Issue #12676 has been updated by hsbt (Hiroshi SHIBATA). Status changed from Assigned to Closed prime is maintained at https://github.com/ruby/prime today. If you still interest this, can you submit this to upstream repo? ---------------------------------------- Feature #12676: Significant performance increase, and code conciseness, for prime_division method in prime.rb https://bugs.ruby-lang.org/issues/12676#change-107591 * Author: jzakiya (Jabari Zakiya) * Status: Closed * Assignee: marcandre (Marc-Andre Lafortune) ---------------------------------------- I earlier posted code to simplify the prime_division method in prime.rb. This made the code much more concise and readable/understandable, while also providing a small speed increase. The code presented here for prime_division2 maintains the conciseness and readability, but uses a different/simpler algorithm to provide a significant speed increase over the current implementation of prime_division in prime.rb. Timings for selected large primes are provided, run on CRuby 2.3.1. System: System76 3.5GHz I7 cpu laptop, Linux 64-bit OS in Virtual Box. ``` n1 = 100_000_000_000_000_003 n2 = 200_000_000_000_000_003 n3 = 1_000_000_000_000_000_003 n1 n2 n3 prime_division 23.7 33.5 74.6 prime_division1 22.9 32.2 72.8 prime_division2 14.8 20.5 45.8 ``` ```ruby def tm; s = Time.now; yield; Time.now - s end irb(main):015:0> n = 100_000_000_000_000_003; tm{ n.prime_division } => 23.730239721 irb(main):016:0> n = 100_000_000_000_000_003; tm{ n.prime_division1 } => 22.877657172 irb(main):017:0> n = 100_000_000_000_000_003; tm{ n.prime_division2 } => 14.758561827 irb(main):018:0> n = 200_000_000_000_000_003; tm{ n.prime_division } => 33.502851342 irb(main):019:0> n = 200_000_000_000_000_003; tm{ n.prime_division1 } => 32.23911595 irb(main):020:0> n = 200_000_000_000_000_003; tm{ n.prime_division2 } => 20.476660683 irb(main):021:0> n = 1_000_000_000_000_000_003; tm{ n.prime_division } => 74.630244055 irb(main):022:0> n = 1_000_000_000_000_000_003; tm{ n.prime_division1 } => 72.778948947 irb(main):023:0> n = 1_000_000_000_000_000_003; tm{ n.prime_division2 } => 45.802756121 ``` 1. Current code for prime_division in prime.rb. ```ruby def prime_division(value, generator = Prime::Generator23.new) raise ZeroDivisionError if value == 0 if value < 0 value = -value pv = [[-1, 1]] else pv = [] end generator.each do |prime| 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 pv end ``` 2. Code simplification for current algorithm, increases conciseness/readability, with slight speedup. ```ruby def prime_division1(value, generator = Prime::Generator23.new) raise ZeroDivisionError if value == 0 pv = value < 0 ? [[-1, 1]] : [] value = value.abs generator.each do |prime| count = 0 while (value1, mod = value.divmod(prime); mod) == 0 value = value1 count += 1 end pv.push [prime, count] unless count == 0 break if prime > value1 end pv.push [value, 1] if value > 1 pv end ``` 3. Change of algorithm, maintains conciseness/readability with significant speed increase. ```ruby def prime_division2(value, generator = Prime::Generator23.new) raise ZeroDivisionError if value == 0 pv = value < 0 ? [-1] : [] value = value.abs sqrt_value = Math.sqrt(value).to_i generator.each do |prime| break if prime > sqrt_value while value % prime == 0 pv << prime value /= prime sqrt_value = Math.sqrt(value).to_i end end pv << value if value > 1 pv.group_by {|prm| prm }.map{|prm, exp| [prm, exp.size] } end ``` -- https://bugs.ruby-lang.org/