Cyclical Arithmetic with Unsigned Integers and Arbitrary Ranges

This library crate provides an extension trait, CycleAdd, for performing cyclical (modular) addition and subtraction with unsigned integer types (u8, u16, and u32). Unlike the default + and - operators, these operations never overflow below zero or beyond the defined modulus.mo

Features

• Cyclical addition and subtraction: Perform modular arithmetic without overflow.
• 1-based series support: Simplifies operations on series starting from 1 (e.g., months, weekdays).
• Lightweight and focused: Extends core unsigned integer types for cryptography, metrology, and other use cases.

Examples

Cyclical Addition

let first_number: u8 = 22;
let second_number: u8 = 6;

let result = first_number.cycle_add(second_number, 24);
// Result: 4 (22 + 6 wraps around at 24)

Cyclical Subtraction

let first_number: u8 = 37;

let result = first_number.cycle_sub(78, 100);
// Result: 59 (37 - 78 wraps around at 100)

1-Based Series Operations

Many common series (e.g., months, weekdays) start from 1. Modular arithmetic typically assumes 0-based indexing, which can lead to unexpected results. The series_add, series_sub, and series_mod methods handle these conversions for you.

let sample_month_1: u8 = 11;
let limit = 12; // Months of the year

let result = sample_month_1.series_add(1, limit);
// Result: 12 (November + 1 = December)

let sample_month_2: u8 = 3;
let result = sample_month_2.series_sub(3, limit);
// Result: 12 (March - 3 = December)

let sample_month_value: u8 = 24; // 24th month
let result = sample_month_value.series_mod(limit);
// Result: 12 (24 wraps around to December)

Comparison with Related Crates

Unlike the Ring360 crate, RotaryAdd focuses exclusively on extending core unsigned integer types. It is designed for use cases such as:

• Cryptography
• Metrology
• Building blocks for other crates (e.g., encoding/decoding operations)

Changelog

Version 0.2.1

• Corrections to README.md, comments and tests only.

Version 0.2.0

• Removed T.rotary_add(&T) and T.rotary_sub(&T) as they were functionally equivalent to T.wrapping_add(T) and T.wrapping_sub(T) in the Rust core library (but with the first parameter passed by reference).
• All remaining trait methods now take the first parameter by value, consistent with other arithmetic methods in the standard library.

Version 0.1.2

• Added series_add, series_sub, and series_mod methods for 1-based series operations.