Dartboard PI - Revision history

Polas: 8 revisions imported

2019-04-15T15:44:44Z

8 revisions imported

Polas: /* Source Code */

2013-02-01T13:12:17Z

‎Source Code

Polas at 18:31, 18 January 2013

2013-01-18T18:31:57Z

Polas: /* Download */

2013-01-18T18:26:24Z

‎Download

Polas: /* Source Code */

2013-01-18T18:25:30Z

‎Source Code

Polas at 14:21, 14 January 2013

2013-01-14T14:21:34Z

Polas at 11:37, 3 July 2010

2010-07-03T11:37:05Z

Polas: /* Download */

2010-01-11T17:25:52Z

‎Download

Polas: Created page with '== Overview == Dartboard method to find PI The dartboard method to find PI is a simple algorithm to find the value of PI. At this point…'

2010-01-10T23:06:06Z

Created page with '== Overview == thumb|260px|right|Dartboard method to find PI The dartboard method to find PI is a simple algorithm to find the value of PI. At this point…'

New page

== Overview ==

[[Image:dartboard.jpg|thumb|260px|right|Dartboard method to find PI]]
The dartboard method to find PI is a simple algorithm to find the value of PI. At this point it must be noted that there are much better methods out there to find PI, however the dartboard method is embarasingly parallel and as such quite simple to parallelise. The basic premise is that you can throw n darts randomly at a round dartboard on a square backing. As each dart is thrown randomly the ratio of darts hitting the board to those landing on the square is equal to the ratio between the two areas - which is PI / 4. Of course, the more darts you simulate throwing at the board, the better the approximation of PI - in our example each process will perform this simulated throwing a number of times, and then each process's approximation of PI is combined and averaged by one of the processes to obtain the result. Very ruffly, this means that with d darts, thrown over r rounds on n processes, the time taken parallely is the time it takes to simulate throwing d * r darts, yet a sequential algorithm would need to simulate throwing d * r * n darts. (We have excluded the consideration of communication costs from the parallel situation to simplify the concept.) Hopefully quite obviously, in the example by changing the number of processes, the number of rounds and the number of darts to throw in each round will directly change the accuracy of the result.

== Source Code ==

var m:=10; // number of processes
var pi:array[Double,m,1]:: allocated[row[] :: horizontal[m] :: single[evendist[]]];
var result:array[Double,m] :: allocated[single[on[0]]];
var mypi:Double;
mypi:=0;
var p;
par p from 0 to m - 1
{
var darts:=1000; // number of darts to simulate throwing each round
var rounds:=100; // number of rounds of darts to throw
var i:=0;
for i from 0 to rounds
{
mypi:= mypi + (4 * (throwdarts[darts] % darts));
};
((pi#p)#0):=(mypi % rounds);
};
result:=pi;
proc 0
{
var avepi:Double;
avepi:=0;
var j:=0;
for j from 0 to m - 1
{
var y:=(result#j);
avepi:=avepi + y;
};
avepi:=avepi % m;
print["PI = ",avepi,"\n"];
};

function Int throwdarts[var darts]
{
darts: Int :: allocated[multiple[]];
var score:=0;
var n:=0;
for n from 0 to darts
{
var r:=randomnumber[0,1]; // random number between 0 and 1
var xcoord:=(2 * r) - 1;
r:=randomnumber[0,1]; // random number between 0 and 1
var ycoord:=(2 * r) - 1;
if ((sqr[xcoord] + sqr[ycoord]) < 1)
{
score:=score + 1; // hit the dartboard!
};
};
return score;
};

== Notes ==

An interesting aside is that we have used a function in this example, yet there is no main function. The throwdarts function will simulate throwing the darts for each round. As already noted in the language documentation, the main function is optional and without it the compiler will set the program entry point to be the start of the source code.
== Download ==

@@ Line 39: / Line 39: @@
   };
-  function Int throwdarts(var darts:Int)
+  function Double throwdarts(var darts:Int)
+  {
-     var score:=0;
+     var score:Double;
      var n:=0;
      for n from 0 to darts - 1 {

← Older revision		Revision as of 18:31, 18 January 2013
Line 55:		Line 55:
	''This code requires at least Mesham version 1.0''		''This code requires at least Mesham version 1.0''

−	~~== Notes ==~~
−
−	An interesting aside is that we have used a function in this example, yet there is no main function. The throwdarts function will simulate throwing the darts for each round. As already noted in the language documentation, the main function is optional and without it the compiler will set the program entry point to be the start of the source code.
	== Download ==		== Download ==

@@ Line 60: / Line 60: @@
 == Download ==
-The dartboard method to compute PI source code is located [http://www.mesham.com/downloads/pi.mesh here]
+The dartboard method to compute PI source code is located [http://www.mesham.com/downloads/pi.mesh here] a legacy version for Mesham 0.5 can be downloaded [http://www.mesham.com/downloads/pi-0.5.mesh here]
 [[Category:Example Codes]]

← Older revision		Revision as of 14:21, 14 January 2013
Line 64:		Line 64:

	The dartboard method to compute PI source code is located [http://www.mesham.com/downloads/pi.mesh here]		The dartboard method to compute PI source code is located [http://www.mesham.com/downloads/pi.mesh here]
		+
		+	[[Category:Example Codes]]

← Older revision		Revision as of 11:37, 3 July 2010
Line 1:		Line 1:
		+	<metadesc>Mesham is a type oriented programming language allowing the writing of high performance parallel codes which are efficient yet simple to write and maintain</metadesc>
	== Overview ==		== Overview ==

← Older revision	Revision as of 15:44, 15 April 2019
(No difference)

@@ Line 7: / Line 7: @@
 == Source Code ==
-  var m:=10; // number of processes
+ #include <maths>
-  var pi:array[Double,m,1]:: allocated[row[] :: horizontal[m] :: single[evendist[]]];
+ #include <io>
-  var result:array[Double,m] :: allocated[single[on[0]]];
+ #include <string>
- var mypi:Double;
- mypi:=0;
+  var m:=64; // number of processes
- var p;
- par p from 0 to m - 1
+  function void main() {
+    var calculatedPi:array[Double,m]:: allocated[single[on[0]]];
-   var darts:=1000; // number of darts to simulate throwing each round
+    var mypi:Double;
-   var rounds:=100; // number of rounds of darts to throw
+    var p;
-   var i:=0;
+    par p from 0 to m - 1 {
-   for i from 0 to rounds
+       var darts:=10000; // number of darts to simulate throwing each round
+       var rounds:=100; // number of rounds of darts to throw
-      mypi:= mypi + (4 * (throwdarts[darts] % darts));
+       var i;
-   };
+       for i from 0 to rounds - 1 {
-   ((pi#p)#0):=(mypi % rounds);
+          mypi:=mypi + (4.0 * (throwdarts(darts) / darts));
   };
-  result:=pi;
-  proc 0
+  function Int throwdarts(var darts:Int)
+  {
-   var avepi:Double;
+    var score:=0;
-   avepi:=0;
+    var n:=0;
-   var j:=0;
+    for n from 0 to darts - 1 {
-   for j from 0 to m - 1
+       var xcoord:=randomnumber(0,1);
+       var ycoord:=randomnumber(0,1);
-      var y:=(result#j);
+       if ((pow(xcoord,2) + pow(ycoord,2)) < 1.0) {
-      avepi:=avepi + y;
+          score++; // hit the dartboard!
-   };
+       };
-   avepi:=avepi % m;
+    };
-   print["PI = ",avepi,"\n"];
+    return score;
   };
-−
- function Int throwdarts[var darts]
+''This code requires at least Mesham version 1.0''
 == Notes ==

← Older revision		Revision as of 17:25, 11 January 2010
Line 61:		Line 61:
	An interesting aside is that we have used a function in this example, yet there is no main function. The throwdarts function will simulate throwing the darts for each round. As already noted in the language documentation, the main function is optional and without it the compiler will set the program entry point to be the start of the source code.		An interesting aside is that we have used a function in this example, yet there is no main function. The throwdarts function will simulate throwing the darts for each round. As already noted in the language documentation, the main function is optional and without it the compiler will set the program entry point to be the start of the source code.
	== Download ==		== Download ==
		+
		+	The dartboard method to compute PI source code is located [http://www.mesham.com/downloads/pi.mesh here]