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arXiv:1901.04289cs.MS

Faster arbitrary-precision dot product and matrix multiplication

Fredrik Johansson

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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.

arXiv comments
Journal reference
26th IEEE Symposium on Computer Arithmetic (ARITH26), Jun 2019, Kyoto, Japan
DOI
Subjects
cs.MSMathematical Software math.NANumerical Analysis

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  1. Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic (2016) 1 comment

    • Author here. I will take the opportunity to advertise my blog at https://fredrikj.net/blog/ where I post occasional development updates about Arb and other projects. Some improvements not covered in the 2016 preprint include much faster code for arithmetic and matrix…

      fdejView on HNParent context

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