BrainFuck part 4 - Advanced maths

Print a number

Now, with euclidean division, we can print number. The process looks like (recursive definition): print(x) = if x < 10 then return x, else return print(quotient x/10) + remainder x/10

In other words, we will divide N successively by 10, store the remainders and fianlly print them all, backards.

Note : the remainders will first be values from 0 to 9. But

• it's uneasy to iterate on null values (see playground about arrays)
• and we need to print chars from "0" to "9" and not just values

Fortunately, "0" is not 0, so we will store remainders + 48

Let's start

• Memory: 0, N, 0, ... (note : we will need a various number of zeros, based on how many digits are displayed)
• Cursor: on N
• Input: any

Process

• Invariant : memory = 0, {some digit chars}, X, 0, 0, 0, 0, 0 with N in base 10 written as "X in base 10" + all the digit chars, reversed
• While X is not null
  • Divide X by 10
  • Add 48 to remainder
  • Replace X cell by remainder
  • Put quotient after X cell
  • Clear all used cells on the right
  • Go to the "new X cell" (on the right of the original)
• Loop
• Memory = 0, {N number in base 10, with reversed digits}, 0, 0, 0, 0, 0
• Print all chars in array, backwards

Code

[                        While X is not null
  >>>>++++++++++<<<<     (10)
  [->+>>+>-[<-]<[<<[->>  Divide X by 10
  >+<<<]>>>>+<<-<]<<]    ** part 2 **
  ++++++++[->++++++<]>   add 48 to remainder
  [-<+>]                 Move remainder at X location
  >>>>[-<<<<+>>>>]       Put quotient at new X location
  <[-]<<<                Reset cells
]                        Loop
<[.<]                    Print backwards

#Minified version

[>>>>++++++++++<<<<[->+>>+>-[<-]<[<<[->>>+<<<]>>>>+<<-<]<<]++++++++[->++++++<]>[-<+>]>>>>[-<<<<+>>>>]<[-]<<<]<[.<]

Final state

• Memory: 0, { reversed digits of N}, 0
• Cursor: on first cell
• Input: unchanged
• Output: N printed, in base 10

Test program

This program reads all chars from the input and print ASCII codes (space separated)

>,[                         for each char read
  [>>>>++++++++++<<<<[->+   Print char code
  >>+>-[<-]<[<<[->>>+<<<]    ** part 2 **
  >>>>+<<-<]<<]++++++++[-    ** part 3 ** 
  >++++++<]>[-<+>]>>>>[-<    ** part 4 ** 
  <<<+>>>>]<[-]<<<]<[.[-]<]  ** part 5 ** Note: the "reset cell" before end of line : chars are deleted after being printed
  ++++++++[->++++<]>.       (32) = space; and print
,]                          Read next char and loop