Current File : /var/lib/rbenv/versions/3.2.2/lib64/ruby/gems/3.2.0/gems/rbs-2.8.2/stdlib/prime/0/prime.rbs
# <!-- rdoc-file=lib/prime.rb -->
# The set of all prime numbers.
#
# ## Example
#
# Prime.each(100) do |prime|
# p prime #=> 2, 3, 5, 7, 11, ...., 97
# end
#
# Prime is Enumerable:
#
# Prime.first 5 # => [2, 3, 5, 7, 11]
#
# ## Retrieving the instance
#
# For convenience, each instance method of `Prime`.instance can be accessed as a
# class method of `Prime`.
#
# e.g.
# Prime.instance.prime?(2) #=> true
# Prime.prime?(2) #=> true
#
# ## Generators
#
# A "generator" provides an implementation of enumerating pseudo-prime numbers
# and it remembers the position of enumeration and upper bound. Furthermore, it
# is an external iterator of prime enumeration which is compatible with an
# Enumerator.
#
# `Prime`::`PseudoPrimeGenerator` is the base class for generators. There are
# few implementations of generator.
#
# `Prime`::`EratosthenesGenerator`
# : Uses Eratosthenes' sieve.
# `Prime`::`TrialDivisionGenerator`
# : Uses the trial division method.
# `Prime`::`Generator23`
# : Generates all positive integers which are not divisible by either 2 or 3.
# This sequence is very bad as a pseudo-prime sequence. But this is faster
# and uses much less memory than the other generators. So, it is suitable
# for factorizing an integer which is not large but has many prime factors.
# e.g. for Prime#prime? .
#
class Prime
include Singleton
include Enumerable[Integer]
extend Enumerable[Integer]
# <!--
# rdoc-file=lib/prime.rb
# - each(ubound = nil, generator = EratosthenesGenerator.new, &block)
# -->
# Iterates the given block over all prime numbers.
#
# ## Parameters
#
# `ubound`
# : Optional. An arbitrary positive number. The upper bound of enumeration.
# The method enumerates prime numbers infinitely if `ubound` is nil.
# `generator`
# : Optional. An implementation of pseudo-prime generator.
#
#
# ## Return value
#
# An evaluated value of the given block at the last time. Or an enumerator which
# is compatible to an `Enumerator` if no block given.
#
# ## Description
#
# Calls `block` once for each prime number, passing the prime as a parameter.
#
# `ubound`
# : Upper bound of prime numbers. The iterator stops after it yields all prime
# numbers p <= `ubound`.
#
def self.each: (?Integer? ubound, ?PseudoPrimeGenerator generator) { (Integer) -> void } -> void
| (?Integer? ubound, ?PseudoPrimeGenerator generator) -> PseudoPrimeGenerator
# <!--
# rdoc-file=lib/prime.rb
# - each(ubound = nil, generator = EratosthenesGenerator.new, &block)
# -->
# Iterates the given block over all prime numbers.
#
# ## Parameters
#
# `ubound`
# : Optional. An arbitrary positive number. The upper bound of enumeration.
# The method enumerates prime numbers infinitely if `ubound` is nil.
# `generator`
# : Optional. An implementation of pseudo-prime generator.
#
#
# ## Return value
#
# An evaluated value of the given block at the last time. Or an enumerator which
# is compatible to an `Enumerator` if no block given.
#
# ## Description
#
# Calls `block` once for each prime number, passing the prime as a parameter.
#
# `ubound`
# : Upper bound of prime numbers. The iterator stops after it yields all prime
# numbers p <= `ubound`.
#
def each: (?Integer? ubound, ?PseudoPrimeGenerator generator) { (Integer) -> void } -> void
| (?Integer? ubound, ?PseudoPrimeGenerator generator) -> PseudoPrimeGenerator
# <!--
# rdoc-file=lib/prime.rb
# - int_from_prime_division(pd)
# -->
# Re-composes a prime factorization and returns the product.
#
# For the decomposition:
#
# [[p_1, e_1], [p_2, e_2], ..., [p_n, e_n]],
#
# it returns:
#
# p_1**e_1 * p_2**e_2 * ... * p_n**e_n.
#
# ## Parameters
# `pd`
# : Array of pairs of integers. Each pair consists of a prime number -- a
# prime factor -- and a natural number -- its exponent (multiplicity).
#
#
# ## Example
# Prime.int_from_prime_division([[3, 2], [5, 1]]) #=> 45
# 3**2 * 5 #=> 45
#
def self.int_from_prime_division: (Array[[ Integer, Integer ]]) -> Integer
# <!--
# rdoc-file=lib/prime.rb
# - int_from_prime_division(pd)
# -->
# Re-composes a prime factorization and returns the product.
#
# For the decomposition:
#
# [[p_1, e_1], [p_2, e_2], ..., [p_n, e_n]],
#
# it returns:
#
# p_1**e_1 * p_2**e_2 * ... * p_n**e_n.
#
# ## Parameters
# `pd`
# : Array of pairs of integers. Each pair consists of a prime number -- a
# prime factor -- and a natural number -- its exponent (multiplicity).
#
#
# ## Example
# Prime.int_from_prime_division([[3, 2], [5, 1]]) #=> 45
# 3**2 * 5 #=> 45
#
def int_from_prime_division: (Array[[ Integer, Integer ]]) -> Integer
# <!--
# rdoc-file=lib/prime.rb
# - prime?(value, generator = Prime::Generator23.new)
# -->
# Returns true if `value` is a prime number, else returns false. Integer#prime?
# is much more performant.
#
# ## Parameters
#
# `value`
# : an arbitrary integer to be checked.
# `generator`
# : optional. A pseudo-prime generator.
#
def self.prime?: (Integer value, ?PseudoPrimeGenerator generator) -> bool
# <!--
# rdoc-file=lib/prime.rb
# - prime?(value, generator = Prime::Generator23.new)
# -->
# Returns true if `value` is a prime number, else returns false. Integer#prime?
# is much more performant.
#
# ## Parameters
#
# `value`
# : an arbitrary integer to be checked.
# `generator`
# : optional. A pseudo-prime generator.
#
def prime?: (Integer value, ?PseudoPrimeGenerator generator) -> bool
# <!--
# rdoc-file=lib/prime.rb
# - prime_division(value, generator = Prime::Generator23.new)
# -->
# Returns the factorization of `value`.
#
# For an arbitrary integer:
#
# p_1**e_1 * p_2**e_2 * ... * p_n**e_n,
#
# prime_division returns an array of pairs of integers:
#
# [[p_1, e_1], [p_2, e_2], ..., [p_n, e_n]].
#
# Each pair consists of a prime number -- a prime factor -- and a natural number
# -- its exponent (multiplicity).
#
# ## Parameters
# `value`
# : An arbitrary integer.
# `generator`
# : Optional. A pseudo-prime generator. `generator`.succ must return the next
# pseudo-prime number in ascending order. It must generate all prime
# numbers, but may also generate non-prime numbers, too.
#
#
# ### Exceptions
# `ZeroDivisionError`
# : when `value` is zero.
#
#
# ## Example
#
# Prime.prime_division(45) #=> [[3, 2], [5, 1]]
# 3**2 * 5 #=> 45
#
def self.prime_division: (Integer, ?PseudoPrimeGenerator generator) -> Array[[ Integer, Integer ]]
# <!--
# rdoc-file=lib/prime.rb
# - prime_division(value, generator = Prime::Generator23.new)
# -->
# Returns the factorization of `value`.
#
# For an arbitrary integer:
#
# p_1**e_1 * p_2**e_2 * ... * p_n**e_n,
#
# prime_division returns an array of pairs of integers:
#
# [[p_1, e_1], [p_2, e_2], ..., [p_n, e_n]].
#
# Each pair consists of a prime number -- a prime factor -- and a natural number
# -- its exponent (multiplicity).
#
# ## Parameters
# `value`
# : An arbitrary integer.
# `generator`
# : Optional. A pseudo-prime generator. `generator`.succ must return the next
# pseudo-prime number in ascending order. It must generate all prime
# numbers, but may also generate non-prime numbers, too.
#
#
# ### Exceptions
# `ZeroDivisionError`
# : when `value` is zero.
#
#
# ## Example
#
# Prime.prime_division(45) #=> [[3, 2], [5, 1]]
# 3**2 * 5 #=> 45
#
def prime_division: (Integer, ?PseudoPrimeGenerator generator) -> Array[[ Integer, Integer ]]
# Returns the singleton instance.
#
def self.instance: () -> Prime
# <!-- rdoc-file=lib/prime.rb -->
# An abstract class for enumerating pseudo-prime numbers.
#
# Concrete subclasses should override succ, next, rewind.
#
class PseudoPrimeGenerator
# <!--
# rdoc-file=lib/prime.rb
# - new(ubound = nil)
# -->
#
def initialize: (?Integer?) -> void
include Enumerable[Integer]
# <!--
# rdoc-file=lib/prime.rb
# - upper_bound()
# -->
# ----
# <!--
# rdoc-file=lib/prime.rb
# - upper_bound=(ubound)
# -->
#
attr_accessor upper_bound(): Integer?
# <!--
# rdoc-file=lib/prime.rb
# - each() { |prime| ... }
# -->
# Iterates the given block for each prime number.
#
def each: () { (Integer) -> void } -> void
# <!--
# rdoc-file=lib/prime.rb
# - next()
# -->
# alias of `succ`.
#
def next: () -> Integer
# <!--
# rdoc-file=lib/prime.rb
# - rewind()
# -->
# Rewinds the internal position for enumeration.
#
# See `Enumerator`#rewind.
#
def rewind: () -> void
# <!--
# rdoc-file=lib/prime.rb
# - size()
# -->
#
def size: () -> Float
# <!--
# rdoc-file=lib/prime.rb
# - succ()
# -->
# returns the next pseudo-prime number, and move the internal position forward.
#
# `PseudoPrimeGenerator`#succ raises `NotImplementedError`.
#
def succ: () -> Integer
end
# <!-- rdoc-file=lib/prime.rb -->
# An implementation of `PseudoPrimeGenerator`.
#
# Uses `EratosthenesSieve`.
#
class EratosthenesGenerator < PseudoPrimeGenerator
end
# <!-- rdoc-file=lib/prime.rb -->
# An implementation of `PseudoPrimeGenerator` which uses a prime table generated
# by trial division.
#
class TrialDivisionGenerator < PseudoPrimeGenerator
end
# <!-- rdoc-file=lib/prime.rb -->
# Generates all integers which are greater than 2 and are not divisible by
# either 2 or 3.
#
# This is a pseudo-prime generator, suitable on checking primality of an integer
# by brute force method.
#
class Generator23 < PseudoPrimeGenerator
end
end
Mini Shell