GMP is available under the LGPL.
GMP is not a common system API like POSIX, so if you rely on it, you actually have to bundle GMP, or otherwise handle the dependency.
LGPL is fine for things like standard C and POSIX, because your program is not tied to that LGPL-ed implementation. The GPL itself recognizes "system library" as a special status. It is permissible for GNU programs to depend on proprietary libraries if they are system libraries. Under very similar reasoning, depending on LGPL-ed libraries is okay in an otherwise completely free program if those LGPL-ed libraries are system libraries.
LGPL limits you to dynamic linking, which is gross for this kind of thing. (Have you looked at a dynamic library function call lately?)
If you make a language depend on a LGPL library for numbers, that turns into GPL if you have to build a static image for an embedded system.
This is not a problem with malloc or printf which you just get from that system, rather than by carrying the GNU C Library into your program.
Legally you may be able to get away with adding a LGPLed library to a MIT or BSD program; in practice, licensing is not purely about "what can I legally get away with". What kind of hassles and restrictions will there be factors into it. Also philosophy factors into it: it's ideologically inappropriate for a liberally licensed (BSD, MIT) program to depend on special-purpose, non-system GNU libraries.
I chose MPI for TXR; LibTomMath, though providing some optimizations like Karatsuba multiplication, just brings in too much cruft.
Quite a few bugs in MPI, but I have a handle on it.
I extended it with bit operations, a faster square root, more conversion routines and such.
http://www.kylheku.com/cgit/txr/log/mpi
I'm familiar with LibTomMath. Tom St. Denis used to post to the comp.lang.c newsgroup years ago. Some 15 years ago I used it (or rather LibTomCrypt, which is based on it) in a commercial project to do some RSA-based authentication on some configuration packets sent to mobile devices.