# BrainFuck part 4 - Advanced maths

DPAmar
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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

## Process

• 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"

## Code

[             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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