NTL is a high-performance, portable C++ library providing data structures and algorithms for manipulating signed, arbitrary length integers, and for vectors, matrices, and polynomials over the integers and over finite fields.
For those keeping score: I did a quick comparison of v9.2 against v5.5 (which was when development kind of lapsed between 2009 and 2013). For one of my basic benchmarks, namely, multiplication of degree 1023 polynomials modulo a 1024-bit prime, I measure a 1.8x speedup. I'm pretty sure a number of other things have improved, too.
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