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

Yves Nievergelt | Zendy

Open Access

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

Author(s) -

Yves Nievergelt

Publication year - 2003

Publication title -

acm transactions on mathematical software

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.767

H-Index - 87

eISSN - 1557-7295

pISSN - 0098-3500

DOI - 10.1145/641876.641878

Subject(s) - quartic function , arithmetic , floating point , scalar (mathematics) , quadratic equation , numerical digit , computation , mathematics , saturation arithmetic , matrix (chemical analysis) , single precision floating point format , algebra over a field , arbitrary precision arithmetic , algorithm , pure mathematics , materials science , geometry , composite material

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.

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