Faster arbitrary-precision dot product and matrix multiplication

Fredrik Johansson 1
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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.
Type de document :
Pré-publication, Document de travail
2019
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https://hal.inria.fr/hal-01980399
Contributeur : Fredrik Johansson <>
Soumis le : lundi 14 janvier 2019 - 13:51:45
Dernière modification le : mercredi 16 janvier 2019 - 09:26:32

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matrix.pdf
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  • HAL Id : hal-01980399, version 1
  • ARXIV : 1901.04289

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Fredrik Johansson. Faster arbitrary-precision dot product and matrix multiplication. 2019. 〈hal-01980399〉

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