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?
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
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.
Thank you. -- Darren Duncan
