better support for u256 and i256

Author: quaternic

libm-test/tests/u256.rs

@@ -111,7 +111,13 @@ fn mp_u256_add() {
         let y = random_u256(&mut rng);
         assign_bigint(&mut bx, x);
         assign_bigint(&mut by, y);
-        let actual = x + y;
+        let actual = if u256::MAX - x >= y {
+            x + y
+        } else {
+            // otherwise (u256::MAX - x) < y, so the wrapped result is
+            // (x + y) - (u256::MAX + 1) == y - (u256::MAX - x) - 1
+            y - (u256::MAX - x) - 1_u128.widen()
+        };
         bx += &by;
         check_one(|| hexu(x), || Some(hexu(y)), actual, &mut bx);
     }

libm/src/math/support/big.rs

@@ -11,10 +11,10 @@ const U128_LO_MASK: u128 = u64::MAX as u128;
 
 /// A 256-bit unsigned integer represented as two 128-bit native-endian limbs.
 #[allow(non_camel_case_types)]
-#[derive(Clone, Copy, Debug, PartialEq, PartialOrd)]
+#[derive(Clone, Copy, Debug, PartialEq, PartialOrd, Eq, Ord)]
 pub struct u256 {
-    pub lo: u128,
     pub hi: u128,
+    pub lo: u128,
 }
 
 impl u256 {
@@ -28,17 +28,17 @@ impl u256 {
     pub fn signed(self) -> i256 {
         i256 {
             lo: self.lo,
-            hi: self.hi,
+            hi: self.hi as i128,
         }
     }
 }
 
 /// A 256-bit signed integer represented as two 128-bit native-endian limbs.
 #[allow(non_camel_case_types)]
-#[derive(Clone, Copy, Debug, PartialEq, PartialOrd)]
+#[derive(Clone, Copy, Debug, PartialEq, PartialOrd, Eq, Ord)]
 pub struct i256 {
+    pub hi: i128,
     pub lo: u128,
-    pub hi: u128,
 }
 
 impl i256 {
@@ -47,7 +47,7 @@ impl i256 {
     pub fn unsigned(self) -> u256 {
         u256 {
             lo: self.lo,
-            hi: self.hi,
+            hi: self.hi as u128,
         }
     }
 }
@@ -73,17 +73,17 @@ impl MinInt for i256 {
 
     type Unsigned = u256;
 
-    const SIGNED: bool = false;
+    const SIGNED: bool = true;
     const BITS: u32 = 256;
     const ZERO: Self = Self { lo: 0, hi: 0 };
     const ONE: Self = Self { lo: 1, hi: 0 };
     const MIN: Self = Self {
-        lo: 0,
-        hi: 1 << 127,
+        lo: u128::MIN,
+        hi: i128::MIN,
     };
     const MAX: Self = Self {
         lo: u128::MAX,
-        hi: u128::MAX >> 1,
+        hi: i128::MAX,
     };
 }
 
@@ -116,23 +116,44 @@ macro_rules! impl_common {
                 unimplemented!("only used to meet trait bounds")
             }
         }
-    };
-}
 
-impl_common!(i256);
-impl_common!(u256);
+        impl ops::Add<Self> for $ty {
+            type Output = Self;
 
-impl ops::Add<Self> for u256 {
-    type Output = Self;
+            fn add(self, rhs: Self) -> Self::Output {
+                let (lo, carry) = self.lo.overflowing_add(rhs.lo);
+                let (hi, of) = Int::carrying_add(self.hi, rhs.hi, carry);
 
-    fn add(self, rhs: Self) -> Self::Output {
-        let (lo, carry) = self.lo.overflowing_add(rhs.lo);
-        let hi = self.hi.wrapping_add(carry as u128).wrapping_add(rhs.hi);
+                #[cfg(debug_assertions)]
+                if of {
+                    panic!("attempt to add with overflow")
+                }
 
-        Self { lo, hi }
-    }
+                Self { lo, hi }
+            }
+        }
+
+        impl ops::Sub<Self> for $ty {
+            type Output = Self;
+
+            fn sub(self, rhs: Self) -> Self::Output {
+                let (lo, borrow) = self.lo.overflowing_sub(rhs.lo);
+                let (hi, of) = Int::borrowing_sub(self.hi, rhs.hi, borrow);
+
+                #[cfg(debug_assertions)]
+                if of {
+                    panic!("attempt to subtract with overflow")
+                }
+
+                Self { lo, hi }
+            }
+        }
+    };
 }
 
+impl_common!(i256);
+impl_common!(u256);
+
 impl ops::Shr<u32> for u256 {
     type Output = Self;
 
@@ -200,19 +221,18 @@ impl HInt for u128 {
     }
 
     fn widen_hi(self) -> Self::D {
-        self.widen() << <Self as MinInt>::BITS
+        u256 { lo: 0, hi: self }
     }
 }
 
 impl HInt for i128 {
     type D = i256;
 
     fn widen(self) -> Self::D {
-        let mut ret = self.unsigned().zero_widen().signed();
-        if self.is_negative() {
-            ret.hi = u128::MAX;
+        i256 {
+            lo: self as u128,
+            hi: if self < 0 { -1 } else { 0 },
         }
-        ret
     }
 
     fn zero_widen(self) -> Self::D {
@@ -228,7 +248,7 @@ impl HInt for i128 {
     }
 
     fn widen_hi(self) -> Self::D {
-        self.widen() << <Self as MinInt>::BITS
+        i256 { lo: 0, hi: self }
     }
 }
 
@@ -252,6 +272,6 @@ impl DInt for i256 {
     }
 
     fn hi(self) -> Self::H {
-        self.hi as i128
+        self.hi
     }
 }

libm/src/math/support/big/tests.rs

@@ -36,7 +36,7 @@ fn widen_i128() {
         (LOHI_SPLIT as i128).widen(),
         i256 {
             lo: LOHI_SPLIT,
-            hi: u128::MAX
+            hi: -1,
         }
     );
     assert_eq!((-1i128).zero_widen().unsigned(), (u128::MAX).widen());
@@ -275,3 +275,26 @@ fn shr_u256_overflow() {
     assert_eq!(u256::MAX >> 257, u256::ZERO);
     assert_eq!(u256::MAX >> u32::MAX, u256::ZERO);
 }
+
+#[test]
+fn u256_ord() {
+    let _1 = u256::ONE;
+    let _2 = _1 + _1;
+    for x in u8::MIN..u8::MAX {
+        let y = x + 1;
+        let wx = (x as u128).widen_hi();
+        let wy = (y as u128).widen_hi();
+        assert!([wx, wx + _1, wx + _2, wy, wy + _1, wy + _2].is_sorted());
+    }
+}
+#[test]
+fn i256_ord() {
+    let _1 = i256::ONE;
+    let _2 = _1 + _1;
+    for x in i8::MIN..i8::MAX {
+        let y = x + 1;
+        let wx = (x as i128).widen_hi();
+        let wy = (y as i128).widen_hi();
+        assert!([wx, wx + _1, wx + _2, wy - _2, wy - _1, wy].is_sorted());
+    }
+}

libm/src/math/support/int_traits.rs

@@ -5,9 +5,12 @@ use core::{cmp, fmt, ops};
 pub trait MinInt:
     Copy
     + fmt::Debug
+    + cmp::Ord
     + ops::BitOr<Output = Self>
     + ops::Not<Output = Self>
     + ops::Shl<u32, Output = Self>
+    + ops::Add<Output = Self>
+    + ops::Sub<Output = Self>
 {
     /// Type with the same width but other signedness
     type OtherSign: MinInt;
@@ -37,8 +40,6 @@ pub trait Int:
     + fmt::Display
     + fmt::Binary
     + fmt::LowerHex
-    + PartialEq
-    + PartialOrd
     + ops::AddAssign
     + ops::SubAssign
     + ops::MulAssign
@@ -51,8 +52,6 @@ pub trait Int:
     + ops::ShlAssign<u32>
     + ops::ShrAssign<u32>
     + ops::ShrAssign<i32>
-    + ops::Add<Output = Self>
-    + ops::Sub<Output = Self>
     + ops::Mul<Output = Self>
     + ops::Div<Output = Self>
     + ops::Rem<Output = Self>
@@ -62,7 +61,6 @@ pub trait Int:
     + ops::Shr<u32, Output = Self>
     + ops::BitXor<Output = Self>
     + ops::BitAnd<Output = Self>
-    + cmp::Ord
     + From<bool>
     + CastFrom<i32>
     + CastFrom<u16>
@@ -102,6 +100,8 @@ pub trait Int:
     fn rotate_left(self, other: u32) -> Self;
     fn overflowing_add(self, other: Self) -> (Self, bool);
     fn overflowing_sub(self, other: Self) -> (Self, bool);
+    fn carrying_add(self, other: Self, carry: bool) -> (Self, bool);
+    fn borrowing_sub(self, other: Self, borrow: bool) -> (Self, bool);
     fn leading_zeros(self) -> u32;
     fn ilog2(self) -> u32;
 }
@@ -174,6 +174,20 @@ macro_rules! int_impl_common {
             #[allow(clippy::incompatible_msrv)]
             <Self>::ilog2(self)
         }
+
+        fn carrying_add(self, other: Self, carry: bool) -> (Self, bool) {
+            let (ab, of1) = self.overflowing_add(other);
+            let (abc, of2) = ab.overflowing_add(Self::from_bool(carry));
+            // `of1 && of2` is possible with signed integers if a negative sum
+            // overflows to `MAX` and adding the carry overflows again back to `MIN`
+            (abc, of1 ^ of2)
+        }
+
+        fn borrowing_sub(self, other: Self, borrow: bool) -> (Self, bool) {
+            let (ab, of1) = self.overflowing_sub(other);
+            let (abc, of2) = ab.overflowing_sub(Self::from_bool(borrow));
+            (abc, of1 ^ of2)
+        }
     };
 }