Add LinePoly

[ajgara]

Add the implementation of LinePoly and eval_at_point, as needed for the Fri Verifier.

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This change is 

[shaharsamocha7]

Reviewed 2 of 3 files at r1, all commit messages.
Reviewable status: 2 of 3 files reviewed, 4 unresolved discussions (waiting on @ajgara)

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stwo_cairo_verifier/src/poly/line.cairo line 6 at r1 (raw file):

#[derive(Drop, Clone)]
pub struct LinePoly {
    pub coeffs: Array<SecureField>,

Those are in bit-reverse order, right?
Please add documentation

Code quote:

pub coeffs: Array<SecureField>,

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stwo_cairo_verifier/src/poly/line.cairo line 16 at r1 (raw file):

    }

    fn eval_at_point(self: @LinePoly, mut x: SecureField) -> SecureField {

Add a TODO to consider replacing the eval_at_point with fft

Code quote:

 fn eval_at_point(self: @LinePoly, mut x: SecureField) -> SecureField {

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stwo_cairo_verifier/src/poly/line.cairo line 21 at r1 (raw file):

        while i < *self.log_size {
            mappings.append(x);
            x = m31(2).into() * x * x - m31(1).into();

more efficient

Suggestion:

let x_square = x * x; 
x = x_square + x_square - m31(1).into();

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stwo_cairo_verifier/src/poly/line.cairo line 40 at r1 (raw file):

        };

        *level[0]

Add an assert that level is of length 1.

Code quote:

        *level[0]

[shaharsamocha7]

Reviewed 1 of 3 files at r1.
Reviewable status: all files reviewed, 4 unresolved discussions (waiting on @ajgara)

[shaharsamocha7]

Reviewed 1 of 1 files at r3, all commit messages.
Reviewable status: all files reviewed, 1 unresolved discussion (waiting on @ajgara)

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stwo_cairo_verifier/src/poly/line.cairo line 13 at r3 (raw file):

/// reversed order is {b₀, b₄, b₂, b₆}.
/// Then, the polynomial p represented by coeffs = [a₀, a₁, a₂, a₃] and log_size = 2 is
/// p = a₀ * b₀ + a₁ * b₄ + a₂ * b₂ + a₃ * b₆.

Please avoid of using unicode chars.
I think that the first line is enough for this doc.

Suggestion:

/// A univariate polynomial represented by its coefficients in the line part of the FFT-basis
/// in bit reversed order.

[schouhy]

Sure! done.

[andrewmilson]

Reviewed 2 of 3 files at r1.
Reviewable status: 2 of 3 files reviewed, 4 unresolved discussions (waiting on @ajgara and @shaharsamocha7)

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stwo_cairo_verifier/src/poly/line.cairo line 42 at r4 (raw file):

            };
            level = new_level;
        };

Can this be done recursively to reflect the code in the Rust implementation https://github.com/starkware-libs/stwo/blob/e4014820ee79ab32025d9bcb80d1bfe8d277d61b/src/core/poly/line.rs#L106

Code quote:

        let mappings = @mappings;
        let mut i = mappings.len();
        while i > 0 {
            i -= 1;
            let mut new_level = array![];
            let mut j = 0;
            while j < level.len() {
                new_level.append(*level[j] + *mappings[i] * *level[j + 1]);
                j += 2;
            };
            level = new_level;
        };

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stwo_cairo_verifier/src/poly/line.cairo line 65 at r4 (raw file):

        };
        let x = m31(590768354);
        let result = line_poly.eval_at_point(x.into());

Arrange Act Assert

Suggestion:

   
   let result = line_poly.eval_at_point(x.into());
   

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stwo_cairo_verifier/src/poly/line.cairo line 76 at r4 (raw file):

        };
        let x = m31(10);
        let result = line_poly.eval_at_point(x.into());

Arrange Act Assert

Suggestion:

        
        let result = line_poly.eval_at_point(x.into());
        

[ajgara]

Reviewable status: 0 of 4 files reviewed, 3 unresolved discussions (waiting on @andrewmilson and @shaharsamocha7)

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stwo_cairo_verifier/src/poly/line.cairo line 13 at r3 (raw file):

Previously, shaharsamocha7 wrote…

Please avoid of using unicode chars.
I think that the first line is enough for this doc.

Done.

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stwo_cairo_verifier/src/poly/line.cairo line 42 at r4 (raw file):

Previously, andrewmilson (Andrew Milson) wrote…

Can this be done recursively to reflect the code in the Rust implementation https://github.com/starkware-libs/stwo/blob/e4014820ee79ab32025d9bcb80d1bfe8d277d61b/src/core/poly/line.rs#L106

Done.

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stwo_cairo_verifier/src/poly/line.cairo line 65 at r4 (raw file):

Previously, andrewmilson (Andrew Milson) wrote…

Arrange Act Assert

Done.

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stwo_cairo_verifier/src/poly/line.cairo line 76 at r4 (raw file):

Previously, andrewmilson (Andrew Milson) wrote…

Arrange Act Assert

Done.

[ajgara]

Let us know if there's anything else to improve! I'm not used to this tool haha.

Reviewable status: 0 of 4 files reviewed, 3 unresolved discussions (waiting on @andrewmilson and @shaharsamocha7)

[andrewmilson]

with comments

Reviewable status: 0 of 4 files reviewed, 4 unresolved discussions (waiting on @ajgara and @shaharsamocha7)

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stwo_cairo_verifier/src/poly/line.cairo line 1 at r5 (raw file):

use core::array::ArrayTrait;

Is this needed?

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stwo_cairo_verifier/src/poly/line.cairo line 20 at r5 (raw file):

    }

    // TODO: Consider replacing with FFT.

I don't think "replacing with FFT" is necessary. The protocol only uses LinePoly to evaluate at a single point.

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stwo_cairo_verifier/src/poly/utils.cairo line 4 at r5 (raw file):

pub fn fold(

Please copy over docs from rust.

[carlogf]

Hi! I addressed the comments and rebased with the last commit in main

Reviewable status: 0 of 4 files reviewed, 4 unresolved discussions (waiting on @ajgara, @andrewmilson, and @shaharsamocha7)

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stwo_cairo_verifier/src/poly/line.cairo line 1 at r5 (raw file):

Previously, andrewmilson (Andrew Milson) wrote…

Is this needed?

Not needed, removed it

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stwo_cairo_verifier/src/poly/line.cairo line 20 at r5 (raw file):

Previously, andrewmilson (Andrew Milson) wrote…

I don't think "replacing with FFT" is necessary. The protocol only uses LinePoly to evaluate at a single point.

makes sense :)

[shaharsamocha7]

Reviewed 2 of 4 files at r5, 1 of 2 files at r6, all commit messages.
Reviewable status: 3 of 4 files reviewed, 4 unresolved discussions (waiting on @ajgara, @andrewmilson, and @carlogf)

[shaharsamocha7]

Reviewed 1 of 2 files at r6.
Reviewable status: all files reviewed, 4 unresolved discussions (waiting on @ajgara and @andrewmilson)