On Wed, Nov 18, 2009 at 12:33:35AM -0800, Darren Duncan wrote:
> Acknowledging that 'FatRat' is current name for above 'Ratio' ...
>
> pugs-comm...@feather.perl6.nl wrote:
>> -For applications that really need arbitrary precision denominators
>> -as well as numerators, C<Ratio> may be used, which is defined as C<Int/Int>.
>> +For applications that really need arbitrary precision denominators as
>> +well as numerators at the cost of performance, C<Ratio> may be used,
>> +which is stored as C<Int/Int>, that is, as arbitrary precision in
>> +both parts. There is no literal form for a C<Ratio>, so it must
>> +be constructed using C<Ratio.new($nu,$de)>. In general, only math
>> +operators with at least one C<Ratio> argument will return another
>> +C<Ratio>, to prevent accidental promotion of reasonably fast C<Rat>
>> +values into arbitrarily slow C<Ratio> values.
>
> Given the above, if one wants to construct a full-precision rational
> value in terms of 3 Int values analogous to a mantissa and radix and
> exponent, what is the best way to write it in Perl 6?
>
> For example, say I want the following expression to result in a FatRat
> because presumably that's the only type which will represent the result
> value exactly:
>
> 45207196 * 10 ** -37
>
> How should that be spelled out in terms of 3 integers?

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why 3?
FatRat.new(45207196, 10**37);
> And note that a decimal-specific answer isn't what I want, since I want
> something that would also work for this:
>
> 45207196 * 11 ** -37
FatRat.new(45207196, 11**37);
> Any thoughts?
>
> Basically where I'm coming from here is the idea that any rational can
> also be expressed as 3 integers like the above, not just the
> numerator/denominator pair; the 3 integers are advantages both for being
> efficient with common pathological cases such as very large or very small
> rationals with a small amount of precision, such as the above, as well as
> for exactly reflecting the concept of a radix-agnostic floating-point
> number.
I think that's an implementation detail. If you care much about it, you'll
have to provide your Rat type.
Cheers,
Moritz