Fast Basecases for Arbitrary-Size Multiplication

Multiple precision libraries typically use assembly-optimized loops for basecase operations on variable-length operands. We consider the alternative of generating lookup tables with hardcoded routines for many fixed sizes, e.g. for all multiplications up to 16 by 8 words. On recent ARM64 and x86-64 CPUs, we demonstrate up to a 2x speedup over GMP for basecase-sized multiplication and a 20% speedup for Karatsuba-sized operands. We pay special attention to the computation of approximate products and demonstrate up to a 3x speedup over GMP/MPFR for floating-point multiplication.