Marxen.c

marxen.c is an entry by Heiner Marxen for the Bignum Bakeoff contest, whose objective is to write a program (in 512 characters or less) that generates the largest possible output. It came in second place in the competition, behind Loader's number.
The program uses a variant of the Goodstein sequence. Its output is lower bounded by \(f_{\omega^{\omega}}(2\uparrow\uparrow 500)\) and upper bounded by \(f_{\varepsilon_{0}+{\omega^3}}(1,000,000)\) in the fast-growing hierarchy.Bignum Bakeoff contest recap by David Moews.
== Code ==
typedef int	J;
J P(J x,J y)	{ return x+y ? x%2 + y%2*2 + P(x/2,y/2)*4 : 0 ;}
J H(J z)	{ return z ? z%2 + 2*H(z/4) : 0 ;}
J I(J f,J e,J r){ return f ? P(P(f,e),r) : r ;}
J M(J x,J e)	{ return x ? I(x%2, M(e,0), M(x/2, e+1)) : 0 ;}
J D(J,J);	 
J E(J f,J e,J r,J b)
{
 return e ? E(1, D(e,b), I(b-1, D(e,b), I(f-1,e,r)), b) : I(f-1,e,r) ;
}
J D(J x,J b)	{ return x ? E( H(H(x)), H(H(x)/2), H(x/2), b) : 0 ;}
J F(J x,J b)	{ return x ? F(D(x,b+1),b+1) : b ;}
J G(J x)	{ return F(M(x,9), 9) ;}
J f(J n,J x)	{ return n ? f(n-1, G(x ? f(n,x-1) : n)) : G(x) ;}
J g(J x)	{ return f(x,x) ;}
J h(J n,J x)	{ return n ? h(n-1, g(x ? h(n,x-1) : n)) : g(x) ;}
J main(void)	{ return h(g(9),9) ;}
==Functions defined in Marxen.c==
In the following, the operator symbol / denotes the integral division and a % b is equivalent to a (mod b).
===P(x,y)===
# If x+y = 0, then P(x,y)=0.
# Otherwise, P(x,y)=x%2 + y%2*2 + 4P(x/2,y/2).
===H(z)===
# If z = 0, then H(z)=0.
# Otherwise, H(z)=z%2 + 2H(z/4)
===I(f,e,r)===
# If f = 0, then I(f,e,r)=r.
# Otherwise, I(f,e,r)=P(P(f,e),r)
===M(x,e)===
# If x = 0, then M(x,e)=0.
# Otherwise, M(x,e)=I(x%2, M(e,0), M(x/2,e+1))
===D(x,b)===
# If x = 0, then D(x,b)=0.
# Otherwise, D(x,b)=E(H(H(x)), H(H(x)/2), H(x/2), b)
===E(f,e,r,b)===
# If e = 0, then E(f,e,r,b)=I(f-1,e,r)
# Otherwise, E(f,e,r,b)=E(1, D(e,b), I(b-1, D(e,b), I(f-1,e,r)), b)
===F(x,b)===
# If x = 0, then F(x,b)=b.
# Otherwise, F(x,b)=F(D(x,b+1),b+1)
===G(x)===
G(x)=F(M(x,9),9)
===f(n,x)===
# If n = 0, then f(n,x)=G(x).
# Else if x = 0, then f(n,x)=f(n-1,G(n))
# Otherwise, f(n,x)=f(n-1,G(f(n,x-1)))
===g(x)===
g(x)=f(x,x)
===h(n,x)===
# If n = 0, then h(n,x)=g(x).
# Else if x = 0, then h(n,x)=h(n-1,g(n))
# Otherwise, h(n,x)=h(n-1,g(h(n,x-1)))
===main()===
main()=h(g(9),9)
This is the number produced by the program, and thus the number submitted to the Bignum Bakeoff.
==Sources==
==See also==
ja:marxen.c
fr:marxen.c
ru:Marxen.c
Category:Bignum Bakeoff contestant
Category:Numbers
Category:Functions
Category:Computers
Category:Eponymous numbers
Category:Exponentiated linear omega level
Category:Epsilon level