Batch inverse (ported from plonky1)

src/field/batch_inverse.rs

@@ -0,0 +1,30 @@
+use crate::field::field::Field;
+
+fn batch_multiplicative_inverse<F: Field>(x: &[F]) -> Vec<F> {
+    // This is Montgomery's trick. At a high level, we invert the product of the given field
+    // elements, then derive the individual inverses from that via multiplication.
+
+    let n = x.len();
+    if n == 0 {
+        return Vec::new();
+    }
+
+    let mut a = Vec::with_capacity(n);
+    a.push(x[0]);
+    for i in 1..n {
+        a.push(a[i - 1] * x[i]);
+    }
+
+    let mut a_inv = vec![F::ZERO; n];
+    a_inv[n - 1] = a[n - 1].try_inverse().expect("No inverse");
+    for i in (0..n - 1).rev() {
+        a_inv[i] = x[i + 1] * a_inv[i + 1];
+    }
+
+    let mut x_inv = Vec::with_capacity(n);
+    x_inv.push(a_inv[0]);
+    for i in 1..n {
+        x_inv.push(a[i - 1] * a_inv[i]);
+    }
+    x_inv
+}

src/field/mod.rs

@@ -1,3 +1,4 @@
+pub(crate) mod batch_inverse;
 pub(crate) mod crandall_field;
 pub(crate) mod field;
 pub(crate) mod field_search;