New submission from Stefan Behnel <stefan...@behnel.de>: I recently read a paper¹ about the difficulty of calculating the most exact midpoint between two floating point values, facing overflow, underflow and rounding errors. The intention is to assure that the midpoint(a,b) is
- actually within the interval [a,b] - the floating point number in that interval that is closest to the real midpoint (i.e. (a+b)/2). It feels like a function that should be part of Python's math module. ¹ https://hal.archives-ouvertes.fr/file/index/docid/576641/filename/computing-midpoint.pdf The author proposes the following implementation (pages 20/21): midpoint(a,b) = a if a == b else # covers midpoint(inf, inf) 0 if a == -b else # covers midpoint(-inf, +inf) -realmax if a == -inf else # min. double value +realmax if b == +inf else # max. double value round_to_nearest_even((a - a/2) + b/2) I guess nans should simply pass through as in other functions, i.e. midpoint(a,nan) == midpoint(nan,b) == nan. The behaviour for [a,inf] is decidedly up for discussion. There are certainly cases where midpoint(a,+inf) would best return +inf, but +realmax as an actual finite value also seems reasonable. OTOH, it's easy for users to promote inf->realmax or realmax->inf or even inf->a themselves, just like it's easy to check for +/-inf before calling the function. It just takes a bit longer to do these checks on user side. There could also be a "mode" argument that makes it return one of: a or b (i.e. the finite bound), +/-realmax or +/-inf in the two half-infinity cases. What do you think about this addition? ---------- components: Library (Lib) messages: 339257 nosy: mark.dickinson, rhettinger, scoder, stutzbach priority: normal severity: normal status: open title: Add math.midpoint(a,b) function type: enhancement versions: Python 3.8 _______________________________________ Python tracker <rep...@bugs.python.org> <https://bugs.python.org/issue36493> _______________________________________ _______________________________________________ Python-bugs-list mailing list Unsubscribe: https://mail.python.org/mailman/options/python-bugs-list/archive%40mail-archive.com
