Error bounds for computer arithmetics

被引：6
作者：
Rump, Siegfried M. [1 ,2 ]
机构：
[1] Hamburg Univ Technol, Inst Reliable Comp, Schwarzenberg Campus 3, D-21071 Hamburg, Germany
[2] Waseda Univ, Fac Sci & Engn, Shinjuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan
来源：
2019 IEEE 26TH SYMPOSIUM ON COMPUTER ARITHMETIC (ARITH) | 2019年
关键词：
FLOATING-POINT SUMMATION; ACCURATE; FAITHFUL;
D O I：
10.1109/ARITH.2019.00011
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
This note summarizes recent progress in error bounds for compound operations performed in some computer arithmetic. Given a general set of real numbers together with some operations satisfying the first standard model, we identify three types A, B, and C of weak sufficient assumptions implying new results and sharper error estimates. Those include linearized error estimates in the number of operations, faithfully rounded and reproducible results. All types of assumptions are satisfied for an IEEE-754 p-digit base-beta floating-point arithmetic.
引用
收藏
页码：1 / 14
页数：14
相关论文
共 43 条
  • [1] [Anonymous], 2003, GAMM MITT GES ANGEW
  • [2] [Anonymous], 2010, Modern Computer Arithmetic, DOI DOI 10.1017/CBO9780511921698
  • [3] A Fortran 90-based multiprecision system
    Bailey, DH
    [J]. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1995, 21 (04): : 379 - 387
  • [4] Boldo S., 2006, Applied Computing 2006. 21st Annual ACM Symposium on Applied Computing, P1328, DOI 10.1145/1141277.1141586
  • [5] On the Robustness of the 2Sum and Fast2Sum Algorithms
    Boldo, Sylvie
    Graillat, Stef
    Muller, Jean-Michel
    [J]. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2017, 44 (01):
  • [6] FLOATING-POINT TECHNIQUE FOR EXTENDING AVAILABLE PRECISION
    DEKKER, TJ
    [J]. NUMERISCHE MATHEMATIK, 1971, 18 (03) : 224 - +
  • [7] Parallel Reproducible Summation
    Demmel, James
    Hong Diep Nguyen
    [J]. IEEE TRANSACTIONS ON COMPUTERS, 2015, 64 (07) : 2060 - 2070
  • [8] Fast Reproducible Floating-Point Summation
    Demmel, James
    Nguyen, Hong Diep
    [J]. 2013 21ST IEEE SYMPOSIUM ON COMPUTER ARITHMETIC (ARITH), 2013, : 163 - 172
  • [9] Demmel J, 2008, ACTA NUMER, V17, P87, DOI 10.1017/S0962492906350015
  • [10] WHAT EVERY COMPUTER SCIENTIST SHOULD KNOW ABOUT FLOATING-POINT ARITHMETIC
    GOLDBERG, D
    [J]. COMPUTING SURVEYS, 1991, 23 (01) : 5 - 48
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