Scalar fused multiply-add instructions produce floating-point matrix arithmetic provably accurate to the penultimate digit

被引：27

作者：

Nievergelt, Y ^{[1
]}

机构：

[1] Eastern Washington Univ, Dept Math, Cheney, WA 99004 USA

来源：

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE | 2003年 / 29卷 / 01期

关键词：

algorithms; design; languages; standardization; theory; doubly compensated summation; floating-point arithmetic; fused multiply-add instruction; matrix arithmetic; provable accuracy; rounding error; RISC; COMPUTATION; COMPUTER; DESIGN;

D O I：

10.1145/641876.641878

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Combined with doubly compensated summation, scalar fused multiply-add instructions redefine the concept of floating-point arithmetic, because they allow for the computation of sums of real or complex matrix products accurate to the penultimate digit. Particular cases include complex arithmetic, dot products, cross products, residuals of linear systems, determinants of small matrices, discriminants of quadratic, cubic, or quartic equations, and polynomials.

引用

页码：27 / 48

页数：22

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