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Conference material: "Scientific service & Internet: proceedings of the 22nd All-Russian Scientific Conference (September 21-25, 2020, online)"
Authors: Nepejvoda N.N., Grigorevskiy I.N., Klimov A. V., Klimov Y. A., Romanenko S. A.
Digit-wise parallelism of addition of real numbers due to redundancy of representation
An introduction and the state of work of the project for the implementation of high-precision arithmetic in an overlaying numeration system, which provides digit-wise parallelism of operations of addition and subtraction of real numbers with restricted carry propagation only by 1–2 bits, is presented. The historical origins of ideas behind such numeration systems in the history of mathematics, dating back to O.-L. Cauchy (1840) and L.E.J. Brouwer (1921), are outlined. A draft of a digit-wise parallel addition circuit with carry propagation only to the next digit in a numeration system with two additional digits is demonstrated.
arbitrary-precision arithmetic, bignum arithmetic, digit-wise parallelism, overlaying numeration system
Publication language: russian,  pages: 13 (p. 486-498)
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About authors:
  • Nepejvoda Nikolai Nikolevich,,  PSI RAN
  • Grigorevskiy Ivan Nikolaevich,,  PSI RAS
  • Klimov Andrei Valentinovich,,  Ailamazyan Program Systems Institute of RAS; KIAM RAS
  • Klimov Yuri Andreevich,,  Ailamazyan Program Systems Institute of RAS; KIAM RAS
  • Romanenko Sergei Anatolievich,,  Ailamazyan Program Systems Institute of RAS; KIAM RAS