Elm Integer

A pure Elm library for computing with the integers, ℤ = { ..., -2, -1, 0, 1, 2, ... }.

What's available?

The integers from -10 to 10

• negativeTen
• negativeNine
• negativeEight
• negativeSeven
• negativeSix
• negativeFive
• negativeFour
• negativeThree
• negativeTwo
• negativeOne
• zero
• one
• two
• three
• four
• five
• six
• seven
• eight
• nine
• ten

Ways to create integers from an Int or a Natural

• fromSafeInt
• fromInt
• fromNatural

Ways to create integers from a String

• fromSafeString
• fromString
• fromBinaryString
• fromOctalString
• fromDecimalString
• fromHexString
• fromBaseBString

Comparison operators

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

Predicates for classification

• isNegative (i.e. < 0)
• isNonNegative (i.e. >= 0)
• isZero (i.e. == 0)
• isNonZero (i.e. /= 0)
• isPositive (i.e. > 0)
• isNonPositive (i.e. <= 0)
• isEven
• isOdd

Arithmetic

• abs
• negate
• add
• sub
• mul
• divModBy (Euclidean division)
• divBy
• modBy
• quotRemBy (differs from divModBy in its handling of negative operands)
• quotBy
• remBy
• exp

Ways to convert to an Int or a Natural

• toInt
• toNatural

N.B. Please remember to use them with caution since they discard information.

Ways to convert to a String

• toString (same as toDecimalString)
• toBinaryString
• toOctalString
• toDecimalString
• toHexString
• toBaseBString

Examples

Calculator - Live Demo

In the examples/calculator directory you will find the implementation of a simple integer calculator web application. The calculator is designed and built to make it easy to test out all the integer input formats, arithmetic operations, and integer output formats that's supported by this library.

You are able to enter your expression using an S-expression based language. The following syntax is supported:

Expr      ::= Integer
            | '(' 'abs' Expr ')'
            | '(' 'negate' Expr ')'
            | '(' 'add' Expr* ')'
            | '(' 'sub' Expr Expr ')'
            | '(' 'mul' Expr* ')'
            | '(' 'div' Expr Expr ')'
            | '(' 'mod' Expr Expr ')'
            | '(' 'quot' Expr Expr ')'
            | '(' 'rem' Expr Expr ')'
            | '(' 'exp' Expr Expr ')'
Integer   ::= Sign Magnitude
Sign      ::= '-'?
Magnitude ::= ('0b' | '0B') Binary
            | ('0o' | '0O') Octal
            | ('0x' | '0X') Hex
            | Decimal
Binary    ::= [0-1]+
Octal     ::= [0-7]+
Hex       ::= [0-9a-fA-F]+
Decimal   ::= [0-9]+

N.B. You must be in the Nix development shell (nix develop) to run the scripts mentioned below.

Build

Build the calculator web application.

$ build-examples-calculator

Run

Serve the calculator web application.

$ serve-examples-calculator

Then, open http://localhost:8000 in your browser to run the calculator.

Performance

TL;DR The performance of this library depends solely on the performance of elm-natural.

This library is built on elm-natural and each function that is implemented using functions from elm-natural only introduces a constant amount of overhead. As a result, the performance characteristics of a given function, f, from this library are directly related to the performance characteristics of the functions from elm-natural that are used to implement f. Practically speaking, this means that any performance gains in elm-natural will necessarily lead to corresponding performance gains within elm-integer.

Resources

• Chapter 18 - Arbitrary-Precision Arithmetic of C Interfaces and Implementations: Techniques for Creating Reusable Software helped me to design, organize and implement the library.
• Euclidean Division: Integer Division with Remainders by Probabilistic World helped me to understand all the competing definitions of integer division with remainders.