float_eq

Compare IEEE floating point values for equality.

Comparing floating point values for equality is notoriously difficult, getting it right requires careful reasoning and iteration. This API provides a variety of comparison algorithms and debugging tools to help make the process more intuitive and your choices explicit and clear to future maintainers.

Background

Given how widely algorithmic requirements can vary, float_eq explores the idea that there are no generally sensible default margins for comparisons. This is in contrast to the approach taken by many other crates, which often provide default epsilon values in checks or implicitly favour particular algorithms. The author's hope is that by exposing the inherent complexity in a uniform way, programmers will find it easier to develop an intuition for effective use of floats.

This work builds on the definitions in Knuth's The Art Of Computer Programming, (Vol. 2, Seminumerical Algorithms, Third Edition, section 4.2.2), and that Random ASCII article on floating point comparison.

Usage

Add this to your cargo.toml:

[dependencies]
float_eq = "0.5"

and, if you're using the 2015 edition, this to your crate root:

extern crate float_eq;

then, you can import items with use:

use float_eq::{assert_float_eq, float_eq};

Comparisons

This crate provides boolean comparison operations:

assert!(float_eq!(1000.0f32, 1000.0002, ulps <= 4));

const ROUNDING_ERROR: f32 = 0.000_345_266_98;
assert!(float_ne!(4.0f32, 4.1, rmax <= ROUNDING_ERROR));

And asserts:

const RECIP_REL_EPSILON: f32 = 0.000_366_210_94; 
assert_float_eq!(0.1f32.recip(), 10.0, r2nd <= RECIP_REL_EPSILON);

assert_float_ne!(0.0f32, 0.000_1, abs <= 0.000_05, ulps <= 4);

Checks are invoked by name and with a threshold, so for example abs <= 0.000_05 should be read as "an absolute epsilon comparison with a maximum difference of less than or equal to 0.000_05". Similarly, rmax, rmin, r1st and r2nd provide a variety of kinds of relative epsilon comparison with thresholds that scale to the granularity of one or input value or the other and ulps is an ULPs based comparison that takes advantage of the underlying bitwise representation. See the API documentation for a long form introduction to the different kinds of checks, their uses and limitations.

Combining checks

If more than one check is specified by a comparison then they are performed in order from left to right. If any check is true, then the two values are considered equal. For example, this expression:

float_eq!(a, b, abs <= 0.000_01, ulps <= 4)

Is equivalent to:

float_eq!(a, b, abs <= 0.000_01) || float_eq!(a, b, ulps <= 4)

This allows you to build comparison expressions as needed, only paying for what you use.

Composite types

Composite types that implement FloatEq may be compared on a field-by-field basis, and types that implement FloatEqAll may be compared with a uniformly applied epsilon value across all fields:

let a = Complex32 { re: 2.0, im: 4.000_002 };
let b = Complex32 { re: 2.000_000_5, im: 4.0 };

assert_float_eq!(a, b, ulps <= Complex32Ulps { re: 2, im: 4 });
assert_float_eq!(a, b, ulps_all <= 4);

Arrays of size 0 to 32 (inclusive) are supported:

let a = [1.0, -2.0, 3.0];
let b = [-1.0, 2.0, 3.5];
assert_float_eq!(a, b, abs <= [2.0, 4.0, 0.5]);
assert_float_eq!(a, b, abs_all <= 4.0);

As are tuples up to size 12 (inclusive):

let a = (1.0f32, 2.0f64);
let b = (1.5f32, -2.0f64);
assert_float_eq!(a, b, abs <= (0.5, 4.0));

There are also blanket trait impls for comparing mutable and immutable reference types, the contents of Cell, RefCell, Rc, Arc and Box instances, as well as for slices, Option, Vec, VecDeque, LinkedList, BTreeMap and HashMap.

Types that also implement AssertFloatEq/AssertFloatEqAll may be used in the assert forms.

Derivable

If the optional "derive" feature is enabled, all of the traits may be implemented using #[derive]. The easiest way to do so is to make use of the #[derive_float_eq] helper macro:

#[derive_float_eq(
    ulps_epsilon = "PointUlps",
    debug_ulps_diff = "PointUlpsDebugUlpsDiff",
    all_epsilon = "f64"
)]
#[derive(Debug, PartialEq, Clone, Copy)]
struct Point {
    x: f64,
    y: f64,
}

let a = Point { x: 1.0, y: -2.0 };
let c = Point { 
    x: 1.000_000_000_000_000_9, 
    y: -2.000_000_000_000_001_3
};
assert_float_eq!(a, c, ulps <= PointUlps { x: 4, y: 3 });
assert_float_eq!(a, c, ulps_all <= 4);

Error messages

Assertion failure output tries to provide useful context information without going overboard. For example, this call:

assert_float_eq!(4.0f32, 4.000_008, rmax <= 0.000_001);

Panics with this error message:

thread 'main' panicked at 'assertion failed: `float_eq!(left, right, rmax <= ε)`
        left: `4.0`,
       right: `4.000008`,
    abs_diff: `0.000008106232`,
   ulps_diff: `Some(17)`,
    [rmax] ε: `0.000004000008`', assert_failure.rs:15:5

The message shows the values of the expressions being compared and the difference between them both in absolute terms and in terms of ULPs. The [rmax] ε line shows the epsilon value that the absolute difference was compared against after being appropriately scaled.

Optional features

This crate can be used without the standard library (#![no_std]) by disabling the default std feature. Use this in Cargo.toml:

[dependencies.float_eq]
version = "0.5"
default-features = false

Other optional features:

derive — provides custom derive macros for all traits.
num — blanket trait impls for num::Complex where it is instanced with a compatible type.

Related efforts

The approx and float-cmp crates provide a similar style of general comparison operations, whereas assert_float_eq focuses specifically on assertions. The almost crate instead divides its API into algorithms comparing against zero and non-zero values. In contrast, efloat takes the approach of tracking the error bounds of values as operations are applied.

Contributing

Constructive feedback, suggestions and contributions welcomed, please open an issue.

Changelog

Release information is available in CHANGELOG.md.

float_eq 0.5.0