## Bug #13503

### Improve performance of some Time & Rational methods

**Description**

Some Time methods will call internal quov() function.

quov() calls Rational#quo -> f_muldiv() -> i_gcd() in rational.c

i_gcd() will calculate GCD using Euclidean's Algorithm and it lose a long time in modulo method (ie "x = y % x;").

This patch will replace i_gcd() with Stein's algorithm which is faster algorithm for GCD.

(https://en.wikipedia.org/wiki/Binary_GCD_algorithm)

Some Rational methods also call i_gcd().

### Before¶

Calculating ------------------------------------- Time#subsec 2.017M (± 8.6%) i/s - 10.052M in 5.020331s Time#- 4.246M (± 1.1%) i/s - 21.259M in 5.006968s Time#round 402.944k (±11.0%) i/s - 1.996M in 5.014424s Time#to_f 5.627M (± 1.3%) i/s - 28.195M in 5.011366s Time#to_r 1.927M (± 8.2%) i/s - 9.590M in 5.009198s Rational#+ 3.894M (± 1.0%) i/s - 19.545M in 5.019923s Rational#- 3.811M (± 1.0%) i/s - 19.125M in 5.018842s Rational#* 5.148M (± 1.1%) i/s - 25.858M in 5.023586s

### After¶

Calculating ------------------------------------- Time#subsec 2.648M (± 3.0%) i/s - 13.257M in 5.010600s Time#- 4.265M (± 1.4%) i/s - 21.372M in 5.012480s Time#round 393.309k (±12.5%) i/s - 1.934M in 5.000319s Time#to_f 5.638M (± 2.0%) i/s - 28.223M in 5.008422s Time#to_r 2.313M (± 5.2%) i/s - 11.568M in 5.015379s Rational#+ 4.366M (± 1.6%) i/s - 21.846M in 5.004487s Rational#- 4.443M (± 1.2%) i/s - 22.255M in 5.009509s Rational#* 5.776M (± 1.1%) i/s - 28.888M in 5.002322s

### Test code¶

require 'benchmark/ips' Benchmark.ips do |x| x.report "Time#subsec" do |t| time = Time.now t.times { time.subsec } end x.report "Time#-" do |t| time1 = Time.now time2 = Time.now t.times { time1 - time2 } end x.report "Time#round" do |t| time = Time.now t.times { time.round } end x.report "Time#to_f" do |t| time = Time.now t.times { time.to_f } end x.report "Time#to_r" do |t| time = Time.now t.times { time.to_r } end x.report "Rational#+" do |t| rat1 = 1/2r rat2 = 1/3r t.times { rat1 + rat2 } end x.report "Rational#-" do |t| rat1 = 1/3r rat2 = 1/2r t.times { rat1 - rat2 } end x.report "Rational#*" do |t| rat1 = 1/3r rat2 = 1/2r t.times { rat1 * rat2 } end end

**Related issues**

#### Updated by watson1978 (Shizuo Fujita) over 3 years ago

#### Updated by normalperson (Eric Wong) over 3 years ago

watson1978@gmail.com wrote:

Bug #13503: Improve performance of some Time & Rational methods

## https://bugs.ruby-lang.org/issues/13503#change-64447¶

Some Time methods will call internal quov() function.

quov() calls Rational#quo -> f_muldiv() -> i_gcd() in rational.c

i_gcd() will calculate GCD using Euclidean's Algorithm and it lose a long time in modulo method (ie "x = y % x;").This patch will replace i_gcd() with Stein's algorithm which is faster algorithm for GCD.

(https://en.wikipedia.org/wiki/Binary_GCD_algorithm)Some Rational methods also call i_gcd().

(+Cc tadf, I guess he has been inactive, lately)

While looking at git history, I noticed we used to use Stein's

algorithm for i_gcd, but tadf reverted it in Aug 2008:

commit 5185955f3f64d53f55e34bfe4eaf059b7b347fc4 (r18925)

I do not know why tadf did it, but I tried your benchmarks

but got some regressions and smaller improvements:

==> before <==

Calculating -------------------------------------

Time#subsec 2.811M (± 6.0%) i/s - 14.024M in 5.008796s

Time#- 4.886M (± 5.8%) i/s - 24.347M in 5.001174s

Time#round 537.049k (± 9.0%) i/s - 2.663M in 5.000207s

Time#to_f 6.974M (± 3.3%) i/s - 34.896M in 5.009425s

Time#to_r 2.878M (± 4.5%) i/s - 14.361M in 5.000027s

Rational#+ 6.691M (± 0.3%) i/s - 33.471M in 5.002484s

Rational#- 6.125M (± 2.2%) i/s - 30.659M in 5.008375s

Rational#* 6.917M (± 0.7%) i/s - 34.684M in 5.014488s

==> after <==

Calculating -------------------------------------

Time#subsec 3.035M (± 4.1%) i/s - 15.163M in 5.003889s

Time#- 4.973M (± 3.6%) i/s - 24.889M in 5.010858s

Time#round 405.146k (± 9.8%) i/s - 2.007M in 5.002065s

Time#to_f 6.588M (± 3.7%) i/s - 32.927M in 5.004823s

Time#to_r 2.280M (± 4.9%) i/s - 11.410M in 5.016082s

Rational#+ 6.242M (± 3.5%) i/s - 31.210M in 5.006053s

Rational#- 6.644M (± 2.2%) i/s - 33.284M in 5.012740s

Rational#* 7.157M (± 1.0%) i/s - 35.873M in 5.012748s

Maybe CPU and compiler differences can account for this.

What CPU and compiler are you using?

I tested with AMD FX-8320 @ 3.5GHz + gcc (via Debian 4.9.2-10)

Thank you (quoting the rest for tadf's benefit)

## Before¶

Calculating ------------------------------------- Time#subsec 1.977M (± 9.0%) i/s - 9.816M in 5.003551s Time#- 3.844M (± 4.9%) i/s - 19.220M in 5.011682s Time#round 397.118k (±10.5%) i/s - 1.976M in 5.032733s Time#to_f 5.566M (± 1.9%) i/s - 27.876M in 5.010230s Time#to_r 1.874M (± 8.7%) i/s - 9.339M in 5.018589s Rational#+ 3.889M (± 0.8%) i/s - 19.521M in 5.019869s Rational#- 3.684M (± 0.9%) i/s - 18.517M in 5.026471s Rational#* 3.681M (± 0.9%) i/s - 18.501M in 5.025969s## After¶

Calculating ------------------------------------- Time#subsec 2.640M (± 3.0%) i/s - 13.204M in 5.005680s Time#- 4.241M (± 2.1%) i/s - 21.225M in 5.006865s Time#round 404.738k (±10.9%) i/s - 2.003M in 5.009187s Time#to_f 5.659M (± 2.1%) i/s - 28.297M in 5.002788s Time#to_r 2.263M (± 7.0%) i/s - 11.307M in 5.024765s Rational#+ 4.386M (± 0.6%) i/s - 22.029M in 5.023014s Rational#- 4.391M (± 0.7%) i/s - 22.037M in 5.018534s Rational#* 4.355M (± 1.7%) i/s - 21.820M in 5.011914s## Test code¶

require 'benchmark/ips' Benchmark.ips do |x| x.report "Time#subsec" do |t| time = Time.now t.times { time.subsec } end x.report "Time#-" do |t| time1 = Time.now time2 = Time.now t.times { time1 - time2 } end x.report "Time#round" do |t| time = Time.now t.times { time.round } end x.report "Time#to_f" do |t| time = Time.now t.times { time.to_f } end x.report "Time#to_r" do |t| time = Time.now t.times { time.to_r } end x.report "Rational#+" do |t| rat1 = 1/2r rat2 = 1/3r t.times { rat1 + rat2 } end x.report "Rational#-" do |t| rat1 = 1/3r rat2 = 1/2r t.times { rat1 + rat2 } end x.report "Rational#*" do |t| rat1 = 1/3r rat2 = 1/2r t.times { rat1 + rat2 } end end

#### Updated by normalperson (Eric Wong) over 3 years ago

Eric Wong normalperson@yhbt.net wrote:

(+Cc tadf, I guess he has been inactive, lately)

tadf@dotrb.org (expanded from tadf@ruby-lang.org): host

dotrb.org[219.94.129.152] said: 553 5.3.0 tadf@dotrb.org... User unknown,

not local address (in reply to RCPT TO command)

Hmm... :<

#### Updated by normalperson (Eric Wong) over 3 years ago

Eric Wong normalperson@yhbt.net wrote:

Maybe CPU and compiler differences can account for this.

What CPU and compiler are you using?

I tested with AMD FX-8320 @ 3.5GHz + gcc (via Debian 4.9.2-10)

Here is my Pentium M laptop @ 1.60GHz (same gcc):

==> before <==

Calculating -------------------------------------

Time#subsec 877.041k (± 4.8%) i/s - 4.376M in 5.003931s

Time#- 641.496k (± 0.8%) i/s - 3.211M in 5.006323s

Time#round 92.460k (± 6.2%) i/s - 461.538k in 5.010971s

Time#to_f 667.671k (± 0.7%) i/s - 3.352M in 5.021237s

Time#to_r 363.584k (± 1.8%) i/s - 1.827M in 5.026851s

Rational#+ 1.905M (± 0.4%) i/s - 9.549M in 5.012380s

Rational#- 1.969M (± 0.6%) i/s - 9.866M in 5.009592s

Rational#* 2.297M (± 0.5%) i/s - 11.499M in 5.007220s

==> after <==

Calculating -------------------------------------

Time#subsec 851.197k (± 3.3%) i/s - 4.266M in 5.017699s

Time#- 620.533k (± 0.6%) i/s - 3.113M in 5.016971s

Time#round 87.844k (± 7.1%) i/s - 438.845k in 5.021267s

Time#to_f 646.047k (± 0.5%) i/s - 3.233M in 5.004371s

Time#to_r 346.689k (± 1.5%) i/s - 1.738M in 5.014382s

Rational#+ 1.922M (± 1.0%) i/s - 9.629M in 5.009889s

Rational#- 2.026M (± 0.4%) i/s - 10.130M in 4.999171s

Rational#* 2.320M (± 0.5%) i/s - 11.618M in 5.007548s

#### Updated by watson1978 (Shizuo Fujita) over 3 years ago

normalperson (Eric Wong) wrote:

Maybe CPU and compiler differences can account for this.

What CPU and compiler are you using?

I tested with AMD FX-8320 @ 3.5GHz + gcc (via Debian 4.9.2-10)

I have used MacBook Pro (Retina, 15-inch, Late 2013) and my enviroment is

- OS : macOS 10.12.4
- CPU : Intel Core i7 2.6 GHz
- Compiler : clang-802.0.42 in Xcode 8.3.2

In additional, I turned off turbo boost feater in Intel CPU when measured the benchmark using https://github.com/rugarciap/Turbo-Boost-Switcher

Thank you.

#### Updated by watson1978 (Shizuo Fujita) over 3 years ago

**Status**changed from*Open*to*Closed*

Applied in changeset trunk|r58922.

Improve performance of some Time & Rational methods

rational.c (i_gcd): replace GCD algorithm from Euclidean algorithm to Stein

algorithm (https://en.wikipedia.org/wiki/Binary_GCD_algorithm).

Some Time methods will call internal quov() function and it calls Rational#quo -> f_muldiv() -> i_gcd() in rational.c And some Rational methods also call i_gcd(). The implementation of Euclidean algorithm spent a long time at modulo operation (ie "x = y % x;"). The Stein algorithm will replace with shift operation which is faster than modulo. Time#subsec -> 36 % up Time#to_r -> 26 % up Rational#+ -> 14 % up Rational#- -> 15 % up Rational#* -> 13 % up [ruby-core:80843] [Bug #13503] [Fix GH-1596]

### Before¶

Time#subsec 2.142M (± 9.8%) i/s - 10.659M in 5.022659s Time#to_r 2.003M (± 9.1%) i/s - 9.959M in 5.012445s Rational#+ 3.843M (± 0.9%) i/s - 19.274M in 5.016254s Rational#- 3.820M (± 1.3%) i/s - 19.149M in 5.014137s Rational#* 5.198M (± 1.4%) i/s - 26.016M in 5.005664s

After

Time#subsec 2.902M (± 2.9%) i/s - 14.505M in 5.001815s

Time#to_r 2.503M (± 4.8%) i/s - 12.512M in 5.011454s

Rational#+ 4.390M (± 1.2%) i/s - 22.001M in 5.012413s

Rational#- 4.391M (± 1.2%) i/s - 22.013M in 5.014584s

Rational#* 5.872M (± 2.2%) i/s - 29.369M in 5.003666sTest code

require 'benchmark/ips'

Benchmark.ips do |x|

x.report "Time#subsec" do |t|

time = Time.now

t.times { time.subsec }

end

x.report "Time#to_r" do |t|

time = Time.now

t.times { time.to_r }

end

x.report "Rational#+" do |t|

rat1 = 1/2r

rat2 = 1/3r

t.times { rat1 + rat2 }

end

x.report "Rational#-" do |t|

rat1 = 1/3r

rat2 = 1/2r

t.times { rat1 - rat2 }

end

x.report "Rational#*" do |t|

rat1 = 1/3r

rat2 = 1/2r

t.times { rat1 * rat2 }

end

end

#### Updated by mame (Yusuke Endoh) about 2 years ago

**Has duplicate***Feature #15161: making gcd faster for 3x3*added