refactor: Don't require trait to invert element

Author: jan-ferdinand

twenty-first/benches/inverses.rs

@@ -5,13 +5,12 @@ use criterion::Criterion;
 use itertools::Itertools;
 use twenty_first::math::b_field_element::BFieldElement;
 use twenty_first::math::other::random_elements;
-use twenty_first::math::traits::Inverse;
 
 /// Run with `cargo criterion --bench inverse`
 fn inverse(c: &mut Criterion) {
     let mut group = c.benchmark_group("Inverses");
     group.sample_size(10); // runs
-    let count = 1024 * 1024; // count of elements to be inversed per run
+    let count = 1024 * 1024; // count of elements to be inverted per run
 
     let rnd_elems: Vec<BFieldElement> = random_elements(count);
 

twenty-first/src/math/b_field_element.rs

@@ -234,6 +234,40 @@ impl BFieldElement {
         self.canonical_representation()
     }
 
+    #[must_use]
+    #[inline]
+    pub fn inverse(&self) -> Self {
+        #[inline(always)]
+        const fn exp(base: BFieldElement, exponent: u64) -> BFieldElement {
+            let mut res = base;
+            let mut i = 0;
+            while i < exponent {
+                res = BFieldElement(BFieldElement::montyred(res.0 as u128 * res.0 as u128));
+                i += 1;
+            }
+            res
+        }
+
+        let x = *self;
+        assert_ne!(
+            x,
+            Self::zero(),
+            "Attempted to find the multiplicative inverse of zero."
+        );
+
+        let bin_2_ones = x.square() * x;
+        let bin_3_ones = bin_2_ones.square() * x;
+        let bin_6_ones = exp(bin_3_ones, 3) * bin_3_ones;
+        let bin_12_ones = exp(bin_6_ones, 6) * bin_6_ones;
+        let bin_24_ones = exp(bin_12_ones, 12) * bin_12_ones;
+        let bin_30_ones = exp(bin_24_ones, 6) * bin_6_ones;
+        let bin_31_ones = bin_30_ones.square() * x;
+        let bin_31_ones_1_zero = bin_31_ones.square();
+        let bin_32_ones = bin_31_ones.square() * x;
+
+        exp(bin_31_ones_1_zero, 32) * bin_32_ones
+    }
+
     #[inline]
     /// Square the base M times and multiply the result by the tail value
     pub const fn power_accumulator<const N: usize, const M: usize>(
@@ -582,35 +616,7 @@ impl Inverse for BFieldElement {
     #[must_use]
     #[inline]
     fn inverse(&self) -> Self {
-        let x = *self;
-        assert_ne!(
-            x,
-            Self::zero(),
-            "Attempted to find the multiplicative inverse of zero."
-        );
-
-        #[inline(always)]
-        const fn exp(base: BFieldElement, exponent: u64) -> BFieldElement {
-            let mut res = base;
-            let mut i = 0;
-            while i < exponent {
-                res = BFieldElement(BFieldElement::montyred(res.0 as u128 * res.0 as u128));
-                i += 1;
-            }
-            res
-        }
-
-        let bin_2_ones = x.square() * x;
-        let bin_3_ones = bin_2_ones.square() * x;
-        let bin_6_ones = exp(bin_3_ones, 3) * bin_3_ones;
-        let bin_12_ones = exp(bin_6_ones, 6) * bin_6_ones;
-        let bin_24_ones = exp(bin_12_ones, 12) * bin_12_ones;
-        let bin_30_ones = exp(bin_24_ones, 6) * bin_6_ones;
-        let bin_31_ones = bin_30_ones.square() * x;
-        let bin_31_ones_1_zero = bin_31_ones.square();
-        let bin_32_ones = bin_31_ones.square() * x;
-
-        exp(bin_31_ones_1_zero, 32) * bin_32_ones
+        self.inverse()
     }
 }
 

twenty-first/src/math/traits.rs

@@ -28,6 +28,12 @@ pub trait Inverse
 where
     Self: Sized + Zero,
 {
+    /// The multiplicative inverse: `a * a.inverse() == 1`
+    ///
+    /// # Panics
+    ///
+    /// Panics if `self` does not have a multiplicative inverse, for example, when
+    /// `self` is zero. (For fields, this is the only case.)
     fn inverse(&self) -> Self;
 
     fn inverse_or_zero(&self) -> Self {

twenty-first/src/math/x_field_element.rs

@@ -278,6 +278,17 @@ impl XFieldElement {
         Self::new([element, zero, zero])
     }
 
+    #[must_use]
+    pub fn inverse(&self) -> Self {
+        assert!(
+            !self.is_zero(),
+            "Cannot invert the zero element in the extension field."
+        );
+        let self_as_poly: Polynomial<BFieldElement> = self.to_owned().into();
+        let (_, a, _) = Polynomial::<BFieldElement>::xgcd(self_as_poly, Self::shah_polynomial());
+        a.into()
+    }
+
     pub fn unlift(&self) -> Option<BFieldElement> {
         if self.coefficients[1].is_zero() && self.coefficients[2].is_zero() {
             Some(self.coefficients[0])
@@ -299,13 +310,7 @@ impl XFieldElement {
 impl Inverse for XFieldElement {
     #[must_use]
     fn inverse(&self) -> Self {
-        assert!(
-            !self.is_zero(),
-            "Cannot invert the zero element in the extension field."
-        );
-        let self_as_poly: Polynomial<BFieldElement> = self.to_owned().into();
-        let (_, a, _) = Polynomial::<BFieldElement>::xgcd(self_as_poly, Self::shah_polynomial());
-        a.into()
+        self.inverse()
     }
 }