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-- returns the 2^n possible n-bit nums (base 2),
--         that is 2^n lines of n chars each.
-- usage: put nBits(n,0&cr&1) into theBits
function nBits n,t 
  if n=1 then return t
  repeat for each line L in t
    put cr & L & "0" after s
    put cr & L & "1" after s
  end repeat
  return nBits(n-1,char 2 to -1 of s)
end nBits

on mouseUp
  put the millisecs into m1
  set cursor to watch; lock messages; lock screen
  put 3 into N -- the num of bits from a field or a scrollbar
    put nBits(N,0&cr&1) into theBits
  put the millisecs-m1 & " ms" into fld "timing"
  -- takes a lot of time, use file instead of a fld
  -- to write the 2^N lines of N chars each for N > 15:
  put theBits into fld "out"
end mouseUp

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on mouseUp
  put the millisecs into m1
  set cursor to watch; lock messages; lock screen
  put 24 into n --> 24*2^24 + 2^24-1 =  419430399 Bytes
  put nBits(n,0&cr&1) into theBits 
  put bitfilename(n) into f
  put theBits into url("file:"&f)
  put "(n+1)*2^n-1="&(n+1)*2^n-1&": "&the millisecs-m1& \
      " ms" into fld "timing"
end mouseUp

function nBits n,t -- returns the 2^n possible n-bit nums
  if n=1 then return t
  repeat for each line L in t
    put cr & L & "0" after s
    put cr & L & "1" after s
  end repeat
  return nBits(n-1,char 2 to -1 of s)
end nBits

function bitfileName n
  put the effective filename of this stack into f
  set itemdel to slash
  put "bits"&format("%02d.text",n) into last item of f
  return f
end bitfileName

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000
001 <-- 1st 1 starts far right
010 <-- 1st 1 moves to middle
100 <-- 1st 1 arrives at end left
101 <-- 2nd 1 starts far right
110 <-- 2nd 1 moves to middle, can not move farther
111 <-- 3rd 1 starts and stops, no further moves

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-- usage: put 50 into N
-- put bogspattern(1,N,0&cr&1) into fld "out"
function bogspattern m,N,t
   if m=N then return t
   repeat with j=1 to m+1
     put cr & "0" & line j of t after s
   end repeat
   repeat for each line L in t
     put cr & "1" & L after s
   end repeat
   return bogspattern(m+1,N,char 2 to -1 of s)
end bogspattern

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on printallStringsFrom s, k
   put empty into fld "list"
   printStrings s, "", the number of chars of s , k
end printallStringsFrom

on printStrings s, prefix, n, k
   if k = 0 then
      put prefix &cr after fld "list"
   else      
      repeat with i = 1 to n step 1
         printStrings s, prefix & char i of s, n, k - 1
      end repeat
   end if
end printStrings

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on mouseUp
   put 3 into stringLength
   printallStringsFrom "01", stringLength
end mouseUp

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   printallStringsFrom "AB", 1
   printallStringsFrom "ABCD", 1
   printallStringsFrom "ABCD", 4
   ....
   

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on mouseUp
   put the ticks into g
   put "000000000000" into zeros
   repeat with y = 1 to 8192
      put baseConvert(y,10,2) into line y of temp
   end repeat
   repeat for each line tLine in temp
      put zeros before tline
      delete char 1 to -14 of tLine
      put tLine & return after accum
   end repeat
   delete the last line of accum
   answer the ticks - g
end mouseUp

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function nBits n,t -- returns the 2^n possible n-bit nums -- from Hermann
   local s
   if n=1 then return t
   repeat for each line L in t
      put cr & L & "0" after s
      put cr & L & "1" after s
   end repeat
   return nBits(n-1,char 2 to -1 of s)
end nBits

function nBits2 pLength -- advantages: no "repeat for each line" and no recursion
   local tStrings
   put cr & "0" & cr & "1" into tStrings
   repeat with i = 2 to pLength
      replace cr with cr & 0 in tStrings -- put 0 before each line
      get tStrings
      replace cr & 0 with cr & 1 in it -- replace each leading 0 with 1
      put it after tStrings
   end repeat
   delete char 1 of tStrings
   return tStrings
end nBits2

on mouseUp
   set cursor to watch
   local tMilliseconds, tStrings, tReport
   repeat with tLength = 2 to 24
      put - the milliseconds into tMilliseconds[ "nBits" ]
      put nBits( tLength, "0" & cr & "1" ) into tStrings[ "nBits" ]
      add the milliseconds to tMilliseconds[ "nBits" ]
      
      put - the milliseconds into tMilliseconds[ "nBits2" ]
      put nBits2( tLength ) into tStrings[ "nBits2" ]
      add the milliseconds to tMilliseconds[ "nBits2" ]
      
      if tMilliseconds[ "nBits" ] > 5 and tMilliseconds[ "nBits2" ] > 0 then
         get tLength \
               && ( number of lines in tStrings[ "nBits" ] ) \
               && ( tStrings[ "nBits" ] = tStrings[ "nBits2" ] ) \
               && tMilliseconds[ "nBits" ] \
               && tMilliseconds[ "nBits2" ] \
               && round( ( tMilliseconds[ "nBits2" ] - tMilliseconds[ "nBits" ] ) * 100 / tMilliseconds[ "nBits" ] ) & "%" \
               & cr
         put it after msg
         put it after tReport
         wait 0 with messages
      end if
   end repeat
   if tReport is not empty then
      replace space with comma in tReport
      put "length,count,nBits=nBits2,nBits ms,nBits2 ms,delta" & cr before tReport
   end if
   breakpoint
end mouseUp

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length,count,nBits=nBits2,nBits ms,nBits2 ms,delta
11,2048,true,7,1,-86%
12,4096,true,16,1,-94%
13,8192,true,31,2,-94%
14,16384,true,61,7,-89%
15,32768,true,141,10,-93%
16,65536,true,276,19,-93%
17,131072,true,590,48,-92%
18,262144,true,1192,122,-90%
19,524288,true,1679,161,-90%
20,1048576,true,3872,534,-86%
21,2097152,true,7767,1060,-86%
22,4194304,true,15950,1563,-90%
23,8388608,true,31288,4428,-86%
24,16777216,true,63586,7792,-88%

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-- usage: put nBits3(n,cr) into theBits 
-- n is the num of digits
function nBits3 n,t0 -- recursion variant
  put t0 into t1
  replace cr with cr&0 in t0
  replace cr with cr&1 in t1
  if n > 1 then return nBits3(n-1,t0&t1)
  else return char 2 to -1 of t0&t1
end nBits3

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-- usage: put nBits2a(n) into theBits 
-- n is the num of digits
function nBits2a pLength -- repeat variant
  local tStrings, tStringx
  put cr & "0" & cr & "1" into tStrings
  repeat pLength-1
    put tStrings into tStringx
    replace cr with cr & "0" in tStrings
    replace cr with cr & "1" in tStringx
    put tStringx after tStrings
  end repeat
  return char 2 to -1 of tStrings
end nBits2a