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
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.
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
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
F64Margin types are provided for specifying margins as
both an epsilon value and an ULPs value, and defaults are provided via
(although there is no perfect default value that is always appropriate, so beware).
Several other traits are provided including
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!; assert! // 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.
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!; assert!;
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
#![no_std] unless you enable the
You can use the
ApproxEq trait directly like so:
We have implemented
F32Margin (and similarly for
so you can use this shorthand:
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!; assert!; assert!; assert!; assert!; assert!; assert!; // 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.
Non floating-point types
ApproxEq can be implemented for non floating-point types as well, since
an associated type.
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 = ().
This crate was inspired by this Random ASCII blog post: