Use double optimization where appropriate

Author: daxpedda

ed448-goldilocks/src/curve/twedwards/extended.rs

@@ -115,7 +115,7 @@ impl ExtendedPoint {
 
         // Compute x
         let xy = x * y;
-        let x_numerator = xy + xy;
+        let x_numerator = xy.double();
         let x_denom = y.square() - (a * x.square());
         let new_x = x_numerator * x_denom.invert();
 

ed448-goldilocks/src/curve/twedwards/extensible.rs

@@ -52,7 +52,7 @@ impl ExtensiblePoint {
     pub fn double(&self) -> ExtensiblePoint {
         let A = self.X.square();
         let B = self.Y.square();
-        let C = self.Z.square() + self.Z.square();
+        let C = self.Z.square().double();
         let D = -A;
         let E = (self.X + self.Y).square() - A - B;
         let G = D + B;

ed448-goldilocks/src/decaf/points.rs

@@ -550,7 +550,7 @@ impl CompressedDecaf {
         let (I, ok) = (v * u1_sqr).inverse_square_root();
 
         let Dx = I * u1;
-        let Dxs = (s + s) * Dx;
+        let Dxs = s.double() * Dx;
 
         let mut X = (Dxs * I) * v;
         let k = Dxs * FieldElement::DECAF_FACTOR;

ed448-goldilocks/src/edwards/extended.rs

@@ -673,7 +673,7 @@ impl EdwardsPoint {
 
         // Compute x
         let xy = x * y;
-        let x_numerator = xy + xy;
+        let x_numerator = xy.double();
         let x_denom = y.square() - (a * x.square());
         let new_x = x_numerator * x_denom.invert();
 

ed448-goldilocks/src/field/element.rs

@@ -317,7 +317,7 @@ impl FieldElement {
     }
 
     pub fn double(&self) -> Self {
-        Self(self.0.add(&self.0))
+        Self(self.0.double())
     }
 
     /// Computes the inverse square root of a field element
@@ -426,7 +426,7 @@ impl FieldElement {
         let b = b - Self::ONE;
 
         let c = a.square();
-        let a = a + a;
+        let a = a.double();
         let e = c + Self::ONE;
         let T = a * e;
         let X = a * b;

ed448-goldilocks/src/field/scalar.rs

@@ -314,7 +314,7 @@ impl<C: CurveWithScalar> Field for Scalar<C> {
     }
 
     fn double(&self) -> Self {
-        self + self
+        self.double()
     }
 
     fn invert(&self) -> CtOption<Self> {
@@ -641,7 +641,7 @@ impl<C: CurveWithScalar> Scalar<C> {
 
     /// Compute `self` + `self` mod ℓ
     pub const fn double(&self) -> Self {
-        self.addition(self)
+        Self::new(self.scalar.double_mod(&ORDER))
     }
 
     /// Compute `self` - `rhs` mod ℓ