Code patterns ControlA counted loop

A counted loop

Runs a piece of program a given number of times.

Watch it run

The form “Using up the counter” works on 3 cells, named “n”, “scratch” and “star”. Press Play, drag the step slider forwards and back, or change n with the slider:

The figure needs JavaScript. The program below is the result for the example values.

The counter is the loop cell. Each round takes 1 off; when it reaches zero the loop ends.

The counter is used up. To keep it, each round also adds 1 to a scratch cell, and one move at the end puts it back (see move a value).

The body may read the counter too, as long as it leaves it where it was: the form The body reads the counter adds the counter itself to a total each round.

The code

This is the program the figure ran. It is brainfuck as it stands: copy it, or open it in the playground, where you can change it:

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

Open in the playground28 characters

What it needs

The body must return to the counter cell.
Any cell size. A count of zero runs the body zero times.

Common mistakes

Taking 1 off at the start of the round in one place and at the end in another. Both work; mixing them up inside one body does not.
A body that is not "flat" (it prints, or holds a loop): the optimiser cannot fold the loop, so the cost is per round. See the cost page.

What it costs

A plain step is one command. An optimised step is one step of an interpreter that folds runs of the same command and flat loops. Choose the values and watch the two bars; What costs what explains how cost is counted:

The figure needs JavaScript. The table below has the measured steps.

Cost as a formula, and measured

**Table 1.** The cost as a function of the values. Exact formulas are checked on every case they run.
Form	Plain steps	Optimised steps
Using up the counter	76 + 7n	3 + 3n
Keeping the counter	79 + 13n	5 + 4n
The body reads the counter	grows with n × n	1 + 4n

**Table 2.** Measured when this page was written.
Form	Values	Bits	Characters	Plain steps	Optimised steps
Using up the counter	n = 0	8	28	76	3
Using up the counter	n = 5	8	28	111	18
Using up the counter	n = 30	8	28	286	93
Keeping the counter	n = 5	8	37	144	25
The body reads the counter	n = 4	8	24	183	17

Other forms

Keeping the counter

Layout: n, keep, star. Every round saves one unit in "keep".

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

Open in the playground37 characters

Run this form step by step

The form “Keeping the counter” works on 3 cells, named “n”, “keep” and “star”. Press Play, drag the step slider forwards and back, or change n with the slider:

The figure needs JavaScript. The program below is the result for the example values.

The body reads the counter

Adds n + (n − 1) + … + 1. Layout: n, total, scratch.

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

Open in the playground24 characters

Run this form step by step

The form “The body reads the counter” works on 3 cells, named “n”, “total” and “scratch”. Press Play, drag the step slider forwards and back, or change n with the slider:

The figure needs JavaScript. The program below is the result for the example values.

Where it is used

Multiply two cells is a counted loop round a copy.
Print a constant string: the loop that seeds the cells.

Sources

Source: Esolang wiki: Brainfuck algorithms: section "Summing 1~n" for the idea of the third form; the code here is our own.

Every program on this page was run on many inputs, in plain and in optimised mode, and compared with JavaScript. The explanations are written for this page.