compute R2 at compile time instead of hardcoding

src/lib.zig

@@ -135,7 +135,9 @@ pub const Element = struct {
     pub const MODULUS: u254 = 0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001;
     /// `R = M % MODULUS` where `M` is the power of `2^64` closest to the number of bits
     ///  required to represent the field modulus.
-    pub const R = (std.math.powi(u257, 2, 256) catch @panic("failed to compute R")) % MODULUS;
+    pub const R: u256 = (std.math.powi(u257, 2, 256) catch @panic("failed to compute R")) % MODULUS;
+    /// `R2 = R^2 % MODULUS`
+    pub const R2: u256 = (std.math.powi(u512, R, 2) catch @panic("failed to compute R2")) % MODULUS;
     /// `INVERSE = -MODULUS ^ (-1) mod 2^254`
     ///
     /// `INVERSE = R ^ (-1)`
@@ -196,6 +198,8 @@ pub const Element = struct {
         const high_mod_prod: u256 = @truncate(mod_prod >> 256);
         const add_overflow: u1 = @addWithOverflow(self.value, low_mod_prod)[1];
         const adjusted_diff = add_overflow + high_mod_prod;
+
+        // TODO: this is just a compare and reduce
         const carry_adjust, const is_carry_adjusted = @subWithOverflow(adjusted_diff, MODULUS);
         const is_negative = @subWithOverflow(0, is_carry_adjusted)[1];
         const result = if (is_negative == 0) carry_adjust else adjusted_diff;
@@ -204,16 +208,17 @@ pub const Element = struct {
 
     /// Translates a field element into of the Montgomery domain.
     pub fn fromInteger(integer: u256) Element {
-        const product = @as(u512, integer) *
-            @as(u512, 0x216d0b17f4e44a58c49833d53bb808553fe3ab1e35c59e31bb8e645ae216da7);
+        const product = @as(u512, integer) * @as(u512, R2);
         const low_prod: u256 = @truncate(product);
         const high_prod: u256 = @truncate(product >> 256);
         const n_prod: u256 = @truncate(@as(u512, low_prod) * @as(u512, INVERSE));
         const mod_prod = @as(u512, n_prod) * MODULUS;
         const low_mod_prod: u256 = @truncate(mod_prod);
         const high_mod_prod: u256 = @truncate(mod_prod >> 256);
         const add_overflow = @addWithOverflow(low_prod, low_mod_prod)[1];
-        const adjusted_diff = (@as(u256, add_overflow) + high_prod) + high_mod_prod;
+        const adjusted_diff = add_overflow + high_prod + high_mod_prod;
+
+        // TODO: this is just a compare and reduce
         const carry_adjust, const is_carry_adjusted = @subWithOverflow(adjusted_diff, MODULUS);
         const is_negative = @subWithOverflow(0, is_carry_adjusted)[1];
         const result = if (is_negative == 0) carry_adjust else adjusted_diff;