2016-09-03 11:17 GMT+02:00 Denis Kudriashov <dionisiydk@gmail.com>:
2016-09-03 9:48 GMT+02:00 Nicolas Cellier <nicolas.cellier.aka.nice@ gmail.com>:
For floating points it would be good to also have something related to unit of least precision like I think it exists in google tests:
assert: aFloat isWithin: anInteger ulpFrom: anotherFloat ^(aFloat - anotherFloat) abs <= (anotherFloat ulp max: aFloat ulp)
It's testing if the result are the same with a tolerance on least significant bits. (anotherFloat ulp max: aFloat ulp) is not really necessary, it's only for making the comparison symmetric. indeed, 2 and 2 predecessor do not have the same exponent, so do not have the same ulp. If we don't have symmetry, then self assert: 2.0 predecessor predecessor isWithin: 1 ulpFrom: 2.0. might differ from: self assert: 2.0 isWithin: 1 ulpFrom: 2.0 predecessor predecessor .
Note that the this message cannot be used to test for zero result (because 0.0 ulp is the smallest denormal). For example: self assert: 2.0 - 2.0 predecessor isWithin: 4 ulpFrom: 0.0. would anwer false, but it makes no sense! One should write self assert: 2.0 isWithin: 4 ulpFrom: 2.0 predecessor.
Bad result will be in other cases too (not only zero):
expected := 8085- 8084.9999. computed := (80.85 * 100) - 8084.9999. (computed - expected) abs <= (computed ulp max: expected ulp) "==> false"
Fine, this result is not within 1 ulp error because of catastrophic
cancellation, the difference is more than 1e7 ulp. That just mean that we have a numerical formulation that is quite unstable (it has half precision of double). I don't see why this invalidate this specific type of assertion, au contraire.