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A note on multiple precision arithmetic

Authors:

Albert G. Cox,

H. A. LutherAuthors Info & Claims

Communications of the ACM, Volume 4, Issue 8

Page 353

https://doi.org/10.1145/366678.366693

Published: 01 August 1961 Publication History

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Abstract

Since computers have means to detect overflow on addition or subtraction, this can be used in a multiple precision addition-subtraction subroutine to obviate a sign analysis. Consider all integers in the computer to be expressed “radix t”, that is, in the form a = a₀ + a₁t + ··· + a_ntⁿ where a_i are of like sign and have magnitudes less than t. t is a positive integer determined by the word length of the computer. Consider the expression c = a ± b = (a₀ ± b₀) + (a₁ ± b₁)t + ··· + (a_n ± b_n)tⁿ. Here a_i ± b_i may exceed the storage capacity of one word or may have a sign different from c.

References

[1]

1. BELLMAN, RICHARD. Introduction to Matrix Analysis, Ch. 4. McGraw-Hill Book Co., New York, (1960).

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[2]

2. DE WITTE, LEENDERT. Least squares fitting of a great circle through points on a sphere. Comm. ACM 3, (Oct. 1960), 611-613.

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Shi ZChen CYang GXiong HLi FHu HWan Z(2023)Design Space Exploration of Galois and Fibonacci Configuration Based on Espresso Stream CipherACM Transactions on Reconfigurable Technology and Systems10.1145/356742816:3(1-24)Online publication date: 20-Jun-2023
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Zhao KMa YHe RZhang JXu NBian J(2023)Adaptive Selection and Clustering of Partial Reconfiguration Modules for Modern FPGA Design FlowACM Transactions on Reconfigurable Technology and Systems10.1145/356742716:2(1-24)Online publication date: 2-Apr-2023
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Soldavini SFriebel KTibaldi MHempel GCastrillon JPilato C(2023)Automatic Creation of High-bandwidth Memory Architectures from Domain-specific Languages: The Case of Computational Fluid DynamicsACM Transactions on Reconfigurable Technology and Systems10.1145/356355316:2(1-34)Online publication date: 11-Mar-2023
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Index Terms

A note on multiple precision arithmetic
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Arbitrary-precision arithmetic
      2. Interval arithmetic

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Published: 01 August 1961

Published in CACM Volume 4, Issue 8

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