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## The iterative way

Factorial can be computed using an iterative way : let result be 1, then for each value V between 1 and N, multiply result by V.

## Let's start

- Memory: N 0 0 0 0 0
- Cursor: first cell
- Input: any

## Process

- set result to 1
- set current index to 0
*invariant: result = (current index)! and first cell + current index = N*- while first cell is not null
- increase index
- multiply result by current index
- decrease first cell

- loop
*first cell = 0, so current index = N and result = N!*

## Code

```
>>>>+ set result to 1 (and current index to 0)
<<<<[ while first cell is not null
>[->+>+<<]>[-<+>]> copy current index
[->[->+>+<<]>[-<+>]<<] multiply result by current index
>>>[-<<+>>]<<<<<+ increase current index and store result x new index into result
<-] decrease first cell and loop
```

## Minified version

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

## Final state

- Memory: 0 N 0 0 N!
- Cursor: first cell
- Input: unchanged
- Output: unchanged

## Test program

This programs prints `x`

, code 120 = 5!

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

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