Feature #5378

Prime.each is slow

Added by Mike Conigliaro over 2 years ago. Updated over 1 year ago.

[ruby-core:39769]
Status:Assigned
Priority:Normal
Assignee:Yuki Sonoda
Category:-
Target version:next minor

Description

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

require 'benchmark'
require 'prime'

def primesupto(n)
s = [nil, nil] + (2..n).toa
(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('primesupto') { primesupto(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) [x8664-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)

prime.patch Magnifier (4.06 KB) Hiroshi Shirosaki, 10/01/2011 03:26 PM

History

#1 Updated by Hiroshi Shirosaki over 2 years ago

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

This patch improves Prime performance.

require 'benchmark'
require 'prime'

def primesupto(n)
s = [nil, nil] + (2..n).toa
(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('primesupto') { p primesupto(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 ~/primebench.rb
ruby 1.9.4dev (2011-10-01 trunk 33368) [x86
64-darwin11.1.0]
user system total real
primesupto 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 ~/primebench.rb
ruby 1.9.4dev (2011-10-01 trunk 33368) [x86
64-darwin11.1.0]
user system total real
primesupto 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)

#2 Updated by Peter Vanbroekhoven over 2 years ago

Note that the primesupto 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 primesupto(n)
s = [nil, nil] + (2..n).toa
(2..(n ** 0.5).to
i).each do |i|
if si.step(n, i) { |j| s[j] = nil }
end
end
s.compact
end

#3 Updated by Yusuke Endoh over 2 years ago

  • Tracker changed from Bug to Feature

#4 Updated by Yusuke Endoh over 2 years ago

  • Status changed from Open to Assigned
  • Assignee set to 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 primesuptoyusuke(n)
primes = [2]
n /= 2
prime
table = [true] * n
i = 1
while i < n
if primetable[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

primesuptomike 1.720000 0.010000 1.730000 ( 1.726733)
primes
uptopeter 0.780000 0.020000 0.800000 ( 0.795156)
primesupto_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 mame@tsg.ne.jp

#5 Updated by Yutaka HARA over 1 year ago

  • Target version set to next minor

#6 Updated by Charles Nutter over 1 year ago

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

mconigliario's version:

               user     system      total        real

primesupto 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

primesupto 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

primesupto 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

primesupto 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

primesupto 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.

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