Here is a question I want to submit to you:

Currently, for determinstic computations, LinBox uses (in some places at
least) the log of the real Hadamard's bound in its machinery, ie,
log (min (prod (|col_i|^2) , prod(|row_i|^2) )
=
min ( sum (log ( |col_i|^2 ) ) , sum (log (|row_i|^2)))

Although the result could be represented as a double float, its
computation need to use gmp integer arithmetic for lar
But to compute it, we use gmp integer arithmetic for computing |col_i| =
sum_j (a[i,j]^2), since it can overflow the double reprensentation
capabilities (not only the mantissa, but also the exponent).

This drawback can be particularly bad  for the case of small matrices
and very large entries.

An alternative could be to use mpfr multiprecision floating point
arithmetic. This makes it much faster, but would require another
dependancy for linbox to compile.

Do you think it would be worth to add this dependency?

Clément

-dave

PS.  Since it is a bound, I would think the mantissa accuracy of double
is sufficient.  But when the exponent is exceeded, well, then you need
realer real numbers!