Serge D. Mechveliani wrote:
Efficient arithmetic algorithms for large numbers is a matter of mathematics. Such algorithms, and libraries, are developed by the best experts in computational mathematics. Maybe, GMP is such.
There isn't too much mathematics in... everything is known for years, published in books: Knuth, etc. The question is efficient implementation and interfacing, and this is not a mathematical issue. Algorithmic, yes. Karatsuba, etc.... GMP has a venerable history, developed for years, well debugged etc. Used in other language processors, e.g. in some implementations of Scheme. The CAS named Pari apparently has its own bignum library, though. There are places where libraries are badly implemented as well. For example the rationals in the standard library of Haskell (this remark may be obsolete. In fact I HOPE it is obsolete...) Jerzy Karczmarczuk