# using  pseudocode for  procedure algorithm.
            3 quantities needed
            target number
            trial_square_root,   w.a. guess
            formula factor , usually 2 or 3
            check approx. root from square side rule with sqrt function in TCL
     ref. errorx procedure        
     check_answer   new area =? desired goal , desired goal reached (yes/no)
     set answers and printout with resulting values

        # pretty print from autoindent and ased editor
        # Indian Bakhshali Square Root calculator
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI, 2oct2017
        # comment follows from gold, 12Dec2018
        # pretty print from autoindent and ased editor
        # Indian Bakhshali Square Root Calculator V2
        # written on Windows XP on TCL
        # working under TCL version 8.6
        # Revamping older program from 2017.
        # Indian Bakhshali Square Root is of
        # historical interest, but not particularly
        # accurate.
        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 {{} {target number N :} }
        lappend names {trial square root:}
        lappend names {formula factor: }
        lappend names {answers: intermediate term in formula }
        lappend names {trial square :}
        lappend names {square root from TCL sqrt function : }
        lappend names {percentage error: }
        lappend names {approximate square root from square side rule :} 
        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 Indian Bakhshali Square Root
            from TCL ,
            # gold on  TCL Club, 12Dec2018 "
            tk_messageBox -title "About" -message $msg } 
        proc self_help {} {
            set msg " Indian Bakhshali Square Root V2
            from TCL Club ,
            # self help listing
            # problem, Indian Bakhshali Square Root V2
            # 3 givens follow.
            1) target number N:
            2) trial square root:
            3) formula factor:
            # Recommended procedure is push testcase
            # and fill frame,
            # change first three entries etc, push solve,
            # and then push report.
            # Report allows copy and paste
            # from console to conventional texteditor.
            # For testcases, testcase number is internal
            # to the calculator and will not be printed
            # until the report button is pushed
            # for the current result numbers.
            # >>> copyright notice <<<
            # This posting, screenshots, and TCL source code is
            # copyrighted under the TCL/TK license terms.
            # Editorial rights and disclaimers
            # retained under the TCL/TK license terms
            # and will be defended as necessary in court.
            Conventional text editor formulas
            or  formulas grabbed from internet
            screens can be pasted into green console.
            # gold on  TCL Club, 12Dec2018 "
            tk_messageBox -title "Self_Help" -message $msg }
       proc ::tcl::mathfunc::precision {precision float}  {
            #  tcl:wiki:Floating-point formatting, [AM]
            set x [ format "%#.5g" $float ]
            return $x
           }   
            #proc errorx always returns a positive error. 
            #Normally assume $aa is human estimate,
            #assume $bb is divinely exact.
       proc errorx  {aa bb} {expr { $aa > $bb ?   (($aa*1.)/$bb -1.)*100. : (($bb*1.)/$aa -1.)*100.}}
       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 target_number $side1
            set trial_square_root $side2
            set formula_factor $side3
            set s $target_number 
            set n $trial_square_root
       #set approximate_root [/ [+ [* [* $n $n ] [+ [* $n $n ] [* 6. $s]]] [* $s $s]] [* 4. $n [+  $s [*  $n $n ] ] ]  ]
       set approximate_root [/ [+ [* [* $n $n ] [+ [* $n $n ] [* 6. $s]]] [* $s $s]] [* 4. $n [+  $s [*  $n $n ] ] ]  ]
            set side4  $approximate_root
            set side5 [* $trial_square_root $trial_square_root]
            set side6 [sqrt $target_number ]  
            set side7 [ errorx $approximate_root [sqrt  $target_number ]   ]
            set side8 $approximate_root
                    }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$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 answer2
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global testcase_number
            console eval {.console config -bg palegreen}
            console eval {.console config -font {fixed 20 bold}}
            console eval {wm geometry . 40x20}
            console eval {wm title . " Indian Bakhshali Square Root V2 Report, screen grab and paste from console 2 to texteditor"}
            console eval {. configure -background orange -highlightcolor brown -relief raised -border 30}
            console show;
            puts "%|table $testcase_number|printed in| tcl wiki format|% "
            puts "&| quantity| value| comment, if any|& "
            puts "&| $testcase_number:|testcase_number | |&"
            puts "&| $side1 :|target number N  |   |&"
            puts "&| $side2 :|trial square root | |& "  
            puts "&| $side3 :|function factor | |& "
            puts "&| $side4 :|answers: intermediate term in formula| |&"
            puts "&| $side5 :|trial square | |&"
            puts "&| $side6 :|square root from TCL sqrt function |  |&"
            puts "&| $side7 :|percentage error |  |&"
            puts "&| $side8 :|approximate square root from from Bakhshali formula |  |&" 
            }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { set side8 0 ; calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 3.  2.0  2.0 1.72  4.0   1.732    0.005366  1.732}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 216.E3 465.0 2.0 464.758 216225.0   464.758 9.E-13  464.758}
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 1296.E4 3601.0 2.0  3600.0  12967201.0    3600.0  6.E-14  3600.}
        ::ttk::button .clearallx -text clear -command {clearx }
        ::ttk::button .about -text about -command {about}
        ::ttk::button .self_help -text self_help -command { self_help }
        ::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 .self_help .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 . "Indian Bakhshali Square Root Calculator V2"     

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

                # pretty print from autoindent and ased editor
                # console program for token multiplication and square root
                # additional verbose  
                # working under TCL version 8.5.6 and eTCL 1.0.1
                # program written on Windows XP on eTCL
                # gold on TCL WIKI, 10Mar2017
                package require Tk
                package require math::numtheory
                namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory }
                set tcl_precision 17
                console show
             global keeper target_number keep_under
             set keeper 0
             proc square_root_functionx { number_for_root  } {  
             global keeper target_number keep_under
             set counter 0
             set epsilon .0001
             while { $counter < 1000.  } {
             set keeper [* $counter $counter 1. ] 
             set target_number $number_for_root
             if { [* $counter $counter 1. ]   > [* $number_for_root 1.] } {break}  
             set keep_under $counter         
             incr counter 
             }   
             return $counter}
            puts " function gives [ square_root_functionx 10. ] ,  root for $target_number between $keep_under and  [ square_root_functionx 10. ] , max square $keeper "
            #returns positive integers under and over root.
            # function gives 4 ,  root for 10. between 3 and  4 , max square 16.0