Modulo Power function in J

Question

If I want to compute a^b mod c then there is an efficient way of doing this, without computing a^b in full.

However, when programming, if I write f g x then g(x) is computed regardless of f.

J provides for composing f and g in special cases, and the modulo power function is one of them. For instance, the following runs extremely quickly.

1000&| @ (2&^) 10000000x

This is because the 'atop' conjunction @ tells the language to compose the functions if possible. If I remove it, it goes unbearably slowly.

If however I want to work with x^x , then ^~ no longer works and I get limit errors for large values. Binding those large values however does work.

So

999&| @ (100333454&^) 100333454x

executes nice and fast but

999&| @ ^~ 100333454x

gives me a limit error - the RHS is too big.

Am I right in thinking that in this case, J is not using an efficient power-modulo algorithm?

Answer 1

Per the special code page:

m&|@^       dyad    avoids exponentiation for integer arguments
m&|@(n&^)   monad   avoids exponentiation for integer arguments

The case for ^~ is not supported by special code.