intrval 0.1.0

Generic intervals (ranges) library
Documentation 
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intrvals
========

[![Build Status](https://github.com/tsionyx/intrval/actions/workflows/rust.yml/badge.svg)](https://github.com/tsionyx/intrval/actions)
[![Latest version](https://img.shields.io/crates/v/intrval.svg)](https://crates.io/crates/intrval)
[![MSRV](https://img.shields.io/crates/msrv/intrval)](https://crates.io/crates/intrval)
[![Documentation](https://docs.rs/intrval/badge.svg)](https://docs.rs/intrval)


`intrvals` is a generic intervals library with basic
[arithmetic](https://en.wikipedia.org/wiki/Interval_arithmetic) (+, -, *)
and sets (_union_, _intersect_, _complement_) operations support.

Its main structure is an `Interval` which represents
a single-dimensioned (possibly unbounded) span of values instantiated by any type `T`.

## macro syntax

Allows to simplify the defintions of an interval
in common inequality and ranges terms.

For the half-open intervals, the inclusive bound is marked with `=` symbol; 
for the closed interval both `[a, b]` and `(=a, =b)` defintions are possible.

```rust
use intrval::{interval, Interval};

let i0: Interval<i16> = interval!(_);
assert_eq!(i0, Interval::Empty);

let igt2: Interval<i16> = interval!(> 2);
assert_eq!(igt2, Interval::GreaterThan(2));

let igt10: Interval<i16> = interval!(> 10);
assert_eq!(igt10, Interval::GreaterThan(10));

let i_2to10_incl: Interval<i16> = interval!([-2, 10]);
assert_eq!(i_2to10_incl, Interval::Closed((-2, 10)));

let i5to20_excl: Interval<i16> = interval!((5, =20));
assert_eq!(i5to20_excl, Interval::LeftOpen((5, 20)));

let iuni: Interval<i16> = interval!(..);
assert_eq!(iuni, Interval::Full);
```

## common functions

```rust
use core::cmp::Ordering;
use intrval::{interval, Size};

assert!(interval!(_: i32).is_empty());
assert!(interval!((1, 0)).is_empty());
assert!(interval!((0, 0)).is_empty());
assert!(!(interval!([0, 0]).is_empty()));
assert!(interval!(..: i32).is_full());

let igt10 = interval!(> 10);
assert!(igt10.contains(&11));
assert!(!(igt10.contains(&10)));
assert!(!(interval!(_).contains(&0)));

assert_eq!(interval!(_: i8).len(), Size::Empty);
assert_eq!(interval!((1, 0)).len(), Size::Empty);
assert_eq!(interval!([1, 1]).len(), Size::SinglePoint);
assert_eq!(interval!((-10, =10)).len(), Size::Finite(20));
assert_eq!(interval!(> 2).len(), Size::Infinite);

let i_left_open = interval!((2, =5));
assert_eq!(i_left_open.clamp(10).unwrap(), (Ordering::Equal, 5));
assert_eq!(i_left_open.clamp(3).unwrap(), (Ordering::Equal, 3));
assert_eq!(i_left_open.clamp(2).unwrap(), (Ordering::Greater, 2));
assert_eq!(i_left_open.clamp(0).unwrap(), (Ordering::Greater, 2));
```

## scalar arithmetic

Add, subtract or multiply the interval bounds with a scalar value of type `U`
if the underlying type `T: {Add, Sub, Mult}<U>`:

```rust
use intrval::{interval, Interval};

// negation changes the sign and flips the bounds
assert_eq!(-interval!(> 2), interval!(< -2));
assert_eq!(-interval!([-2, 10]), interval!([-10, 2]));

// full and empy does not change with scalars
assert_eq!(interval!(_) + 5, interval!(_));
assert_eq!(interval!(_: i32) * 2, interval!(_));
assert_eq!(interval!(..) - 100, interval!(..));
assert_eq!(interval!(..: i32) * -5, interval!(..));
// however, multiplying by 0 is different
assert_eq!(interval!(..: i32) * 0, interval!([0, 0]));

assert_eq!(interval!(> 2) + 3, interval!(> 5));
assert_eq!(interval!(> 10) - 5, interval!(> 5));
assert_eq!(interval!(> 2) * 5, interval!(> 10));
assert_eq!(interval!((5, =20)) / 5, Interval::LeftOpen((1, 4)));
// multiplying/dividing by negative flips the bounds
assert_eq!(interval!([-2, 10]) * -4, interval!([-40, 8]));
assert_eq!(interval!([16, 79]) / -8, Interval::Closed((-9, -2)));
```

## interval arithmetic

Add, subtract or multiply an `Interval<T>` with an `Interval<U>`
to produce another `Interval<Z>`
if the underlying type `T: {Add, Sub, Mult}<U, Output=Z>`:

```rust
use intrval::interval;

let i0 = interval!(_: i32);
let igt10 = interval!(> 10);
let i_2to10_incl = interval!([-2, 10]);
let i5to20_excl = interval!((5, =20));
let iuni = interval!(..: i32);

assert_eq!(igt10 + i_2to10_incl, interval!(> 8));
// adding degenerate does not change the normal one
assert_eq!(igt10 + interval!((1, 0)), igt10);
assert_eq!(interval!((1, 0)) + igt10, igt10);

assert_eq!(i_2to10_incl - i5to20_excl, interval!((=-22, 5)));
// subtracting degenerate does not change the normal one
assert_eq!(igt10 - interval!((1, 0)), igt10);
// subtracting _from_ degenerate negates the normal one
assert_eq!(interval!((2, 0)) - i_2to10_incl, -i_2to10_incl);

// Interval::Empty is neutral over multiplication
assert_eq!(i0 * i_2to10_incl, i0);
// positive (+inf) times positive is positive
assert_eq!(interval!(> 2) * igt10, interval!(> 20));
// positive (+inf) times (negative and positive) is (-inf, +inf)
assert_eq!(igt10 * i_2to10_incl, interval!(..));
assert_eq!(igt10 * i5to20_excl, interval!(> 50));
// Interval::Full is neutral over multiplication
assert_eq!(i5to20_excl * iuni, iuni);
```

## set operations

```rust
use intrval::{interval, Bounded as _};

let igt2 = interval!(> 2);
let igt10 = interval!(> 10);

assert_eq!(igt2.complement().into_single().unwrap(), interval!(<= 2));
// `.complement` is aliased with `!`
assert_eq!(
    (!interval!([-2, 10])).into_pair().unwrap(),
    (interval!(< -2), igt10)
);

assert_eq!(igt2.intersect(igt10).unwrap(), igt10);
// `.intersect` is aliased with `&` (falling back to Interval::Empty)
assert!((igt10 & interval!([-2, 10])).is_empty());
assert_eq!(
    interval!([-2, 10]) & interval!((5, =20)),
    interval!((5, =10))
);

assert_eq!(
    igt10
        .union(interval!([-2, 10]))
        .unwrap()
        .into_single()
        .unwrap(),
    interval!(>= -2)
);
// `.union` is aliased with `|` (falling back to the first non-empty if possible)
assert_eq!(
    (interval!([-2, 10]) | igt2).into_single().unwrap(),
    interval!(>= -2)
);
assert_eq!(
    (interval!((5, 10)) | interval!([3, 4]))
        .into_pair()
        .unwrap(),
    // reorders the input intervals in left-to-right order if they do not intersect
    (interval!([3, 4]), interval!((5, 10)))
);
assert_eq!((interval!(_) | igt2).into_single().unwrap(), igt2);
assert_eq!((igt2 | interval!(_)).into_single().unwrap(), igt2);

assert_eq!(
    interval!([-2, 10]).enclosure(igt10 * 2).unwrap(),
    interval!(>= -2)
);
```