Alright, alright, looking for these better math libraries is getting quite annoying. Surely, if someone else hadn’t made an integer arithmetic version of BLAS, they’d made an arbitrary precision version of BLAS? Indeed, they did, it was done in the past, but not anymore. The library I’ve found hasn’t been updated in 8 years. Also, you’re asking about libraries using double-width intermediates during multiplications? Yes, indeed this MPACK library does make reference to a floating point equivalent, QD/DD (quad-double, double-double arithmetic). Alas, that too is no longer maintained, nor is the original webpage even on the Internet anymore!
Original BLAS, floating point only.
20200527/http://www.netlib.org/blas/
MPACK, arbitrary precision BLAS and LAPACK.
20200527/DuckDuckGo gmp blas
20200527/http://mplapack.sourceforge.net/
QD/DD, quad-double, double-double floating point arithmetic.
20200527/https://web.archive.org/web/20100502022120/http://www.cs.berkeley.edu/~yozo/
Now, what about CGAL in the midst of all this? CGAL touts using arbitrary precision arithmetic for all operations. Well, reading this page on information about CGAL’s philosophy on exact computation, I’m finding some striking similarities between my own library and what CGAL is doing internally. Except, for CGAL, of course, they are doing it exclusively for geometric computation, to the exclusion of exposing a general-purpose library for linear algebra.
20200527/https://www.cgal.org/exact.html
So, at the end of all of this, I can conclude that yes, there are a variety of libraries that do things similar to the way I’m doing it in my own library, but nothing quite fits the bill as nicely about what I’m looking for as my own library does.
Also, there is something to be said about this kind of software appearing in more commercial contexts as of late. For many years, this may have only been the interest of academia, but with the advent of Tensor Processing Units (TPUs) using integer arithmetic extensively to accelerate artificial intelligence computation and the like, there is certainly a lot more commercial interest, and with that, the desire to make the results of the development proprietary. So that may partially explain why we’ve been seeing such developments so publicly available in the late 2000s, but then they suddenly dropped off a cliff and fell into dis-maintenance after the year 2012. Google wanted to sweep up all of that math tech talent for themselves.