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Diffstat (limited to 'ruby_1_9_3/lib/prime.rb')
| -rw-r--r-- | ruby_1_9_3/lib/prime.rb | 509 |
1 files changed, 0 insertions, 509 deletions
diff --git a/ruby_1_9_3/lib/prime.rb b/ruby_1_9_3/lib/prime.rb deleted file mode 100644 index 4a20d93fb7..0000000000 --- a/ruby_1_9_3/lib/prime.rb +++ /dev/null @@ -1,509 +0,0 @@ -# -# = prime.rb -# -# Prime numbers and factorization library. -# -# Copyright:: -# Copyright (c) 1998-2008 Keiju ISHITSUKA(SHL Japan Inc.) -# Copyright (c) 2008 Yuki Sonoda (Yugui) <yugui@yugui.jp> -# -# Documentation:: -# Yuki Sonoda -# - -require "singleton" -require "forwardable" - -class Integer - # Re-composes a prime factorization and returns the product. - # - # See Prime#int_from_prime_division for more details. - def Integer.from_prime_division(pd) - Prime.int_from_prime_division(pd) - end - - # Returns the factorization of +self+. - # - # See Prime#prime_division for more details. - def prime_division(generator = Prime::Generator23.new) - Prime.prime_division(self, generator) - end - - # Returns true if +self+ is a prime number, false for a composite. - def prime? - Prime.prime?(self) - end - - # Iterates the given block over all prime numbers. - # - # See +Prime+#each for more details. - def Integer.each_prime(ubound, &block) # :yields: prime - Prime.each(ubound, &block) - end -end - -# -# 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 [2, 3, 5, 7, 11] -# -# == Retrieving the instance -# -# +Prime+.new is obsolete. Now +Prime+ has the default instance and you can -# access it as +Prime+.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. -# Futhermore, it is a external iterator of prime enumeration which is -# compatible to an Enumerator. -# -# +Prime+::+PseudoPrimeGenerator+ is the base class for generators. -# There are few implementations of generator. -# -# [+Prime+::+EratosthenesGenerator+] -# Uses eratosthenes's sieve. -# [+Prime+::+TrialDivisionGenerator+] -# Uses the trial division method. -# [+Prime+::+Generator23+] -# Generates all positive integers which is not divided by 2 nor 3. -# This sequence is very bad as a pseudo-prime sequence. But this -# is faster and uses much less memory than 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 Enumerable - @the_instance = Prime.new - - # obsolete. Use +Prime+::+instance+ or class methods of +Prime+. - def initialize - @generator = EratosthenesGenerator.new - extend OldCompatibility - warn "Prime::new is obsolete. use Prime::instance or class methods of Prime." - end - - class << self - extend Forwardable - include Enumerable - # Returns the default instance of Prime. - def instance; @the_instance end - - def method_added(method) # :nodoc: - (class<< self;self;end).def_delegator :instance, method - end - end - - # 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 - # yields all prime numbers p <= +ubound+. - # - # == Note - # - # +Prime+.+new+ returns a object extended by +Prime+::+OldCompatibility+ - # in order to compatibility to Ruby 1.8, and +Prime+#each is overwritten - # by +Prime+::+OldCompatibility+#+each+. - # - # +Prime+.+new+ is now obsolete. Use +Prime+.+instance+.+each+ or simply - # +Prime+.+each+. - def each(ubound = nil, generator = EratosthenesGenerator.new, &block) - generator.upper_bound = ubound - generator.each(&block) - end - - - # Returns true if +value+ is prime, false for a composite. - # - # == Parameters - # - # +value+:: an arbitrary integer to be checked. - # +generator+:: optional. A pseudo-prime generator. - def prime?(value, generator = Prime::Generator23.new) - value = -value if value < 0 - return false if value < 2 - for num in generator - q,r = value.divmod num - return true if q < num - return false if r == 0 - end - end - - # Re-composes a prime factorization and returns the product. - # - # == Parameters - # +pd+:: Array of pairs of integers. The each internal - # pair consists of a prime number -- a prime factor -- - # and a natural number -- an exponent. - # - # == Example - # For <tt>[[p_1, e_1], [p_2, e_2], ...., [p_n, e_n]]</tt>, it returns: - # - # p_1**e_1 * p_2**e_2 * .... * p_n**e_n. - # - # Prime.int_from_prime_division([[2,2], [3,1]]) #=> 12 - def int_from_prime_division(pd) - pd.inject(1){|value, (prime, index)| - value *= prime**index - } - end - - # Returns the factorization of +value+. - # - # == Parameters - # +value+:: An arbitrary integer. - # +generator+:: Optional. A pseudo-prime generator. - # +generator+.succ must return the next - # pseudo-prime number in the ascendent - # order. It must generate all prime numbers, - # but may generate non prime numbers. - # - # === Exceptions - # +ZeroDivisionError+:: when +value+ is zero. - # - # == Example - # For an arbitrary integer: - # - # n = p_1**e_1 * p_2**e_2 * .... * p_n**e_n, - # - # prime_division(n) returns: - # - # [[p_1, e_1], [p_2, e_2], ...., [p_n, e_n]]. - # - # Prime.prime_division(12) #=> [[2,2], [3,1]] - # - def prime_division(value, generator= Prime::Generator23.new) - raise ZeroDivisionError if value == 0 - if value < 0 - value = -value - pv = [[-1, 1]] - else - pv = [] - end - for prime in generator - count = 0 - while (value1, mod = value.divmod(prime) - mod) == 0 - value = value1 - count += 1 - end - if count != 0 - pv.push [prime, count] - end - break if value1 <= prime - end - if value > 1 - pv.push [value, 1] - end - return pv - end - - # An abstract class for enumerating pseudo-prime numbers. - # - # Concrete subclasses should override succ, next, rewind. - class PseudoPrimeGenerator - include Enumerable - - def initialize(ubound = nil) - @ubound = ubound - end - - def upper_bound=(ubound) - @ubound = ubound - end - def upper_bound - @ubound - end - - # returns the next pseudo-prime number, and move the internal - # position forward. - # - # +PseudoPrimeGenerator+#succ raises +NotImplementedError+. - def succ - raise NotImplementedError, "need to define `succ'" - end - - # alias of +succ+. - def next - raise NotImplementedError, "need to define `next'" - end - - # Rewinds the internal position for enumeration. - # - # See +Enumerator+#rewind. - def rewind - raise NotImplementedError, "need to define `rewind'" - end - - # Iterates the given block for each prime numbers. - def each(&block) - return self.dup unless block - if @ubound - last_value = nil - loop do - prime = succ - break last_value if prime > @ubound - last_value = block.call(prime) - end - else - loop do - block.call(succ) - end - end - end - - # see +Enumerator+#with_index. - alias with_index each_with_index - - # see +Enumerator+#with_object. - def with_object(obj) - return enum_for(:with_object) unless block_given? - each do |prime| - yield prime, obj - end - end - end - - # An implementation of +PseudoPrimeGenerator+. - # - # Uses +EratosthenesSieve+. - class EratosthenesGenerator < PseudoPrimeGenerator - def initialize - @last_prime = nil - super - end - - def succ - @last_prime = @last_prime ? EratosthenesSieve.instance.next_to(@last_prime) : 2 - end - def rewind - initialize - end - alias next succ - end - - # An implementation of +PseudoPrimeGenerator+ which uses - # a prime table generated by trial division. - class TrialDivisionGenerator<PseudoPrimeGenerator - def initialize - @index = -1 - super - end - - def succ - TrialDivision.instance[@index += 1] - end - def rewind - initialize - end - alias next succ - end - - # Generates all integer which are greater than 2 and - # are not divided by 2 nor 3. - # - # This is a pseudo-prime generator, suitable on - # checking primality of a integer by brute force - # method. - class Generator23<PseudoPrimeGenerator - def initialize - @prime = 1 - @step = nil - super - end - - def succ - loop do - if (@step) - @prime += @step - @step = 6 - @step - else - case @prime - when 1; @prime = 2 - when 2; @prime = 3 - when 3; @prime = 5; @step = 2 - end - end - return @prime - end - end - alias next succ - def rewind - initialize - end - end - - # Internal use. An implementation of prime table by trial division method. - class TrialDivision - include Singleton - - def initialize # :nodoc: - # These are included as class variables to cache them for later uses. If memory - # usage is a problem, they can be put in Prime#initialize as instance variables. - - # There must be no primes between @primes[-1] and @next_to_check. - @primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101] - # @next_to_check % 6 must be 1. - @next_to_check = 103 # @primes[-1] - @primes[-1] % 6 + 7 - @ulticheck_index = 3 # @primes.index(@primes.reverse.find {|n| - # n < Math.sqrt(@@next_to_check) }) - @ulticheck_next_squared = 121 # @primes[@ulticheck_index + 1] ** 2 - end - - # Returns the cached prime numbers. - def cache - return @primes - end - alias primes cache - alias primes_so_far cache - - # Returns the +index+th prime number. - # - # +index+ is a 0-based index. - def [](index) - while index >= @primes.length - # Only check for prime factors up to the square root of the potential primes, - # but without the performance hit of an actual square root calculation. - if @next_to_check + 4 > @ulticheck_next_squared - @ulticheck_index += 1 - @ulticheck_next_squared = @primes.at(@ulticheck_index + 1) ** 2 - end - # Only check numbers congruent to one and five, modulo six. All others - - # are divisible by two or three. This also allows us to skip checking against - # two and three. - @primes.push @next_to_check if @primes[2..@ulticheck_index].find {|prime| @next_to_check % prime == 0 }.nil? - @next_to_check += 4 - @primes.push @next_to_check if @primes[2..@ulticheck_index].find {|prime| @next_to_check % prime == 0 }.nil? - @next_to_check += 2 - end - return @primes[index] - end - end - - # Internal use. An implementation of eratosthenes's sieve - class EratosthenesSieve - include Singleton - - BITS_PER_ENTRY = 16 # each entry is a set of 16-bits in a Fixnum - NUMS_PER_ENTRY = BITS_PER_ENTRY * 2 # twiced because even numbers are omitted - ENTRIES_PER_TABLE = 8 - NUMS_PER_TABLE = NUMS_PER_ENTRY * ENTRIES_PER_TABLE - FILLED_ENTRY = (1 << NUMS_PER_ENTRY) - 1 - - def initialize # :nodoc: - # bitmap for odd prime numbers less than 256. - # For an arbitrary odd number n, @tables[i][j][k] is - # * 1 if n is prime, - # * 0 if n is composite, - # where i,j,k = indices(n) - @tables = [[0xcb6e, 0x64b4, 0x129a, 0x816d, 0x4c32, 0x864a, 0x820d, 0x2196].freeze] - end - - # returns the least odd prime number which is greater than +n+. - def next_to(n) - n = (n-1).div(2)*2+3 # the next odd number to given n - table_index, integer_index, bit_index = indices(n) - loop do - extend_table until @tables.length > table_index - for j in integer_index...ENTRIES_PER_TABLE - if !@tables[table_index][j].zero? - for k in bit_index...BITS_PER_ENTRY - return NUMS_PER_TABLE*table_index + NUMS_PER_ENTRY*j + 2*k+1 if !@tables[table_index][j][k].zero? - end - end - bit_index = 0 - end - table_index += 1; integer_index = 0 - end - end - - private - # for an odd number +n+, returns (i, j, k) such that @tables[i][j][k] represents primarity of the number - def indices(n) - # binary digits of n: |0|1|2|3|4|5|6|7|8|9|10|11|.... - # indices: |-| k | j | i - # because of NUMS_PER_ENTRY, NUMS_PER_TABLE - - k = (n & 0b00011111) >> 1 - j = (n & 0b11100000) >> 5 - i = n >> 8 - return i, j, k - end - - def extend_table - lbound = NUMS_PER_TABLE * @tables.length - ubound = lbound + NUMS_PER_TABLE - new_table = [FILLED_ENTRY] * ENTRIES_PER_TABLE # which represents primarity in lbound...ubound - (3..Integer(Math.sqrt(ubound))).step(2) do |p| - i, j, k = indices(p) - next if @tables[i][j][k].zero? - - start = (lbound.div(p)+1)*p # least multiple of p which is >= lbound - start += p if start.even? - (start...ubound).step(2*p) do |n| - _, j, k = indices(n) - new_table[j] &= FILLED_ENTRY^(1<<k) - end - end - @tables << new_table.freeze - end - end - - # Provides a +Prime+ object with compatibility to Ruby 1.8 when instantiated via +Prime+.+new+. - module OldCompatibility - # Returns the next prime number and forwards internal pointer. - def succ - @generator.succ - end - alias next succ - - # Overwrites Prime#each. - # - # Iterates the given block over all prime numbers. Note that enumeration - # starts from the current position of internal pointer, not rewound. - def each(&block) - return @generator.dup unless block_given? - loop do - yield succ - end - end - end -end |