On Thu, Oct 8, 2020, at 13:17, Tim Peters wrote:
> [Random832 <random...@fastmail.com>]
> > I was making a "convert Fraction to Decimal, exactly if possible" function
> > and
> > ran into a wall: it's not possible to do some of the necessary operations
> > with
> > exact precision in decimal:
> >
> > - multiplication
> > - division where the result can be represented exactly [the divisor is an
> > integer whose prime factors are only two and five, or a rational number
> > whose numerator qualifies]
>
> Without you supplying careful concrete examples, I really have no idea
> what you're looking for.
I don't understand what's unclear - I was suggesting there should be an easy
way to have the exact result for all operations on Decimal operands that have
exact results representable as Decimal.
I did misunderstand part of the documentation, though... the documentation
claims "Some operations like addition, subtraction, and multiplication by an
integer will automatically preserve fixed point. ", and I assumed without
checking that this applied even if the size of the operands was greater than
the context precision, and therefore that addition and subtraction were always
exact. This is why my post was so focused on multiplication and division.
Sine correcting that misunderstanding, I've looked over the implementation and
I no longer think this is worth adding without a concrete use case, since
supporting adding very large and very small numbers together would introduce
more inefficiencies than it's worth.
Incidentally, I also noticed the procedure suggested by the documentation for
doing fixed point arithmetic can result in incorrect double rounding in some
situations:
>>> (D('1.01')*D('1.46')).quantize(TWOPLACES) # true result is 1.4746
Decimal('1.48')
> Integers have unbounded precision, so stick to those when part of a
> computation needs to be unbounded. If by "Decimal" you mean Python's
> "decimal.Decimal" class, the constructor ignores the context
> precision, and retains all the info passed to it, So there's no need
> at all to change Decimal precision.
This only applies to the constructor though, not the arithmetic operators.
> Here's a guess at what you want:
That works for the specific use case of converting Fraction to Decimal- I
didn't know that Decimal supported E notation in the constructor, so I thought
I would have to multiply or divide by a power of ten directly [which would
therefore have to be rounded]... going through the string constructor seems
extremely inefficient and inelegant, though, I'd like a way to losslessly
multiply or divide a decimal by a power of ten at least... a sort of decimal
equivalent to ldexp.
And I guess for the other operations it's possible to work around by doing the
operations in Fraction and converting to Decimal in the end - that also seems
inelegant, but oh well.
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