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Signed also tends to mean modular arithmetic. It's just with a different definition of modular arithmetic than the Euclidean one. See Boute's 1992 paper "The Eu
by SAI_Peregrinus 5y ago
Signed also tends to mean modular arithmetic. It's just with a different definition of modular arithmetic than the Euclidean one. See Boute's 1992 paper "The Euclidean Definition of the Functions div
and mod" [1] for details on the various definitions.
Both signed and unsigned arithmetic are using finite fields, instead of Abelian rings as most people expect.
[1] https://biblio.ugent.be/publication/314490/file/452146.pdf https://biblio.ugent.be/publication/314490/file/452146.pdf
- jacobolus 5y ago> Both signed and unsigned arithmetic are using finite fields, This is not correct. They are rings with some additional (not mathematically standard) operations thrown in. 'Finite field' means something very specific, and quite different. https://en.wikipedia.org/wiki/Finite_field https://en.wikipedia.org/wiki/Finite_field Computer integer arithmetic hardware can be used to implement finite field arithmetic, but even the 2^n case takes quite a bit of trickery. https://en.wikipedia.org/wiki/Finite_field_arithmetic https://en.wikipedia.org/wiki/Finite_field_arithmetic