiting on @liorgold2 and @spapinistarkware)

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corelib/src/test/math_test.cairo line 101 at r5 (raw file):

Previously, liorgold2 wrote…

Add another test with b==n==256-bit odd number. This will test the branch where g1 is large.

Done.

[liorgold2]

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

[liorgold2]

Reviewable status: complete! all files reviewed, all discussions resolved (waiting on @spapinistarkware)