Precise Floating-Point Summation and Dot Product Computation for Sunway

The Sunway platform, as a representative of domestic high-performance processors, is widely used in scientific computing, but it has certain limitations in hardware support for floating-point operations, especially in high-precision calculations. To address this issue, the cumulative effect of rounding errors in floating-point addition and dot product operations was explored. Subsequently, based on the error-free transformation technique and the SIMD instructions and floating-point vector registers on the Sunway1621 platform, the floating-point summing SimdSum algorithm and the dot product SimdDot algorithm were designed and implemented. On the test set generated by GenDot2, the relative error of the computation results of the SimdDot algorithm compared to double-precision results was reduced by an average of 99.9%, demonstrating better stability and the ability to adapt to a larger range of condition numbers. On the test data set generated by the Sin function, the computational accuracy of the SimdSum algorithm reached the level of computational accuracy of the long double type on the Intel platform. When comparing the proposed algorithms with double-precision operations on the Sunway1621 processor, on different scales of test sets randomly generated in Python, although the average running time of the SimdSum and SimdDot algorithms was about 13.06 times that of double precision, the precision of the computational results was significantly improved.