Explicitly bounded comparison of floating point numbers.
Comparing floating point values for equality is really hard. To get it right requires careful thought and iteration based on the needs of each specific algorithm's inputs and error margins. This API provides a toolbox of components to make your options clear and your choices explicit 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 how
to write effective comparisons. The trade-off is that each individual
comparison requires more iteration time and thought.
And yes, this is yet another crate built on the principles described in that Random ASCII [floating point comparison] article, which is highly recommended background reading 🙂.
Add this to your cargo.toml:
[dependencies]
float_eq = "0.3"
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, rel <= ROUNDINGERROR)); ```
And asserts:
```rust const RECIPRELEPSILON: f32 = 0.00036621094; assertfloateq!(0.1f32.recip(), 10.0, rel <= RECIPREL_EPSILON);
assertfloatne!(0.0f32, 0.0001, abs <= 0.00005, ulps <= 4); ```
Where rel <= ROUNDING_ERROR should be read as "a relative epsilon comparison
with a maximum difference of less than or equal to ROUNDING_ERROR", and
similarly for abs and ulps. 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 using the abs, rel, and ulps comparisons, and types that implement
FloatEqAll may be compared with a uniformly applied epsilon value using the
abs_all, rel_all and ulps_all variants:
```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));
Types that also implement FloatDiff and FloatEqDebug/FloatEqAllDebug may
be used in the assert forms.
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, rel <= 0.000_001);
Panics with this error message:
thread 'test' panicked at 'assertion failed: `float_eq!(left, right, rel <= ε)`
left: `4.0`,
right: `4.000008`,
abs_diff: `0.000008106232`,
ulps_diff: `Some(17)`,
[rel] ε: `0.000004000008`', assert_failure.rs:15:5
The message provides abs_diff and ulps_diff regardless of which kinds of
checks are chosen. The [rel] ε line gives the epsilon value that abs_diff is
checked against in the comparison, which has been scaled based on the size of
the inputs. Absolute epsilon and ULPs based checks would provide different
output, see the [API documentation] for more details.
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 = "0.3"
default-features = false
Other optional features:
- num — implements FloatEq, FloatEqDebug and FloatDiff 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.
Further support for basic Rust container and wrapper types.
Checks that use a precision relative to the minimum of the two input values, or to the first or second operand.
#[derive] support for comparison of custom types that are composed of
already comparable floating point values.