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

Nepejvoda Nikolai Nikolevich,  ,  orcid.org/0000-0002-7869-8053,  PSI RAN

Grigorevskiy Ivan Nikolaevich,  ,  orcid.org/0000-0001-8078-1238,  PSI RAS

Klimov Andrei Valentinovich,  ,  orcid.org/0000-0003-0418-7311,  Ailamazyan Program Systems Institute of RAS; KIAM RAS

Klimov Yuri Andreevich,  ,  orcid.org/0000-0001-5081-1547,  Ailamazyan Program Systems Institute of RAS; KIAM RAS

Romanenko Sergei Anatolievich,  ,  orcid.org/0000-0002-2971-9647,  Ailamazyan Program Systems Institute of RAS; KIAM RAS