## Feature #5378

### Prime.each is slow

**Description**

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)

**Related issues**

### History

#### #1 [ruby-core:39806] Updated by h.shirosaki (Hiroshi Shirosaki) over 6 years ago

**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)

#### #2 [ruby-core:39854] Updated by calamitas (Peter Vanbroekhoven) over 6 years ago

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 si.step(n, i) { |j| s[j] = nil }

end

end

s.compact

end

#### #3 Updated by mame (Yusuke Endoh) over 6 years ago

**Tracker**changed from*Bug*to*Feature*

#### #4 [ruby-core:39872] Updated by mame (Yusuke Endoh) over 6 years ago

**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 mame@tsg.ne.jp

#### #5 [ruby-core:48484] Updated by yhara (Yutaka HARA) over 5 years ago

**Target version**set to*2.6*

#### #6 [ruby-core:48681] Updated by headius (Charles Nutter) over 5 years ago

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.

#### #7 Updated by marcandre (Marc-Andre Lafortune) over 3 years ago

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

#### #8 Updated by naruse (Yui NARUSE) 5 months ago

**Target version**deleted ()*2.6*