spectral-norm benchmark N=5,500

Each chart bar shows how many times slower, one ↓ spectral-norm program was, compared to the fastest program.

These are not the only programs that could be written. These are not the only compilers and interpreters. These are not the only programming languages.

Column × shows how many times more each program used compared to the benchmark program that used least.

    sort sortsort
  ×   Program Source Code CPU secs Elapsed secs Memory KB Code B ≈ CPU Load
1.0C gcc #5 7.891.98752569  99% 99% 100% 100%
1.0Fortran Intel #3 7.982.001,328638  100% 100% 100% 100%
1.0Fortran Intel 7.912.011,348568  99% 99% 99% 99%
1.0Ada 2005 GNAT #4 7.882.011,9282762  99% 99% 99% 99%
1.3C++ g++ #6 10.092.544961044  99% 99% 100% 100%
1.3C++ g++ #5 10.092.544961044  100% 100% 100% 100%
1.3C gcc #4 10.652.684961139  100% 100% 100% 100%
1.4C++ g++ #8 10.682.684961278  100% 100% 100% 100%
2.0C gcc #3 15.753.95752463  100% 100% 100% 100%
2.0Go #3 15.703.961,816536  99% 99% 99% 99%
2.0Haskell GHC #4 15.704.041,940984  97% 97% 97% 97%
2.1Go #2 15.774.111,296668  96% 96% 96% 96%
2.1Lisp SBCL #2 15.914.1223,184906  96% 97% 97% 97%
2.1Lisp SBCL #3 15.914.1323,184883  97% 97% 96% 97%
2.2Ada 2005 GNAT #3 16.914.341,9241702  99% 99% 99% 94%
2.3Java  #2 17.804.5921,132950  97% 96% 99% 96%
2.3Scala #2 17.814.6325,420720  100% 95% 95% 95%
2.4OCaml #3 16.824.783,512938  93% 91% 92% 90%
2.6Clojure #8 18.305.2564,960918  84% 83% 98% 85%
2.7Racket #3 20.665.4126,372627  95% 95% 98% 95%
2.8Clojure #6 18.765.5364,384808  83% 81% 81% 95%
2.8Clojure #7 18.785.5860,924762  82% 81% 82% 93%
2.8C# Mono #2 21.955.6424,7641063  98% 98% 97% 97%
3.7F# Mono #2 22.317.3730,580852  73% 76% 75% 80%
4.0Fortran Intel #2 7.857.85788513  1% 0% 0% 100%
6.1Erlang HiPE #2 47.4812.0922,836747  99% 98% 98% 98%
7.9Rust #2 15.6915.694,788525  0% 1% 100% 0%
7.9OCaml #2 15.6915.701,804377  42% 0% 0% 58%
7.9Rust 15.6915.704,912492  1% 1% 100% 0%
7.9Go 15.7115.701,296411  1% 1% 0% 99%
7.9Pascal Free Pascal 15.7115.728423  1% 0% 100% 0%
8.6Java  17.1217.0620,908514  99% 1% 1% 1%
8.8Scala 17.5917.5123,204404  1% 0% 1% 100%
9.5Hack #3 73.7618.89188,2281195  98% 97% 98% 98%
10Haskell GHC #2 42.1620.294,724403  100% 37% 37% 35%
10C gcc 20.6920.70468383  1% 0% 1% 100%
10C++ g++ 20.7520.761,072452  1% 0% 100% 1%
11Lisp SBCL 21.2821.2912,752625  0% 1% 100% 0%
11Ada 2005 GNAT 21.7621.771,492710  1% 1% 100% 0%
11C# Mono 21.8621.8720,092459  0% 1% 0% 100%
11Dart 22.0721.9318,056457  1% 1% 1% 100%
19Erlang #2 145.6136.7816,772747  99% 99% 99% 99%
19Racket #2 37.7937.7923,340532  0% 1% 100% 0%
20Racket 40.1640.1619,828446  33% 1% 67% 0%
24Perl #4 183.4747.039,340551  98% 97% 98% 97%
29Erlang HiPE 56.7756.7817,920507  75% 25% 0% 0%
35Hack #2 68.9468.9756,400398  0% 100% 1% 1%
50Ruby #3 6 min98.7042,696828  96% 96% 97% 97%
57PHP #3 7 min113.8524,4081193  98% 97% 100% 98%
101Perl 200.90200.975,516333  0% 0% 0% 100%
106Python 3 #5 13 min209.7643,728437  98% 98% 98% 98%
112Erlang 222.95223.0319,936507  90% 10% 0% 0%
119Perl #3 15 min235.3610,404846  100% 100% 100% 100%
124Ruby JRuby #4 251.58245.32660,988326  29% 35% 17% 24%
126Ruby JRuby #2 16 min250.73668,044776  98% 98% 98% 98%
133Ruby JRuby 270.56263.82656,884292  34% 22% 18% 31%
163Ruby #4 5 min5 min9,452326  1% 100% 0% 0%
196Ruby 6 min6 min8,972292  1% 100% 0% 0%
225PHP #2 7 min7 min7,244397  96% 0% 5% 0%
383Python 3 #6 12 min12 min6,464328  1% 0% 0% 100%
467Python 3 #8 15 min15 min5,600449  0% 1% 100% 0%
471Perl #2 15 min15 min3,972343  85% 15% 0% 0%
Scala #4 Failed1006
Scala #3 Failed982
"wrong" (different) algorithm / less comparable programs
1.0C++ g++ #2 7.921.994961330
1.1C++ g++ #7 8.492.144921283
1.2C gcc #2 2.332.34236,904669
5.6Python 3 #2 11.0111.02489,356233
49Python 3 #3 96.4397.021,197,752379

 spectral-norm benchmark : Eigenvalue using the power method

You can write your own program for this task and contribute to the benchmarks game by following these general instructions.

More specifically:

diff program output N = 100 with this output file to check your program is correct before contributing.

We are trying to show the performance of various programming language implementations - so we ask that contributed programs not only give the correct result, but also use the same algorithm to calculate that result.

Each program should calculate the spectral norm of an infinite matrix A, with entries a11=1, a12=1/2, a21=1/3, a13=1/4, a22=1/5, a31=1/6, etc

Each program must implement 4 separate functions / procedures / methods like the C# program.

For more information see challenge #3 in Eric W. Weisstein, "Hundred-Dollar, Hundred-Digit Challenge Problems" and "Spectral Norm".

From MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/Hundred-DollarHundred-DigitChallengeProblems.html
http://mathworld.wolfram.com/SpectralNorm.html

Thanks to Sebastien Loisel for this benchmark.

Revised BSD license

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