Actions

## Feature #10354

closed

### Optimize Integer#prime?

Status:
Closed
Priority:
Normal
Target version:
-
[ruby-core:65580]

Description

Nick Slocum shows in https://github.com/ruby/ruby/pull/736 that Integer#prime? can be optimized quite a bit.

First, that's because there are some basic things to avoid in the current lib, like needlessly capturing blocks and there's a useless `loop do` too.

I'm attaching a patch that fixes many of these things.

Even after these fixes applied, Nick's version is still faster and I don't see why we would not use it for Fixnum#prime?

For Bignum#prime?, since division costs more, we can go slightly faster with the following implementation:

```class Integer
# Returns true if +self+ is a prime number, else returns false.
def prime?
return true if self == 2
return false if self % 2 == 0 || self % 3 == 0 || self < 2
skip_division = true
(5..(self**0.5).floor).step(2) do |i|
return false if skip_division && self % i == 0
skip_division = !skip_division
end
true
end
end
```

Files

Related issues

 Is duplicate of Ruby master - Feature #5378: Prime.each is slow Assigned yugui (Yuki Sonoda) Actions

#### Updated by marcandre (Marc-Andre Lafortune)almost 7 years ago

Oups, it would help if I gave the right implementation for Bignum#prime? See below

Here are some benchmarks:

Benchmark over 1..1_000_000
Current prime lib: 15.54
Fixed prime lib: 7.13
Nick's: 2.49

Benchmark for ((1 << 65) + 5).prime?:
Current prime lib: 11.83
Fixed prime lib: 6.82
Nick's: 5.32
Mine: 4.91

```class Integer
# Returns true if +self+ is a prime number, else returns false.
def prime?
return true if self == 2
return false if (self % 2 == 0) || (self % 3 == 0) || (self < 2)
skip_division = 3
(5..(self**0.5).floor).step(2) { |i|
if (skip_division -= 1) == 0
skip_division = 3
next
end
return false if self % i == 0
}
true
end
end
```

#### Updated by Anonymous almost 7 years ago

I rewrote #prime? again using a better algorithm. It's about 2x faster. This version is for `Integer`, but could be reworked for `BigNum`.

```class Integer
def prime?
return self >= 2 if self <= 3
return false if self % 2 == 0 or self % 3 == 0
(5..(self**0.5).floor).step(6).each do |i|
if self % i == 0 || self % (i + 2) == 0
return false
end
end
true
end
end
```

Benchmarked with ruby-2.1.3
my first version: 4.27

#### Updated by marcandre (Marc-Andre Lafortune)almost 7 years ago

Dear Yugui,

Do you have an objection that I commit my fixes (which are really bug fixes) while you decide if you want to go in the direction of Nick's optimization?

Thanks

Actions #4

Actions #5

#### Updated by marcandre (Marc-Andre Lafortune)almost 6 years ago

• Status changed from Open to Closed

Applied in changeset r52200.

• lib/prime.rb: Optimize Integer#prime? Patch by Nick Slocum [Bug #10354]
Actions

Also available in: Atom PDF