diff options
author | yugui <yugui@b2dd03c8-39d4-4d8f-98ff-823fe69b080e> | 2008-09-03 13:57:21 +0000 |
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committer | yugui <yugui@b2dd03c8-39d4-4d8f-98ff-823fe69b080e> | 2008-09-03 13:57:21 +0000 |
commit | fce093432eadc191b3647f116a9c2f6748efda3e (patch) | |
tree | 08292b34a1435b87391cf0c11e042fca14443d00 /lib/prime.rb | |
parent | 9cab7d15ca791d0b14db03217485a7c756097a71 (diff) | |
download | ruby-fce093432eadc191b3647f116a9c2f6748efda3e.tar.gz |
* lib/mathn.rb (Integer): moved into prime.rb.
(Prime): ditto.
* lib/prime.rb (Integer): moved from mathn.rb.
(Integer.each_prime): added.
(Integer#prime?): added.
(Prime): moved from mathn.rb.
Its implmentation was rewritten. see [ruby-dev:35863].
And patched by Keiju ISHITSUKA <keiju@ishitsuka.com>,
see [ruby-dev:36128].
(Prime.new): obsolete.
(Prime.instance): added.
(Prime.each): added.
(Prime.int_from_prime_division): added.
(Prime.prime_division): added.
(Prime.prime?): added.
Patch by TOYOFUKU Chikanobu
<nobu_toyofuku at nifty.com> in [ruby-dev:36067].
(Prime.cache): removed.
(Prime.primes): removed.
(Prime.primes_so_far): removed.
(Prime#int_from_prime_division): added.
(Prime#prime_division): added.
(Prime#prime?): added.
(Prime#primes): removed.
(Prime#primes_so_far): removed.
(Prime::PseudoPrmeGenerator): added.
(Prime::EratosthenesGenerator): added.
(Prime::TrialDivisionGenerator): added.
(Prime::Generator23): added.
(Prime::TrialDivision): added.
Extracted from the previous implementation of Prime
by Keiju ISHITSUKA.
(Prime::EratosthenesSieve): added.
* lib/.document (prime.rb): added
* lib/README (prime.rb): added
* test/test_prime.rb: added.
git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@19095 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
Diffstat (limited to 'lib/prime.rb')
-rw-r--r-- | lib/prime.rb | 446 |
1 files changed, 446 insertions, 0 deletions
diff --git a/lib/prime.rb b/lib/prime.rb new file mode 100644 index 0000000000..be1c8b42a0 --- /dev/null +++ b/lib/prime.rb @@ -0,0 +1,446 @@ +# +# = 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 +# +# == 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 + + module OldCompatibility + def succ + @generator.succ + end + alias next succ + + def each(&block) + loop do + yield succ + end + end + 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 numer, passing the prime as + # a parameter. + # + # +ubound+:: + # Upper bound of prime numbers. The iterator stops after + # yields all prime numbers p <= +ubound+. + 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) + 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 [[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. + # + # 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 + pv = [] + 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. + # +ubound+:: + def each(&block) + return self.dup unless block + if @ubound + loop do + p = succ + break if p > @ubound + block.call p + 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 + 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 + 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 + 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 + + + + + # 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 + + # An implementation of eratosthenes's sieve + class EratosthenesSieve + include Singleton + + def initialize # :nodoc: + # bitmap for odd prime numbers less than 256. + # For an arbitrary odd number n, @table[i][j] is 1 when n is prime where i,j = n.divmod(32) . + @table = [0xcb6e, 0x64b4, 0x129a, 0x816d, 0x4c32, 0x864a, 0x820d, 0x2196] + 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 of given n + i,j = n.divmod(32) + loop do + extend_table until @table.length > i + if !@table[i].zero? + (j...32).step(2) do |j| + return 32*i+j if !@table[i][j.div(2)].zero? + end + end + i += 1; j = 1 + end + end + + private + def extend_table + orig_len = @table.length + new_len = [orig_len**2, orig_len+256].min + lbound = orig_len*32 + ubound = new_len*32 + @table.fill(0xFFFF, orig_len...new_len) + (3..Integer(Math.sqrt(ubound))).step(2) do |p| + i, j = p.divmod(32) + next if @table[i][j.div(2)].zero? + + start = (lbound.div(2*p)*2+1)*p # odd multiple of p which is greater than or equal to lbound + (start...ubound).step(2*p) do |n| + i, j = n.divmod(32) + @table[i] &= 0xFFFF ^ (1<<(j.div(2))) + end + end + end + end +end |