perf: stack-backed storage for exact arithmetic kernels

Cargo.toml

@@ -48,6 +48,11 @@ name = "vs_linalg"
 harness = false
 required-features = [ "bench" ]
 
+[[bench]]
+name = "exact"
+harness = false
+required-features = [ "bench", "exact" ]
+
 [profile.release]
 lto = "fat"
 codegen-units = 1

benches/exact.rs

@@ -0,0 +1,166 @@
+//! Benchmarks for exact arithmetic operations.
+//!
+//! These benchmarks measure the performance of the `exact` feature's
+//! arbitrary-precision methods across dimensions D=2..5 (the primary
+//! target for geometric predicates).
+
+use criterion::Criterion;
+use la_stack::{Matrix, Vector};
+use pastey::paste;
+use std::hint::black_box;
+
+#[inline]
+#[allow(clippy::cast_precision_loss)]
+const fn matrix_entry<const D: usize>(r: usize, c: usize) -> f64 {
+    if r == c {
+        (r as f64).mul_add(1.0e-3, (D as f64) + 1.0)
+    } else {
+        0.1 / ((r + c + 1) as f64)
+    }
+}
+
+#[inline]
+const fn make_matrix_rows<const D: usize>() -> [[f64; D]; D] {
+    let mut rows = [[0.0; D]; D];
+    let mut r = 0;
+    while r < D {
+        let mut c = 0;
+        while c < D {
+            rows[r][c] = matrix_entry::<D>(r, c);
+            c += 1;
+        }
+        r += 1;
+    }
+    rows
+}
+
+#[inline]
+#[allow(clippy::cast_precision_loss)]
+fn make_vector_array<const D: usize>() -> [f64; D] {
+    let mut data = [0.0; D];
+    let mut i = 0;
+    while i < D {
+        data[i] = (i as f64) + 1.0;
+        i += 1;
+    }
+    data
+}
+
+/// Near-singular matrix: base singular matrix + tiny perturbation.
+/// This forces the exact Bareiss fallback in `det_sign_exact` (the fast
+/// f64 filter cannot resolve the sign).
+#[inline]
+fn near_singular_3x3() -> Matrix<3> {
+    let perturbation = f64::from_bits(0x3CD0_0000_0000_0000); // 2^-50
+    Matrix::<3>::from_rows([
+        [1.0 + perturbation, 2.0, 3.0],
+        [4.0, 5.0, 6.0],
+        [7.0, 8.0, 9.0],
+    ])
+}
+
+macro_rules! gen_exact_benches_for_dim {
+    ($c:expr, $d:literal) => {
+        paste! {{
+            let a = Matrix::<$d>::from_rows(make_matrix_rows::<$d>());
+            let rhs = Vector::<$d>::new(make_vector_array::<$d>());
+
+            let mut [<group_d $d>] = ($c).benchmark_group(concat!("exact_d", stringify!($d)));
+
+            // === f64 baselines ===
+            [<group_d $d>].bench_function("det", |bencher| {
+                bencher.iter(|| {
+                    let det = black_box(a)
+                        .det(la_stack::DEFAULT_PIVOT_TOL)
+                        .expect("should not fail");
+                    black_box(det);
+                });
+            });
+
+            [<group_d $d>].bench_function("det_direct", |bencher| {
+                bencher.iter(|| {
+                    let det = black_box(a).det_direct();
+                    black_box(det);
+                });
+            });
+
+            // === det_exact (BigRational result) ===
+            [<group_d $d>].bench_function("det_exact", |bencher| {
+                bencher.iter(|| {
+                    let det = black_box(a).det_exact().expect("should not fail");
+                    black_box(det);
+                });
+            });
+
+            // === det_exact_f64 (exact → f64) ===
+            [<group_d $d>].bench_function("det_exact_f64", |bencher| {
+                bencher.iter(|| {
+                    let det = black_box(a).det_exact_f64().expect("should not fail");
+                    black_box(det);
+                });
+            });
+
+            // === det_sign_exact (adaptive: fast filter + exact fallback) ===
+            [<group_d $d>].bench_function("det_sign_exact", |bencher| {
+                bencher.iter(|| {
+                    let sign = black_box(a).det_sign_exact().expect("should not fail");
+                    black_box(sign);
+                });
+            });
+
+            // === solve_exact (BigRational result) ===
+            [<group_d $d>].bench_function("solve_exact", |bencher| {
+                bencher.iter(|| {
+                    let x = black_box(a).solve_exact(black_box(rhs)).expect("should not fail");
+                    black_box(x);
+                });
+            });
+
+            // === solve_exact_f64 (exact → f64) ===
+            [<group_d $d>].bench_function("solve_exact_f64", |bencher| {
+                bencher.iter(|| {
+                    let x = black_box(a).solve_exact_f64(black_box(rhs)).expect("should not fail");
+                    black_box(x);
+                });
+            });
+
+            [<group_d $d>].finish();
+        }};
+    };
+}
+
+fn main() {
+    let mut c = Criterion::default().configure_from_args();
+
+    #[allow(unused_must_use)]
+    {
+        gen_exact_benches_for_dim!(&mut c, 2);
+        gen_exact_benches_for_dim!(&mut c, 3);
+        gen_exact_benches_for_dim!(&mut c, 4);
+        gen_exact_benches_for_dim!(&mut c, 5);
+    }
+
+    // Near-singular 3×3: forces Bareiss fallback in det_sign_exact.
+    {
+        let m = near_singular_3x3();
+        let mut group = c.benchmark_group("exact_near_singular_3x3");
+
+        group.bench_function("det_sign_exact", |bencher| {
+            bencher.iter(|| {
+                let sign = black_box(m).det_sign_exact().expect("should not fail");
+                black_box(sign);
+            });
+        });
+
+        group.bench_function("det_exact", |bencher| {
+            bencher.iter(|| {
+                let det = black_box(m).det_exact().expect("should not fail");
+                black_box(det);
+            });
+        });
+
+        group.finish();
+    }
+
+    c.final_summary();
+}