Add unreduced field arithmetic (#116)

stwo_cairo_verifier/src/fields/cm31.cairo

@@ -1,5 +1,6 @@
 use core::num::traits::{One, Zero};
-use super::m31::{M31, m31, M31Trait};
+use core::ops::{AddAssign, MulAssign, SubAssign};
+use super::m31::{M31, M31Impl, m31, M31Trait};
 
 #[derive(Copy, Drop, Debug, PartialEq)]
 pub struct CM31 {
@@ -14,34 +15,104 @@ pub impl CM31Impl of CM31Trait {
         let denom_inverse: M31 = (self.a * self.a + self.b * self.b).inverse();
         CM31 { a: self.a * denom_inverse, b: -self.b * denom_inverse }
     }
+
+    /// Computes all `1/arr[i]` with a single call to `inverse()` using Montgomery batch inversion.
+    fn batch_inverse(arr: Array<CM31>) -> Array<CM31> {
+        // Construct array `1, z, zy, ..., zy..b`.
+        let mut prefix_product_rev = array![];
+        let mut cumulative_product: CM31 = One::one();
+
+        let mut i = arr.len();
+        while i != 0 {
+            i -= 1;
+            prefix_product_rev.append(cumulative_product);
+            cumulative_product *= *arr[i];
+        };
+
+        // Compute `1/zy..a`.
+        let mut cumulative_product_inv = cumulative_product.inverse();
+        // Compute all `1/a = zy..b/zy..a, 1/b = zy..c/zy..b, ...`.
+        let mut inverses = array![];
+
+        let mut i = prefix_product_rev.len();
+        for v in arr {
+            i -= 1;
+            inverses.append(cumulative_product_inv * *prefix_product_rev[i]);
+            cumulative_product_inv *= v;
+        };
+
+        inverses
+    }
+
+    // TODO(andrew): When associated types are supported, support `Mul<CM31, M31>`.
+    #[inline]
+    fn mul_m31(self: CM31, rhs: M31) -> CM31 {
+        CM31 { a: self.a * rhs, b: self.b * rhs }
+    }
+
+    // TODO(andrew): When associated types are supported, support `Sub<CM31, M31>`.
+    #[inline]
+    fn sub_m31(self: CM31, rhs: M31) -> CM31 {
+        CM31 { a: self.a - rhs, b: self.b }
+    }
 }
 
 pub impl CM31Add of core::traits::Add<CM31> {
+    #[inline]
     fn add(lhs: CM31, rhs: CM31) -> CM31 {
         CM31 { a: lhs.a + rhs.a, b: lhs.b + rhs.b }
     }
 }
+
 pub impl CM31Sub of core::traits::Sub<CM31> {
+    #[inline]
     fn sub(lhs: CM31, rhs: CM31) -> CM31 {
         CM31 { a: lhs.a - rhs.a, b: lhs.b - rhs.b }
     }
 }
+
 pub impl CM31Mul of core::traits::Mul<CM31> {
+    #[inline]
     fn mul(lhs: CM31, rhs: CM31) -> CM31 {
         CM31 { a: lhs.a * rhs.a - lhs.b * rhs.b, b: lhs.a * rhs.b + lhs.b * rhs.a }
     }
 }
+
+pub impl CM31AddAssign of AddAssign<CM31, CM31> {
+    #[inline]
+    fn add_assign(ref self: CM31, rhs: CM31) {
+        self = self + rhs
+    }
+}
+
+pub impl CM31SubAssign of SubAssign<CM31, CM31> {
+    #[inline]
+    fn sub_assign(ref self: CM31, rhs: CM31) {
+        self = self - rhs
+    }
+}
+
+pub impl CM31MulAssign of MulAssign<CM31, CM31> {
+    #[inline]
+    fn mul_assign(ref self: CM31, rhs: CM31) {
+        self = self * rhs
+    }
+}
+
 pub impl CM31Zero of Zero<CM31> {
     fn zero() -> CM31 {
         cm31(0, 0)
     }
+
     fn is_zero(self: @CM31) -> bool {
         (*self).a.is_zero() && (*self).b.is_zero()
     }
+
     fn is_non_zero(self: @CM31) -> bool {
         (*self).a.is_non_zero() || (*self).b.is_non_zero()
     }
 }
+
 pub impl CM31One of One<CM31> {
     fn one() -> CM31 {
         cm31(1, 0)
@@ -53,17 +124,28 @@ pub impl CM31One of One<CM31> {
         (*self).a.is_non_one() || (*self).b.is_non_zero()
     }
 }
+
 pub impl M31IntoCM31 of core::traits::Into<M31, CM31> {
+    #[inline]
     fn into(self: M31) -> CM31 {
         CM31 { a: self, b: m31(0) }
     }
 }
+
 pub impl CM31Neg of Neg<CM31> {
+    #[inline]
     fn neg(a: CM31) -> CM31 {
         CM31 { a: -a.a, b: -a.b }
     }
 }
 
+impl CM31PartialOrd of PartialOrd<CM31> {
+    fn lt(lhs: CM31, rhs: CM31) -> bool {
+        lhs.a < rhs.a || (lhs.a == rhs.a && lhs.b < rhs.b)
+    }
+}
+
+#[inline]
 pub fn cm31(a: u32, b: u32) -> CM31 {
     CM31 { a: m31(a), b: m31(b) }
 }

stwo_cairo_verifier/src/fields/m31.cairo

@@ -1,28 +1,45 @@
 use core::num::traits::{WideMul, CheckedSub};
+use core::ops::{AddAssign, MulAssign, SubAssign};
 use core::option::OptionTrait;
 use core::traits::TryInto;
 
+/// Equals `2^31 - 1`.
 pub const P: u32 = 0x7fffffff;
+
+/// Equals `2^31 - 1`.
 const P32NZ: NonZero<u32> = 0x7fffffff;
+
+/// Equals `2^31 - 1`.
 const P64NZ: NonZero<u64> = 0x7fffffff;
 
+/// Equals `2^31 - 1`.
+const P128NZ: NonZero<u128> = 0x7fffffff;
+
 #[derive(Copy, Drop, Debug, PartialEq)]
 pub struct M31 {
     pub inner: u32
 }
 
 #[generate_trait]
 pub impl M31Impl of M31Trait {
+    #[inline]
     fn reduce_u32(val: u32) -> M31 {
         let (_, res) = core::integer::u32_safe_divmod(val, P32NZ);
         M31 { inner: res.try_into().unwrap() }
     }
 
+    #[inline]
     fn reduce_u64(val: u64) -> M31 {
         let (_, res) = core::integer::u64_safe_divmod(val, P64NZ);
         M31 { inner: res.try_into().unwrap() }
     }
 
+    #[inline]
+    fn reduce_u128(val: u128) -> M31 {
+        let (_, res) = core::integer::u128_safe_divmod(val, P128NZ);
+        M31 { inner: res.try_into().unwrap() }
+    }
+
     #[inline]
     fn sqn(v: M31, n: usize) -> M31 {
         if n == 0 {
@@ -43,45 +60,81 @@ pub impl M31Impl of M31Trait {
     }
 }
 pub impl M31Add of core::traits::Add<M31> {
+    #[inline]
     fn add(lhs: M31, rhs: M31) -> M31 {
         let res = lhs.inner + rhs.inner;
         let res = res.checked_sub(P).unwrap_or(res);
         M31 { inner: res }
     }
 }
+
 pub impl M31Sub of core::traits::Sub<M31> {
+    #[inline]
     fn sub(lhs: M31, rhs: M31) -> M31 {
         lhs + (-rhs)
     }
 }
+
 pub impl M31Mul of core::traits::Mul<M31> {
+    #[inline]
     fn mul(lhs: M31, rhs: M31) -> M31 {
         M31Impl::reduce_u64(lhs.inner.wide_mul(rhs.inner))
     }
 }
+
+pub impl M31AddAssign of AddAssign<M31, M31> {
+    #[inline]
+    fn add_assign(ref self: M31, rhs: M31) {
+        self = self + rhs
+    }
+}
+
+pub impl M31SubAssign of SubAssign<M31, M31> {
+    #[inline]
+    fn sub_assign(ref self: M31, rhs: M31) {
+        self = self - rhs
+    }
+}
+
+pub impl M31MulAssign of MulAssign<M31, M31> {
+    #[inline]
+    fn mul_assign(ref self: M31, rhs: M31) {
+        self = self * rhs
+    }
+}
+
 pub impl M31Zero of core::num::traits::Zero<M31> {
+    #[inline]
     fn zero() -> M31 {
         M31 { inner: 0 }
     }
+
     fn is_zero(self: @M31) -> bool {
         *self.inner == 0
     }
+
     fn is_non_zero(self: @M31) -> bool {
         *self.inner != 0
     }
 }
+
 pub impl M31One of core::num::traits::One<M31> {
+    #[inline]
     fn one() -> M31 {
         M31 { inner: 1 }
     }
+
     fn is_one(self: @M31) -> bool {
         *self.inner == 1
     }
+
     fn is_non_one(self: @M31) -> bool {
         *self.inner != 1
     }
 }
+
 pub impl M31Neg of Neg<M31> {
+    #[inline]
     fn neg(a: M31) -> M31 {
         if a.inner == 0 {
             M31 { inner: 0 }
@@ -90,16 +143,55 @@ pub impl M31Neg of Neg<M31> {
         }
     }
 }
+
 impl M31IntoFelt252 of Into<M31, felt252> {
+    #[inline]
     fn into(self: M31) -> felt252 {
         self.inner.into()
     }
 }
 
+impl M31PartialOrd of PartialOrd<M31> {
+    fn ge(lhs: M31, rhs: M31) -> bool {
+        lhs.inner >= rhs.inner
+    }
+
+    fn lt(lhs: M31, rhs: M31) -> bool {
+        lhs.inner < rhs.inner
+    }
+}
+
+#[inline]
 pub fn m31(val: u32) -> M31 {
     M31Impl::reduce_u32(val)
 }
 
+#[derive(Copy, Drop, Debug)]
+pub struct UnreducedM31 {
+    pub inner: felt252,
+}
+
+pub impl UnreducedM31Sub of Sub<UnreducedM31> {
+    #[inline]
+    fn sub(lhs: UnreducedM31, rhs: UnreducedM31) -> UnreducedM31 {
+        UnreducedM31 { inner: lhs.inner - rhs.inner }
+    }
+}
+
+pub impl UnreducedM31Add of Add<UnreducedM31> {
+    #[inline]
+    fn add(lhs: UnreducedM31, rhs: UnreducedM31) -> UnreducedM31 {
+        UnreducedM31 { inner: lhs.inner + rhs.inner }
+    }
+}
+
+impl M31IntoUnreducedM31 of Into<M31, UnreducedM31> {
+    #[inline]
+    fn into(self: M31) -> UnreducedM31 {
+        UnreducedM31 { inner: self.inner.into() }
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::{m31, P, M31Trait};