(well that should be called areclose too! 🙂)
Determining whether two input values are close to each other or not is done according to given absolute and relative tolerances.
Absolute tolerance is obvious, as the maximum allowed difference between the two input values. This tolerance value must be at least zero.
The default value for this is 0 because it is not possible to determine an appropriate tolerance without knowing the likely values expected in a given use case.
Relative tolerance is the maximum allowed difference, but, relative to the larger absolute input value of the two. A relative tolerance of 5% is specified as 0.05. This value must be greater than zero and normally less than 1 to be meaningful.
A good default value for this is 1e-09, which assures that the two values are the same within about 9 decimal digits.
Using an absolute tolerance is important for comparisons near zero. This is because when both input values are lesser in magnitude than 1, a relative comparison test is very unlikely to be satisfied.
Providing 0 as input for either kind of tolerance will switch off that type of tolerance checking.
The IEEE 754 special values of NaN, inf, and -inf will be handled according to IEEE rules. Specifically, NaN is not considered close to any other value, including NaN. inf and -inf are only considered close to themselves.
If passed invalid tolerance values false is always returned.
The implementation is based on CPython, but has one small improvement from Boost.
Copy-paste the appropriate header for your language into your project and #include it where required.
bool areclose(double a, double b)
… is for testing with default tolerances.
bool areclose2(double a, double b, double abs_tol, double rel_tol)
… allows you to customize the tolerance values.
All the functionality is embodied in the AreClose functor class. Its members are as follows:
The default constructor AreClose() initializes a functor with default tolerances.
The constructor AreClose(double absTol, double relTol) allows you to specify the tolerances.
isValid returns whether an functor has valid tolerances. An invalid functor will always test false.
double absoluteTolerance() and double relativeTolerance() are getters.
bool setAbsoluteTolerance(double) and bool setRelativeTolerance(double) are setters. They return the success status based on whether the input value is valid. Invalid values are not set.
static bool invalidTolerance(double) checks for invalid tolerance values.
Use as:
AreClose areclose{2e-12, 4 * DBL_EPSILON};
if (areclose(a, b)) …
© 2021, Shriramana Sharma, samjnaa-at-gmail-dot-com
Use, modification and distribution are permitted subject to the "BSD-2-Clause"-type license stated in the accompanying file LICENSE.txt.