finding out the precision of floats

[casevh at gmail.com]

> Why should you? It only gives you 28 significant digits, while 64-bit
> float (as in 32-bit version of Python) gives you 53 significant
> digits. Also note, that on x86 FPU uses 80-bit registers. An then
> Decimal executes over 1500 times slower.

64-bit floating point only gives you 53 binary bits, not 53 digits.
That's approximately 16 decimal digits. And anyway, Decimal can be
configured to support than 28 digits.

>
> >>> from timeit import Timer
> >>> t1 = Timer('(1.0/3.0)*3.0 - 1.0')
> >>> t2 = Timer('(Decimal(1)/Decimal(3))*Decimal(3)-Decimal(1)',
>
> 'from decimal import Decimal')>>> t2.timeit()/t1.timeit()
>
> 1621.7838879255889
>
> If that's not enough to forget about Decimal, take a look at this:
>
> >>> (Decimal(1)/Decimal(3))*Decimal(3) == Decimal(1)
> False
> >>> ((1.0/3.0)*3.0) == 1.0
>
> True

Try ((15.0/11.0)*11.0) == 15.0. Decimal is actually returning the
correct result. Your example was just lucky.

Decimal was intended to solve a different class of problems. It
provides predictable arithmetic using "decimal" floating point.
IEEE-754 provides predictable arithmetic using "binary" floating
point.

casevh