[Jprogramming] Crash calculating large hyper operations

[Dan Bron]

The notion of “hyper operation” extends the intuition that multiplication is repeated addition, exponentiation is repeated multiplication, tetration is repeated exponentiation, and so on.

Hyperoperation can be defined piecewise (per Wikipedia) as:

            / b+1 if n = 0
            | a if n  = 1, b = 0
 H_n(a,b) = | 0 if n  = 2, b = 0
            | 1 if n >= 3, b = 0
            \ H_n-1( a, H_n(a, b-1) ) otherwise

Or, in J:

H =: adverb define
:
  if. 0=m do.
    1+y
  elseif. (m > 0) *. (0=y) do.
    (<:3<.m) { x,0,1
  elseif. do.
    x (<:m) H x m H <:y
  end.
)

Now, while J likes 2 (0 H) 3, 2 (1 H) 3, 2 (2 H) 3, and 2 (3 H) 3 just fine, producing the expected results [1], it silently crashes (i.e. the IDE simply disappears) on 2 (4 H) 3 .

Now, I’m sure  2 tetration 3  is some absurdly large number and I wouldn’t expect a result, but I’d prefer a stack error (or whatever) to a crash.

-Dan

[1]  Representing successor, addition, multiplication, and exponentiation respectively.