Announcing elm-integer

I am happy to announce the release of elm-integer.

elm-integer is a pure Elm library for computing with the integers, ℤ = { ..., -2, -1, 0, 1, 2, ... }. It uses arbitrary-precision arithmetic so the magnitude of the numbers you can compute with is only limited by the available memory. It is extensively tested for correctness and has reasonable performance characteristics.

Try it out

I built an integer calculator that allows you to test out all the integer input formats, arithmetic operations, and integer output formats that's supported by elm-integer. Feel free to use the calculator to explore the limits of the library.

Compared to cmditch/elm-bigint

Commonly used small integers are named

The integers from -10 to 10 are already named. In particular, zero, one, two, ten, and negativeOne are available for immediate use.

Large integers are easy to create

fromSafeString is useful for establishing large constants in a calculation.

Multiple integer input formats are supported

Any base from 2 to 36 is supported using fromBaseBString and shortcuts are provided for binary, octal, decimal, and hexadecimal input formats.

Multiple integer output formats are supported

Any base from 2 to 36 is supported using toBaseBString and shortcuts are provided for binary, octal, decimal, and hexadecimal output formats.

There are useful predicates

With these predicates it's easy to check if your integer is zero (== 0), negative (< 0), non-negative (>= 0), positive (> 0), or non-positive (<= 0).

== and /= work as expected so if you wanted to know if your integer, z, is equal to -1 then z == negativeOne is all you have to do.

Arithmetic is performant

This library is built on elm-natural which currently outperforms cmditch/elm-bigint in multiplication, division with remainder, and exponentiation.

divModBy defines Euclidean division

cmditch/elm-bigint's divmod operation defines truncated division (or T-division) according to Daan Leijen's paper, Division and Modulus for Computer Scientists. It is the equivalent of quot/rem in Haskell. No equivalent of Euclidean division is provided.

N.B. You can check out this Ellie of divmod to confirm the above statements.

However, Boute argues that Euclidean division is superior to the other definitions of the div and mod functions in terms of regularity and useful mathematical properties.

Hence, divModBy in elm-integer defines Euclidean division and truncated division is provided by quotRemBy.

Feedback is appreciated

If you happen to use the library in an application, I would greatly appreciate your feedback.

Thank you for reading!