modedecimal

Modedecimal is a term used to describe a numeric representation and arithmetic approach that combines decimal fixed-point numbers with modular arithmetic. In this scheme, decimal values are encoded as integers by applying a fixed scale factor, then reduced modulo a chosen modulus. The approach aims to provide wrap-around behavior with exact decimal fractions, useful in contexts where overflow protection or cyclic arithmetic is desired. The term is not standardized and may refer to a family of techniques rather than a single formal system.

Representation and operations: A value x with d decimal places is encoded as e = floor(x × 10^d) mod M, where M is the modulus. Arithmetic is performed on the encoded integers modulo M. For example, with d = 2 and M = 100000, 12.34 becomes 1234 and 5.50 becomes 550; their sum is 1784, representing 17.84 after decoding. Division is defined only when the divisor has a modular inverse modulo M, and may require special handling. Precision is bounded by d and M; choosing M large relative to the value range reduces wrap-around.

Advantages and limitations: Modedecimal can prevent unbounded growth and provides deterministic wrap-around behavior. It can allow using integer hardware paths without floating-point. However, it introduces artificial cyclic limits, complicates comparisons across wrap boundaries, and requires careful handling of carries, scaling, and division. It is not a standard numeric type in most languages, and practical use tends to be niche or experimental.

Relationship and applications: The concept overlaps with fixed-point arithmetic, modular arithmetic, and finite-field representations used in cryptography, digital signal processing, and error detection. It is sometimes discussed in theoretical contexts or in libraries that implement modular fixed-point numbers for specialized tasks.

See also: Fixed-point arithmetic, modular arithmetic, finite fields, modular inverses, big integers.