Where is your phone number in Pi?

[Wanderer]

So here is my first X11-Basic program which I got to work (more or less) as it should. I am not yet quite happy with it because I had to use workarounds for several bugs or missing features in X11-Basic, but I arrived finally at a working version.
This program calculates Pi, e, and square roots, to as many digits as you wish (if you have time to wait...), and lets you search for any numeric string - for example your phone number - within them.

(Note: The next post contains the program as an attached *.bas file. I did not find any option for attaching files to the first post of a thread.)

' "Where is your phone number in Pi?"
' -----------------------------------
' Programming Language: X11-Basic
'
' Demonstrates some of the "big integer" capacities of X11-Basic,
' applied also to fractional numbers.
' May be used and extended freely.
'
' This program lets you search for your phone number (or any other numeric
' string) in as many digits of Pi as you wish.
' Instead of Pi you can also calculate and search e, the square root of 2,
' or (almost) any other square root.
'
' The program writes every number it calculates to a text file,
' so you can later open or edit it in a text editor. 
' The names of these files are "bn_pi.txt", "bn_e.txt", and "bn_sqrt2.txt".
' These are initialized to 10000 digits the first time the program is run.
' Then they can be extended by means of the "Recalculate" option. 
' The files for other square roots are accordingly called e.g. "bn_sqrt7" for
' the square root of 7, etc.
'
' IMPORTANT: This program works only when compiled to bytecode,
' but NOT in the X11-Basic interpreter (at least not in the Windows version), 
' because of several bugs in the interpreter.
'
' Also, if you wish to calculate millions of digits, the interpreter
' would be far too slow. Remember that you would have to calculate about
' ten million digits if you want to have a reasonable chance to find a 
' seven-digit phone number within them.
' On a Pentium IV 2.66 GHz running Windows XP, calculating 100,000 digits of Pi
' took 37 seconds for the bytecode file. (Most of this time was used for conver-
' ting the calculated number into a string.) Since the computing time increases
' approximately proportional to the square of the number of digits, calculating
' ten million digits would take approximately 100 hours.
'
' Note: The "Blink" mechanism for the wait screen could be implemented in a
' more elegant way using EVERY, but I found this feature to be still unreliable.
'
' - Some PRINT statements which give feedback about program progress are left
' in the code; these might be annoying when running under Android where console
' and graphics screen are identical, so just comment them out.

If android?
  baseDir$="/mnt/sdcard/bas/"
Else
  baseDir$=""
EndIf

Dim fixedNum$(5)
'Dim filename$() = [" ", "bn_pi.txt", "bn_e.txt", "bn_sqrt2.txt", " "]
'Dim numberName$() = [" ", "Pi", "e", "Sqrt(2)", " "]
'Above lines were rejected by the compiler/interpreter.
Dim filename$(5)
filename$(1) = "bn_pi.txt"
filename$(2) = "bn_e.txt"
filename$(3) = "bn_sqrt2.txt"
Dim numberName$(5)
numberName$(1) = "Pi"
numberName$(2) = "e"
numberName$(3) = "Sqrt(2)"
searchNumber$ = "       234"
squareNumber$ = "        3"

waitX1%=0
waitY1%=0
scrsave$=" "

openw 1
get_geometry 1, scrx%, scry%, scrw%, scrh%
textW = max(min(min(scrw%,scrh%)/30, 16),8)
linelength% = Int(scrw%/textW)
Color color_rgb(0,0,0)
pbox 0,0, scrw%-1, scrh%-1
Dim WaitText$(2)
WaitText$(0) = "Initializing Numbers"
WaitText$(1) = "Please Wait"
ret = @OpenWaitScreen(WaitText$())
For i% = 1 To 3
  If exist(baseDir$+filename$(i%))    !Loads Pi, e, and sqrt(2) from existing files.
    fixedNum$(i%) = @MyBLoad$(baseDir$+filename$(i%))
  Else     !Initialize Pi, e, and sqrt(2) to 10000 digits.
    Select i%
    Case 1
      fixedNum$(1) = @PiString$(10000)
    Case 2
      fixedNum$(2) = @EString$(10000)
    Case 3
      fixedNum$(3) = @SqrtString$(2,10000)
    endselect
    ret% = @myBSave%(baseDir$+filename$(i%), fixedNum$(i%))
  EndIf  
Next i%
ret = @CloseWaitScreen()
Dim waitText$(3)

'Start of main loop:
Do
startAgain:
  'Dialog for choosing number:
  '===========================
  txt$ = "Choose a number where to search:"
  btns$ = "Pi|e|sqrt(2)|sqrt(n)|EXIT"
  alert 0, txt$, 0, btns$, selection%
  Exit If selection%=5
  If selection%=4    !Arbitrary square root
                     !=====================
    txt$ = "Search square root of: "+Chr$(27)+squareNumber$
    alert 0, txt$, 0, "OK|Cancel", sele%, reTxt$
    If sele%=2
      GoTo startAgain
    EndIf
    squareNumber$ = word$(reTxt$,1,Chr$(13))
    sqN% = Val(Trim$(squareNumber$))
    If sqN%<0 
      sqN%=0
    EndIf
    filename$(4)="bn_sqrt"+Str$(sqN%)+".txt"
    numberName$(4)="Sqrt("+Str$(sqN%)+")"
    If exist(baseDir$+filename$(4))
      fixedNum$(4) = @MyBLoad$(baseDir$+filename$(4))
    Else     !Initialize sqrt(sqN%) to 10000 digits.
      WaitText$(0) = "Recalculating "+numberName$(selection%)
      WaitText$(1) = "to 10000 digits."
      WaitText$(2) = "Please wait."
      ret = @OpenWaitScreen(WaitText$())
      fixedNum$(4) = @SqrtString$(sqN%,10000)
      ret = @CloseWaitScreen()
      ret% = @myBSave%(baseDir$+filename$(4), fixedNum$(4))
    EndIf  
  EndIf
  'Search/Recalculate Dialog:
  '==========================
  digits% = Len(fixedNum$(selection%))-InStr(fixedNum$(selection%),".")
  txt$ = numberName$(selection%) + " is calculated with "
  txt$ = txt$+Chr$(27)+Str$(digits%)+"     |"
  txt$ = txt$+"digits. (Edit to recalculate.)|Input your phone number|or any other number|(without spaces):"+Chr$(27)+searchNumber$
  btns$ = "Search|Recalculate|Cancel"
  alert 0, txt$, 0, btns$, sele2%, reTxt$
      'Print selection%; " - "; sele2%; " |"; reTxt$; "|"
  newDigits% = Val(Trim$(word$(reTxt$, 1, Chr$(13))))
  searchNumber$ = word$(reTxt$, 2, Chr$(13))
  'Note: we should not TRIM searchNumber$ itself,
  ' because we use it as the new default text in the next ALERT,
  ' and ALERT does not allow to input a string longer than the default text.
  Select sele2%
  Case 1              !Search for a number
                      !===================
    posi% = InStr(fixedNum$(selection%), Trim$(searchNumber$))
    Color color_rgb(1,1,0.4)
    If posi%
      ltext 0,0, "Found "+Trim$(searchNumber$)+" in "+numberName$(selection%)
      ltext 0,textW*2, "at position "+Str$(posi%-2)+":"
      ret = @PrintFoundNumber(fixedNum$(selection%))
         'Print "Found at "; posi%-2
    Else
      ltext 0,0, Trim$(searchNumber$)+" was not found in "+Str$(Len(fixedNum$(selection%))-2)+" digits"
      ltext 0,textW*2, "of "+numberName$(selection%)+"."
          'Print "Not found"
    EndIf
    ltext 0,textW*16, "Press any key"
    ltext 0,textW*18, "or click mouse to continue."
    showpage
    x$ = @WaitMouseOrKey$()
    Color color_rgb(0,0,0)
    pbox 0,0, scrw%-1,scrh%-1
    showpage
  Case 2              !Recalculate a number
                      !====================
    If newDigits%<=digits%
      txt$ = "New number of digits is not greater|than the current one.|"
      txt$ = txt$ + "Recalculating makes no sense."
      alert 1, txt$, 1, "OK", s%
      GoTo startAgain
    EndIf
    digits% = newDigits%
    WaitText$(0) = "Recalculating "+numberName$(selection%)
    WaitText$(1) = "to "+Str$(digits%)+" digits."
    WaitText$(2) = "Please wait."
    ret = @OpenWaitScreen(WaitText$())
      tt = Timer
    Select selection%
    Case 1
      fixedNum$(1) = @PiString$(digits%)
    Case 2
      fixedNum$(2) = @EString$(digits%)
    Case 3
      fixedNum$(3) = @SqrtString$(2, digits%)
    Case 4
      fixedNum$(4) = @SqrtString$(sqN%, digits%)
    EndSelect
      Print "Calculation "; selection%; " = "; Timer-tt; " seconds."
    ret% = @myBSave%(baseDir$+filename$(selection%), fixedNum$(selection%))
    ret = @CloseWaitScreen()
  Case 3
    'Cancelled (nothing to do)
  endselect
Loop
End

Function PrintFoundNumber(nString$)
  'Following is a workaround for printing text with background color,
  ' which does not yet work properly.
  Local startString%, startX%, 
  startString% = max(posi%-(lineLength%-Len(Trim$(searchNumber$)))/2, 1)
  startX% = ltextlen(Mid$(nString$, startString%, posi%-startString%))
  Color color_rgb(1,0,0)
  pbox startX%, textW*4, startX%+ltextlen(Trim$(searchNumber$)), textW*6
  Color color_rgb(1,1,0.4)
  ltext 0, textW*4, Mid$(nString$, startString%, lineLength%)
  Return 0
EndFunction

Function MyBLoad$(file$)
  'Workaround because of a bug in the Windows version.
  Local f%, temp$, bytes%
  If exist(file$)
    bytes% = size(file$)
    temp$ = Space$(bytes%)
    f%=FreeFile()
    Open "I", f%, file$
    bget f%, VarPtr(temp$), bytes%
    Close f%
    Return temp$
  Else
    Return ""
  EndIf 
EndFunction

Function MyBSave%(file$, s$)
  'Workaround because of a bug in the Windows version.
  Local f%, bytes%
  bytes% = Len(s$)
  f%=FreeFile()
  Open "O", f%, file$
  bput f%, VarPtr(s$), bytes%
  Close f%
  Return bytes%
EndFunction

Function PiString$(digits%)
  Local expon%, myPi&, denom&
  expon% = (digits%+26)/9    !Use more digits because of rounding errors.
  Locate 1,1
  Print "Preparing denominator..."
  denom& = @bn_power&(1000000000, expon%)
  Locate 1,1
  Print "Calculating Pi...       "
  myPi& = @bnx_pi&(denom&)
  ret = @BlinkWaitScreen(waitText$())
  Locate 1,1
  Print "Generating string...    "
  Return Left$(@bnx_radixPower$(myPi&, 9*expon%, 10), digits%+2)
EndFunction

Function EString$(digits%)
  Local expon%, denom&, e&
  expon% = (digits%+26)/9
  Locate 1,1
  Print "Preparing denominator..."
  denom& = @bn_power&(1000000000, expon%)
  Locate 1,1
  Print "Calculating e...        "
  e& = @bnx_e&(denom&)
  Locate 1,1
  Print "Generating string...    "
  Return Left$(@bnx_radixPower$(e&, 9*expon%, 10), digits%+2)
EndFunction

Function SqrtString$(n%, digits%)
  Local expon%, denom&, root&
  expon% = (digits%+17)/9
  denom& = @bn_power&(1000000000, expon%)
  Locate 1,1
  Print "Calculating square root..."
  root& = sqrt(n%*denom&*denom&)
  Locate 1,1
  Print "Generating string...      "
  Return Left$(@bnx_radixPower$(root&, 9*expon%, 10), digits%+4)
EndFunction

Function bnx_pi&(denom&)
    'Calculates Pi (Gauss-Legendre Algorithm), returns numerator.
    Local a&, olda&, b&, t&, x&
    a& = denom&
    b& = sqrt(denom&*denom& div 2)
    t& = denom& div 4
    x& = 1
    Repeat
        olda& = a&
        a& = (a&+b&) div 2
        ret = @BlinkWaitScreen(waitText$())
        b& = Sqrt(b&*olda&)
        Sub olda&, a&
        ret = @BlinkWaitScreen(waitText$())
        t& = t&-((x&*olda&*olda&) div denom&)
        Add x&, x&
        ret = @BlinkWaitScreen(waitText$())
    Until olda&=0
  Return (a&*a&) div t&
EndFunction

Function bnx_e&(denom&)
  'Return value / denom& = e.
  Local divisor&, diff&, num&
  num& = denom&
  diff& = denom&
  divisor& = 1
  repeat
    div diff&, divisor&
    inc divisor&
    Add num&, diff&
    ret = @BlinkWaitScreen(waitText$())
  Until diff&=0
  Return num&
EndFunction

Function bn_power&(a&, b%)
  ' (Returns 1 if b% negative - not quite logical...)
  Local c&, i%
  c& = 1
  For i% = 1 To b%
    c& = c&*a&
    ret = @BlinkWaitScreen(waitText$())
  Next i%
  Return c&
EndFunction

Function bn_radix$(a&,base%)
  'for arbitrary precision integers
  Local temp2$, sign$

  If base%>64 Or base%<2 
    Return ""
  EndIf
  sign$=""         !Initialize local variables
  temp2$ = ""
  If a&<0 Then
    sign$="-"
    a& = -a&
  EndIf
  repeat
    temp2$ = @bn_makedigit$(a& Mod base%) + temp2$
    div a&, base%
  Until a&=0
  Return sign$+temp2$
EndFunction

Function bnx_radix$(a&,b&,base%,maxlen%)
  'Returns a&/b& in base base%, max. maxlen% digits.
  'Is actually not used by this program since we can use the function
  ' bnx_radixPower$() below, which is about twice as fast.
  Local temp$, n&

  If b&=0
    Return ""
  EndIf
  temp$ = ""
  If Sgn(a&)<>Sgn(b&)
    temp$="-"
  EndIf
  a& = Abs(a&)
  b& = Abs(b&)
  n& = a& div b&      !Integer part
  temp$ = temp$ + @bn_radix$(n&,base%)+"."
  If temp$="."
    Return ""         !Invalid base%
  endif
  n& = a& Mod b&      !Residue
  repeat
    mul n&,base%
    temp$ = temp$+@bn_makedigit$(n& div b&)
    n& = n& Mod b&
    ret = @BlinkWaitScreen(waitText$())
  Until (Len(temp$)>=maxlen%) Or (n&=0)
  Return temp$
EndFunction

Function bnx_radixPower$(a&,b%,base%)
  'Returns a&/(base%^b%) in base base%, b% "decimal" digits.
  Local temp$, sign&, i%

  If base%>64 Or base%<2     !Invalid base
    Return ""
  EndIf
  sign$=""                   !Initialize local variables
  temp$=""
  If a&<0 Then
    sign$="-"
    a& = -a&
  EndIf
  For i% = 1 To b%
    temp$ = @bn_makedigit$(a& Mod base%) + temp$
    div a&, base%
    ret = @BlinkWaitScreen(waitText$())
  Next i%
  temp$ = "."+temp$
  repeat
    temp$ = @bn_makedigit$(a& Mod base%) + temp$
    div a&, base%
  Until a&=0
  Return sign$+temp$
EndFunction

Function bn_makedigit$(dig&)
'"else..if" must be nested, because of a bug in the Windows version.
'dig& could be a normal integer if the result of a big integer division
' or of big integer MOD could be assigned to a normal integer. 
' In the bytecode file this works, but the interpreter yields wrong results
' when doing this; so I decided to use a big integer here.
' However, in the Windows version, the interpreter now crashes when using this function!
  Local digi%
      'Print "Entered MakeDigit."
  digi% = dig&  
  If (digi%<10)
  Return Chr$(digi%+48)
  Else 
    If (digi%<36)
    Return Chr$(digi%+55)
    Else 
      If (digi%<62)
      Return Chr$(digi%+61)
      Else 
        If (digi%=62)
        Return "@"
        Else 
          If (digi%=63)
          Return "$"
          Else
            Return "!"
          EndIf
        EndIf
      EndIf
    EndIf
    EndIf
EndFunction

Function OpenWaitScreen(t$())
  Local maxLen%, i%, y%
  deftext 0, textW/100, textW/75, 0
  maxLen% = 0
  For i% = 0 To Dim?(t$())-1
    maxLen% = max(ltextlen(t$(i)), maxLen%)
  Next i%
  waitW% = maxLen%+2*textW
  waitH% = (Dim?(t$())+1)*textW*2
  waitX1% = (scrw%-waitW%)/2
  waitY1% = (scrh%-waitH%)/2
  Color color_rgb(0.3,0.3,0.3)
  pbox waitX1%, waitY1%, waitX1%+waitW%-1, waitY1%+waitH%-1
  Color color_rgb(1,1,0.4)
  y% = waitY1% + textW
  For i% = 0 To Dim?(t$())-1
    ltext waitX1%+textW, y%, t$(i%)
    Add y%, (textW*2)
  Next i%
  showpage
  waitT = Timer
  Return 0
EndFunction

Function BlinkWaitScreen(t$())
  Local i%, y%
  If Timer<waitT+1
    Return 0
  EndIf
  waitT = Timer
  blink% = blink% Xor 1
  If blink%
    Color color_rgb(0.3,0.7,0.7)
  Else
    Color color_rgb(0.3,0.3,0.3)
  EndIf
  pbox waitX1%, waitY1%, waitX1%+waitW%-1, waitY1%+waitH%-1
  Color color_rgb(1,1,0.4)
  y% = waitY1% + textW
  For i% = 0 To Dim?(t$())-1
    ltext waitX1%+textW, y%, t$(i%)
    Add y%, (textW*2)
  Next i%
  showpage
  Return 1
EndFunction

Function CloseWaitScreen()
  Color color_rgb(0,0,0)
  pbox waitX1%, waitY1%, waitX1%+waitW%-1, waitY1%+waitH%-1
  showpage
  Return 0
EndFunction

Function WaitMouseOrKey$()
  While InKey$<>""
  Wend
  repeat
    m$=InKey$
  Until (m$<>"") Or ((mousek And 7)<>0)
  Return m$
EndFunction

[Wanderer]

Here the program attached as a *.bas file.
(Funny thing in this forum: There is no option for attaching a file to the first post of a thread, but the following posts support attachments...)