sed is a very powerful tool. A simple sed statement may turn a cat into cement. Observe: echo cat | sed statement

I was asked by mariom@ircnet whether is it possible to implement the Euklidean algorithm (the one that computes the greatest common divisor) in awk. awk is a Turing complete language, so the answer is yes, it is possible. There is a snippet proposed by mariom:

{ a = $1; b = $2; while (b != 0) { c = a % b; a = b; b = c; } print a }

Anyway, my response was that it is possible even in sed. Is it? Of course! Sed is a Turing complete language. Though I had no idea how to write it in sed. I use sed for simple substitutions only, but I could not admit that!

I started googling for arithmetic operations in sed and I found a dc implementation in pure sed. So the next question is how to implement the Euklidean algorithm in dc. It turned out to be quite simple, see:

[lalb%sclbsalcsblb0

This code assumes that there are two integers on the stack. So you can test it with something like that:

echo '20 25 [lalb%sclbsalcsblb0

Let’s analyze what is happening there. There is F macro that is equivalent of “while” loop in awk code. It **l**oads the values of **a** and **b** registers on the stack. Then replaces them with their reminder and **s**aves it in the **c** registers.

lbsalcsb

statement just copies the value of **b** to **a** and **c** to **b**. Finaly it compares the value of **b** with **0**. If former is greater it executes **F** (note: recurrence. It is the only way to implement a loop in dc). Otherwise it quits.

sasblFxlap

statement is an entry point. It saves values from stack in the **a** and **b** registers, then executes **F** and prints the content of the **a** register. So this sed script is an equivalent of awk script that executes Euklidean algothm.

Now it is enough to embed the dc script into dc.sed, et voila! Enjoy: Euclidean algorithm implemented in pure sed.