An Efficient Complex-CSR Sparse Matrix-Vector Multiplication Framework Under Dynamic Arbitrary-Precision Ball Arithmetic

Abstract

State-of-the-art multi-precision mathematical libraries, such as FLINT and Arb, lack optimized native subroutines for sparse matrix-vector multiplication (SpMV) when operating under dynamic runtime arbitrary-precision complex interval arithmetic (acb mat). Consequently, representing sparse topologies through standard dense structures incurs severe computational penalties due to redundant zero-element evaluations and persistent cache thrashing. To address this architectural gap, we present a novel standalone C++ framework utilizing a modified Compressed Sparse Row layout tailored for complex ball entities (Complex-CSR) powered by a dynamic MPFR backend. Evaluated under strict structural densities of 0.05% across variable mantissa limits up to 500 decimal digits, our unified, unrolled row-pointer execution model completely eliminates algebraic overhead on empty cells. Empirical execution metrics demonstrate that the proposed framework achieves ultra-low latencies (0.016s at 100 digits and 0.024s at 500 digits), proving high performance scalability while guaranteeing exact bit-level consistency in interval radius bounding.