Factorial in Brainfuck

Example for versions EsCo 0.511 (Brainfuck), Müller's Brainfuck 2.0

This example uses iterative definition of factorial. Last calculated factorial is stored in variable c6 and on each step it is multiplied by next number (stored in c5). A low-level description is given in the comments, notation “cXvY” meaning that after execution of the commands in the line the data pointer is at cell X, and the value at this cell is Y. A total of 13 memory cells is used.

This example uses one minor cheat: classic Brainfuck interpreter uses byte variables to store values of memory cells, so 6! and further will cause overflow. Writing long arithmetics in Brainfuck is a bit of overkill, so in this example we assume that memory cells can store integer values. Besides, factorial length grows fast along with execution time of Brainfuck program, so the above code is limited to calculating and printing first 7 factorials.

+++++++++++++++++++++++++++++++++			c1v33 : ASCII code of !
+++++++++++++++++++++++++++++++				c2v61 : ASCII code of =
>++++++++++						c3v10 : ASCII code of EOL
>+++++++						c4v7  : quantity of numbers to be calculated
>							c5v0  : current number (one digit)
>+							c6v1  : current value of factorial (up to three digits)
<<							c4    : loop counter
[							block : loop to print one line and calculate next
>++++++++++++++++++++++++++++++++++++++++++++++++.	c5    : print current number
------------------------------------------------	c5    : back from ASCII to number
<<<<.-.>.<.+						c1    : print !_=_

>>>>>							block : print c6 (preserve it)
>							c7v0  : service zero
>++++++++++						c8v10 : divizor
<<							c6    : back to dividend
[->+>-[>+>>]>[+[-<+>]>+>>]<<<<<<]			c6v0  : divmod algo borrowed from esolangs; results in 0 n d_n%d n%d n/d
>[<+>-]							c6    : move dividend back to c6 and clear c7
>[-]							c8v0  : clear c8

>>							block : c10 can have two digits; divide it by ten again
>++++++++++						c11v10: divizor
<							c10   : back to dividend
[->-[>+>>]>[+[-<+>]>+>>]<<<<<]				c10v0 : another divmod algo borrowed from esolangs; results in 0 d_n%d n%d n/d
>[-]							c11v0 : clear c11
>>[++++++++++++++++++++++++++++++++++++++++++++++++.[-]]c13v0 : print nonzero n/d (first digit) and clear c13
<[++++++++++++++++++++++++++++++++++++++++++++++++.[-]] c12v0 : print nonzero n%d (second digit) and clear c12
<<<++++++++++++++++++++++++++++++++++++++++++++++++.[-]	c9v0  : print any n%d (last digit) and clear c9

<<<<<<.							c3    : EOL
>>+							c5    : increment current number
							block : multiply c6 by c5 (don't preserve c6)
>[>>+<<-]						c6v0  : move c6 to c8
>>							c8v0  : repeat c8 times
<<<[>+>+<<-]						c5v0  : move c5 to c6 and c7
>>[<<+>>-]						c7v0  : move c7 back to c5
<<<<-							c4    : decrement loop counter