BigNum optimizations


#1

Time for multiplication of BigNums grows quadratically with number of
digits (ruby 1.8.7). And in ruby 1.9 is lower than in ruby 1.8:

require ‘benchmark’

Benchmark.bmbm do |b|
[100, 200, 400, 800, 1600].each do |n|
num = 1123 ** n
b.report “#{n}” do
1000.times{num*num}
end
end
end

ruby -v a.rb
ruby 1.8.7 (2008-08-11 patchlevel 72) [i486-linux]
Rehearsal ----------------------------------------
100 0.010000 0.000000 0.010000 ( 0.010418)
200 0.030000 0.000000 0.030000 ( 0.036871)
400 0.130000 0.000000 0.130000 ( 0.125760)
800 0.460000 0.000000 0.460000 ( 0.482740)
1600 1.810000 0.000000 1.810000 ( 1.903963)
------------------------------- total: 2.440000sec

       user     system      total        real

100 0.020000 0.000000 0.020000 ( 0.008206)
200 0.020000 0.000000 0.020000 ( 0.029941)
400 0.120000 0.000000 0.120000 ( 0.115787)
800 0.460000 0.000000 0.460000 ( 0.459517)
1600 1.770000 0.020000 1.790000 ( 1.807655)

Exit code: 0

$ ruby1.9 -v a.rb
ruby 1.9.0 (2008-06-20 revision 17482) [i486-linux]
Rehearsal ----------------------------------------
100 0.020000 0.000000 0.020000 ( 0.013167)
200 0.040000 0.000000 0.040000 ( 0.046076)
400 0.150000 0.000000 0.150000 ( 0.150487)
800 0.540000 0.010000 0.550000 ( 0.589719)
1600 2.200000 0.000000 2.200000 ( 2.258581)
------------------------------- total: 2.960000sec

       user     system      total        real

100 0.000000 0.000000 0.000000 ( 0.009808)
200 0.040000 0.000000 0.040000 ( 0.037194)
400 0.140000 0.000000 0.140000 ( 0.144723)
800 0.560000 0.000000 0.560000 ( 0.587338)
1600 2.210000 0.000000 2.210000 ( 2.254998)

Exit code: 0

+1 for making it faster, i.e. N log N.

It looks like BigNum will be faster in next release
(http://redmine.ruby-lang.org/search/index/ruby-19?q=Karatsuba), is it
true?
But why Karatsuba? It is only O(N**1.585) while Schönhage–Strassen is
O(N log N).

I guess it is more reasonable to implement


or take use of any GPL soft

See also talk
http://blade.nagaokaut.ac.jp/cgi-bin/scat.rb/ruby/ruby-talk/77470
dated 30 Jul 2003

Artem V.


#2

Hi,

In message “Re: BigNum optimizations”
on Tue, 17 Mar 2009 07:49:20 +0900, Artem V.
removed_email_address@domain.invalid writes:

|+1 for making it faster, i.e. N log N.
|
|It looks like BigNum will be faster in next release
|(http://redmine.ruby-lang.org/search/index/ruby-19?q=Karatsuba), is it
|true?

True.

% ruby -v a.rb
ruby 1.8.7 (2008-08-11 patchlevel 72) [i486-linux]
Rehearsal ----------------------------------------
100 0.020000 0.000000 0.020000 ( 0.024290)
200 0.070000 0.000000 0.070000 ( 0.072934)
400 0.120000 0.000000 0.120000 ( 0.123551)
800 0.490000 0.000000 0.490000 ( 0.514302)
1600 1.900000 0.000000 1.900000 ( 1.971061)
------------------------------- total: 2.600000sec

       user     system      total        real

100 0.010000 0.000000 0.010000 ( 0.015825)
200 0.030000 0.000000 0.030000 ( 0.048896)
400 0.120000 0.000000 0.120000 ( 0.124947)
800 0.480000 0.000000 0.480000 ( 0.490557)
1600 1.900000 0.000000 1.900000 ( 1.905196)

% ruby1.9 -v a.rb
ruby 1.9.2dev (2009-03-15 trunk 22972) [i686-linux]
Rehearsal ----------------------------------------
100 0.020000 0.000000 0.020000 ( 0.030905)
200 0.040000 0.000000 0.040000 ( 0.045328)
400 0.080000 0.000000 0.080000 ( 0.084670)
800 0.250000 0.000000 0.250000 ( 0.275130)
1600 0.770000 0.000000 0.770000 ( 0.796491)
------------------------------- total: 1.160000sec

       user     system      total        real

100 0.010000 0.000000 0.010000 ( 0.007731)
200 0.020000 0.000000 0.020000 ( 0.026167)
400 0.070000 0.000000 0.070000 ( 0.092874)
800 0.260000 0.000000 0.260000 ( 0.256951)
1600 0.770000 0.000000 0.770000 ( 0.807816)

|But why Karatsuba? It is only O(N**1.585) while Schönhage–Strassen is
|O(N log N).

It’s matter of the resource we have. If some one would volunteer to
implement it, we’d love to merge.

          matz.

#3

Hi,

In message “Re: BigNum optimizations”
on Wed, 18 Mar 2009 04:11:34 +0900, “M. Edward (Ed) Borasky”
removed_email_address@domain.invalid writes:

|It might be easier to link to a standard open-source multi-precision
|library that it would be to revise the one that’s built into the Ruby
|interpreters. I haven’t benchmarked these against each other, but the
|two I know about are GMP http://gmplib.org/ and CLN
|http://www.ginac.de/CLN/. Both are GPL.

We cannot link pure GPLed library to Ruby for licensing issue. Last
time I checked none of these multi precision numeric libraries
satisfied our criteria (license, portability, etc). GMP (or CLN or
whatever) can be used via extension, and we are happy to offer help if
required.

          matz.

#4

On Tue, Mar 17, 2009 at 5:56 PM, Yukihiro M. removed_email_address@domain.invalid
wrote:

We cannot link pure GPLed library to Ruby for licensing issue. Â Last
time I checked none of these multi precision numeric libraries
satisfied our criteria (license, portability, etc). Â GMP (or CLN or
whatever) can be used via extension, and we are happy to offer help if
required.

I just checked … GMP is LGPL. Would that work?

                            matz.


M. Edward (Ed) Borasky
http://www.linkedin.com/in/edborasky

I’ve never met a happy clam. In fact, most of them were pretty steamed.


#5

On Mon, Mar 16, 2009 at 4:23 PM, Yukihiro M. removed_email_address@domain.invalid
wrote:

------------------------------- total: 2.600000sec
Rehearsal ----------------------------------------
400 Â Â 0.070000 Â 0.000000 Â 0.070000 ( Â 0.092874)
800 Â Â 0.260000 Â 0.000000 Â 0.260000 ( Â 0.256951)
1600 Â 0.770000 Â 0.000000 Â 0.770000 ( Â 0.807816)

|But why Karatsuba? It is only O(N**1.585)  while Schönhage–Strassen is
|O(N log N).

It’s matter of the resource we have. Â If some one would volunteer to
implement it, we’d love to merge.

                            matz.

It might be easier to link to a standard open-source multi-precision
library that it would be to revise the one that’s built into the Ruby
interpreters. I haven’t benchmarked these against each other, but the
two I know about are GMP http://gmplib.org/ and CLN
http://www.ginac.de/CLN/. Both are GPL. GMP is available in just about
every Linux distro I know about; CLN may be a little harder to find,
but it’s in Debian and Gentoo. I don’t know about other platforms, but
at least GMP is “pure-enough” GNU that it should compile on Windows
and Macs and Solaris.

Ezra … is this something Engine Y. could do for 1.8.6 / Rubinius?
I think the jRuby people are working on their Bignum performance too.


M. Edward (Ed) Borasky
http://www.linkedin.com/in/edborasky

I’ve never met a happy clam. In fact, most of them were pretty steamed.


#6

Hi,

In message “Re: BigNum optimizations”
on Wed, 18 Mar 2009 10:01:07 +0900, “M. Edward (Ed) Borasky”
removed_email_address@domain.invalid writes:

|> We cannot link pure GPLed library to Ruby for licensing issue. Last
|> time I checked none of these multi precision numeric libraries
|> satisfied our criteria (license, portability, etc). GMP (or CLN or
|> whatever) can be used via extension, and we are happy to offer help if
|> required.
|
|I just checked … GMP is LGPL. Would that work?

Well, it’s not impossible (i.e. 1.8 regex was LGPL), but not ideal.
Some commercial Ruby users had to replace 1.8 regex by Oniguruma only
for a license issue. I don’t want to see same situation for bignums.

          matz.

#7

M. Edward (Ed) Borasky wrote:

Ezra … is this something Engine Y. could do for 1.8.6 / Rubinius?
I think the jRuby people are working on their Bignum performance too.

We’re mostly just wrapping the JDK’s builtin BigInteger class, which is
not known for its scorching performance. BigInteger.doubleValue actually
passes the number through a a String and re-parses it (a contributor
implemented a replacement, for obvious reasons). There are alternative
libraries, but we have not merged them in to avoid bloating the size of
JRuby’s distribution.

Of course almost all of them can be called directly through our Java
integration layer, so if people need the performance they can do that.
Java 7 is supposed to include a number of performance improvements for
BigInteger as well.

We would not decline a clean-room implementation of Bignum that uses the
latest and greatest algorithms :slight_smile: It would probably be easier in Java
than in C.

  • Charlie

#8

On Wed, Mar 18, 2009 at 10:10:45AM +0900, Yukihiro M. wrote:

|
|I just checked … GMP is LGPL. Would that work?

Well, it’s not impossible (i.e. 1.8 regex was LGPL), but not ideal.
Some commercial Ruby users had to replace 1.8 regex by Oniguruma only
for a license issue. I don’t want to see same situation for bignums.

How about libtommath/libtomfastmath ? there is a gem of it available:

http://math.libtomcrypt.com/

enjoy,

-jeremy


#9

On Tue, Mar 17, 2009 at 6:10 PM, Yukihiro M. removed_email_address@domain.invalid
wrote:

|I just checked … GMP is LGPL. Would that work?

Well, it’s not impossible (i.e. 1.8 regex was LGPL), but not ideal.
Some commercial Ruby users had to replace 1.8 regex by Oniguruma only
for a license issue. Â I don’t want to see same situation for bignums.

                            matz.

Yeah … the PostgreSQL community mostly uses BSD-style licenses
specifically because of the “chilling effect” of GPL on commercial
users. Actually, given that a lot of BigNum work came out of MIT, I’m
surprised there isn’t an MIT-licensed BigNum library running around
somewhere. Let me dig around into what’s in Sage (sagemath.org) and
what’s in Python. This is a wheel we shouldn’t have to re-invent or
even re-code. :slight_smile:

M. Edward (Ed) Borasky
http://www.linkedin.com/in/edborasky

I’ve never met a happy clam. In fact, most of them were pretty steamed.


#10

Hi,

In message “Re: BigNum optimizations”
on Fri, 20 Mar 2009 12:07:50 +0900, Jeremy H.
removed_email_address@domain.invalid writes:

|How about libtommath/libtomfastmath ? there is a gem of it available:
|
| http://math.libtomcrypt.com/

It’s public domain. We will have no licensing problem. The only
concern is that the last release was April 2006. I hope it does not
have any issues.

          matz.