Add WideningMul trait

Adds a trait for performing widening multiplication, with an output
whose size is equal to the sum of the inputs.

Author: tarcieri

src/traits.rs

@@ -272,7 +272,7 @@ pub trait CheckedSub<Rhs = Self>: Sized {
 /// value as the least significant value.
 pub trait Concat: ConcatMixed<Self, MixedOutput = Self::Output> {
     /// Concatenated output: twice the width of `Self`.
-    type Output;
+    type Output: Integer;
 
     /// Concatenate the two halves, with `self` as most significant and `lo`
     /// as the least significant.
@@ -285,7 +285,7 @@ pub trait Concat: ConcatMixed<Self, MixedOutput = Self::Output> {
 /// value as the least significant value.
 pub trait ConcatMixed<Lo: ?Sized = Self> {
     /// Concatenated output: combination of `Lo` and `Self`.
-    type MixedOutput;
+    type MixedOutput: Integer;
 
     /// Concatenate the two values, with `self` as most significant and `lo`
     /// as the least significant.
@@ -416,3 +416,12 @@ pub trait Invert: Sized {
     /// Computes the inverse.
     fn invert(&self) -> Self::Output;
 }
+
+/// Widening multiply: returns a value with a number of limbs equal to the sum of the inputs.
+pub trait WideningMul<Rhs = Self>: Sized {
+    /// Output of the widening multiplication.
+    type Output: Integer;
+
+    /// Perform widening multiplication.
+    fn widening_mul(&self, rhs: Rhs) -> Self::Output;
+}

src/uint/boxed/mul.rs

@@ -1,6 +1,6 @@
 //! [`BoxedUint`] multiplication operations.
 
-use crate::{uint::mul::mul_limbs, BoxedUint, CheckedMul, Limb, Wrapping, Zero};
+use crate::{uint::mul::mul_limbs, BoxedUint, CheckedMul, Limb, WideningMul, Wrapping, Zero};
 use core::ops::{Mul, MulAssign};
 use subtle::{Choice, CtOption};
 
@@ -26,6 +26,14 @@ impl BoxedUint {
     }
 }
 
+impl CheckedMul<BoxedUint> for BoxedUint {
+    type Output = Self;
+
+    fn checked_mul(&self, rhs: BoxedUint) -> CtOption<Self> {
+        self.checked_mul(&rhs)
+    }
+}
+
 impl CheckedMul<&BoxedUint> for BoxedUint {
     type Output = Self;
 
@@ -43,6 +51,24 @@ impl CheckedMul<&BoxedUint> for BoxedUint {
     }
 }
 
+impl WideningMul for BoxedUint {
+    type Output = Self;
+
+    #[inline]
+    fn widening_mul(&self, rhs: BoxedUint) -> Self {
+        self.mul(&rhs)
+    }
+}
+
+impl WideningMul<&BoxedUint> for BoxedUint {
+    type Output = Self;
+
+    #[inline]
+    fn widening_mul(&self, rhs: &BoxedUint) -> Self {
+        self.mul(&rhs)
+    }
+}
+
 impl Mul<Wrapping<BoxedUint>> for Wrapping<BoxedUint> {
     type Output = Self;
 

src/uint/mul.rs

@@ -2,7 +2,10 @@
 
 // TODO(tarcieri): use Karatsuba for better performance
 
-use crate::{Checked, CheckedMul, Concat, ConcatMixed, Limb, Uint, WideWord, Word, Wrapping, Zero};
+use crate::{
+    Checked, CheckedMul, Concat, ConcatMixed, Limb, Uint, WideWord, WideningMul, Word, Wrapping,
+    Zero,
+};
 use core::ops::{Mul, MulAssign};
 use subtle::CtOption;
 
@@ -165,15 +168,49 @@ impl<const LIMBS: usize> Uint<LIMBS> {
     }
 }
 
+impl<const LIMBS: usize, const HLIMBS: usize> CheckedMul<Uint<HLIMBS>> for Uint<LIMBS> {
+    type Output = Self;
+
+    #[inline]
+    fn checked_mul(&self, rhs: Uint<HLIMBS>) -> CtOption<Self> {
+        self.checked_mul(&rhs)
+    }
+}
+
 impl<const LIMBS: usize, const HLIMBS: usize> CheckedMul<&Uint<HLIMBS>> for Uint<LIMBS> {
     type Output = Self;
 
+    #[inline]
     fn checked_mul(&self, rhs: &Uint<HLIMBS>) -> CtOption<Self> {
         let (lo, hi) = self.mul_wide(rhs);
         CtOption::new(lo, hi.is_zero())
     }
 }
 
+impl<const LIMBS: usize, const HLIMBS: usize> WideningMul<Uint<HLIMBS>> for Uint<LIMBS>
+where
+    Uint<HLIMBS>: ConcatMixed<Self>,
+{
+    type Output = <Uint<HLIMBS> as ConcatMixed<Self>>::MixedOutput;
+
+    #[inline]
+    fn widening_mul(&self, rhs: Uint<HLIMBS>) -> Self::Output {
+        self.mul(&rhs)
+    }
+}
+
+impl<const LIMBS: usize, const HLIMBS: usize> WideningMul<&Uint<HLIMBS>> for Uint<LIMBS>
+where
+    Uint<HLIMBS>: ConcatMixed<Self>,
+{
+    type Output = <Uint<HLIMBS> as ConcatMixed<Self>>::MixedOutput;
+
+    #[inline]
+    fn widening_mul(&self, rhs: &Uint<HLIMBS>) -> Self::Output {
+        self.mul(rhs)
+    }
+}
+
 impl<const LIMBS: usize, const HLIMBS: usize> Mul<Wrapping<Uint<HLIMBS>>>
     for Wrapping<Uint<LIMBS>>
 {