num-ord 0.1.0

#![no_std]
#![warn(
    invalid_html_tags,
    missing_debug_implementations,
    trivial_casts,
    unused_lifetimes,
    unused_import_braces
)]
#![deny(missing_docs, unaligned_references)]

//! # num-ord
//!
//! This crate provides a numerically ordered wrapper type, [`NumOrd`]. This
//! type implements the [`PartialOrd`] and [`PartialEq`] traits for all the
//! possible combinations of built-in integer types, in a mathematically correct
//! manner without overflows.
//!
//! For example, comparing an `x: i64` and a `y: f64` is actually quite
//! difficult.  Neither `(x as f64) < y` nor `x < (y as i64)` is correct. But
//! `NumOrd(x) < NumOrd(y)` is:
//! ```rust
//! use num_ord::NumOrd;
//!
//! let x = 3_i64;
//! let y = 3.5_f64;
//! assert_eq!(x < (y as i64), false); // Incorrect.
//! assert_eq!(NumOrd(x) < NumOrd(y), true); // Correct.
//!
//! let x = 9007199254740993_i64;
//! let y = 9007199254740992_f64;
//! assert_eq!(format!("{}", y), "9007199254740992"); // No rounded constant trickery!
//! assert_eq!((x as f64) <= y, true); // Incorrect.
//! assert_eq!(NumOrd(x) <= NumOrd(y), false); // Correct.
//! ```

use core::cmp::Ordering;


/// A numerically ordered wrapper type.
///
/// See the crate docs for more details.
#[derive(Copy, Clone, Debug, Hash, PartialEq, Eq, PartialOrd, Ord)]
#[repr(transparent)]
pub struct NumOrd<T>(pub T);


macro_rules! common_type_impl_body {
    ($Lhs:ty, $Rhs:ty, $CommonT:ty, $lhs:expr, $rhs:expr, $op:ident, $less:expr, $greater:expr, $nan:expr) => {{
        ($lhs as $CommonT).$op(&($rhs as $CommonT))
    }};
}

macro_rules! int_float_impl_body {
    ($IntT:ty, $FloatT:ty, $_UnusedT:ty, $lhs:expr, $rhs:expr, $op:ident, $less:expr, $greater:expr, $nan:expr) => {{
        let lhs = $lhs;
        let rhs = $rhs;

        // Range in which FloatT is dense in the integers.
        const FLOAT_DENSE_INT_MIN: $IntT =
            (0 as $IntT).saturating_sub(1) << <$FloatT>::MANTISSA_DIGITS;
        const FLOAT_DENSE_INT_MAX: $IntT = 1 << <$FloatT>::MANTISSA_DIGITS;

        // One above IntT::MAX as FloatT. May be infinite.
        const INT_MAX_POWER_OF_TWO: $IntT = <$IntT>::MAX ^ (<$IntT>::MAX >> 1);
        const INT_ONE_ABOVE_MAX_AS_FLOAT: $FloatT = 2.0 * (INT_MAX_POWER_OF_TWO as $FloatT);

        if FLOAT_DENSE_INT_MIN <= lhs && lhs <= FLOAT_DENSE_INT_MAX {
            // lhs is exactly representable as an integer valued float.
            (lhs as $FloatT).$op(&rhs)
        } else if INT_ONE_ABOVE_MAX_AS_FLOAT <= rhs {
            $less
        } else if <$IntT>::MIN as $FloatT > rhs {
            $greater
        } else if rhs.is_nan() {
            $nan
        } else {
            // The rounding to integer can't affect the outcome, since we know that
            // `lhs` is sufficiently large such that if `rhs` is close, it must be
            // an integer.
            lhs.$op(&(rhs as $IntT))
        }
    }};
}

// Must have IntT <= UintT in width.
macro_rules! int_uint_impl_body {
    ($IntT:ty, $UintT:ty, $_UnusedT:ty, $lhs:expr, $rhs:expr, $op:ident, $less:expr, $greater:expr, $nan:expr) => {{
        let lhs = $lhs;
        let rhs = $rhs;

        if lhs < 0 {
            $less
        } else {
            (lhs as $UintT).$op(&rhs)
        }
    }};
}

macro_rules! apply_impl_body {
    ($impl_body:ident, $Lhs:ty, $Rhs:ty, $CommonT:ty) => {
        impl PartialEq<NumOrd<$Rhs>> for NumOrd<$Lhs> {
            fn eq(&self, other: &NumOrd<$Rhs>) -> bool {
                $impl_body!($Lhs, $Rhs, $CommonT, self.0, other.0, eq, false, false, false)
            }
        }

        impl PartialOrd<NumOrd<$Rhs>> for NumOrd<$Lhs> {
            fn partial_cmp(&self, other: &NumOrd<$Rhs>) -> Option<Ordering> {
                $impl_body!(
                    $Lhs,
                    $Rhs,
                    $CommonT,
                    self.0,
                    other.0,
                    partial_cmp,
                    Some(Ordering::Less),
                    Some(Ordering::Greater),
                    None
                )
            }

            fn lt(&self, other: &NumOrd<$Rhs>) -> bool {
                $impl_body!($Lhs, $Rhs, $CommonT, self.0, other.0, lt, true, false, false)
            }

            fn le(&self, other: &NumOrd<$Rhs>) -> bool {
                $impl_body!($Lhs, $Rhs, $CommonT, self.0, other.0, le, true, false, false)
            }

            fn gt(&self, other: &NumOrd<$Rhs>) -> bool {
                $impl_body!($Lhs, $Rhs, $CommonT, self.0, other.0, gt, false, true, false)
            }

            fn ge(&self, other: &NumOrd<$Rhs>) -> bool {
                $impl_body!($Lhs, $Rhs, $CommonT, self.0, other.0, ge, false, true, false)
            }
        }

        // Reverse implementation.
        impl PartialEq<NumOrd<$Lhs>> for NumOrd<$Rhs> {
            fn eq(&self, other: &NumOrd<$Lhs>) -> bool {
                other == self
            }
        }

        impl PartialOrd<NumOrd<$Lhs>> for NumOrd<$Rhs> {
            fn partial_cmp(&self, other: &NumOrd<$Lhs>) -> Option<Ordering> {
                other.partial_cmp(self).map(|o| o.reverse())
            }

            fn lt(&self, other: &NumOrd<$Lhs>) -> bool {
                other > self
            }

            fn le(&self, other: &NumOrd<$Lhs>) -> bool {
                other >= self
            }

            fn gt(&self, other: &NumOrd<$Lhs>) -> bool {
                other < self
            }

            fn ge(&self, other: &NumOrd<$Lhs>) -> bool {
                other <= self
            }
        }
    };
}

apply_impl_body!(int_float_impl_body, i64, f32, ());
apply_impl_body!(int_float_impl_body, i128, f32, ());
apply_impl_body!(int_float_impl_body, i64, f64, ());
apply_impl_body!(int_float_impl_body, i128, f64, ());
apply_impl_body!(int_float_impl_body, u64, f32, ());
apply_impl_body!(int_float_impl_body, u128, f32, ());
apply_impl_body!(int_float_impl_body, u64, f64, ());
apply_impl_body!(int_float_impl_body, u128, f64, ());

apply_impl_body!(int_uint_impl_body, i8, u128, ());
apply_impl_body!(int_uint_impl_body, i16, u128, ());
apply_impl_body!(int_uint_impl_body, i32, u128, ());
apply_impl_body!(int_uint_impl_body, i64, u128, ());
apply_impl_body!(int_uint_impl_body, i128, u128, ());


macro_rules! impl_common_type {
    ($($T:ty, $U:ty => $C:ty;)*) => {$(
        apply_impl_body!(common_type_impl_body, $T, $U, $C);
    )*}
}

impl_common_type! {
    // See tools/gen.py.
      u8,   i8 =>  i16;
      u8,  u16 =>  u16;
      u8,  i16 =>  i16;
      u8,  u32 =>  u32;
      u8,  i32 =>  i32;
      u8,  u64 =>  u64;
      u8,  i64 =>  i64;
      u8, u128 => u128;
      u8, i128 => i128;
      u8,  f32 =>  f32;
      u8,  f64 =>  f64;
      i8,  u16 =>  i32;
      i8,  i16 =>  i16;
      i8,  u32 =>  i64;
      i8,  i32 =>  i32;
      i8,  u64 => i128;
      i8,  i64 =>  i64;
      i8, i128 => i128;
      i8,  f32 =>  f32;
      i8,  f64 =>  f64;
     u16,  i16 =>  i32;
     u16,  u32 =>  u32;
     u16,  i32 =>  i32;
     u16,  u64 =>  u64;
     u16,  i64 =>  i64;
     u16, u128 => u128;
     u16, i128 => i128;
     u16,  f32 =>  f32;
     u16,  f64 =>  f64;
     i16,  u32 =>  i64;
     i16,  i32 =>  i32;
     i16,  u64 => i128;
     i16,  i64 =>  i64;
     i16, i128 => i128;
     i16,  f32 =>  f32;
     i16,  f64 =>  f64;
     u32,  i32 =>  i64;
     u32,  u64 =>  u64;
     u32,  i64 =>  i64;
     u32, u128 => u128;
     u32, i128 => i128;
     u32,  f32 =>  f64;
     u32,  f64 =>  f64;
     i32,  u64 => i128;
     i32,  i64 =>  i64;
     i32, i128 => i128;
     i32,  f32 =>  f64;
     i32,  f64 =>  f64;
     u64,  i64 => i128;
     u64, u128 => u128;
     u64, i128 => i128;
     i64, i128 => i128;
     f32,  f64 =>  f64;
}