MVPoly: util to compute nested loops indices

It will be used later in the cross-term computation to perform the multi-nomial
sum

mvpoly/src/utils.rs

@@ -219,3 +219,50 @@ pub fn compute_all_two_factors_decomposition(
         factors
     }
 }
+
+/// Compute the list of indices to perform N nested loops of different size each.
+/// In other words, if we have to perform the 3 nested loops:
+/// ```rust
+/// let n1 = 3;
+/// let n2 = 3;
+/// let n3 = 5;
+/// for i in 0..n1 {
+///   for j in 0..n2 {
+///     for k in 0..n3 {
+///     }
+///   }
+/// }
+/// ```
+/// the output will be all the possible values of `i`, `j`, and `k`.
+/// The algorithm is as follows:
+/// ```rust
+/// for l in 0..(n1 * n2 * n3) {
+///   i = l               % n1;
+///   j = (l / n1)        % n2;
+///   k = (l / (n1 * n2)) % n3;
+/// }
+/// ```
+/// For N nested loops, the algorithm is the same, with the division increasing
+/// by the factor `N_k` for the index `i_(k + 1)`
+pub fn compute_indices_nested_loop(nested_loop_sizes: Vec<usize>) -> Vec<Vec<usize>> {
+    let n = nested_loop_sizes.iter().product();
+    (0..n)
+        .map(|i| {
+            let mut div = 1;
+            // Compute indices for the loop, step i
+            let indices: Vec<usize> = nested_loop_sizes
+                .iter()
+                .map(|n_i| {
+                    let k = (i / div) % n_i;
+                    div *= n_i;
+                    k
+                })
+                .collect();
+            assert!(
+                div == n,
+                "The division must be equal to the number of terms at the end"
+            );
+            indices
+        })
+        .collect()
+}

mvpoly/tests/utils.rs

@@ -1,8 +1,8 @@
 use std::collections::HashMap;
 
 use mvpoly::utils::{
-    compute_all_two_factors_decomposition, get_mapping_with_primes, is_prime, naive_prime_factors,
-    PrimeNumberGenerator,
+    compute_all_two_factors_decomposition, compute_indices_nested_loop, get_mapping_with_primes,
+    is_prime, naive_prime_factors, PrimeNumberGenerator,
 };
 
 pub const FIRST_FIFTY_PRIMES: [usize; 50] = [
@@ -225,3 +225,74 @@ pub fn test_compute_all_two_factors_decomposition_with_multiplicity() {
         .to_vec()
     );
 }
+
+#[test]
+pub fn test_compute_indices_nested_loop() {
+    let nested_loops = vec![2, 2];
+    // sorting to get the same order
+    let mut exp_indices = vec![vec![0, 0], vec![0, 1], vec![1, 0], vec![1, 1]];
+    exp_indices.sort();
+    let mut comp_indices = compute_indices_nested_loop(nested_loops);
+    comp_indices.sort();
+    assert_eq!(exp_indices, comp_indices);
+
+    let nested_loops = vec![3, 2];
+    // sorting to get the same order
+    let mut exp_indices = vec![
+        vec![0, 0],
+        vec![0, 1],
+        vec![1, 0],
+        vec![1, 1],
+        vec![2, 0],
+        vec![2, 1],
+    ];
+    exp_indices.sort();
+    let mut comp_indices = compute_indices_nested_loop(nested_loops);
+    comp_indices.sort();
+    assert_eq!(exp_indices, comp_indices);
+
+    let nested_loops = vec![3, 3, 2, 2];
+    // sorting to get the same order
+    let mut exp_indices = vec![
+        vec![0, 0, 0, 0],
+        vec![0, 0, 0, 1],
+        vec![0, 0, 1, 0],
+        vec![0, 0, 1, 1],
+        vec![0, 1, 0, 0],
+        vec![0, 1, 0, 1],
+        vec![0, 1, 1, 0],
+        vec![0, 1, 1, 1],
+        vec![0, 2, 0, 0],
+        vec![0, 2, 0, 1],
+        vec![0, 2, 1, 0],
+        vec![0, 2, 1, 1],
+        vec![1, 0, 0, 0],
+        vec![1, 0, 0, 1],
+        vec![1, 0, 1, 0],
+        vec![1, 0, 1, 1],
+        vec![1, 1, 0, 0],
+        vec![1, 1, 0, 1],
+        vec![1, 1, 1, 0],
+        vec![1, 1, 1, 1],
+        vec![1, 2, 0, 0],
+        vec![1, 2, 0, 1],
+        vec![1, 2, 1, 0],
+        vec![1, 2, 1, 1],
+        vec![2, 0, 0, 0],
+        vec![2, 0, 0, 1],
+        vec![2, 0, 1, 0],
+        vec![2, 0, 1, 1],
+        vec![2, 1, 0, 0],
+        vec![2, 1, 0, 1],
+        vec![2, 1, 1, 0],
+        vec![2, 1, 1, 1],
+        vec![2, 2, 0, 0],
+        vec![2, 2, 0, 1],
+        vec![2, 2, 1, 0],
+        vec![2, 2, 1, 1],
+    ];
+    exp_indices.sort();
+    let mut comp_indices = compute_indices_nested_loop(nested_loops);
+    comp_indices.sort();
+    assert_eq!(exp_indices, comp_indices);
+}