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

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 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). Evaluated at 128-bit precision on massive matrices up to 50,000×50,000 with a 0.05% structural density, our unified, unrolled row-pointer execution model completely eliminates algebraic overhead on empty cells. Empirical execution metrics demonstrate that the proposed framework processes 1, 248, 919 active elements in 1.988 seconds—achieving a terminal throughput of 25, 151 rows per second—while guaranteeing exact bit-level consistency in interval radius bounding.