Title: Faster arbitrary-precision dot product and matrix multiplication,
Abstract: We present algorithms for real and complex dot product and matrix
multiplication in arbitrary-precision floating-point and ball arithmetic. A
low-overhead dot product is implemented on the level of GMP limb arrays; it is
about twice as fast as previous code in MPFR and Arb at precision up to several
hundred bits. Up to 128 bits, it is 3-4 times as fast, costing 20-30 cycles per
term for floating-point evaluation and 40-50 cycles per term for balls. We
handle large matrix multiplications even more efficiently via blocks of scaled
integer matrices. The new methods are implemented in Arb and significantly
speed up polynomial operations and linear algebra.