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Edit File: 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 # - 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 # - 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_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 ]] # 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