BrainFuck part 4 - Advanced maths


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Evaluate greater / less functions

We already know how to evaluate whether 2 numbers are equals. Given 2 numbers A and B, let's see now how to check if A is less than to B (LT) or greater or equal to B (GE).

This code can be obviously adapted from GE / LT to LE / GT

Let's start

  • Memory: A, B, 0, 0
  • Cursor: on A
  • Input: any


  • Invariant : first cell - second cell is always d = A - B. If B ends to 0, then d > 0; if A ends to 0 first then d <= 0
  • While A is not null
    • Set else flag on 3rd cell
    • Decrease A
    • If B is not null
      • Decrease B
      • Reset else flag
    • If B is null
      • A is greater than B, no need to continue the loop : reset A
  • Loop
  • Result is on B: "B not null" == "A < B"


[             while A is not null
  -           decrease A
  >>+         set else flag
  <[          if B is not null
    ->-       decrease B and reset else flag
  ]>          B not null : on 4th cell; B null : on 3rd cell set to 1
  [<<[-]>>->] so if B null reset A
  <<<         back to A
]             loop
>[[-]<+>]<    a bit formatting (if result is true then clear B and put 1 into A)

Minified version


Final state

  • Memory: result, 0, 0, 0 with result = 1 if B > A and 0 if A >= B
  • Cursor: on result
  • Input: unchanged
  • Output: unchanged

Test program

This program reads 2 chars. It first copies these chars, then compares to print in alphabetical order

,[->+>+<<]>[-<+>],[->>+>+<<<]>>>[-<<<+>>>]<<   read 2 chars and copy
[->>+<[->-]>[<<[-]>>->]<<<]>[[-]<+>]<          compare the 2 copies
>+<[>-<-<<.>.>]                                set else bit; if A less than B print A then B (and reset result)
>[-<<.<.>>>]                                   otherwise print B then A
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