Monte Carlo methods: Difference between revisions
Content added Content deleted
(Added Dart) |
m (→{{header|REXX}}: used a simplier comma function, added/changed whitespace and comments, expanded range of iterations.) |
||
| Line 1,887: | Line 1,887: | ||
=={{header|REXX}}== |
=={{header|REXX}}== |
||
A specific-purpose commatizer function is included to format the number of iterations. |
|||
<lang rexx>/*REXX program computes and displays the value of pi÷4 using the Monte Carlo algorithm*/ |
<lang rexx>/*REXX program computes and displays the value of pi÷4 using the Monte Carlo algorithm*/ |
||
/*true pi*/ pi=3.141592653589793238462643383279502884197169399375105820974944592307816406 |
|||
pi=3.141592653589793238462643383279502884197169399375105820974944592307816406 /*true pi.*/ |
|||
say ' 1 2 3 4 5 6 7 ' |
say ' 1 2 3 4 5 6 7 ' |
||
say 'scale: 1·234567890123456789012345678901234567890123456789012345678901234567890123' |
say 'scale: 1·234567890123456789012345678901234567890123456789012345678901234567890123' |
||
say /* [↑] a two-line scale for showing pi*/ |
say /* [↑] a two-line scale for showing pi*/ |
||
say 'true pi=' |
say 'true pi= ' pi"+" /*we might as well brag about true pi.*/ |
||
numeric digits length(pi) - 1 /*this program uses these decimal digs.*/ |
numeric digits length(pi) - 1 /*this program uses these decimal digs.*/ |
||
parse arg times chunk . /*does user want a specific number? */ |
parse arg times chunk . /*does user want a specific number? */ |
||
if times=='' | times=="," then times= |
if times=='' | times=="," then times=5000000000 /*five billion should do it, hopefully.*/ |
||
if chunk=='' | chunk=="." then chunk= 10000 /*perform Monte Carlo in 10k chunks.*/ |
if chunk=='' | chunk=="." then chunk= 10000 /*perform Monte Carlo in 10k chunks.*/ |
||
limit=10000-1 /*REXX random generates only integers. */ |
limit=10000-1 /*REXX random generates only integers. */ |
||
limitSq=limit**2 /*··· so, instead of one, use limit**2.*/ |
limitSq=limit**2 /*··· so, instead of one, use limit**2.*/ |
||
accur=0 /*accuracy of Monte Carlo pi (so far). */ |
accur=0 /*accuracy of Monte Carlo pi (so far). */ |
||
!=0; @reps='repetitions: Monte Carlo pi is' |
!=0; @reps= 'repetitions: Monte Carlo pi is' /*pi decimal digit accuracy (so far).*/ |
||
say /*a blank line, just for the eyeballs.*/ |
say /*a blank line, just for the eyeballs.*/ |
||
do j=1 for times%chunk |
do j=1 for times % chunk |
||
do chunk /*do Monte Carlo, one chunk at-a-time.*/ |
|||
if random(0, limit)**2 + random(0, limit)**2 <= limitSq then !=!+1 |
|||
end /*chunk*/ |
|||
reps=chunk* |
reps=chunk * j /*calculate the number of repetitions. */ |
||
_=compare(4*! / reps, pi) /*compare apples and ··· crabapples. */ |
_=compare(4*! / reps, pi) /*compare apples and ··· crabapples. */ |
||
if _<=accur then iterate /*if not better accuracy, keep trukin'.*/ |
if _<=accur then iterate /*if not better accuracy, keep trukin'.*/ |
||
say right( |
say right(comma(reps), 20) @reps 'accurate to' _-1 "places." /*-1 for dec. pt.*/ |
||
accur=_ /*use this accuracy for next baseline. */ |
accur=_ /*use this accuracy for next baseline. */ |
||
end /*j*/ |
end /*j*/ |
||
exit /*stick a fork in it, we're all done. */ |
exit /*stick a fork in it, we're all done. */ |
||
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
||
comma: procedure; arg _; do k=length(_) to 1 by -3; _=insert(',',_,k); end; return _</lang> |
|||
e=verify(n, #'0', , verify(n, #"0.", 'M') ) - 4 |
|||
do j=e to b by -3; _=insert(',',_,j); end /*j*/; return _</lang> |
|||
'''output''' when using the default inputs: |
'''output''' when using the default inputs: |
||
<pre> |
<pre> |
||