Elm Natural

An Elm library for computing with the natural numbers, ℕ = { 0, 1, 2, ... }.

What's available?

The natural numbers from 0 to 10

• zero
• one
• two
• three
• four
• five
• six
• seven
• eight
• nine
• ten

Ways to create natural numbers from Int values

• fromInt
• fromSafeInt

Ways to create natural numbers from String values

• fromBinaryString
• fromOctalString
• fromHexString
• fromString (supports binary, octal, hexadecimal, and decimal input formats)
• fromSafeString
• fromBaseBString

Comparison operators

• ==
• compare
• isLessThan
• isLessThanOrEqual
• isGreaterThan
• isGreaterThanOrEqual
• max
• min

Predicates for classification

• isZero
• isOne
• isPositive
• isEven
• isOdd

Arithmetic

• add
• sub (saturating subtraction)
• mul
• divModBy (Euclidean division)
• divBy
• modBy
• exp

A way to convert to an Int

• toInt (use with caution)

Ways to convert to a String representation

• toBinaryString
• toOctalString
• toHexString
• toString (decimal representation)
• toBaseBString

Examples

As a simple example we can implement the factorial function.

import Natural as N exposing (Natural)

fact : Natural -> Natural
fact n =
    if N.isZero n then
      N.one

    else
      N.mul n <| fact (N.sub n N.one)

And then we can use it to compute 100!.

N.toString (fact (N.fromSafeInt 100)) == "93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000"

Many more examples can be found in the examples/src directory.

• Fibonacci.elm - Computes up to the 1000th Fibonacci number.
• Pi.elm - Computes the first 100 digits of π.
• E.elm - Computes the first 100 digits of e.
• BaseConversion.elm - Converts decimal numbers to their binary, octal, and hexadecimal representations.

References

• Chapter 17 - Extended Precision Arithmetic of C Interfaces and Implementations: Techniques for Creating Reusable Software helped me figure out how to design, organize and build the library from the ground up.
• Lua Bint inspired the examples.