# Trait hacspec_lib::prelude::traits::float::TotalOrder

source · [−]## Expand description

Trait for floating point numbers that provide an implementation
of the `totalOrder`

predicate as defined in the IEEE 754 (2008 revision)
floating point standard.

## Required Methods

Return the ordering between `self`

and `other`

.

Unlike the standard partial comparison between floating point numbers,
this comparison always produces an ordering in accordance to
the `totalOrder`

predicate as defined in the IEEE 754 (2008 revision)
floating point standard. The values are ordered in the following sequence:

- negative quiet NaN
- negative signaling NaN
- negative infinity
- negative numbers
- negative subnormal numbers
- negative zero
- positive zero
- positive subnormal numbers
- positive numbers
- positive infinity
- positive signaling NaN
- positive quiet NaN.

The ordering established by this function does not always agree with the
`PartialOrd`

and `PartialEq`

implementations. For example,
they consider negative and positive zero equal, while `total_cmp`

doesn’t.

The interpretation of the signaling NaN bit follows the definition in the IEEE 754 standard, which may not match the interpretation by some of the older, non-conformant (e.g. MIPS) hardware implementations.

##### Examples

```
use num_traits::float::TotalOrder;
use std::cmp::Ordering;
use std::{f32, f64};
fn check_eq<T: TotalOrder>(x: T, y: T) {
assert_eq!(x.total_cmp(&y), Ordering::Equal);
}
check_eq(f64::NAN, f64::NAN);
check_eq(f32::NAN, f32::NAN);
fn check_lt<T: TotalOrder>(x: T, y: T) {
assert_eq!(x.total_cmp(&y), Ordering::Less);
}
check_lt(-f64::NAN, f64::NAN);
check_lt(f64::INFINITY, f64::NAN);
check_lt(-0.0_f64, 0.0_f64);
```