The (long standard) functions frexp & ldexp allow the consultation and manipulation of
the (binary) exponent of IEEE floating point arithmetic.
In particular, one can utilize frexp & ldexp to pre-condition certain computations to
increase precision and avoid exponent overflow/underflow.
The graphics community makes minor use of frexp & ldexp, but a Google search produced
_zero_ papers on the use of these functions in large scale matrix operations.
Should I be Google searching with different terms, or has frexp/ldexp fallen into
the blind spot of numerical mathematicians?
One example:
One can "factor out" a 2^k factor from each row and column of a matrix (different
k for each row & column); this factoring _preserves all bits_ & is thus invertible.
These kinds of things were done in the dawn of computing (1950's/1960's), but
seem to have completely fallen out of favor.