Feature #5378: Prime.each is slow

• Status: Closed
• Assignee: yugui (Yuki Sonoda)
• Target version: -

[mconigliaro (Mike Conigliaro)]

See discussion here: https://gist.github.com/1246868

require 'benchmark'
require 'prime'

def primes_up_to(n)
s = [nil, nil] + (2..n).to_a
(2..(n ** 0.5).to_i).reject { |i| s[i].nil? }.each do |i|
(i ** 2).step(n, i) { |j| s[j] = nil }
end
s.compact
end

Benchmark.bm(12) do |x|
x.report('primes_up_to') { primes_up_to(2000000).inject(0) { |memo,obj| memo + obj } }
x.report('Prime.each') { Prime.each(2000000).inject(0) { |memo,obj| memo + obj } }
end

$ ruby -v
ruby 1.9.2p290 (2011-07-09 revision 32553) [x86_64-darwin10.8.0]
$ ruby lol.rb
user system total real
primes_up_to 1.470000 0.020000 1.490000 ( 1.491340)
Prime.each 7.820000 0.010000 7.830000 ( 7.820969)

[h.shirosaki (Hiroshi Shirosaki)]

• File prime.patch prime.patch added

It seems that converting from integer to bitmap tables in EratosthenesSieve class is slow.

This patch improves Prime performance.

require 'benchmark'
require 'prime'

def primes_up_to(n)
s = [nil, nil] + (2..n).to_a
(2..(n ** 0.5).to_i).reject { |i| s[i].nil? }.each do |i|
(i ** 2).step(n, i) { |j| s[j] = nil }
end
s.compact
end
Benchmark.bm(12) do |x|
x.report('primes_up_to') { p primes_up_to(1500000).inject(0) { |memo,obj| memo + obj } }
2.times do
x.report('Prime.each') { p Prime.each(1500000).inject(0) { |memo,obj| memo + obj } }
end
end

before

$ ruby -v ~/prime_bench.rb
ruby 1.9.4dev (2011-10-01 trunk 33368) [x86_64-darwin11.1.0]
user system total real
primes_up_to 2.530000 0.020000 2.550000 ( 2.550595)
Prime.each 6.450000 0.010000 6.460000 ( 6.461948)
Prime.each 0.880000 0.000000 0.880000 ( 0.877138)

after

$ ruby -v -Ilib ~/prime_bench.rb
ruby 1.9.4dev (2011-10-01 trunk 33368) [x86_64-darwin11.1.0]
user system total real
primes_up_to 2.560000 0.020000 2.580000 ( 2.583900)
Prime.each 4.630000 0.010000 4.640000 ( 4.633154)
Prime.each 0.330000 0.000000 0.330000 ( 0.325838)

[calamitas (Peter Vanbroekhoven)]

Note that the primes_up_to method Mike posted is not quite optional in that the intended optimization in the form of the reject doesn't do anything. The reject is executed before the loop and so the loop is still executed for all numbers instead of just for the primes.

If you use the version below instead, it is over 2.5 times faster for 2 mil primes on my machine. That would make the new built-in version still almost 5 times slower than the pure-Ruby version. Note also that in my benchmarks I changed the inject block to just return memo and not calculate the sum because that skews the results by quite a bit; there's the extra summing, but the sum gets in the Bignum range and so it adds object creation and garbage collection.

def primes_up_to(n)
s = [nil, nil] + (2..n).to_a
(2..(n ** 0.5).to_i).each do |i|
if s[i]
(i ** 2).step(n, i) { |j| s[j] = nil }
end
end
s.compact
end

[mame (Yusuke Endoh)]

• Tracker changed from Bug to Feature

[mame (Yusuke Endoh)]

• Status changed from Open to Assigned
• Assignee set to yugui (Yuki Sonoda)

Hello,

Just slowness is not a bug unless it is a regression, I think.
So I moved this ticket to the feature tracker.

I believe that there is no perfect algorithm to enumerate
primes. Any algorithm has drawback and advantage. Note that
speed is not the single important thing. I could be wrong,
but I guess that prime.rb does not priotize speed (especially,
linear-order cost), but high-abstract design.

Even in terms of speed, my version is about 2 times faster
than Peter's, though it uses extra memory. So, there are
trade-offs.

def primes_up_to_yusuke(n)
primes = [2]
n /= 2
prime_table = [true] * n
i = 1
while i < n
if prime_table[i]
primes << j = i * 2 + 1
k = i + j
while k < n
prime_table[k] = false
k += j
end
end
i += 1
end
primes
end

              user     system      total        real

primes_up_to_mike 1.720000 0.010000 1.730000 ( 1.726733)
primes_up_to_peter 0.780000 0.020000 0.800000 ( 0.795156)
primes_up_to_yusuke 0.410000 0.000000 0.410000 ( 0.419209)
Prime.each 4.760000 0.010000 4.770000 ( 4.765654)

I think every prime-aholic should implement their own favorite
algorithm by himself :-)

--
Yusuke Endoh [e-mail]

[yhara (Yutaka HARA)]

• Target version set to 2.6

[headius (Charles Nutter)]

JRuby numbers for the various implementations proposed (best times out of ten in-process iterations):

mconigliario's version:

               user     system      total        real

primes_up_to 2.100000 0.000000 2.100000 ( 1.062000)
Prime.each 0.980000 0.010000 0.990000 ( 0.883000)

h.shirosaki's version:

               user     system      total        real

primes_up_to 2.100000 0.010000 2.110000 ( 1.014000)
Prime.each 1.030000 0.000000 1.030000 ( 0.930000)

calamitas's version:

               user     system      total        real

primes_up_to 1.130000 0.020000 1.150000 ( 0.467000)
Prime.each 1.020000 0.000000 1.020000 ( 0.908000)

mame's version:

               user     system      total        real

primes_up_to 0.180000 0.000000 0.180000 ( 0.143000)
Prime.each 0.970000 0.000000 0.970000 ( 0.948000)

Ruby 1.9.3p286 running mame's version:

               user     system      total        real

primes_up_to 0.380000 0.000000 0.380000 ( 0.382392)
Prime.each 0.790000 0.000000 0.790000 ( 0.793005)

Definitely some room for improvement over the base implementation.

[marcandre (Marc-Andre Lafortune)]

• Has duplicate Feature #10354: Optimize Integer#prime? added

[naruse (Yui NARUSE)]

• Target version deleted (2.6)

[hsbt (Hiroshi SHIBATA)]

• Status changed from Assigned to Closed

prime.rb was extracted to https://github.com/ruby/prime as the bundled gems.

If you still have the motivation of this proposal, can you file this to the new canonical repository? Thanks.