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0.8.0 | May 4, 2020 |
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0.0.3 | Mar 10, 2015 |
#45 in Rust patterns
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float-cmp
Documentation is available at https://docs.rs/float-cmp
float-cmp defines and implements traits for approximate comparison of floating point types
which have fallen away from exact equality due to the limited precision available within
floating point representations. Implementations of these traits are provided for f32
and f64
types.
When I was a kid in the '80s, the programming rule was "Never compare floating point numbers". If you can follow that rule and still get the outcome you desire, then more power to you. However, if you really do need to compare them, this crate provides a reasonable way to do so.
Another crate efloat
offers another solution by providing a floating point type that
tracks its error bounds as operations are performed on it, and thus can implement the
ApproxEq
trait in this crate more accurately, without specifying a Margin
.
The recommended go-to solution (although it may not be appropriate in all cases) is the
approx_eq()
function in the ApproxEq
trait (or better yet, the macros). For f32
and f64
, the F32Margin
and F64Margin
types are provided for specifying margins as
both an epsilon value and an ULPs value, and defaults are provided via Default
(although there is no perfect default value that is always appropriate, so beware).
Several other traits are provided including Ulps
, ApproxEqUlps
, ApproxOrdUlps
, and
ApproxEqRatio
.
The problem
Floating point operations must round answers to the nearest representable number. Multiple operations may result in an answer different from what you expect. In the following example, the assert will fail, even though the printed output says "0.45 == 0.45":
let a: f32 = 0.15 + 0.15 + 0.15;
let b: f32 = 0.1 + 0.1 + 0.25;
println!("{} == {}", a, b);
assert!(a==b) // Fails, because they are not exactly equal
This fails because the correct answer to most operations isn't exactly representable, and so your computer's processor chooses to represent the answer with the closest value it has available. This introduces error, and this error can accumulate as multiple operations are performed.
The solution
With ApproxEq
, we can get the answer we intend:
let a: f32 = 0.15 + 0.15 + 0.15;
let b: f32 = 0.1 + 0.1 + 0.25;
println!("{} == {}", a, b);
assert!( approx_eq!(f32, a, b, ulps = 2) );
Some explanation
We use the term ULP (units of least precision, or units in the last place) to mean the difference between two adjacent floating point representations (adjacent meaning that there is no floating point number between them). This term is borrowed from prior work (personally I would have chosen "quanta"). The size of an ULP (measured as a float) varies depending on the exponents of the floating point numbers in question. That is a good thing, because as numbers fall away from equality due to the imprecise nature of their representation, they fall away in ULPs terms, not in absolute terms. Pure epsilon-based comparisons are absolute and thus don't map well to the nature of the additive error issue. They work fine for many ranges of numbers, but not for others (consider comparing -0.0000000028 to +0.00000097).
Using this crate
By default this crate enables the ratio
module providing the ApproxEqRatio
trait. This
feature pulls in num-traits
. If you disable this feature, you'll need to either enable
num-traits
directly or else enable the std
feature; otherwise it won't compile. This crate
is #![no_std]
unless you enable the std
feature.
You can use the ApproxEq
trait directly like so:
assert!( a.approx_eq(b, F32Margin { ulps: 2, epsilon: 0.0 }) );
We have implemented From<(f32,i32)>
for F32Margin
(and similarly for F64Margin
)
so you can use this shorthand:
assert!( a.approx_eq(b, (0.0, 2)) );
With macros, it is easier to be explicit about which type of margin you wish to set, without mentioning the other one (the other one will be zero). But the downside is that you have to specify the type you are dealing with:
assert!( approx_eq!(f32, a, b, ulps = 2) );
assert!( approx_eq!(f32, a, b, epsilon = 0.00000003) );
assert!( approx_eq!(f32, a, b, epsilon = 0.00000003, ulps = 2) );
assert!( approx_eq!(f32, a, b, (0.0, 2)) );
assert!( approx_eq!(f32, a, b, F32Margin { epsilon: 0.0, ulps: 2 }) );
assert!( approx_eq!(f32, a, b, F32Margin::default()) );
assert!( approx_eq!(f32, a, b) ); // uses the default
For most cases, I recommend you use a smallish integer for the ulps
parameter (1 to 5
or so), and a similar small multiple of the floating point's EPSILON constant (1.0 to 5.0
or so), but there are plenty of cases where this is insufficient.
Implementing these traits
You can implement ApproxEq
for your own complex types like shown below.
The floating point type F
must be Copy
, but for large types you can implement
it for references to your type as shown.
use float_cmp::ApproxEq;
pub struct Vec2<F> {
pub x: F,
pub y: F,
}
impl<'a, M: Copy, F: Copy + ApproxEq<Margin=M>> ApproxEq for &'a Vec2<F> {
type Margin = M;
fn approx_eq<T: Into<Self::Margin>>(self, other: Self, margin: T) -> bool {
let margin = margin.into();
self.x.approx_eq(other.x, margin)
&& self.y.approx_eq(other.y, margin)
}
}
Non floating-point types
ApproxEq
can be implemented for non floating-point types as well, since Margin
is
an associated type.
The efloat
crate implements (or soon will implement) ApproxEq
for a compound type
that tracks floating point error bounds by checking if the error bounds overlap.
In that case type Margin = ()
.
Inspiration
This crate was inspired by this Random ASCII blog post:
https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
Dependencies
~38KB