How To Cube A Number In Factor?

Question

I'm playing with Factor trying to get a little understanding of concatenative programming. Writing a word to square a number is trivial:

: square ( n -- n ) dup * ;

But for the life of me I can't seem to figure out how to cube a number:

: cube ( n -- n ) * * ;  ! Form a

Doesn't work because the inferred stack effect is ( x x x -- x ) Similarly

: cube ( n -- n ) dup * * ; ! Form b

also fails.

If I were to hard code a cube I would do something like this:

3 3 * 3 *

Which is why my naive guess would be form b.

As I say I'm just playing with Factor and would love to know what I'm missing here--but it's mostly for my curiosity.

Answer 1

There is a builtin word for that:

IN: scratchpad 3 3 ^ .
27

Or if you want to write the word yourself:

: pow ( x n -- y ) 1 - over '[ _ * ] times ;
IN: scratchpad 5 3 pow .
125

You could also formulate cube using square:

: cube ( n -- n' ) dup square * ;
IN: scratchpad 6 cube .
216

Answer 2

In case anyone else runs across this and wants to know how to do this:

: cube ( n -- n ) dup dup * * ;

The dup dup will add the value to the top of the stack twice and then the * * will multiply twice. I'd bet there's a less hacky way to do this but, as I say, in case anyone else is curious.

Answer 3

This might be interesting to you:

: double ( n -- n ) dup + ;   ! add 2 times
: square ( n -- n ) dup * ;   ! multiply 2 times

So what about 3 times?

: triple ( n -- n ) dup dup + + ;   ! add 3 times
: cube   ( n -- n ) dup dup * * ;   ! multiply 3 times

(I wonder if there is a way to generalize the pattern [..a a a b b b..])

What about the next higher order operation: Tetration:

: tetrate2 ( n -- n ) dup ^ ;         ! raise to power twice
: tetrate3 ( n -- n ) dup dup ^ ^ ;   ! raise to power thrice

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You could probably also generalize the other way, implementing hyper-operations like Knuth's up arrow. It's not immediately apparent to me how one would go about doing that, but Björn's answer seems to hint at it. The actual source has a lot of abstraction layers optimizing for the different datatypes. Clicking thru until it reaches (^fixnum) gives something similar