Tak (function)

The Tak function , named after Ikuo Takeuchi (竹 内 郁 雄), is a recursive function that is defined as follows:

${\displaystyle t(x,y,z):={\begin{cases}y&{\text{falls }}x\leq y\\t{\big (}t(x-1,y,z),t(y-1,z,x),t(z-1,z,y){\big )}&{\text{andernfalls}}\end{cases}}}$

Expressed differently:

${\displaystyle t(x,y,z)={\begin{cases}y&{\text{falls }}x\leq y\\{\begin{cases}z&{\text{falls }}y\leq z\\x&{\text{andernfalls}}\end{cases}}&{\text{andernfalls}}\end{cases}}}$

It is often used as a benchmark for programming languages ​​that are optimized for recursion .

Web links

• Eric W. Weisstein : TAK Function . In: MathWorld (English).