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 if tolerant_equal(x, y) or abs(x-y) <= 1e-10: .. than if tolerant_equal(x, y, atol=1e-10): .. [1] http://www.jsoftware.com/help/dictionary/d000.htm [2] http://www.dyalog.com/uploads/documents/Papers/tolerant_comparison/tolerant_...