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September 2017 Update

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Ingy döt Net 2017-09-23 10:01:46 +02:00
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Task/Monte-Carlo-methods/REXX/monte-carlo-methods.rexx
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/*REXX program computes and displays the value of pi÷4 using the Monte Carlo algorithm*/
pi=3.141592653589793238462643383279502884197169399375105820974944592307816406 /*true pi.*/
say ' 1 2 3 4 5 6 7 '
say 'scale: 1·234567890123456789012345678901234567890123456789012345678901234567890123'
/*true pi*/ pi=3.141592653589793238462643383279502884197169399375105820974944592307816406
say ' 1 2 3 4 5 6 7 '
say 'scale: 1·234567890123456789012345678901234567890123456789012345678901234567890123'
say /* [↑] a two-line scale for showing pi*/
say 'true pi='pi"+" /*we might as well brag about 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.*/
parse arg times chunk . /*does user want a specific number? */
if times=='' | times=="," then times=1000000000 /*one billion should do it, hopefully. */
if chunk=='' | chunk=="." then chunk= 10000 /*perform Monte Carlo in 10k chunks.*/
limit=10000-1 /*REXX random generates only integers. */
if times=='' | times=="," then times=5e12 /*five trillion should do it, hopefully*/
if chunk=='' | chunk=="." then chunk=100000 /*perform Monte Carlo in 100k chunks.*/
limit=10000 - 1 /*REXX random generates only integers. */
limitSq=limit**2 /*··· so, instead of one, use limit**2.*/
accur=0 /*accuracy of Monte Carlo pi (so far). */
!=0; @reps='repetitions: Monte Carlo pi is' /*pi decimal digit accuracy (so far).*/
accuracy=0 /*accuracy of Monte Carlo pi (so far).*/
!=0; @reps= 'repetitions: Monte Carlo pi is' /*pi decimal digit accuracy (so far).*/
say /*a blank line, just for the eyeballs.*/
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*j /*calculate the number of repetitions. */
do j=1 for times % chunk
do chunk /*do Monte Carlo, one chunk at-a-time.*/
if random(, limit)**2 + random(, limit)**2 <= limitSq then !=! + 1
end /*chunk*/
reps=chunk * j /*calculate the number of repetitions. */
_=compare(4*! / reps, pi) /*compare apples and ··· crabapples. */
if _<=accur then iterate /*if not better accuracy, keep trukin'.*/
say right(commas(reps),20) @reps 'accurate to' _-1 "places." /*-1 for dec. pt.*/
accur=_ /*use this accuracy for next baseline. */
if _<=accuracy then iterate /*Not better accuracy? Keep truckin'. */
say right(comma(reps), 20) @reps 'accurate to' _-1 "places." /*─1 ≡ dec. point*/
accuracy=_ /*use this accuracy for next baseline. */
end /*j*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: procedure; parse arg _; n=_'.9'; #=123456789; b=verify(n,#,"M")
e=verify(n, #'0', , verify(n, #"0.", 'M') ) - 4
do j=e to b by -3; _=insert(',',_,j); end /*j*/; return _
comma: procedure; arg _; do k=length(_)-3 to 1 by -3; _=insert(',',_,k); end; return _