Monte Carlo methods: Difference between revisions

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A specific-purpose commatizer function is included to format the number of iterations.
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*/
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numeric digits 20 /*use 20 decimal digits to handle args.*/
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/*true pi*/ pi=3.141592653589793238462643383279502884197169399375105820974944592307816406
parse arg times chunk digs r? . /*does user want a specific number? */
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if times=='' | times=="," then times= 5e12 /*five trillion should do it, hopefully*/
if chunk=='' | chunk=="," then chunk= 100000 /*perform Monte Carlo in 100k chunks.*/
if digs =='' | digs=="," then digs= 99 /*indicates to use length of PI - 1. */
if datatype(r?, 'W') then call random ,,r? /*Is there a random seed? Then use it.*/
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/* [↓] pi meant to line─up with a SAY.*/
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pi= 3.141592653589793238462643383279502884197169399375105820974944592307816406
pi= strip( left(pi, digs + length(.) ) ) /*obtain length of pi to what's wanted.*/
numeric digits length(pi) - 1 /*define decimal digits as length PI -1*/
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= ' 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.*/
say /*display a blank line for separation. */
parse arg times chunk . /*does user want a specific number? */
limit = 10000 - 1 /*REXX random generates only integers. */
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limitSq = limit **2 /*··· so, instead of one, use limit**2.*/
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if times=='' | times=="," then times=5e12 /*five trillion should do it, hopefully*/
if chunk=='' | chunk=="." then chunk=100000 /*perform Monte Carlo in 100k chunks.*/
accuracy= 0 /*accuracy of Monte Carlo pi (so far).*/
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@reps= 'repetitions: Monte Carlo pi is' /*a handy─dandy short literal for a SAY*/
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limit=10000 - 1 /*REXX random generates only integers. */
limitSq=limit**2 /*··· so, instead of one, use limit**2.*/
!= 0 /*!: is the accuracy of pi (so far). */
do j=1 for times % chunk
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accuracy=0 /*accuracy of Monte Carlo pi (so far).*/
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do chunk /*do Monte Carlo, one chunk at─a─time. */
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!=0; @reps= 'repetitions: Monte Carlo pi is' /*pi decimal digit accuracy (so far).*/
say /*a blank line, just for the eyeballs.*/
if random(, limit)**2 + random(, limit)**2 <= limitSq then != ! + 1
do j=1 for times % chunk
end /*chunk*/
do chunk /*do Monte Carlo, one chunk at-a-time.*/
reps= chunk * j /*calculate the number of repetitions. */
if random(, limit)**2 + random(, limit)**2 <= limitSq then !=! + 1
_= compare(4*! / reps, pi) /*compare apples and ··· crabapples. */
end /*chunk*/
if _<=accuracy then iterate /*Not better accuracy? Keep truckin'. */
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say right(commas(reps), 20) @reps 'accurate to' _-1 "places." /*─1≡dec. point*/
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reps=chunk * j /*calculate the number of repetitions. */
_=compare(4*! / reps, pi) /*compare apples and ··· crabapples. */
accuracy= _ /*use this accuracy for next baseline. */
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end /*j*/
if _<=accuracy then iterate /*Not better accuracy? Keep truckin'. */
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exit 0 /*stick a fork in it, we're all done. */
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say right(comma(reps), 20) @reps 'accurate to' _-1 "places." /*─1 ≡ dec. point*/
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accuracy=_ /*use this accuracy for next baseline. */
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end /*j*/
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exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
comma: procedure; arg _; do k=length(_)-3 to 1 by -3; _=insert(',',_,k); end; return _</lang>
commas: procedure; arg _; do k=length(_)-3 to 1 by -3; _=insert(',',_,k); end; return _</lang>
{{out|output|text=&nbsp; when using the default input:}}
{{out|output|text=&nbsp; when using the default input:}}
<pre>
<pre>
Retrieved from "https://rosettacode.org/wiki/Monte_Carlo_methods"