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2016 Update

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Tina Müller 2016-12-05 22:15:40 +01:00
parent 948b86eafa
commit dcf5d15da3
7965 changed files with 139854 additions and 31002 deletions
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62
Task/Monte-Carlo-methods/REXX/monte-carlo-methods.rexx
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@ -1,32 +1,30 @@
/*REXX program computes pi ÷ 4 using the Monte Carlo algorithm. */
parse arg times chunks . /*does user want a specific number? */
if times=='' then times=1000000000 /*one billion should do it, me thinks. */
if chunks=='' then chunks=10000 /*do Monte Carlo in 10,000 chunks. */
limit=10000-1 /*REXX random generates only integers. */
limitSq=limit**2 /*··· so, instead of one, use limit**2.*/
!=0 /*the number of "pi hits" (so far). */
accur=0 /*accuracy of Monte Carlo pi (so far). */
if 1=='f1'x then piChar='pi' /*if EBCDIC, then use literal. */
else piChar='e3'x /* " ASCII, " " pi glyph, */
pi=3.14159265358979323846264338327950288419716939937511 /*this, da real McCoy*/
numeric digits length(pi) /*this program uses these decimal digs.*/
say 'real pi='pi"+" /*we might as well brag about it. */
say /*a blank line, just for the eyeballs. */
do j=1 for times%chunks
do chunks /*do Monte Carlo, one chunk-at-a-time.*/
if random(0,limit)**2 + random(0,limit)**2 <=limitSq then !=!+1
end /*chunks*/
reps=chunks*j /*compute the number of repetitions. */
piX=4*!/reps /*let's see how this puppy does so far.*/
_=compare(piX,pi) /*compare apples and ··· crabapples. */
if _<=accur then iterate /*if not better accuracy, keep going. */
say right(commas(reps),20) 'repetitions: Monte Carlo' piChar,
"is accurate to" _-1 'places.' /*subtract one for decimal point.*/
accur=_ /*use this accuracy for the 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 _
/*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'
say /* [↑] a two-line scale for showing 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. */
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 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. */
_=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. */
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 _