* lib/prime.rb (Prime::EratosthenesGenerator,

Prime::EratosthenesSieve): New implementation by
  robertjlooby <robertjlooby AT gmail.com>.

* test/test_prime.rb: updated with new method name

commit 4b6090ea852d63b26e02796c69b41caa0fa95077
Merge: ceda881 c8f7809
Author: Yuki Sonoda (Yugui) <yugui@yugui.jp>
Date:   Mon Jul 15 12:50:04 2013 +0900

    Merge commit 'c8f780987fbdfbae428977487e1cf793c4c36d3f'

    Conflicts:
    	lib/prime.rb

commit c8f780987f
Author: robertjlooby <robertjlooby@gmail.com>
Date:   Thu Jun 27 23:04:45 2013 -0500

    updated test/test_prime.rb with new method name

commit 996517bdbb
Author: robertjlooby <robertjlooby@gmail.com>
Date:   Thu Jun 27 22:59:39 2013 -0500

    new implementation of Prime::EratosthenesGenerator and Prime::EratosthenesSieve

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@41982 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

ChangeLog

@@ -1,3 +1,11 @@
+Mon Jul 15 13:07:27 2013  Yuki Yugui Sonoda  <yugui@yugui.jp>
+
+	* lib/prime.rb (Prime::EratosthenesGenerator,
+	  Prime::EratosthenesSieve): New implementation by
+	  robertjlooby <robertjlooby AT gmail.com>.
+
+	* test/test_prime.rb: updated with new method name
+
 Mon Jul 15 11:32:46 2013  Zachary Scott  <e@zzak.io>
 
 	* numeric.c (rb_cNumeric): [DOC] Added comment for Numeric to fix doc

lib/prime.rb

@@ -306,12 +306,13 @@ class Prime
   # Uses +EratosthenesSieve+.
   class EratosthenesGenerator < PseudoPrimeGenerator
     def initialize
-      @last_prime = nil
+      @last_prime_index = -1
       super
     end
 
     def succ
-      @last_prime = @last_prime ? EratosthenesSieve.instance.next_to(@last_prime) : 2
+      @last_prime_index += 1
+      EratosthenesSieve.instance.get_nth_prime(@last_prime_index)
     end
     def rewind
       initialize
@@ -422,68 +423,48 @@ class Prime
   class EratosthenesSieve
     include Singleton
 
-    BITS_PER_ENTRY = 16  # each entry is a set of 16-bits in a Fixnum
+    def initialize
-    NUMS_PER_ENTRY = BITS_PER_ENTRY * 2 # twiced because even numbers are omitted
+      @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]
-    ENTRIES_PER_TABLE = 8
+      # @max_checked must be an even number
-    NUMS_PER_TABLE = NUMS_PER_ENTRY * ENTRIES_PER_TABLE
+      @max_checked = @primes.last + 1
-    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 get_nth_prime(n)
-    def next_to(n)
+      compute_primes while @primes.size <= n
-      n = (n-1).div(2)*2+3 # the next odd number to given n
+      @primes[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 primality of the number
+    def compute_primes
-    def indices(n)
+      # max_segment_size must be an even number
-      #   binary digits of n: |0|1|2|3|4|5|6|7|8|9|10|11|....
+      max_segment_size = 1e6.to_i
-      #   indices:            |-|    k  |  j  |     i
+      max_cached_prime = @primes.last
-      # because of NUMS_PER_ENTRY, NUMS_PER_TABLE
+      # do not double count primes if #compute_primes is interrupted
+      # by Timeout.timeout
+      @max_checked = max_cached_prime + 1 if max_cached_prime > @max_checked
 
-      k = (n & 0b00011111) >> 1
+      segment_min = @max_checked
-      j = (n & 0b11100000) >> 5
+      segment_max = [segment_min + max_segment_size, max_cached_prime * 2].min
-      i = n >> 8
+      root = Integer(Math.sqrt(segment_max).floor)
-      return i, j, k
-    end
 
-    def extend_table
+      sieving_primes = @primes[1 .. -1].take_while { |prime| prime <= root }
-      lbound = NUMS_PER_TABLE * @tables.length
+      offsets = Array.new(sieving_primes.size) do |i|
-      ubound = lbound + NUMS_PER_TABLE
+        (-(segment_min + 1 + sieving_primes[i]) / 2) % sieving_primes[i]
-      new_table = [FILLED_ENTRY] * ENTRIES_PER_TABLE # which represents primality in lbound...ubound
+      end
-      (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
+      segment = ((segment_min + 1) .. segment_max).step(2).to_a
-        start += p if start.even?
+      sieving_primes.each_with_index do |prime, index|
-        (start...ubound).step(2*p) do |n|
+        composite_index = offsets[index]
-          _, j, k = indices(n)
+        while composite_index < segment.size do
-          new_table[j] &= FILLED_ENTRY^(1<<k)
+          segment[composite_index] = nil
+          composite_index += prime
         end
       end
-      @tables << new_table.freeze
+
+      segment.each do |prime|
+        @primes.push prime unless prime.nil?
+      end
+      @max_checked = segment_max
     end
   end
 

test/test_prime.rb

@@ -154,7 +154,7 @@ class TestPrime < Test::Unit::TestCase
       # simulates that Timeout.timeout interrupts Prime::EratosthenesSieve#extend_table
       def sieve.Integer(n)
         n = super(n)
-        sleep 10 if /extend_table/ =~ caller.first
+        sleep 10 if /compute_primes/ =~ caller.first
         return n
       end