From: jzakiya@... Date: 2016-10-08T04:08:35+00:00 Subject: [ruby-core:77525] [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. I am confused some by these recent comments, and would appreciate clarification. Since 1 is not prime and returns [] then for mathematical consistency and correctness so should -1. I don't understand how the code I presented created a problem. It presents no problems in my benchmarks. The alternative to it then would be: ``` return [] if self == 0 or self.abs == 1 ``` Actually, the code fixes handling -1 correctly and also correctly mathematically handles 0 (no error raised). If you allow these mathematical errors to remain the code produces the same results as `prime_division` and is thus a drop in replacement for it (but much faster). Have you tested it? Besides these math errors, the current version of `prime_divison` is slow and uses much more code than necessary. My purpose is to make prime factorization in `prime.rb` as fast as possible, particulary to exceed Matz's Ruby 3x3 goal. The code I've presented is orders of magnitude faster than 3x, with the added benefit of greatly reducing the codebase necessary to achieve this performance increase. On my 3.5GHz I7 Linux laptop it can factor 30+ digit numbers in seconds. Have you benchmarked it against `prime_division`? Are there other more important metrics that the code is being judged against? As a user of Ruby for math and engineering purposes I need accuracy, speed, and ease of use. The present handling of -1 and 0 are just plain mathematical errors. In fact, from a mathematical perspective *all negative integers are defined as non-prime*, so from that perspective you don't even need to try to prime factor negative numbers. In my `primes-utils` gem I just do `self.abs` to require processing only positve integers. Also, by using the `OpenSSL` Standard Library you can replace the slow implementation of `prime?` with it's counterpart to increase performance, and save code too. Below is the even more concise improved code. As you see, it's much shorter than the current codebase in `prime.rb`. If Ruby ever gets true parallel programming capabilities it could possibly be upgraded to take advantage of that too. If you have questions please let me know. ``` require 'openssl' class Integer def prime? self.to_bn.prime? end def prime_division9(pg_selector = 0) return [] if self.abs | 1 == 1 return [[self, 1]] if self.prime? pv = self < 0 ? [-1] : [] value = self.abs base_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47] base_primes.each {|prm| (pv << prm; value /= prm) while value % prm == 0 } unless value.prime? or value == 1 residues, *, mod = init_generator1(Math.sqrt(value).to_i, pg_selector) rn = residues.size - 1 modk = r = 0 until value.prime? or value == 1 while (prime = modk + residues[r]) (pv << prime; value /= prime; break) if value % prime == 0 r += 1; (r = 0; modk += mod) if r > rn end end 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 < 21 * 10**6 + 1000 return 7 if num < 20 * 10**9 + 1000 return 11 if num < 10 * 10**12 + 1000 return 13 if num < 70 * 10**14 - 1000 return 17 if num < 43 * 10**17 - 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-60797 * Author: Jabari Zakiya * Status: Assigned * Priority: Normal * Assignee: 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/ Unsubscribe: