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https://github.com/dwayne/elm-integer
The integers, ℤ = { ..., -2, -1, 0, 1, 2, ... }.
https://github.com/dwayne/elm-integer
arbitrary-precision bignum elm extended-precision integers multiple-precision
Last synced: 4 months ago
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The integers, ℤ = { ..., -2, -1, 0, 1, 2, ... }.
- Host: GitHub
- URL: https://github.com/dwayne/elm-integer
- Owner: dwayne
- License: bsd-3-clause
- Created: 2023-11-15T21:25:19.000Z (about 1 year ago)
- Default Branch: master
- Last Pushed: 2024-03-12T20:56:32.000Z (11 months ago)
- Last Synced: 2024-09-30T05:07:52.625Z (4 months ago)
- Topics: arbitrary-precision, bignum, elm, extended-precision, integers, multiple-precision
- Language: Elm
- Homepage: https://package.elm-lang.org/packages/dwayne/elm-integer/latest/
- Size: 111 KB
- Stars: 5
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Elm Integer
A pure Elm library for computing with the [integers](https://en.wikipedia.org/wiki/Integer),
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`][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`][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](https://dwayne.github.io/elm-integer/)
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](https://en.wikipedia.org/wiki/S-expression) based language. The
following syntax is supported:
```txt
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.
```sh
$ build-examples-calculator
```
#### Run
Serve the calculator web application.
```sh
$ 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`][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][elm-natural-performance]
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](https://archive.org/details/cinterfacesimple0000hans) helped me to design, organize and implement the library.
- [Euclidean Division: Integer Division with Remainders](https://www.probabilisticworld.com/euclidean-division-integer-division-with-remainders/) by Probabilistic World helped me to understand all the competing definitions of integer division with remainders.
[elm-natural]: https://package.elm-lang.org/packages/dwayne/elm-natural/1.1.1
[Natural]: https://package.elm-lang.org/packages/dwayne/elm-natural/1.1.1/Natural
[elm-natural-performance]: https://github.com/dwayne/elm-natural/tree/1.1.1#performance