In October 2017 I received a program, {goldstoner.c}, in the format of
the BIGNUM BAKEOFF contest from Arnaldur Bjarnason, <aarnaldur@gmail.com>.
The main function, A(n, s, d),  is first called with s != 0 and d = 0 and
then calls itself recursively with s >= d = 1; calls to A(n, s, d) with
s > d > 0 result in recursive calls with s the same and d increased
by 1, eventually bottoming out when s = d, in which case
A(n, s, d) = n.  Following this recursive pattern and with a series of
inductions over the loops in A(n, s, d), it is possible to show that

1 + F[1 + 2(s - d)](n - 1) <= A(n, s, d) <= F[1 + 2(s - d)](2n + 1),
                       n >= 2,  s > d > 0.

Plugging these bounds into the initial call to A(n, s, 0) and making
another series of inductions gives

      F[1, 2](n - 1) + 1 <= A(n, s, 0) <= F[1, 2](2n + 1),
                       n >= 3, s != 0.

The output of {goldstoner.c} is therefore between F[1, 2](98) + 1 and
F[1, 2](199), i.e., between {ioannis.c} and {chan-2.c} in the
BIGNUM BAKEOFF results.





# goldstoner.c #

#include <stdlib.h>

typedef int I;

I A(I n, I s, I d) {
    if (d == s) {
        return n;
    }
	I* a = malloc(n);
	I  i;
    for (i = 0; i < n; ++i) {
        a[i] = n;
    }
    I o = n;
    I l = 1;
    while (l) {
        l = 0;
        I i;
        for (i = 0; i < n; ++i) {
            a[i] += l ? A(a[i] << a[i - 1], !d ? a[i] << a[i - 1] : s, d + 1) : -1;
            a[i] = a[i] < 1 ? 0 : a[i];
            o <<= a[i];
            l = a[i];
        }
    }
    return o;
}

I main() { return A(99, 99, 0); }