# using pseudocode for Babylonian Multiplication Algorithm   
       # possible problem instances, almost square fields
       # babylonian multiplication  rule  a * b = ((a + b)/2)^2 - ((a - b)/2)^2      
      initialize algorithm_result = 1.
      term1 = ((a + b)/2)
      term2 = ((a - b)/2)
      #  babylonian  looks up squares in table
      algorithm_result = tranformed  square (term1 ) -  square (term2 )
      # probably should put algorithm in subroutine or procedure for
      # transfer to other program
      check algorithm 
      check_product = expr a * b 
      set answers and printout with resulting values 
      pseudocode: need test cases > small,medium, giant 
      pseudocode: need testcases within range of expected operation.
      pseudocode: are there any cases too small or large to be solved?

        # pretty print from autoindent and ased editor
        # Babylonian Multiplication Algorithm calculator
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI, 15jan2017
        package require Tk
        package require math::numtheory
        namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
        set tcl_precision 17
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} { long side meters  :} }
        lappend names { short front side meters :}
        lappend names { optional meters : }
        lappend names { answers: ratio long over short : }
        lappend names { squared term1 :}
        lappend names { squared term2 : }
        lappend names { check product (expr a*b) square meters : }
        lappend names { product from algorithm square meters :} 
        foreach i {1 2 3 4 5 6 7 8} {
            label .frame.label$i -text [lindex $names $i] -anchor e
            entry .frame.entry$i -width 35 -textvariable side$i
            grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 }
        proc about {} {
            set msg "Calculator for Babylonian Multiplication Algorithm   
            from TCL WIKI,
            written on eTCL "
            tk_messageBox -title "About" -message $msg } 
       proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 side8 
            global testcase_number 
            incr testcase_number 
            set side1 [* $side1 1. ]
            set side2 [* $side2 1. ]
            set side3 [* $side3 1. ]
            set side4 [* $side4 1. ]
            set side5 [* $side5 1. ]
            set side6 [* $side6 1. ]
            set side7 [* $side7 1. ]
            set side8 [* $side8 1. ] 
            set long_side $side1
            set short_front_side $side2
            set height $side3
            # babylonian multiplication  rule  a * b = ((a + b)/2)^2 - ((a - b)/2)^2
            set term1  [* [+ $long_side $short_front_side ] .5 ]
            set term1  [** $term1 2 ]
            set term2  [* [- $long_side $short_front_side ] .5 ]
            set term2  [** $term2 2 ]
            # babylonian uses table lookup here
            set algorithm_result [- $term1 $term2 ]
            set check_product_tcl [expr { $long_side * $short_front_side }]
            set ratio_long_over_short [/  $long_side $short_front_side ]
            set side4 $ratio_long_over_short
            set side5 $term1
            set side6 $term2
            set side7 $check_product_tcl 
            set side8 $algorithm_result 
                    }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$aa"
            .frame.entry2 insert 0 "$bb"
            .frame.entry3 insert 0 "$cc"
            .frame.entry4 insert 0 "$dd"
            .frame.entry5 insert 0 "$ee"
            .frame.entry6 insert 0 "$ff" 
            .frame.entry7 insert 0 "$gg"
            .frame.entry8 insert 0 "$hh" 
             }
        proc clearx {} {
            foreach i {1 2 3 4 5 6 7 8 } {
                .frame.entry$i delete 0 end } }
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global testcase_number reference_factor flag
            console show;
            puts "%|table $testcase_number|printed in| tcl wiki format|% "
            puts "&| quantity| value| comment, if any|& "
            puts "&| $testcase_number:|testcase_number | |& "
            puts "&| $side1 :|long side meters |   |&"
            puts "&| $side2 :|short front side meters| |& "  
            puts "&| $side3 :|optional meters| |& "
            puts "&| $side4 :|answers: ratio long over short | |&"
            puts "&| $side5 :|squared term1   | |&"
            puts "&| $side6 :|squared term2  |  |&"
            puts "&| $side7 :|check product (expr a*b) square meters |  |&"
            puts "&| $side8 :|product from algorithm square meters |  |&" 
            }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 11.0 10.0  1.0 1.1  110.25  0.25 110. 110.}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 61. 60. 1. 1.01  3660.25  0.25 3660. 3660. }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 3601.0  3600.0  1.0 1.0001  12963600.0  0.25  12963600. 12963600.0 }
        ::ttk::button .clearallx -text clear -command {clearx }
        ::ttk::button .about -text about -command {about}
        ::ttk::button .cons -text report -command { reportx }
        ::ttk::button .exit -text exit -command {exit}
        pack .calculator  -in .buttons -side top -padx 10 -pady 5
        pack  .clearallx .cons .about .exit .test4 .test3 .test2   -side bottom -in .buttons
        grid .frame .buttons -sticky ns -pady {0 10}
               . configure -background aquamarine4 -highlightcolor brown -relief raised -border 30
        wm title . "Babylonian Multiplication Algorithm Calculator"   

  puts " %| testcase $testcase_number | value| units |comment |%"
  puts " &| volume| $volume| cubic meters |based on length $side1 and width $side2   |&"