Optimized transpose (#191)

* Start work on optimized transpose

* Optimized transpose: 12-14% improvement on benchmark

* Transpose: Avoid bounds checks and change order of loops dynamically

* Transpose: re-enable bounds checks

src/util/mod.rs

@@ -38,12 +38,32 @@ pub(crate) fn transpose_poly_values<F: Field>(polys: Vec<PolynomialValues<F>>) -
 pub fn transpose<F: Field>(matrix: &[Vec<F>]) -> Vec<Vec<F>> {
     let l = matrix.len();
     let w = matrix[0].len();
-    let mut transposed = vec![vec![F::ZERO; l]; w];
+
+    let mut transposed = vec![vec![]; w];
     for i in 0..w {
-        for j in 0..l {
-            transposed[i][j] = matrix[j][i];
+        transposed[i].reserve_exact(l);
+        unsafe {
+            // After .reserve_exact(l), transposed[i] will have capacity at least l. Hence, set_len
+            // will not cause the buffer to overrun.
+            transposed[i].set_len(l);
         }
     }
+
+    // Optimization: ensure the larger loop is outside.
+    if w >= l {
+        for i in 0..w {
+            for j in 0..l {
+                transposed[i][j] = matrix[j][i];
+            }
+        }
+    } else {
+        for j in 0..l {
+            for i in 0..w {
+                transposed[i][j] = matrix[j][i];
+            }
+        }
+    }
+
     transposed
 }