Add support for euclidean division and modulation

build.rs

@@ -19,6 +19,7 @@ fn main() {
     ac.emit_expression_cfg("1u32.reverse_bits()", "has_reverse_bits");
     ac.emit_expression_cfg("1u32.trailing_ones()", "has_leading_trailing_ones");
     ac.emit_expression_cfg("{ let mut x = 1; x += &2; }", "has_int_assignop_ref");
+    ac.emit_expression_cfg("1u32.div_euclid(1u32)", "has_div_euclid");
 
     autocfg::rerun_path("build.rs");
 }

src/lib.rs

@@ -40,6 +40,7 @@ pub use int::PrimInt;
 pub use ops::checked::{
     CheckedAdd, CheckedDiv, CheckedMul, CheckedNeg, CheckedRem, CheckedShl, CheckedShr, CheckedSub,
 };
+pub use ops::euclid::{CheckedEuclid, Euclid};
 pub use ops::inv::Inv;
 pub use ops::mul_add::{MulAdd, MulAddAssign};
 pub use ops::saturating::{Saturating, SaturatingAdd, SaturatingMul, SaturatingSub};

src/ops/euclid.rs

@@ -0,0 +1,347 @@
+use core::ops::{Div, Rem};
+
+pub trait Euclid: Sized + Div<Self, Output = Self> + Rem<Self, Output = Self> {
+    /// Calculates Euclidean division, the matching method for `rem_euclid`.
+    ///
+    /// This computes the integer `n` such that
+    /// `self = n * v + self.rem_euclid(v)`.
+    /// In other words, the result is `self / v` rounded to the integer `n`
+    /// such that `self >= n * v`.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num_traits::Euclid;
+    ///
+    /// let a: i32 = 7;
+    /// let b: i32 = 4;
+    /// assert_eq!(Euclid::div_euclid(&a, &b), 1); // 7 > 4 * 1
+    /// assert_eq!(Euclid::div_euclid(&-a, &b), -2); // -7 >= 4 * -2
+    /// assert_eq!(Euclid::div_euclid(&a, &-b), -1); // 7 >= -4 * -1
+    /// assert_eq!(Euclid::div_euclid(&-a, &-b), 2); // -7 >= -4 * 2
+    /// ```
+    fn div_euclid(&self, v: &Self) -> Self;
+
+    /// Calculates the least nonnegative remainder of `self (mod v)`.
+    ///
+    /// In particular, the return value `r` satisfies `0.0 <= r < v.abs()` in
+    /// most cases. However, due to a floating point round-off error it can
+    /// result in `r == v.abs()`, violating the mathematical definition, if
+    /// `self` is much smaller than `v.abs()` in magnitude and `self < 0.0`.
+    /// This result is not an element of the function's codomain, but it is the
+    /// closest floating point number in the real numbers and thus fulfills the
+    /// property `self == self.div_euclid(v) * v + self.rem_euclid(v)`
+    /// approximatively.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use num_traits::Euclid;
+    ///
+    /// let a: i32 = 7;
+    /// let b: i32 = 4;
+    /// assert_eq!(Euclid::rem_euclid(&a, &b), 3);
+    /// assert_eq!(Euclid::rem_euclid(&-a, &b), 1);
+    /// assert_eq!(Euclid::rem_euclid(&a, &-b), 3);
+    /// assert_eq!(Euclid::rem_euclid(&-a, &-b), 1);
+    /// ```
+    fn rem_euclid(&self, v: &Self) -> Self;
+}
+
+macro_rules! euclid_forward_impl {
+    ($($t:ty)*) => {$(
+        #[cfg(has_div_euclid)]
+        impl Euclid for $t {
+            #[inline]
+            fn div_euclid(&self, v: &$t) -> Self {
+                <$t>::div_euclid(*self, *v)
+            }
+
+            #[inline]
+            fn rem_euclid(&self, v: &$t) -> Self {
+                <$t>::rem_euclid(*self, *v)
+            }
+        }
+    )*}
+}
+
+macro_rules! euclid_int_impl {
+    ($($t:ty)*) => {$(
+        euclid_forward_impl!($t);
+
+        #[cfg(not(has_div_euclid))]
+        impl Euclid for $t {
+            #[inline]
+            fn div_euclid(&self, v: &$t) -> Self {
+                let q = self / v;
+                if self % v < 0 {
+                    return if *v > 0 { q - 1 } else { q + 1 }
+                }
+                q
+            }
+
+            #[inline]
+            fn rem_euclid(&self, v: &$t) -> Self {
+                let r = self % v;
+                if r < 0 {
+                    if *v < 0 {
+                        r - v
+                    } else {
+                        r + v
+                    }
+                } else {
+                    r
+                }
+            }
+        }
+    )*}
+}
+
+macro_rules! euclid_uint_impl {
+    ($($t:ty)*) => {$(
+        euclid_forward_impl!($t);
+
+        #[cfg(not(has_div_euclid))]
+        impl Euclid for $t {
+            #[inline]
+            fn div_euclid(&self, v: &$t) -> Self {
+                self / v
+            }
+
+            #[inline]
+            fn rem_euclid(&self, v: &$t) -> Self {
+                self % v
+            }
+        }
+    )*}
+}
+
+euclid_int_impl!(isize i8 i16 i32 i64);
+euclid_uint_impl!(usize u8 u16 u32 u64);
+#[cfg(has_i128)]
+euclid_int_impl!(i128);
+#[cfg(has_i128)]
+euclid_uint_impl!(u128);
+
+#[cfg(all(has_div_euclid, feature = "std"))]
+euclid_forward_impl!(f32 f64);
+
+#[cfg(not(all(has_div_euclid, feature = "std")))]
+impl Euclid for f32 {
+    #[inline]
+    fn div_euclid(&self, v: &f32) -> f32 {
+        let q = <f32 as ::float::FloatCore>::trunc(self / v);
+        if self % v < 0.0 {
+            return if *v > 0.0 { q - 1.0 } else { q + 1.0 };
+        }
+        q
+    }
+
+    #[inline]
+    fn rem_euclid(&self, v: &f32) -> f32 {
+        let r = self % v;
+        if r < 0.0 {
+            r + <f32 as ::float::FloatCore>::abs(*v)
+        } else {
+            r
+        }
+    }
+}
+
+#[cfg(not(all(has_div_euclid, feature = "std")))]
+impl Euclid for f64 {
+    #[inline]
+    fn div_euclid(&self, v: &f64) -> f64 {
+        let q = <f64 as ::float::FloatCore>::trunc(self / v);
+        if self % v < 0.0 {
+            return if *v > 0.0 { q - 1.0 } else { q + 1.0 };
+        }
+        q
+    }
+
+    #[inline]
+    fn rem_euclid(&self, v: &f64) -> f64 {
+        let r = self % v;
+        if r < 0.0 {
+            r + <f64 as ::float::FloatCore>::abs(*v)
+        } else {
+            r
+        }
+    }
+}
+
+pub trait CheckedEuclid: Euclid {
+    /// Performs euclid division that returns `None` instead of panicking on division by zero
+    /// and instead of wrapping around on underflow and overflow.
+    fn checked_div_euclid(&self, v: &Self) -> Option<Self>;
+
+    /// Finds the euclid remainder of dividing two numbers, checking for underflow, overflow and
+    /// division by zero. If any of that happens, `None` is returned.
+    fn checked_rem_euclid(&self, v: &Self) -> Option<Self>;
+}
+
+macro_rules! checked_euclid_forward_impl {
+    ($($t:ty)*) => {$(
+        #[cfg(has_div_euclid)]
+        impl CheckedEuclid for $t {
+            #[inline]
+            fn checked_div_euclid(&self, v: &$t) -> Option<Self> {
+                <$t>::checked_div_euclid(*self, *v)
+            }
+
+            #[inline]
+            fn checked_rem_euclid(&self, v: &$t) -> Option<Self> {
+                <$t>::checked_rem_euclid(*self, *v)
+            }
+        }
+    )*}
+}
+
+macro_rules! checked_euclid_int_impl {
+    ($($t:ty)*) => {$(
+        checked_euclid_forward_impl!($t);
+
+        #[cfg(not(has_div_euclid))]
+        impl CheckedEuclid for $t {
+            #[inline]
+            fn checked_div_euclid(&self, v: &$t) -> Option<$t> {
+                if *v == 0 || (*self == Self::min_value() && *v == -1) {
+                    None
+                } else {
+                    Some(Euclid::div_euclid(self, v))
+                }
+            }
+
+            #[inline]
+            fn checked_rem_euclid(&self, v: &$t) -> Option<$t> {
+                if *v == 0 || (*self == Self::min_value() && *v == -1) {
+                    None
+                } else {
+                    Some(Euclid::rem_euclid(self, v))
+                }
+            }
+        }
+    )*}
+}
+
+macro_rules! checked_euclid_uint_impl {
+    ($($t:ty)*) => {$(
+        checked_euclid_forward_impl!($t);
+
+        #[cfg(not(has_div_euclid))]
+        impl CheckedEuclid for $t {
+            #[inline]
+            fn checked_div_euclid(&self, v: &$t) -> Option<$t> {
+                if *v == 0 {
+                    None
+                } else {
+                    Some(Euclid::div_euclid(self, v))
+                }
+            }
+
+            #[inline]
+            fn checked_rem_euclid(&self, v: &$t) -> Option<$t> {
+                if *v == 0 {
+                    None
+                } else {
+                    Some(Euclid::rem_euclid(self, v))
+                }
+            }
+        }
+    )*}
+}
+
+checked_euclid_int_impl!(isize i8 i16 i32 i64);
+checked_euclid_uint_impl!(usize u8 u16 u32 u64);
+#[cfg(has_i128)]
+checked_euclid_int_impl!(i128);
+#[cfg(has_i128)]
+checked_euclid_uint_impl!(u128);
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn euclid_unsigned() {
+        macro_rules! test_euclid {
+            ($($t:ident)+) => {
+                $(
+                    {
+                        let x: $t = 10;
+                        let y: $t = 3;
+                        assert_eq!(Euclid::div_euclid(&x, &y), 3);
+                        assert_eq!(Euclid::rem_euclid(&x, &y), 1);
+                    }
+                )+
+            };
+        }
+
+        test_euclid!(usize u8 u16 u32 u64);
+    }
+
+    #[test]
+    fn euclid_signed() {
+        macro_rules! test_euclid {
+            ($($t:ident)+) => {
+                $(
+                    {
+                        let x: $t = 10;
+                        let y: $t = -3;
+                        assert_eq!(Euclid::div_euclid(&x, &y), -3);
+                        assert_eq!(Euclid::div_euclid(&-x, &y), 4);
+                        assert_eq!(Euclid::rem_euclid(&x, &y), 1);
+                        assert_eq!(Euclid::rem_euclid(&-x, &y), 2);
+                        let x: $t = $t::min_value() + 1;
+                        let y: $t = -1;
+                        assert_eq!(Euclid::div_euclid(&x, &y), $t::max_value());
+                    }
+                )+
+            };
+        }
+
+        test_euclid!(isize i8 i16 i32 i64);
+    }
+
+    #[test]
+    fn euclid_float() {
+        macro_rules! test_euclid {
+            ($($t:ident)+) => {
+                $(
+                    {
+                        let x: $t = 12.1;
+                        let y: $t = 3.2;
+                        assert!(Euclid::div_euclid(&x, &y) * y + Euclid::rem_euclid(&x, &y) - x
+                        <= 46.4 * <$t as ::float::FloatCore>::epsilon());
+                        assert!(Euclid::div_euclid(&x, &-y) * -y + Euclid::rem_euclid(&x, &-y) - x
+                        <= 46.4 * <$t as ::float::FloatCore>::epsilon());
+                        assert!(Euclid::div_euclid(&-x, &y) * y + Euclid::rem_euclid(&-x, &y) + x
+                        <= 46.4 * <$t as ::float::FloatCore>::epsilon());
+                        assert!(Euclid::div_euclid(&-x, &-y) * -y + Euclid::rem_euclid(&-x, &-y) + x
+                        <= 46.4 * <$t as ::float::FloatCore>::epsilon());
+                    }
+                )+
+            };
+        }
+
+        test_euclid!(f32 f64);
+    }
+
+    #[test]
+    fn euclid_checked() {
+        macro_rules! test_euclid_checked {
+            ($($t:ident)+) => {
+                $(
+                    {
+                        assert_eq!(CheckedEuclid::checked_div_euclid(&$t::min_value(), &-1), None);
+                        assert_eq!(CheckedEuclid::checked_rem_euclid(&$t::min_value(), &-1), None);
+                        assert_eq!(CheckedEuclid::checked_div_euclid(&1, &0), None);
+                        assert_eq!(CheckedEuclid::checked_rem_euclid(&1, &0), None);
+                    }
+                )+
+            };
+        }
+
+        test_euclid_checked!(isize i8 i16 i32 i64);
+    }
+}

src/ops/mod.rs

@@ -1,4 +1,5 @@
 pub mod checked;
+pub mod euclid;
 pub mod inv;
 pub mod mul_add;
 pub mod overflowing;