Data commit

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*/
+numeric digits 20                                /*use 20 decimal digits to handle args.*/
+parse arg times chunk digs r? .                  /*does user want a specific number?    */
+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.*/
+                                                 /* [↓]  pi meant to line─up with a SAY.*/
+           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 'scale:    1·234567890123456789012345678901234567890123456789012345678901234567890123'
+say                                              /* [↑]  a two─line scale for showing pi*/
+say 'true pi= '       pi"+"                      /*we might as well brag about true  pi.*/
+say                                              /*display a blank line for separation. */
+limit   = 10000 - 1                              /*REXX random generates only integers. */
+limitSq = limit **2                              /*··· so, instead of one, use limit**2.*/
+accuracy= 0                                      /*accuracy of Monte Carlo pi  (so far).*/
+@reps= 'repetitions:  Monte Carlo  pi  is'       /*a handy─dandy short literal for a SAY*/
+!= 0                                             /*!:  is the accuracy of pi  (so far). */
+       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 _<=accuracy  then iterate              /*Not better accuracy?  Keep truckin'. */
+       say right(commas(reps), 20) @reps  'accurate to'  _-1  "places."  /*─1≡dec. point*/
+       accuracy= _                               /*use this accuracy for next baseline. */
+       end   /*j*/
+exit 0                                           /*stick a fork in it,  we're all done. */
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+commas: procedure; arg _; do k=length(_)-3  to 1  by -3; _=insert(',',_,k); end;  return _