From ab135be4834195b446986dc848513b70933bc645 Mon Sep 17 00:00:00 2001
From: Jan Ferdinand Sauer <ferdinand@neptune.cash>
Date: Fri, 22 Mar 2024 14:20:59 +0100
Subject: [PATCH] =?UTF-8?q?test:=20benchmark=20B=C3=A9zout=20coefficient?=
 =?UTF-8?q?=20computation?=
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---
 triton-vm/Cargo.toml               |  4 ++
 triton-vm/benches/bezout_coeffs.rs | 63 ++++++++++++++++++++++++++++++
 triton-vm/src/table/ram_table.rs   | 14 ++++---
 3 files changed, 76 insertions(+), 5 deletions(-)
 create mode 100644 triton-vm/benches/bezout_coeffs.rs

diff --git a/triton-vm/Cargo.toml b/triton-vm/Cargo.toml
index 9cd9105d..7d62b2bb 100644
--- a/triton-vm/Cargo.toml
+++ b/triton-vm/Cargo.toml
@@ -51,6 +51,10 @@ test-strategy.workspace = true
 [lints]
 workspace = true
 
+[[bench]]
+name = "bezout_coeffs"
+harness = false
+
 [[bench]]
 name = "mem_io"
 harness = false
diff --git a/triton-vm/benches/bezout_coeffs.rs b/triton-vm/benches/bezout_coeffs.rs
new file mode 100644
index 00000000..118bb42a
--- /dev/null
+++ b/triton-vm/benches/bezout_coeffs.rs
@@ -0,0 +1,63 @@
+use criterion::criterion_group;
+use criterion::criterion_main;
+use criterion::Criterion;
+use num_traits::Zero;
+use twenty_first::prelude::b_field_element::BFIELD_ONE;
+use twenty_first::prelude::*;
+
+use triton_vm::prelude::*;
+use triton_vm::table::ram_table::RamTable;
+
+criterion_main!(benches);
+criterion_group!(
+    name = benches;
+    config = Criterion::default().sample_size(10);
+    targets = current_design<10>,
+              current_design<100>,
+              current_design<1_000>,
+              current_design<10_000>,
+              with_xgcd<10>,
+              with_xgcd<100>,
+              with_xgcd<1_000>,
+              with_xgcd<10_000>,
+);
+
+fn with_xgcd<const N: u64>(c: &mut Criterion) {
+    let roots = unique_roots::<N>();
+    let bench_id = format!("Bézout coefficients (XGCD) (degree {N})");
+    c.bench_function(&bench_id, |b| b.iter(|| bezout_coeffs_xgcd(&roots)));
+}
+
+fn current_design<const N: u64>(c: &mut Criterion) {
+    let roots = unique_roots::<N>();
+    let bench_id = format!("Bézout coefficients (current design) (degree {N})");
+    c.bench_function(&bench_id, |b| {
+        b.iter(|| RamTable::bezout_coefficient_polynomials_coefficients(&roots))
+    });
+}
+
+fn unique_roots<const N: u64>() -> Vec<BFieldElement> {
+    (0..N).map(BFieldElement::new).collect()
+}
+
+fn bezout_coeffs_xgcd(
+    unique_ram_pointers: &[BFieldElement],
+) -> (Vec<BFieldElement>, Vec<BFieldElement>) {
+    let linear_poly_with_root = |&r: &BFieldElement| Polynomial::new(vec![-r, BFIELD_ONE]);
+
+    let polynomial_with_ram_pointers_as_roots = unique_ram_pointers
+        .iter()
+        .map(linear_poly_with_root)
+        .reduce(|accumulator, linear_poly| accumulator * linear_poly)
+        .unwrap_or_else(Polynomial::zero);
+    let formal_derivative = polynomial_with_ram_pointers_as_roots.formal_derivative();
+
+    let (_, bezout_poly_0, bezout_poly_1) =
+        Polynomial::xgcd(polynomial_with_ram_pointers_as_roots, formal_derivative);
+
+    let mut coefficients_0 = bezout_poly_0.coefficients;
+    let mut coefficients_1 = bezout_poly_1.coefficients;
+    coefficients_0.resize(unique_ram_pointers.len(), bfe!(0));
+    coefficients_1.resize(unique_ram_pointers.len(), bfe!(0));
+    (coefficients_0, coefficients_1)
+}
diff --git a/triton-vm/src/table/ram_table.rs b/triton-vm/src/table/ram_table.rs
index 88dc574e..0ff3e0c6 100644
--- a/triton-vm/src/table/ram_table.rs
+++ b/triton-vm/src/table/ram_table.rs
@@ -101,12 +101,16 @@ impl RamTable {
         compare_ram_pointers.then(compare_clocks)
     }
 
-    fn bezout_coefficient_polynomials_coefficients(
-        unique_ram_pointers: &[BFieldElement],
+    /// Compute the [Bézout coefficients](https://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity)
+    /// of the polynomial with the given roots and its formal derivative.
+    ///
+    /// All roots _must_ be unique. That is, the corresponding polynomial must be square free.
+    pub fn bezout_coefficient_polynomials_coefficients(
+        unique_roots: &[BFieldElement],
     ) -> (Vec<BFieldElement>, Vec<BFieldElement>) {
         let linear_poly_with_root = |&r: &BFieldElement| Polynomial::new(vec![-r, BFIELD_ONE]);
 
-        let polynomial_with_ram_pointers_as_roots = unique_ram_pointers
+        let polynomial_with_ram_pointers_as_roots = unique_roots
             .iter()
             .map(linear_poly_with_root)
             .reduce(|accumulator, linear_poly| accumulator * linear_poly)
@@ -118,8 +122,8 @@ impl RamTable {
 
         let mut coefficients_0 = bezout_poly_0.coefficients;
         let mut coefficients_1 = bezout_poly_1.coefficients;
-        coefficients_0.resize(unique_ram_pointers.len(), bfe!(0));
-        coefficients_1.resize(unique_ram_pointers.len(), bfe!(0));
+        coefficients_0.resize(unique_roots.len(), bfe!(0));
+        coefficients_1.resize(unique_roots.len(), bfe!(0));
         (coefficients_0, coefficients_1)
     }