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.
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].
Add this to your cargo.toml:
[dependencies]
float_eq = "0.5"
and, if you're using the 2015 edition, this to your crate root:
rust
extern crate float_eq;
then, you can import items with use:
rust
use float_eq::{assert_float_eq, float_eq};
This crate provides boolean comparison operations:
```rust assert!(float_eq!(1000.0f32, 1000.0002, ulps <= 4));
const ROUNDINGERROR: f32 = 0.00034526698; assert!(floatne!(4.0f32, 4.1, rmax <= ROUNDINGERROR)); ```
And asserts:
```rust const RECIPRELEPSILON: f32 = 0.00036621094; assertfloateq!(0.1f32.recip(), 10.0, r2nd <= RECIPREL_EPSILON);
assertfloatne!(0.0f32, 0.0001, abs <= 0.00005, 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.
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:
rust
float_eq!(a, b, abs <= 0.000_01, ulps <= 4)
Is equivalent to:
rust
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 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:
```rust let a = Complex32 { re: 2.0, im: 4.000002 }; let b = Complex32 { re: 2.000000_5, im: 4.0 };
assertfloateq!(a, b, ulps <= Complex32Ulps { re: 2, im: 4 }); assertfloateq!(a, b, ulps_all <= 4); ```
Arrays of size 0 to 32 (inclusive) are supported:
rust
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):
rust
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.
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:
```rust
ulps_epsilon = "PointUlps",
debug_ulps_diff = "PointUlpsDebugUlpsDiff",
all_epsilon = "f64"
)]
struct Point { x: f64, y: f64, }
let a = Point { x: 1.0, y: -2.0 }; let c = Point { x: 1.0000000000000009, y: -2.0000000000000013 }; assertfloateq!(a, c, ulps <= PointUlps { x: 4, y: 3 }); assertfloateq!(a, c, ulps_all <= 4); ```
Assertion failure output tries to provide useful context information without going overboard. For example, this call:
rust
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.
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.
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.
Constructive feedback, suggestions and contributions welcomed, please [open an issue].
Release information is available in CHANGELOG.md.