GMP Inputs

[Hans Aberg]

Here are some inputs about multi-precision numbers in general:

- Apart from the data types "integer", "rational", and "floating", I have
identified a data type "fixed" for fixed point numbers. This would be like
quotient pairs (p, q), where p, q are integers, and q > 0 is held fixed,
and 1/q is the precision. For example, to be used for computations with
money, time.

Perhaps exotic, but I mention it anyhow.

- As for the inaccuracy (inverted value of precision) of floating and fixed
point numbers, I think that a fairly correct mathematical way would be to
use differentials of the operations involved to compute the new inaccuracy.
That is, unless the user specifically requests a round-off.

For the floating type, one would use logarithmic differentials dlog f :=
(df)/f, and for the fixed point type regular differentials. For example,
floating multiplication gives the new inaccuracy dlog(x*y) = dlog x + log
y, which is no worse than max(dlog x, log y), or the minimum precision of x
and y.

  Hans Aberg