Sync

Task/Average-loop-length/Go/average-loop-length.go

@@ -0,0 +1,44 @@
+package main
+
+import (
+    "fmt"
+    "math"
+    "math/rand"
+)
+
+const nmax = 20
+
+func main() {
+    fmt.Println(" N    average    analytical    (error)")
+    fmt.Println("===  =========  ============  =========")
+    for n := 1; n <= nmax; n++ {
+        a := avg(n)
+        b := ana(n)
+        fmt.Printf("%3d  %9.4f  %12.4f  (%6.2f%%)\n",
+            n, a, b, math.Abs(a-b)/b*100)
+    }
+}
+
+func avg(n int) float64 {
+    const tests = 1e4
+    sum := 0
+    for t := 0; t < tests; t++ {
+        var v [nmax]bool
+        for x := 0; !v[x]; x = rand.Intn(n) {
+            v[x] = true
+            sum++
+        }
+    }
+    return float64(sum) / tests
+}
+
+func ana(n int) float64 {
+    nn := float64(n)
+    term := 1.
+    sum := 1.
+    for i := nn - 1; i >= 1; i-- {
+        term *= i / nn
+        sum += term
+    }
+    return sum
+}

Task/Average-loop-length/REXX/average-loop-length.rexx

@@ -1,36 +1,38 @@
-/*REXX program to read a config file and assign VARs as found within.   */
-numeric digits 10000                   /*be able to calculate  !(runs). */
+/*REXX pgmm computes avg loop length mapping a random field 1..N to 1..N*/
 parse arg runs tests seed .
 if  runs ==','  |   runs ==''  then runs  =      40     /*num of runs.  */
 if tests ==','  |  tests ==''  then tests = 1000000     /*num of trials.*/
 if  seed\==','  &   seed\==''  then call random ,,seed  /*repeatability?*/
+numeric digits 100000;  !.=0;  !.0=1   /*be able to calculate  !(25000).*/
 numeric digits max(9,length(!(runs)))  /*set NUMERIC digits for !(runs).*/
 say right(     runs, 24)  'runs'       /*display # of runs   we're using*/
 say right(    tests, 24)  'tests'      /*   "    "  " tests    "     "  */
 say right( digits(), 24)  'digits'     /*   "    "  " digits   "     "  */
 say
 say '        N    average     exact     % error'        /*headers & pad.*/
-h=  '       ───  ─────────  ─────────  ─────────'; say h;   pad=left('',3)
+h=  '       ───  ─────────  ─────────  ─────────';  say h;  pad=left('',3)
 
       do #=1  for runs;  ##=right(#,9) /*## is used for indenting output*/
-        a= format(exact(#)       ,,4)  /*use 4 digits past decimal point*/
-        e= format(exper(#)       ,,4)  /* "  "    "     "     "      "  */
-      err= format(abs(e-a)*100/a ,,4)  /* "  "    "     "     "      "  */
-      if err=0  then err=err/1         /*present a clean & concise zero.*/
-      say ##  pad  e  pad  a  pad  err /*display a line of statistics.  */
+      avg = fmtD(exact(#))             /*use 4 digits past decimal point*/
+      exa = fmtD(exper(#))             /* "  "    "     "     "      "  */
+      err = fmtD(abs(exa-avg)*100/avg) /* "  "    "     "     "      "  */
+      say ## pad exa pad avg pad err   /*display a line of statistics.  */
       end   /*#*/
 say h                                  /*display the final header bar.  */
 exit                                   /*stick a fork in it, we're done.*/
 /*──────────────────────────────────! subroutine────────────────────────*/
-!: procedure; !=1;      do j=2  to arg(1);   !=!*j;   end;        return !
+!: procedure expose !.;  parse arg z;          if !.z\==0  then return !.z
+!=1;   do j=1  for z;    !=!*j; !.j=!;    end;                  return !
 /*──────────────────────────────────EXACT subroutine────────────────────*/
 exact: parse arg x; s=0; do j=1 for x; s=s+!(x)/!(x-j)/x**j; end; return s
 /*──────────────────────────────────EXPER subroutine────────────────────*/
 exper: parse arg n
-k=0;                do tests;  !.=0    /*repeat TESTS times, reset found*/
-                    !.=0               /*stemmed array: expected results*/
-                        do n;     r=random(1,n);        if !.r  then leave
-                        !.r=1;    k=k+1                 /*bump the ctr. */
+k=0;                do tests;  $.=0    /*repeat TESTS times, reset FOUND*/
+                        do n;     r=random(1,n);        if $.r  then leave
+                        $.r=1;    k=k+1                 /*bump the ctr. */
                         end   /*n*/
                     end       /*tests*/
 return k/tests
+/*──────────────────────────────────FMTD subroutine─────────────────────*/
+fmtD: parse arg y,d;  d=word(d 4,1);   y=format(y,,d); parse var y w '.' f
+if f=0  then return w || left('',d+1); return y