On 22 September 2017 at 13:38, Guido van Rossum <gu...@python.org> wrote: > On Thu, Sep 21, 2017 at 8:30 PM, David Mertz <me...@gnosis.cx> wrote: >> >> Simply because the edge cases for working with e.g. '0xC.68p+2' in a >> hypothetical future Python are less obvious and less simple to demonstrate, >> I feel like learners will be tempted to think that using this base-2/16 >> representation saves them all their approximation issues and their need >> still to use isclose() or friends. > > Show them 1/49*49, and explain why for i < 49, (1/i)*i equals 1 (lucky > rounding).
If anything, I'd expect the hex notation to make the binary vs decimal representational differences *easier* to teach, since instructors would be able to directly show things like: >>> 0.5 == 0x0.8 == 0o0.4 == 0b0.1 # Negative power of two! True >>> (0.1 + 0.2) == 0.3 # Not negative powers of two False >>> 0.3 == 0x1.3333333333333p-2 True >>> (0.1 + 0.2) == 0x1.3333333333334p-2 True While it's possible to provide a demonstration along those lines today, it means writing the last two lines as: >>> 0.3.hex() == "0x1.3333333333333p-2" True >>> (0.1 + 0.2).hex() == "0x1.3333333333334p-2" True (Which invites the question "Why does 'hex(3)' work, but I have to write '0.3.hex()' instead"?) To illustrate that hex floating point literals don't magically solve all your binary floating point rounding issues, an instructor could also demonstrate: >>> one_tenth = 0x1.0 / 0xA.0 >>> two_tenths = 0x2.0 / 0xA.0 >>> three_tenths = 0x3.0 / 0xA.0 >>> three_tenths == one_tenth + two_tenths False Again, a demonstration along those lines is already possible, but it involves using integers in the rational expressions, rather than floats. Given syntactic support, it would also be reasonable for the hex()/oct()/bin() builtins to be expanded to handle printing floating point numbers in those formats, and for floats to gain support for the corresponding print formatting codes. So overall, I'm still +0, on the grounds of improving int/float API consistency. While I'm sympathetic to the concerns about potentially changing the way the binary/decimal representation distinction is taught for floating point values, I don't think having better support for more native representations of binary floats is likely to make that harder than it already is. Cheers, Nick. -- Nick Coghlan | ncogh...@gmail.com | Brisbane, Australia _______________________________________________ Python-ideas mailing list Python-ideas@python.org https://mail.python.org/mailman/listinfo/python-ideas Code of Conduct: http://python.org/psf/codeofconduct/