phoenix-254 / perfect-squares-distributed-systems

A distributed system for finding perfect squares that are sums of consecutive squares

perfect-squares

An interesting problem in arithmetic with deep implications to elliptic curve theory is the problem of finding perfect squares that are sums of consecutive squares. A classic example is the Pythagorean identity:

that reveals that the sum of squares of 3, 4 is itself a square.

A more interesting example is Lucas' Square Pyramid:

In both of these examples, sums of squares of consecutive integers form the square of another integer.

The goal of this project is to use F# and the actor model to build a good solution to this problem that runs well on multi-core machines.

Instruction to run

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1. This project has been developed using Visual Studio Code and ionide extension ref. Also make sure you have dotnet sdk installed.
2. Program.fsx file contains the main logic for the project. To run the program locally use the command:
   dotnet fsi --langversion:preview Program.fsx 40 24
   Here, --langversion:preview is needed when I am writing this, may not be needed in future.
3. To run the program remotely use the command:
   dotnet fsi --langversion:preview Program.fsx 40 24 true
   Here, true is the argument tells the program that it should use remote actors.

Result

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I have achieved parallelism of around 7-8 times by using Akka actor model in this project. Some examples that I tested it on are as follows. [See screenshots]

Example: 1

• Input:
  N = 10^10, K = 2
  
• Output:
  3, 20, 119, 696, 4059, 23660, 137903, 803760, 4684659, 27304196, 159140519, 9113711091, 9174492471, 9201170207, 9203501348, 4228898943, 4294967295, 9361954743, 9417254376, 9482878311, 3427722904, 3463683303, 927538920, 6134308447
  
• Run time:
  real 0m38.907s
  user 4m27.674s
  sys 0m0.514s
  CPU time to Real time ratio : 6.8
  

Example: 2

• Input:
  N = 10^11, K = 2
  
• Output:
  3, 20, 119, 696, 4059, 23660, 137903, 803760, 4684659, 27304196, 159140519, 927538920, 75957200803, 76058624475, 51027785007, 76105188675, 38657389187, 14397045560, 39578320631, 77428752055, 64963961119, 15295287404, 3427722904, 3463683303, 78435184395, 78907549580, 16443921616, 4228898943, 4294967295, 91615519499, 29455579727, 67865704712, 68182518911, 6134308447, 44168195899, 69867701407, 95317973280, 82885205951, 82942587616, 45660904536, 33439886731, 20617974291, 96089133283, 71281441355, 9113711091, 21268305827, 9174492471, 9201170207, 9203501348, 71613130771, 9361954743, 9417254376, 9482878311, 84163829912, 84186789032, 96718872692, 97184579827, 97190222672, 97190607696, 97194169356, 97209046447, 97279817676, 84882215608, 72893482071, 85323105696, 48024363619, 85630496859, 61271285392, 61434523891, 48877375123, 86279592264, 12270139684, 12271335131, 24350538803, 24372902768, 99459260204, 87056560363
  
• Run time:
  real 6m2.195s
  user 47m1.980s
  sys 0m0.697s
  CPU time to Real time ratio : 7.8