Customizable behavior for nearlyEqual: relative or absolute difference

[chidiwilliams]

package.json

"mathjs": "^5.0.1"

I'm trying to set the epsilon value for comparing equality of two numbers. I want all numbers within a range of 1e-5 and below to be considered equal.

I'm doing:

const math = require('mathjs');

math.config({
  epsilon: 1e-5,
});

console.log(math.equal(5e-10, 0));

But this gives an output of:

false

I've also tried:

const math = require('mathjs');
const mth = math.create({
  epsilon: 1e-5,
});

console.log(mth.equal(5e-10, 0));

But it prints the same output.

What's going on or what am I doing wrong?

[josdejong]

The equal function calculates the relative difference, not the absolute difference:

http://mathjs.org/docs/datatypes/numbers.html#equality

[gwhitney]

Actually, equal() is (currently) an undocumented mix of relative and absolute approximate comparisons. See #2838 for some proposals on how this might be systematized, and therefore cover your use case.

[chidiwilliams]

Ah, I see. I would love to see a method to compare absolute difference with EPSILON. Thanks anyway.

[josdejong]

Yes makes sense.

As a workaround you could implement an equal function which does do two checks: one for the value itself, and one for value+1, something like:

math.import({
  absEqual: (a, b) => math.equal(a, b) || math.equal(math.add(a, 1), math.add(b, 1))
})

math.config({epsilon: 1e-5})
console.log(math.equal(0, 1e-6))    // false
console.log(math.absEqual(0, 1e-6)) // true

If we implement absolute nearly equal functionality I think it should go in a new config option. It makes sense, let's give this some more thought. I will reopen this issue and change the title accordingly.