Safe Haskell	Safe-Inferred
Language	Haskell98

Factory.Math.Pi

Contents

Description

AUTHOR: Dr. Alistair Ward
DESCRIPTION: Defines the classes of Pi-algorithm which have been implemented.

Synopsis

Type-classes

class Algorithmic algorithm where Source

Defines the methods expected of a Pi-algorithm.
Most of the implementations naturally return a Rational, but the spigot-algorithms naturally produce a [Int]; though representing Pi as a big integer with the decimal point removed is clearly incorrect.
Since representing Pi as either a Rational or promoted to an Integer, is inconvenient, an alternative decimal String-representation is provided.

Minimal complete definition

Methods

Arguments

:: algorithm
-> DecimalDigits
-> Rational	Returns the value of Pi as a `Rational`.

Arguments

:: algorithm
-> DecimalDigits
-> Integer	Returns the value of Pi, promoted by the required precision to form an integer.

Arguments

:: algorithm
-> DecimalDigits
-> String	Returns the value of Pi as a decimal `String`.

Instances

Algorithmic Algorithm
Algorithmic Algorithm
Algorithmic squareRootAlgorithm => Algorithmic (Algorithm squareRootAlgorithm)
(Algorithmic squareRootAlgorithm, Algorithmic factorialAlgorithm) => Algorithmic (Algorithm squareRootAlgorithm factorialAlgorithm)
(Algorithmic squareRootAlgorithm, Algorithmic factorialAlgorithm) => Algorithmic (Algorithm squareRootAlgorithm factorialAlgorithm)
(Algorithmic agm, Algorithmic bbp, Algorithmic borwein, Algorithmic ramanujan, Algorithmic spigot) => Algorithmic (Category agm bbp borwein ramanujan spigot)

Types

data Category agm bbp borwein ramanujan spigot Source

Categorises the various algorithms.

Constructors

AGM agm	Algorithms based on the Arithmetic-geometric Mean.
BBP bbp	http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula.
Borwein borwein	http://en.wikipedia.org/wiki/Borwein%27s_algorithm.
Ramanujan ramanujan	http://www.pi314.net/eng/ramanujan.php.
Spigot spigot	Algorithms from which the digits of Pi slowly drip, one by one.

Instances

(Eq agm, Eq bbp, Eq borwein, Eq ramanujan, Eq spigot) => Eq (Category agm bbp borwein ramanujan spigot)
(Read agm, Read bbp, Read borwein, Read ramanujan, Read spigot) => Read (Category agm bbp borwein ramanujan spigot)
(Show agm, Show bbp, Show borwein, Show ramanujan, Show spigot) => Show (Category agm bbp borwein ramanujan spigot)
(Defaultable agm, Defaultable bbp, Defaultable borwein, Defaultable ramanujan, Defaultable spigot) => Defaultable (Category agm bbp borwein ramanujan spigot)
(Algorithmic agm, Algorithmic bbp, Algorithmic borwein, Algorithmic ramanujan, Algorithmic spigot) => Algorithmic (Category agm bbp borwein ramanujan spigot)