Schleifen
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## Schleifen

### While-Schleifen

Syntax:

    while <expression1> do <expression2>
    until <expression1> do <expression2>
    do <expression2> while <expression1>
    do <expression2> until <expression1>

These are similar to other languages. However, as in GEL it is simply an expression that must have some return value, these constructs will simply return the result of the last iteration or `NULL` if no iteration was done. In the boolean expression, `=` is translated into `==` just as for the `if` statement.

### For-Schleifen

Syntax:

    for <identifier> = <from> to <to> do <body>
    for <identifier> = <from> to <to> by <increment> do <body>

Loop with identifier being set to all values from `<from>` to `<to>`, optionally using an increment other than 1. These are faster, nicer and more compact than the normal loops such as above, but less flexible. The identifier must be an identifier and can't be a dereference. The value of identifier is the last value of identifier, or `<from>` if body was never evaluated. The variable is guaranteed to be initialized after a loop, so you can safely use it. Also the `<from>`, `<to>` and `<increment>` must be non complex values. The `<to>` is not guaranteed to be hit, but will never be overshot, for example the following prints out odd numbers from 1 to 19:

    for i = 1 to 20 by 2 do print(i)

When one of the values is a floating point number, then the final check is done to within 2^-20 of the step size. That is, even if we overshoot by 2^-20 times the "by" above, we still execute the last iteration. This way

    for x = 0 to 1 by 0.1 do print(x)

does the expected even though adding 0.1 ten times becomes just slightly more than 1.0 due to the way that floating point numbers are stored in base 2 (there is no 0.1, the actual number stored is just ever so slightly bigger). This is not perfect but it handles the majority of the cases. If you want to avoid dealing with this issue, use actual rational numbers for example:

    for x = 0 to 1 by 1/10 do print(x)

This check is done only from version 1.0.16 onwards, so execution of your code may differ on older versions.

### Foreach-Schleifen

Syntax:

    for <identifier> in <matrix> do <body>

For each element in the matrix, going row by row from left to right we execute the body with the identifier set to the current element. To print numbers 1,2,3 and 4 in this order you could do:

    for n in [1,2:3,4] do print(n)

If you wish to run through the rows and columns of a matrix, you can use the RowsOf and ColumnsOf functions, which return a vector of the rows or columns of the matrix. So,

    for n in RowsOf ([1,2:3,4]) do print(n)

will print out [1,2] and then [3,4].

### Break and Continue

You can also use the `break` and `continue` commands in loops. The continue `continue` command will restart the current loop at its next iteration, while the `break` command exits the current loop.

    while(<expression1>) do (
      if(<expression2>) break
      else if(<expression3>) continue;
      <expression4>
    )

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