ResidueNumerals

A residue number system: the digits are $n \bmod$ each modulus, with no place values at all — which is what makes addition and multiplication carry-free and parallel. It is a bijection onto $[0, \prod m_i)$ exactly when the moduli are pairwise coprime.

ResidueNumerals(moduli)the system for the given moduli

Typed signatures

Type	Package	Applies
(list<integer>) -> value	numerals	always

Domain: Numeral systems

Examples

Basic #

$42 \bmod 16$ and $42 \bmod 625$: no place values

live ↗

In$\mathrm{IntegerDigits}(42, \mathrm{ResidueNumerals}(\bigl\lbrack16, 625\bigr\rbrack))$Out$\bigl\lbrack10, 42\bigr\rbrack$

$100 \bmod 7$ and $100 \bmod 11$

live ↗

In$\mathrm{IntegerDigits}(100, \mathrm{ResidueNumerals}(\bigl\lbrack7, 11\bigr\rbrack))$Out$\mathrm{IntegerDigits}(100, \mathrm{ResidueNumerals}(\bigl\lbrack7, 11\bigr\rbrack))$

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Examples	2

See also: IntegerDigits, ResidueSystem