Issue #14383 has been updated by shevegen (Robert A. Heiler).


I won't go into all points since your issue makes even my issue
requests seem small. :-)

It may be easier to split your suggestions into separate issues
tough.

For example, the 0 and -1 situation, if it is a bug (probably
is but I have not checked the official math definition for 
prime divisions myself yet), it may be better to split it into
another issue and detach it from your other statements made,
e. g. the code quality or the speedup gain from optimizing
the ruby code.

I don't think that the ruby core devs are against smaller
improvements at all, irrespective of the 3.x goal (which I
think will be achieved via the JIT/mjit anyway) but it 
may be simpler to have smaller issues. Some of the bigger
issues take longer to resolve. At any rate, that is just my
opinion - feel free to ignore it. :)

----------------------------------------
Feature #14383: Making prime_division in prime.rb Ruby 3 ready.
https://bugs.ruby-lang.org/issues/14383#change-69681

* Author: jzakiya (Jabari Zakiya)
* Status: Open
* Priority: Normal
* Assignee: 
* Target version: 
----------------------------------------
I have been running old code in Ruby 2.5.0 (released 2017.12.25) to check for
speed and compatibility. I still see the codebase in `prime.rb` hardly has
changed at all (except for replacing `Math.sqrt` with `Integer.sqrt`).

To achieve the Ruby 3 goal to make it at least three times faster than Ruby 2
there are three general areas where Ruby improvements can occur.

* increase the speed of its implementation at the machine level
* rewrite its existing codebase in a more efficient|faster manner
* use faster algorithms to implement routines and functions

I want to suggest how to address the later two ways to improve performance of
specifically the `prime_division` method in the `prime.rb` library.


I've raised and made suggestions to some of these issues here
 [ruby-issues forum](https://bugs.ruby-lang.org/issues/12676) and now hope to invigorate additional discussion.


Hopefully with the release of 2.5.0, and Ruby 3 conceptually closer to reality,
more consideration will be given to coding and algorithmic improvements to
increase its performance too.

**Mathematical correctness**

First I'd like to raise what I consider *math bugs* in `prime_division`, in how
it handles `0` and `-1` inputs.

```
> -1.prime_division
 => [[-1,1]]

> 0.prime_division
Traceback (most recent call last):
        4: from /home/jzakiya/.rvm/rubies/ruby-2.5.0/bin/irb:11:in `<main>'
        3: from (irb):85
        2: from /home/jzakiya/.rvm/rubies/ruby-2.5.0/lib/ruby/2.5.0/prime.rb:30:in `prime_division'
        1: from /home/jzakiya/.rvm/rubies/ruby-2.5.0/lib/ruby/2.5.0/prime.rb:203:in `prime_division'
ZeroDivisionError (ZeroDivisionError)
```
First, `0` is a perfectly respectable integer, and is non-prime, so its output should be `[]`, 
an empty array to denote it has no prime factors. The existing behavior is solely a matter of 
`prime_division`'s' implementation, and does not take this mathematical reality into account.

The output for `-1` is also mathematically wrong because `1` is also non-prime (and correctly 
returns `[]`), well then mathematically so should `-1`.  Thus, `prime_division` treats `-1` as 
a new prime number, and factorization, that has no mathematical basis.  Thus, for mathematical 
correctness and consistency `-1` and `0` should both return `[]`, as none have prime factors.

```
> -1.prime_division
 => []

> 0.prime_division
 => []

> 1.prime_division
 => []
```
There's a very simple one-line fix to `prime_division` to do this:

```
# prime.rb

class Prime

  def prime_division(value, generator = Prime::Generator23.new)
    -- raise ZeroDivisionError if value == 0
    ++ return [] if (value.abs | 1) == 1
```

**Simple Code and Algorithmic Improvements**

As stated above, besides the machine implementation improvements, the other
areas of performance improvements will come from coding rewrites and better
algorithms. Below is the coding of `prime_division`. This coding has existed at
least since Ruby 2.0 (the farthest I've gone back).

```
# prime.rb

class Integer

  # Returns the factorization of +self+.
  #
  # See Prime#prime_division for more details.
  def prime_division(generator = Prime::Generator23.new)
    Prime.prime_division(self, generator)
  end

end

class Prime

  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

end
```

This can be rewritten in more modern and idiomatic Ruby, to become much shorter
and easier to understand.

```
require 'prime.rb'

class Integer
  def prime_division1(generator = Prime::Generator23.new)
    Prime.prime_division1(self, generator)
  end
end

class Prime

  def prime_division1(value, generator = Prime::Generator23.new)
    # raise ZeroDivisionError if value == 0
    return [] if (value.abs | 1) == 1
    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

end
```
By merely rewriting it we get smaller|concise code, that's easier to understand,
which is slightly faster. A *triple win!* Just paste the above code into a 2.5.0
terminal session, and run the benchmarks below.

```
def tm; s=Time.now; yield; Time.now-s end

 n = 500_000_000_000_000_000_008_244_213; tm{ pp n.prime_division }
[[3623, 1], [61283, 1], [352117631, 1], [6395490847, 1]]
 => 27.02951016

 n = 500_000_000_000_000_000_008_244_213; tm{ pp n.prime_division1 }
[[3623, 1], [61283, 1], [352117631, 1], [6395490847, 1]]
 => 25.959149721
```
Again, we get a *triple win* to this old codebase by merely rewriting it. It can
be made 3x faster by leveraging the `prime?` method from the `OpenSSL` library to
perform a more efficient|faster factoring algorithm, and implementation.

```
require 'prime.rb'
require 'openssl'

class Integer

  def prime_division2(generator = Prime::Generator23.new)
    return [] if (self.abs | 1) == 1
    pv = self < 0 ? [-1] : []
    value = self.abs
    prime = generator.next
    until value.to_bn.prime? or value == 1
      while prime
        (pv << prime; value /= prime; break) if value % prime == 0
        prime = generator.next
      end
    end
    pv << value if value > 1
    pv.group_by {|prm| prm }.map{|prm, exp| [prm, exp.size] }
  end

end
```
Here we're making much better use of Ruby idioms and libraries (`enumerable` and
`openssl`), leading to a much greater performance increase. A bigger *triple win*.
Pasting this code into a 2.5.0 terminal session gives the following results.

```
# Hardware: System76 laptop; I7 cpu @ 3.5GHz, 64-bit Linux

def tm; s=Time.now; yield; Time.now-s end

 n = 500_000_000_000_000_000_008_244_213; tm{ pp n.prime_division }
[[3623, 1], [61283, 1], [352117631, 1], [6395490847, 1]]
 => 27.02951016

 n = 500_000_000_000_000_000_008_244_213; tm{ pp n.prime_division1 }
[[3623, 1], [61283, 1], [352117631, 1], [6395490847, 1]]
 => 25.959149721

 n = 500_000_000_000_000_000_008_244_213; tm{ pp n.prime_division2 }
[[3623, 1], [61283, 1], [352117631, 1], [6395490847, 1]]
 => 9.39650374
```
`prime_division2` is much more usable for significantly larger numbers and use
cases than `prime_division`. I can even do multiple times better than this, if
you review the above cited forum thread.

My emphasis here is to show there are a lot of possible *low hanging fruit*
performance gains ripe for the picking to achieve Ruby 3 performance goals, if we
look (at minimum) for simpler|better code rewrites, and then algorithmic upgrades.

So the question is, are the devs willing to upgrade the codebase to provide the
demonstrated performance increases shown here for `prime_division`?



-- 
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