From: jzakiya@... Date: 2016-08-24T15:57:47+00:00 Subject: [ruby-core:77045] [Ruby trunk Feature#12676] Significant performance increase, and code conciseness, for prime_division method in prime.rb Issue #12676 has been updated by Jabari Zakiya. One last simple tweek to increase overall peformance, in prime_division5. Instead of selecting the optimum pg based on the number's size, first suck out any factors of some base primes, then determine the optimum pg based on the sqrt of the reduced factored number. This significantly speedups large factorable numbers (while maintaining the same performance for large primes) by choosing the optimun pg for smaller numbers resulting from the factoring by the base primes. ``` class Integer def prime_division5(pg_selector = 0) raise ZeroDivisionError if self == 0 base_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47] pv = self < 0 ? [-1] : [] value = self.abs base_primes.each {|prm| (pv << prm; value /= prm) while value % prm == 0 } sqrt_value = Math.sqrt(value).to_i num = self.abs == value ? value : sqrt_value residues, *, mod = init_generator1(num, pg_selector) rn = residues.size - 1; # last_residue_index modk = r = 0 while (prime = modk + residues[r]) <= sqrt_value while value % prime == 0; pv << prime value /= prime sqrt_value = Math.sqrt(value).to_i end r +=1; (r = 0; modk += mod) if r > rn end pv << value if value > 1 pv.group_by {|prm| prm }.map{|prm, exp| [prm, exp.size] } end private def init_generator1(num, pg_selector) base_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23] pg_selector = select_pg(num.abs) unless base_primes.include? pg_selector # puts "Using P#{pg_selector}" base_primes.select! {|prm| prm <= pg_selector } mod = base_primes.reduce(:*) residues = []; 3.step(mod, 2) {|r| residues << r if mod.gcd(r) == 1 } [residues << mod + 1, base_primes, mod] end def select_pg(num) # adaptively select fastest SP Prime Generator return 5 if num < 1 * 10**7 + 1000 return 7 if num < 1 * 10**10 + 1000 return 11 if num < 1 * 10**13 + 1000 return 13 if num < 7 * 10**15 + 1000 return 17 if num < 4 * 10**18 + 1000 19 end end ``` ---------------------------------------- Feature #12676: Significant performance increase, and code conciseness, for prime_division method in prime.rb https://bugs.ruby-lang.org/issues/12676#change-60270 * Author: Jabari Zakiya * Status: Open * Priority: Normal * Assignee: ---------------------------------------- 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 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. 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. 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. 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/ Unsubscribe: