Reverse Concat(Mixed)/Split(Mixed) argument ordering (#526)

Changes to a "little endian" `lo, hi` convention for the ordering of
arguments to concatenation methods and the ordering of the returned
2-tuple from split methods.

This is more consistent with the rest of the crate, and the
`Uint { limbs }` array which uses a little endian ordering.

Closes #519

src/modular.rs

@@ -121,7 +121,7 @@ mod tests {
     #[test]
     fn test_reducing_r2_wide() {
         // Divide the value ONE^2 by R, which should equal ONE
-        let (hi, lo) = Modulus2::ONE.square().split();
+        let (lo, hi) = Modulus2::ONE.square().split();
         assert_eq!(
             montgomery_reduction::<{ Modulus2::LIMBS }>(
                 &(lo, hi),
@@ -157,9 +157,9 @@ mod tests {
 
         // Computing xR mod modulus without Montgomery reduction
         let (lo, hi) = x.split_mul(&Modulus2::ONE);
-        let c = hi.concat(&lo);
-        let red = c.rem_vartime(&NonZero::new(U256::ZERO.concat(&Modulus2::MODULUS)).unwrap());
-        let (hi, lo) = red.split();
+        let c = lo.concat(&hi);
+        let red = c.rem_vartime(&NonZero::new(Modulus2::MODULUS.0.concat(&U256::ZERO)).unwrap());
+        let (lo, hi) = red.split();
         assert_eq!(hi, Uint::ZERO);
 
         assert_eq!(

src/modular/monty_form.rs

@@ -46,9 +46,9 @@ impl<const LIMBS: usize> MontyParams<LIMBS> {
         // `R^2 mod modulus`, used to convert integers to Montgomery form.
         let r2 = one
             .square()
-            .rem(&NonZero(Uint::<LIMBS>::ZERO.concat(&modulus.0)))
+            .rem(&NonZero(modulus.0.concat(&Uint::ZERO)))
             .split()
-            .1;
+            .0;
 
         // The modular inverse should always exist, because it was ensured odd above, which also ensures it's non-zero
         let inv_mod = modulus

src/traits.rs

@@ -467,49 +467,46 @@ pub trait CheckedSub<Rhs = Self>: Sized {
     fn checked_sub(&self, rhs: &Rhs) -> CtOption<Self>;
 }
 
-/// Concatenate two numbers into a "wide" double-width value, using the `lo`
-/// value as the least significant value.
+/// Concatenate two numbers into a "wide" double-width value, using the `hi` value as the most
+/// significant portion of the resulting value.
 pub trait Concat: ConcatMixed<Self, MixedOutput = Self::Output> {
     /// Concatenated output: twice the width of `Self`.
     type Output: Integer;
 
-    /// Concatenate the two halves, with `self` as most significant and `lo`
-    /// as the least significant.
-    fn concat(&self, lo: &Self) -> Self::Output {
-        self.concat_mixed(lo)
+    /// Concatenate the two halves, with `self` as least significant and `hi` as the least
+    /// significant.
+    fn concat(&self, hi: &Self) -> Self::Output {
+        self.concat_mixed(hi)
     }
 }
 
-/// Concatenate two numbers into a "wide" combined-width value, using the `lo`
-/// value as the least significant value.
-pub trait ConcatMixed<Lo: ?Sized = Self> {
-    /// Concatenated output: combination of `Lo` and `Self`.
+/// Concatenate two numbers into a "wide" combined-width value, using the `hi` value as the most
+/// significant value.
+pub trait ConcatMixed<Hi: ?Sized = Self> {
+    /// Concatenated output: combination of `Self` and `Hi`.
     type MixedOutput: Integer;
 
-    /// Concatenate the two values, with `self` as most significant and `lo`
-    /// as the least significant.
-    fn concat_mixed(&self, lo: &Lo) -> Self::MixedOutput;
+    /// Concatenate the two values, with `self` as least significant and `hi` as the most
+    /// significant.
+    fn concat_mixed(&self, hi: &Hi) -> Self::MixedOutput;
 }
 
-/// Split a number in half, returning the most significant half followed by
-/// the least significant.
+/// Split a number in half, returning the least significant half followed by the most significant.
 pub trait Split: SplitMixed<Self::Output, Self::Output> {
-    /// Split output: high/low components of the value.
+    /// Split output: low/high components of the value.
     type Output;
 
-    /// Split this number in half, returning its high and low components
-    /// respectively.
+    /// Split this number in half, returning its low and high components respectively.
     fn split(&self) -> (Self::Output, Self::Output) {
         self.split_mixed()
     }
 }
 
-/// Split a number into parts, returning the most significant part followed by
-/// the least significant.
-pub trait SplitMixed<Hi, Lo> {
-    /// Split this number into parts, returning its high and low components
-    /// respectively.
-    fn split_mixed(&self) -> (Hi, Lo);
+/// Split a number into parts, returning the least significant part followed by the most
+/// significant.
+pub trait SplitMixed<Lo, Hi> {
+    /// Split this number into parts, returning its low and high components respectively.
+    fn split_mixed(&self) -> (Lo, Hi);
 }
 
 /// Encoding support.

src/uint/concat.rs

@@ -40,21 +40,21 @@ mod tests {
         let hi = U64::from_u64(0x0011223344556677);
         let lo = U64::from_u64(0x8899aabbccddeeff);
         assert_eq!(
-            hi.concat(&lo),
+            lo.concat(&hi),
             U128::from_be_hex("00112233445566778899aabbccddeeff")
         );
     }
 
     #[test]
     fn concat_mixed() {
-        let a = U64::from_u64(0x0011223344556677);
-        let b = U128::from_u128(0x8899aabbccddeeff_8899aabbccddeeff);
+        let hi = U64::from_u64(0x0011223344556677);
+        let lo = U128::from_u128(0x8899aabbccddeeff_8899aabbccddeeff);
         assert_eq!(
-            a.concat_mixed(&b),
+            lo.concat_mixed(&hi),
             U192::from_be_hex("00112233445566778899aabbccddeeff8899aabbccddeeff")
         );
         assert_eq!(
-            b.concat_mixed(&a),
+            hi.concat_mixed(&lo),
             U192::from_be_hex("8899aabbccddeeff8899aabbccddeeff0011223344556677")
         );
     }

src/uint/from.rs

@@ -198,19 +198,19 @@ impl<const LIMBS: usize> From<Limb> for Uint<LIMBS> {
 
 impl<const L: usize, const H: usize, const LIMBS: usize> From<(Uint<L>, Uint<H>)> for Uint<LIMBS>
 where
-    Uint<H>: ConcatMixed<Uint<L>, MixedOutput = Uint<LIMBS>>,
+    Uint<L>: ConcatMixed<Uint<H>, MixedOutput = Uint<LIMBS>>,
 {
     fn from(nums: (Uint<L>, Uint<H>)) -> Uint<LIMBS> {
-        nums.1.concat_mixed(&nums.0)
+        nums.0.concat_mixed(&nums.1)
     }
 }
 
 impl<const L: usize, const H: usize, const LIMBS: usize> From<&(Uint<L>, Uint<H>)> for Uint<LIMBS>
 where
-    Uint<H>: ConcatMixed<Uint<L>, MixedOutput = Uint<LIMBS>>,
+    Uint<L>: ConcatMixed<Uint<H>, MixedOutput = Uint<LIMBS>>,
 {
     fn from(nums: &(Uint<L>, Uint<H>)) -> Uint<LIMBS> {
-        nums.1.concat_mixed(&nums.0)
+        nums.0.concat_mixed(&nums.1)
     }
 }
 

src/uint/macros.rs

@@ -77,8 +77,8 @@ macro_rules! impl_uint_concat_split_mixed {
         {
             type MixedOutput = $name;
 
-            fn concat_mixed(&self, lo: &Uint<{ U64::LIMBS * $size }>) -> Self::MixedOutput {
-                $crate::uint::concat::concat_mixed(lo, self)
+            fn concat_mixed(&self, hi: &Uint<{ U64::LIMBS * $size }>) -> Self::MixedOutput {
+                $crate::uint::concat::concat_mixed(self, hi)
             }
         }
 
@@ -107,16 +107,16 @@ macro_rules! impl_uint_concat_split_even {
         {
             type MixedOutput = $name;
 
-            fn concat_mixed(&self, lo: &Uint<{ <$name>::LIMBS / 2 }>) -> Self::MixedOutput {
-                $crate::uint::concat::concat_mixed(lo, self)
+            fn concat_mixed(&self, hi: &Uint<{ <$name>::LIMBS / 2 }>) -> Self::MixedOutput {
+                $crate::uint::concat::concat_mixed(self, hi)
             }
         }
 
         impl Uint<{ <$name>::LIMBS / 2 }> {
             /// Concatenate the two values, with `self` as most significant and `rhs`
             /// as the least significant.
-            pub const fn concat(&self, lo: &Uint<{ <$name>::LIMBS / 2 }>) -> $name {
-                $crate::uint::concat::concat_mixed(lo, self)
+            pub const fn concat(&self, hi: &Uint<{ <$name>::LIMBS / 2 }>) -> $name {
+                $crate::uint::concat::concat_mixed(self, hi)
             }
         }
 

src/uint/mul.rs

@@ -358,15 +358,15 @@ mod tests {
     #[test]
     fn square() {
         let n = U64::from_u64(0xffff_ffff_ffff_ffff);
-        let (hi, lo) = n.square().split();
+        let (lo, hi) = n.square().split();
         assert_eq!(lo, U64::from_u64(1));
         assert_eq!(hi, U64::from_u64(0xffff_ffff_ffff_fffe));
     }
 
     #[test]
     fn square_larger() {
         let n = U256::MAX;
-        let (hi, lo) = n.square().split();
+        let (lo, hi) = n.square().split();
         assert_eq!(lo, U256::ONE);
         assert_eq!(hi, U256::MAX.wrapping_sub(&U256::ONE));
     }

src/uint/split.rs

@@ -1,11 +1,10 @@
 use crate::{Limb, Uint};
 
-/// Split this number in half, returning its high and low components
-/// respectively.
+/// Split this number in half, returning its low and high components respectively.
 #[inline]
 pub(crate) const fn split_mixed<const L: usize, const H: usize, const O: usize>(
     n: &Uint<O>,
-) -> (Uint<H>, Uint<L>) {
+) -> (Uint<L>, Uint<H>) {
     let top = L + H;
     let top = if top < O { top } else { O };
     let mut lo = [Limb::ZERO; L];
@@ -21,7 +20,7 @@ pub(crate) const fn split_mixed<const L: usize, const H: usize, const O: usize>(
         i += 1;
     }
 
-    (Uint { limbs: hi }, Uint { limbs: lo })
+    (Uint { limbs: lo }, Uint { limbs: hi })
 }
 
 #[cfg(test)]
@@ -30,8 +29,8 @@ mod tests {
 
     #[test]
     fn split() {
-        let (hi, lo) = U128::from_be_hex("00112233445566778899aabbccddeeff").split();
-        assert_eq!(hi, U64::from_u64(0x0011223344556677));
+        let (lo, hi) = U128::from_be_hex("00112233445566778899aabbccddeeff").split();
         assert_eq!(lo, U64::from_u64(0x8899aabbccddeeff));
+        assert_eq!(hi, U64::from_u64(0x0011223344556677));
     }
 }