Recursive Integer Guessing Game

A recursive algorithm that queries an objective function to guess an unknown integer.

An integer guessing 'game' for a
function `isleq', that returns true for
all values less than or equal to a
mystery number.

Syntax: z=guessgame(isleq,n,k)

In tertiary function notation:

g(n,k) =
| k==0 :: isleq(n) ? n : n+1;
| k>0 :: isleq(n+(2^k)-1) ?
g(n,k-1) : g(n+2^k,k-1);
| k<0 :: isleq(n+(2^(-k))-1) ?
g(n,(-k)-1) : g(n+(2^(-k)),k-1);

g(n,-k) for -k negative refers to an
unbounded search [n,inf] with current
search depth up to (n+2^(-k)-1) :

e.g. g(15,-4) denotes [15,30].

g(n,k) for k positive refers to a
search over the interval
[n,(n+(2^(k+1))-1)] :

e.g. guess(63,5) denotes [63,126].

Initial function should be run with n
set as a lower bound (default 1).

Function isleq can be replaced with an
integer instead.