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* lib/mathn.rb (Integer): moved into prime.rb.

Browse source 
(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
This commit is contained in:
yugui 2008-09-03 13:57:21 +00:00
parent 9cab7d15ca
commit fce093432e
6 changed files with 618 additions and 95 deletions
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43
ChangeLog
View file

@ -1,3 +1,46 @@
Wed Sep 3 22:31:11 2008 Yuki Sonoda (Yugui) <yugui@yugui.jp>
* 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.
Wed Sep 3 21:49:00 2008 David A. Black <dblack@rubypal.com>
* lib/scanf.rb: fixed bug involving matching literal '['

1
lib/.document
View file

@ -59,6 +59,7 @@ pathname.rb
ping.rb
pp.rb
prettyprint.rb
prime.rb
profile.rb
profiler.rb
pstore.rb

1
lib/README
View file

@ -42,6 +42,7 @@ parsedate.rb parses date string (obsolete)
pathname.rb Object-Oriented Pathname Class
pp.rb pretty print objects
prettyprint.rb pretty printing algorithm
prime.rb prime numbers and factorization
profile.rb runs ruby profiler
profiler.rb ruby profiler module
pstore.rb persistent object strage using marshal

96
lib/mathn.rb
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@ -12,101 +12,7 @@
require "complex.rb"
require "rational.rb"
require "matrix.rb"
class Integer
def Integer.from_prime_division(pd)
value = 1
for prime, index in pd
value *= prime**index
end
value
end
def prime_division
raise ZeroDivisionError if self == 0
ps = Prime.new
value = self
pv = []
for prime in ps
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 prime * prime >= value
end
if value > 1
pv.push [value, 1]
end
return pv
end
end
class Prime
include Enumerable
# 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
class << self
# Return the prime cache.
def cache
return @@primes
end
alias primes cache
alias primes_so_far cache
end
def initialize
@index = -1
end
# Return primes given by this instance so far.
def primes
return @@primes[0, @index + 1]
end
alias primes_so_far primes
def succ
@index += 1
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
alias next succ
def each
return to_enum(:each) unless block_given?
loop do
yield succ
end
end
end
require "prime.rb"
class Fixnum
remove_method :/

446
lib/prime.rb Normal file
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@ -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

126
test/test_prime.rb Normal file
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@ -0,0 +1,126 @@
require 'test/unit'
require 'prime'
require 'stringio'
class TestPrime < Test::Unit::TestCase
# The first 100 prime numbers
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, 103, 107, 109, 113, 127, 131,
137, 139, 149, 151, 157, 163, 167, 173, 179,
181, 191, 193, 197, 199, 211, 223, 227, 229,
233, 239, 241, 251, 257, 263, 269, 271, 277,
281, 283, 293, 307, 311, 313, 317, 331, 337,
347, 349, 353, 359, 367, 373, 379, 383, 389,
397, 401, 409, 419, 421, 431, 433, 439, 443,
449, 457, 461, 463, 467, 479, 487, 491, 499,
503, 509, 521, 523, 541,
]
def test_each
primes = []
Prime.each do |p|
break if p > 541
primes << p
end
assert_equal PRIMES, primes
end
def test_each_by_prime_number_theorem
3.upto(15) do |i|
max = 2**i
primes = []
Prime.each do |p|
break if p >= max
primes << p
end
# Prime number theorem
assert primes.length >= max/Math.log(max)
delta = 0.05
li = (2..max).step(delta).inject(0){|sum,x| sum + delta/Math.log(x)}
assert primes.length <= li
end
end
def test_each_without_block
enum = Prime.each
assert enum.respond_to?(:each)
assert enum.kind_of?(Enumerable)
assert enum.respond_to?(:with_index)
assert enum.respond_to?(:next)
assert enum.respond_to?(:succ)
assert enum.respond_to?(:rewind)
end
def test_new
buf = StringIO.new('', 'w')
orig, $stderr = $stderr, buf
enum = Prime.new
assert !buf.string.empty?
$stderr = orig
assert enum.respond_to?(:each)
assert enum.kind_of?(Enumerable)
assert enum.respond_to?(:succ)
assert Prime === enum
ensure
$stderr = orig
end
def test_enumerator_succ
enum = Prime.each
assert_equal PRIMES[0, 50], 50.times.map{ enum.succ }
assert_equal PRIMES[50, 50], 50.times.map{ enum.succ }
enum.rewind
assert_equal PRIMES[0, 100], 100.times.map{ enum.succ }
end
def test_enumerator_with_index
enum = Prime.each
last = -1
enum.with_index do |p,i|
break if i >= 100
assert_equal last+1, i
assert_equal PRIMES[i], p
last = i
end
end
class TestInteger < Test::Unit::TestCase
def test_prime_division
pd = PRIMES.inject(&:*).prime_division
assert_equal PRIMES.map{|p| [p, 1]}, pd
end
def test_from_prime_division
assert_equal PRIMES.inject(&:*), Integer.from_prime_division(PRIMES.map{|p| [p,1]})
end
def test_prime?
# small primes
assert 2.prime?
assert 3.prime?
# squared prime
assert !4.prime?
assert !9.prime?
# mersenne numbers
assert (2**31-1).prime?
assert !(2**32-1).prime?
# fermat numbers
assert (2**(2**4)+1).prime?
assert !(2**(2**5)+1).prime? # Euler!
# large composite
assert !((2**13-1) * (2**17-1)).prime?
# factorial
assert !(2...100).inject(&:*).prime?
end
end
end