Formal polynomial evaluator.

[Alon-Ti]

Formal polynomial evaluator.

Added rational functions for formal polynomial evaluator.

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This change is 

[Alon-Ti]

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• Formal polynomial evaluator. #836 👈
• Formal polynomials. #835
• Change Eval Framework Copy requirement to Clone. #834
• dev

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[codecov-commenter]

Codecov Report

Attention: Patch coverage is 51.92308% with 100 lines in your changes missing coverage. Please review.

Project coverage is 90.95%. Comparing base (5a971e9) to head (0989676).

Files with missing lines	Patch %	Lines
crates/prover/src/constraint_framework/rational.rs	21.05%	45 Missing ⚠️
crates/prover/src/core/lookups/utils.rs	40.62%	19 Missing ⚠️
crates/prover/src/constraint_framework/poly.rs	73.13%	17 Missing and 1 partial ⚠️
...rates/prover/src/constraint_framework/poly_eval.rs	65.38%	18 Missing ⚠️

Additional details and impacted files

@@                   Coverage Diff                   @@
##           alont/symbolic-poly     #836      +/-   ##
=======================================================
- Coverage                91.53%   90.95%   -0.59%     
=======================================================
  Files                       91       93       +2     
  Lines                    12629    12832     +203     
  Branches                 12629    12832     +203     
=======================================================
+ Hits                     11560    11671     +111     
- Misses                     953     1045      +92     
  Partials                   116      116              

Flag	Coverage Δ
	90.95% <51.92%> (-0.59%)	⬇️

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[andrewmilson]

with comment

Reviewable status: 0 of 5 files reviewed, 2 unresolved discussions (waiting on @Alon-Ti)

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crates/prover/src/constraint_framework/poly.rs line 25 at r2 (raw file):

    fn default() -> Monomial {
        Monomial { vars: [].into() }
    }

Remove in favour of One?

Code quote:

    fn default() -> Monomial {
        Monomial { vars: [].into() }
    }

---

crates/prover/src/constraint_framework/poly_eval.rs line 83 at r2 (raw file):

        assert_eq!(eval.constraints[0].to_string(), "(x₀x₁x₂) / (x₀ + x₁)");
    }
}

Suggestion:

#[cfg(test)]
mod tests {
    use super::PolyEvaluator;
    use crate::constraint_framework::{EvalAtRow, FrameworkEval};
    use crate::core::fields::FieldExpOps;

    #[test]
    fn test_poly_eval() {
        let test_struct = TestStruct {};
        let eval = test_struct.evaluate(PolyEvaluator {
            cur_var_index: 0,
            constraints: vec![],
        });

        assert_eq!(eval.constraints[0].to_string(), "(x₀x₁x₂) / (x₀ + x₁)");
    }
    
    struct TestStruct {}
    
    impl FrameworkEval for TestStruct {
        fn log_size(&self) -> u32 {
            1 << 16
        }

        fn max_constraint_log_degree_bound(&self) -> u32 {
            1 << 17
        }

        fn evaluate<E: EvalAtRow>(&self, mut eval: E) -> E {
            let x0 = eval.next_trace_mask();
            let x1 = eval.next_trace_mask();
            let x2 = eval.next_trace_mask();

            eval.add_constraint(x0.clone() * x1.clone() * x2 * (x0 + x1).inverse());
            eval
        }
    }
}