I'm replying to my own post.. ;^)
On Nov 30, 2007, at 3:05 AM, Alan K. Stebbens wrote:
There is an interesting benchmarks "contest" at
http://shootout.alioth.debian.org/
...
I've included my tentative submission below.
Before submitting this script to the contest, I would like to get
it reviewed and possibly improved (it seems to already outperform
all the other systems in the benchmark -- but I've not done a
thorough evaluation either).
I've significantly modified the script to include caching of
recurring expressions across different sums. These optimizations
seems to roughly double the performance. Here are the timings:
time '1 sumfor 25000'
...
0.294027
time '0 sumfor 25000'
...
0.457404
Here's the newest script, which I will post in the next few days
unless there are other improvements suggested from this list.
NB. partial-sums
NB.
NB. The Computer Language Benchmarks Game
NB. http://shootout.alioth.debian.org/
NB.
NB. contributed by Alan K. Stebbens <[EMAIL PROTECTED]>
NB. modified by
NB.
NB.
NB. This script implements the partial-sums benchmark,
NB. as defined at:
NB. http://shootout.alioth.debian.org/gp4/benchmark.php?
test=partialsums&lang=all
NB.
NB.
NB. The "correct" output file for this benchmark test is defined
NB. at http://shootout.alioth.debian.org/gp4/iofile.php?
test=partialsums&lang=all&file=output
NB.
NB. I've included the correct output here, for easy reference:
NB.
NB. 3.000000000 (2/3)^k
NB. 314.770573775 k^-0.5
NB. 0.999960002 1/k(k+1)
NB. 30.314520404 Flint Hills 1/( k^3 * sin(k)^2 )
NB. 42.994899946 Cookson Hills 1/( k^3 * cos(k)^2 )
NB. 10.703866769 Harmonic 1/k
NB. 1.644894068 Riemann Zeta 1/(k^2)
NB. 0.693127181 Alternating Harmonic -1^(k+1) / k
NB. 0.785388163 Gregory -1^(k+1) / ( 2k - 1 )
NB. require 'conlib'
echo=: 0 0&$ @ (1!:2&2)
time =: 6!:2
n =: 25000
fmt =: 0j9&": NB. 9 digits precision sum
sin =: 1&o.
cos =: 2&o.
NB. makesums cacheflag -- flag for caching
makesums=: 3 : 0
k =: i.n
sum1 =: +/(2%3)^k NB. (2/3)^k
if. y do. NB. argument == caching flag
k1 =. >:k NB. k+1
k1sq =. *:k1 NB. k^2
k1cube =. k1^3 NB. k^3
m1pow =. _1^>:k1 NB. -1^(k+1)
sum2 =: +/k1^_0.5 NB. k^(-0.5)
sum3 =: +/%k1sq + k1 NB. 1/(k * (k + 1))
sum4 =: +/%k1cube * (sin k1)^2 NB. 1/((k^3)*(sin(k)^2))
sum5 =: +/%k1cube * (cos k1)^2 NB. 1/((k^3)*(cos(k)^2))
sum6 =: +/%k1 NB. 1/k
sum7 =: +/%k1sq NB. 1/(k^2)
sum8 =: +/m1pow%k1 NB. -1^(k+1) / k
sum9 =: +/m1pow%<:+:k1 NB. -1^(k+1) / (2k - 1)
else.
sum2 =: +/_0.5^~>:k NB. k^(-0.5)
sum3 =: +/%([ * >:)>:k NB. 1/(k * (k + 1))
sum4 =: +/%((]^&3)*(*:@sin))>:k NB. 1/((k^3)*(sin(k)^2))
sum5 =: +/%((]^&3)*(*:@cos))>:k NB. 1/((k^3)*(cos(k)^2))
sum6 =: +/%>:k NB. 1/k
sum7 =: +/%*:>:k NB. 1/(k^2)
sum8 =: +/((_1&^@>:)%])>:k NB. -1^(k+1) / k
sum9 =: +/((_1&^@>:)%(<:@+:))>:k NB. -1^(k+1) / (2k - 1)
end.
)
NB. cacheflag sumfor range
sumfor =: 3 : 0
1 sumfor y
:
if. y-:'' do. n=.25000
else. n=.y end.
makesums x
echo (fmt sum1),' (2/3)^k'
echo (fmt sum2),' k^-0.5'
echo (fmt sum3),' 1/k(k+1)'
echo (fmt sum4),' Flint Hills'
echo (fmt sum5),' Cookson Hills'
echo (fmt sum6),' Harmonic'
echo (fmt sum7),' Riemann Zeta'
echo (fmt sum8),' Alternating Harmonic'
echo (fmt sum9),' Gregory'
)
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