Safe Haskell	None
Language	Haskell2010

Factory.Math.Pi

Contents

Type-classes
Types
- Data-types

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

openR

Methods

openR :: algorithm -> DecimalDigits -> Rational Source #

openI :: algorithm -> DecimalDigits -> Integer Source #

openS :: algorithm -> DecimalDigits -> String Source #

Instances

Algorithmic Algorithm Source #
Methods openR :: Algorithm -> DecimalDigits -> Rational Source # openI :: Algorithm -> DecimalDigits -> Integer Source # openS :: Algorithm -> DecimalDigits -> String Source #
Algorithmic Algorithm Source #
Methods openR :: Algorithm -> DecimalDigits -> Rational Source # openI :: Algorithm -> DecimalDigits -> Integer Source # openS :: Algorithm -> DecimalDigits -> String Source #
Algorithmic squareRootAlgorithm => Algorithmic (Algorithm squareRootAlgorithm) Source #
Methods openR :: Algorithm squareRootAlgorithm -> DecimalDigits -> Rational Source # openI :: Algorithm squareRootAlgorithm -> DecimalDigits -> Integer Source # openS :: Algorithm squareRootAlgorithm -> DecimalDigits -> String Source #
(Algorithmic squareRootAlgorithm, Algorithmic factorialAlgorithm) => Algorithmic (Algorithm squareRootAlgorithm factorialAlgorithm) Source #
Methods openR :: Algorithm squareRootAlgorithm factorialAlgorithm -> DecimalDigits -> Rational Source # openI :: Algorithm squareRootAlgorithm factorialAlgorithm -> DecimalDigits -> Integer Source # openS :: Algorithm squareRootAlgorithm factorialAlgorithm -> DecimalDigits -> String Source #
(Algorithmic squareRootAlgorithm, Algorithmic factorialAlgorithm) => Algorithmic (Algorithm squareRootAlgorithm factorialAlgorithm) Source #
Methods openR :: Algorithm squareRootAlgorithm factorialAlgorithm -> DecimalDigits -> Rational Source # openI :: Algorithm squareRootAlgorithm factorialAlgorithm -> DecimalDigits -> Integer Source # openS :: Algorithm squareRootAlgorithm factorialAlgorithm -> DecimalDigits -> String Source #
(Algorithmic agm, Algorithmic bbp, Algorithmic borwein, Algorithmic ramanujan, Algorithmic spigot) => Algorithmic (Category agm bbp borwein ramanujan spigot) Source #
Methods openR :: Category agm bbp borwein ramanujan spigot -> DecimalDigits -> Rational Source # openI :: Category agm bbp borwein ramanujan spigot -> DecimalDigits -> Integer Source # openS :: Category agm bbp borwein ramanujan spigot -> DecimalDigits -> String Source #

Types

Data-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	https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula.
Borwein borwein	https://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 spigot, Eq ramanujan, Eq borwein, Eq bbp, Eq agm) => Eq (Category agm bbp borwein ramanujan spigot) Source #
Methods (==) :: Category agm bbp borwein ramanujan spigot -> Category agm bbp borwein ramanujan spigot -> Bool # (/=) :: Category agm bbp borwein ramanujan spigot -> Category agm bbp borwein ramanujan spigot -> Bool #
(Read spigot, Read ramanujan, Read borwein, Read bbp, Read agm) => Read (Category agm bbp borwein ramanujan spigot) Source #
Methods readsPrec :: Int -> ReadS (Category agm bbp borwein ramanujan spigot) # readList :: ReadS [Category agm bbp borwein ramanujan spigot] # readPrec :: ReadPrec (Category agm bbp borwein ramanujan spigot) # readListPrec :: ReadPrec [Category agm bbp borwein ramanujan spigot] #
(Show spigot, Show ramanujan, Show borwein, Show bbp, Show agm) => Show (Category agm bbp borwein ramanujan spigot) Source #
Methods showsPrec :: Int -> Category agm bbp borwein ramanujan spigot -> ShowS # show :: Category agm bbp borwein ramanujan spigot -> String # showList :: [Category agm bbp borwein ramanujan spigot] -> ShowS #
Default bbp => Default (Category agm bbp borwein ramanujan spigot) Source #
Methods def :: Category agm bbp borwein ramanujan spigot #
(Algorithmic agm, Algorithmic bbp, Algorithmic borwein, Algorithmic ramanujan, Algorithmic spigot) => Algorithmic (Category agm bbp borwein ramanujan spigot) Source #
Methods openR :: Category agm bbp borwein ramanujan spigot -> DecimalDigits -> Rational Source # openI :: Category agm bbp borwein ramanujan spigot -> DecimalDigits -> Integer Source # openS :: Category agm bbp borwein ramanujan spigot -> DecimalDigits -> String Source #