Research Software
An AVX-optimized Julia library for fast Tanh-Sinh quadrature. Achieved up to 62x speedup in 1D, 35,700x in 2D, and successful microsecond-scale convergence in 3D boundary-singular integrals where competing libraries failed to meet tolerance.
FastTanhSinhQuadrature.jl implements high-performance tanh-sinh quadrature in Julia for difficult one-, two-, and three-dimensional integrals, especially near endpoint or boundary singularities. The library combines the robustness of double-exponential quadrature with careful vectorization and low-level performance work, delivering large speedups over baseline implementations while preserving stringent accuracy targets. It is intended for workloads where both numerical reliability and throughput matter.
The repository’s convergence figure reflects why tanh-sinh is the right method for this class of problems: double-exponential node clustering reaches high accuracy quickly even when the integrand has difficult endpoint behavior.
The benchmark summary highlights that the performance gains are not only mathematical. SIMD-specialized kernels and cache reuse are layered on top of the quadrature method, which is what makes the library competitive across repeated integration workloads.
