Factory.Math.Implementations.Primes.Algorithm

AUTHOR

Dr. Alistair Ward

DESCRIPTION

• Generates the constant list of prime-numbers, by a variety of different algorithms.
• http://www.haskell.org/haskellwiki/Prime_numbers.
• http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.31.3936&rep=rep1&type=pdf.
• http://larc.unt.edu/ian/pubs/sieve.pdf.

Types

Data-types

data Algorithm

The implemented methods by which the primes may be generated.

Constructors

SieveOfAtkin Integer

The Sieve of Atkin, optimised using a PrimeWheel of optimal size, for primes up to the specified maximum bound; https://en.wikipedia.org/wiki/Sieve_of_Atkin.

SieveOfEratosthenes NPrimes

The Sieve of Eratosthenes (https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes), optimised using a PrimeWheel.

TrialDivision NPrimes

For each candidate, confirm indivisibility, by all primes smaller than its square-root, optimised using a PrimeWheel.

TurnersSieve

For each prime, the infinite list of candidates greater than its square, is filtered for indivisibility; http://www.haskell.org/haskellwiki/Prime_numbers#Turner.27s_sieve_-_Trial_division.

WheelSieve Int

wheelSieve.

Instances

Eq Algorithm

Methods

(==) :: Algorithm -> Algorithm -> Bool

(/=) :: Algorithm -> Algorithm -> Bool

Read Algorithm

Methods

readsPrec :: Int -> ReadS Algorithm

readList :: ReadS [Algorithm]

readPrec :: ReadPrec Algorithm

readListPrec :: ReadPrec [Algorithm]

Show Algorithm

Methods

showsPrec :: Int -> Algorithm -> ShowS

show :: Algorithm -> String

showList :: [Algorithm] -> ShowS

Default Algorithm

Methods

def :: Algorithm

Algorithmic Algorithm

Methods

primes :: (NFData i, Ix i, Integral i) => Algorithm -> [i]