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Task/Left-factorials/REXX/left-factorials.rexx

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+/*REXX pgm computes/shows the left factorial (or width) of N (or range).*/
+parse arg bot top inc .                /*obtain optional args from C.L. */
+if bot==''  then bot=1                 /*BOT defined?  Then use default.*/
+td= bot<0                              /*if BOT < 0,   only show # digs.*/
+bot=abs(bot)                           /*use the |bot|  for the DO loop.*/
+if top==''  then top=bot               /* "   "   top    "   "   "   "  */
+if inc=''   then inc=1                 /* "   "   inc    "   "   "   "  */
+@='left ! of '                         /*a literal used in the display. */
+w=length(H)                            /*width of largest number request*/
+           do j=bot  to top  by inc    /*traipse through  #'s requested.*/
+           if td  then say @ right(j,w)  " ───► "  length(L!(j)) ' digits'
+                  else say @ right(j,w)  " ───► "  L!(j)
+           end   /*j*/                  /* [↑]  show either L! or #digits*/
+exit                                   /*stick a fork in it, we're done.*/
+/*──────────────────────────────────L! subroutine───────────────────────*/
+L!: procedure; parse arg x .;  if x<3  then return x;  s=4  /*shortcuts.*/
+!=2;     do f=3  to x-1                /*compute L! for all numbers───►X*/
+         !=!*f                         /*compute intermediate factorial.*/
+         if pos(.,!)\==0 then numeric digits digits()*1.5%1 /*bump digs.*/
+         s=s+!                         /*add the factorial ───► L!  sum.*/
+         end   /*f*/                   /* [↑]  handles gi-hugeic numbers*/
+return s                               /*return the sum (L!) to invoker.*/