'+----------------------------------------+
'|                                        |
'|     C h a i n F r a c t i o n s        |
'|                                        |
'| Wilf Hey  2006                         |
'+----------------------------------------+

 template$ = "##.########"

 do
  print "Please key a decimal fraction"
  input "more than 0, less than 10:  ";InputNbr$

'+----------------------------+
'| validate the keyed number  |
'+----------------------------+
  Valid = 0
  if len(InputNbr$) > 0 then
    Valid = 1
    for i = 1 to len(InputNbr$)
      x$ = mid$(InputNbr$, i, 1)
      if instr("0123456789.", x$) = 0 then
        Valid = 0
      end if
    next
'+----------------------------+
'| confirm its range          |
'+----------------------------+
    a = instr(InputNbr$, ".")
    x$ = mid$(x$, a+1)
    if instr(x$, ".") > 0 then
      Valid = 0
    end if
  end if
  if Valid = 1 then
    a = val(InputNbr$)
    if (a > 0) and (a < 10) then
      Valid = a
      exit do
    end if
    Valid = 0
  end if
  print "ERROR"
 loop until Valid > 0
 x$ = using(template$, Valid)
 a = val(x$)
'+----------------------------+
'| abbreviate to 8 decimals   |
'+----------------------------+
 if a <> Valid then print "Taken as ";x$

'+----------------------------+
'| generate Chain Fraction    |
'+----------------------------+
 print
 Chain$ = ""
 fracobject = 1 / Valid

 do until fracobject < 0.0000001 'very small remainder
   object = 1 / fracobject
   intobject = int(object)
   Chain$ = Chain$ + str$(intobject) + " "
   fracobject = object - intobject
   if len(Chain$) > 50 then fracobject = 0 'force end
 loop
 i = 0
 do
   i = i + 1
 loop until word$(Chain$, i) = ""
 Chainlen = i - 1

'+----------------------------+
'| Expand chain at each size  |
'+----------------------------+
 i = 0
 do
   print
   i = i + 1
   x$ = "("
'+----------------------------+
'| insert commas between      |
'|   terms in the chain       |
'+----------------------------+
   for j = 1 to i
     x$ = x$ + word$( Chain$, j) + ","
   next
   x$ = left$( x$, len(x$)-1)
   x$ = x$ + ")"
'+----------------------------+
'| generate a two-digit       |
'|   sequence number          |
'+----------------------------+
   print "<";right$(str$(100+i), 2);">  ";x$

'+----------------------------+
'| evaluate the value of      |
'|   the chain                |
'+----------------------------+
   BaseVal = 0
   FractionA = 0 : FractionB = 1
   for j = i to 1 step -1
     a = val(word$( Chain$, j))
     BaseVal = BaseVal + a
     FractionA = FractionA + FractionB * a
     if j <> 1 then
       BaseVal = 1/BaseVal
       a = FractionA
       FractionA = FractionB
       FractionB = a
     end if
   next
   x$ = using(template$, BaseVal)
   x$ = trim$(x$)
   lenx = len(x$)
'+----------------------------+
'| suppress trailing zeros    |
'+----------------------------+
   do
     if right$(x$,1) <> "0" then exit do
     x$ = left$(x$, len(x$)-1)
   loop until lenx = 0
'+----------------------------+
'| suppress decimal point     |
'|   if it isn't needed       |
'+----------------------------+
   if right$(x$,1) = "." then
     x$ = left$(x$, len(x$)-1)
   end if
   x$ = left$(x$ + space$(lenx), lenx)
   print "      ";x$;
'+----------------------------+
'| calculate error magnitude  |
'+----------------------------+
   x$ = using(template$,BaseVal - Valid)
   x$ = trim$(x$)
   if left$(x$, 1) <> "-" then x$ = "+" + x$
   if x$ = "+0.00000000" then x$ = " "
'+----------------------------+
'| if spot on, stop going for |
'|   more items in the chain  |
'+----------------------------+
''   if x$ = " " then
''     print : exit do
''   end if
     if x$ = " " then x$ = "0."
'+----------------------------+
'| print the error            |
'|   with trailing zero       |
'|   suppression)             |
'+----------------------------+
   lenx = len(x$)
   do
     if right$(x$,1) <> "0" then exit do
     x$ = left$(x$, len(x$)-1)
   loop until lenx = 0 'this will never happen
   if right$(x$,1) = "." then
     x$ = left$(x$, len(x$)-1)
   end if
   x$ = left$(x$ + space$(lenx), lenx)
   if val(x$) = 0 then
     print
   else
     print "  error ";x$
   end if
   print FractionA;" / ";FractionB
' retire if extremely close (insignificant error)
   if val(x$) = 0 then exit do
 loop until i = Chainlen

 stop