On Sat, Aug 5, 2017 at 4:03 AM, Ian Kelly <ian.g.ke...@gmail.com> wrote: > On Fri, Aug 4, 2017 at 11:59 AM, Ian Kelly <ian.g.ke...@gmail.com> wrote: >> On Fri, Aug 4, 2017 at 11:50 AM, Chris Angelico <ros...@gmail.com> wrote: >>> My logic was that floating point rounding is easiest to notice when >>> you're working with a number that's very close to something, and since >>> we're working with square roots, "something" should be a perfect >>> square. The integer square root of n**2 is n, the ISR of n**2+1 is >>> also n, and the ISR of n**2-1 should be n-1. I actually wanted to >>> start at 2**53, but being an odd power, that doesn't have an integer >>> square root, so I started at 2**52, which has an ISR of 2**26. >> >> A slight irony here is that it actually would have taken your script a >> *very* long time to get to 2**53 having started at 2**52, even only >> iterating over the perfect squares. > > Never mind, I just tried it and it's a few seconds. I guess there are > not as many perfect squares in that range as I thought.
There are about thirty million of them. Python can calculate square roots in a handful of nanoseconds on my system, so "a few seconds" sounds about right. >>> math.sqrt(2**53) - math.sqrt(2**52) 27797401.62425156 >>> 2**26 * 0.41421356 27797401.46499584 ChrisA -- https://mail.python.org/mailman/listinfo/python-list
