## FANDOM

10,010 Pages

Loader's number is the output of loader.c, a C program by Ralph Loader that came in first place for the Bignum Bakeoff contest, whose objective was to write a C program (in 512 characters or less) that generates the largest possible output on a theoretical machine with infinite memory. It is among the largest computable numbers ever devised.

The program diagonalizes over the Huet-Coquand calculus of constructions. Its output, affectionately nicknamed Loader's number, is defined as $$D^5(99)=D(D(D(D(D(99)))))$$, where $$D(k)$$ is the sum of all possible bit strings described by the first k expressions of the calculus of constructions (encoding everything as binary numbers).

David Moews has shown that $$D(99)$$ is larger than $$2↑↑30,419$$ (where ↑↑ is tetration), and that even $$D^2(99)$$ would be much larger than $$f_{\varepsilon_0+\omega^3}(1,000,000)$$ in the fast-growing hierarchy, using Cantor's definition of fundamental sequences. $$D^2(99)$$ thus is obviously much larger than the output of Marxen.c, which is upper bounded at the aforementioned $$f_{\varepsilon_0+\omega^3}(1,000,000)$$.

The final output of $$D^5(99)$$ is much larger than TREE(3), SCG(13), and, say, BH(100). It is probably overpowered by finite promise games and greedy clique sequences. Loader's function is computable, so $$\Sigma(n) > D^5(99)$$ for relatively small n, say, n = 100.

## Code Edit

#define R { return
#define P P (
#define L L (
#define T S (v, y, c,
#define C ),
#define X x)
#define F );}

int r, a;
P y, X
R y - ~y << x;
}
Z (X
R r = x % 2 ? 0 : 1 + Z (x / 2 F
L X
R x / 2 >> Z (x F
#define U = S(4,13,-4,
T  t)
{
int
f = L t C
x = r;
R
f - 2 ?
f > 2 ?
f - v ? t - (f > v) * c : y :
P f, P T  L X  C
S (v+2, t  U y C  c, Z (X )))
:
A (T  L X  C
T  Z (X ) F
}
A (y, X
R L y) - 1
? 5 << P y, X
: S (4, x, 4, Z (r) F
#define B (x /= 2) % 2 && (
D (X
{
int
f,
d,
c = 0,
t = 7,
u = 14;
while (x && D (x - 1 C  B 1))
d = L L D (X ) C
f = L r C
x = L r C
c - r || (
L u) || L r) - f ||
B u = S (4, d, 4, r C
t = A (t, d) C
f / 2 & B  c = P d, c C
t  U t C
u  U u) )
C
c && B
t = P
~u & 2 | B
u = 1 << P L c C  u) C
P L c C  t) C
c = r  C
u / 2 & B
c = P t, c C
u  U t C
t = 9 );
R a = P P t, P u, P x, c)) C
a F
}
main ()
R D (D (D (D (D (99)))) F