On Tue, Jan 27, 2015 at 11:20 AM, Guido van Rossum <guido@python.org> wrote:
It feels like absolute tolerance is a completely different test. And it is a much simpler test for which w don't need a helper function -- it's just abs(x) < tolerance.
+1
Just as a point of reference, APL and its derivatives use tolerant comparison in the default equal (=) operator. The definition that they use for finite x and y is simply
x = y <=> abs(x-y) <= tol * max(abs(x), abs(y))
The tolerance can be adjusted globally or in some languages (such as J [1]) in the expression using additional syntax.
In J, the default tolerance is 2**-44, which is about 5.7e-14. APL restricts the range of tolerance values to 0 through 2**-32.
I would be +0 on adding something like
def tolerant_equal(x, y, tol=2**-44):
return abs(x-y) <= tol * max(abs(x), abs(y))
(name subject to bikeshedding)
to math, but -1 on anything more complicated. I would rather see