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DPAmar
4,416 views

Multiply numbers

Multiplication (AxB) is a math algorithm to avoid doing B successive additions. However, BF does not even allows additions : as explained we can only increase or decrease values !

If additions are implemented using "successive +1", then multiplications will be done using "successive successive +1"

To compute AxB, we'll have to sum B, A times. And, as sum destroys operands, we need to copy B for the next loop.

Let's start

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

Process

4 cells : [m,n,o,p]

  • while m is not null
    • invariant : p=Bx(A-m) + (B-n), o= B-n
    • while n is not null
      • decrease n
      • increase o
      • increase p
    • loop
    • while o is not null
      • decrease o
      • increase n
    • loop
    • decrease m
  • loop
  • m=0, n=B, p=BxA, o=0
  • and optionally, do some cleansing

Code

[       while m is not null
  >[    while n is not null
    -   decrease n
    >+  increase o
    >+  increase p
  <<]   loop
  >[    while o is not null
    -   decrease o
    <+  increase n
  >]    loop
  <<-   decrease m
]       loop

Minified version

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

Final state

  • Memory: 0, B, 0 , AxB
  • Cursor: on first cell
  • Input: unchanged
  • Output: unchanged

Optional cleansing

  • Move result to first cell
  • Clear second cell
[>[->+>+<<]>[-<+>]<<-]  mult
>[-]                    clear second cell
>>[-<<<+>>>]<<<         move result

Test program

++++++++++               (10)
>+++++<                  (5)
[>[->+>+<<]>[-<+>]<<-]   multiply
>[-]>>[-<<<+>>>]<<<      cleansing
.                        print 5x10 = 50 ('2' in ASCII)
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