Monte Carlo methods: Difference between revisions

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m (→‎{{header|REXX}}: used a simplier comma function, added/changed whitespace and comments, expanded range of iterations.)
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=={{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*/
/*true pi*/ pi=3.141592653589793238462643383279502884197169399375105820974944592307816406
pi=3.141592653589793238462643383279502884197169399375105820974944592307816406 /*true pi.*/
say ' 1 2 3 4 5 6 7 '
say 'scale: 1·234567890123456789012345678901234567890123456789012345678901234567890123'
say /* [↑] a two-line scale for showing pi*/
say 'true pi= '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=10000000005000000000 /*onefive 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. */
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).*/
say /*a blank line, just for the eyeballs.*/
do j=1 for times % chunk
do 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 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(commascomma(reps), 20) @reps 'accurate to' _-1 "places." /*-1 for dec. pt.*/
accur=_ /*use this accuracy for next baseline. */
end /*j*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commascomma: procedure; parse arg _; do nk=length(_'.9';) to 1 by -3; #_=123456789insert(',',_,k); end; return b=verify(n,#,"M")_</lang>
e=verify(n, #'0', , verify(n, #"0.", 'M') ) - 4
do j=e to b by -3; _=insert(',',_,j); end /*j*/; return _</lang>
'''output''' &nbsp; when using the default inputs:
<pre>
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