Issue #12676 has been updated by Jabari Zakiya.

We can make it faster across ranges, with just a little bit more code,
by adaptively selecting the Prime Generator to use based on the number size.
The method select_pg has a profile of the best PG to use for given number ranges.
It's added to init_generator (along with the number), and provides an adaptively
selected pg, instead of a hard default previously used.

In prime_division4, if no pg_selector is given then its chosen by select_pg;
otherwise, if a valid pg_select value is given then it's used.

```
class Integer
def prime_division4(pg_selector = 0)
raise ZeroDivisionError if self == 0
residues, base_primes, mod = init_generator1(self, pg_selector)
residues = base_primes + residues
r1 = base_primes.size      # first_residue_index
rn = residues.size - 1     # last_residue_index
modk = r = 0

factors = self < 0 ? [-1] : []
n = self.abs
sqrt_n = Math.sqrt(n).to_i
while (p = modk + residues[r]) <= sqrt_n
while n % p == 0; factors << p; n /= p; sqrt_n = Math.sqrt(n).to_i end
r += 1; (r = r1; modk += mod) if r > rn
end
factors << n if n > 1
factors.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
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-60236

* 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: <mailto:ruby-core-request / ruby-lang.org?subject=unsubscribe>
<http://lists.ruby-lang.org/cgi-bin/mailman/options/ruby-core>