Er, yes, I'm aware why this happened, my point is that this happens in the hardware floating point, but Python is as slow as the non-accelerated big rationals in my realistic::Real (it's actually markedly slower than the more appropriate realistic::Rational but that's not what my existing benchmarks cared about)
Not really. It's a limitation of the IEEE floating point format used in most programming languages. Some numbers that look nice in base 10 don't have an exact representation in base 2.
Rational numbers where the denominator is a multiple of the prime factors of the base have an exact fractional representation in that base.
1/3 doesn't have an exact representation in base 10 or base 2. 1/5th does have an exact representation in base 10 (0.2), but doesn't in base 2. 1/4th has an exact representation in base 10 (0.25) and in base 2 (0.01)
