Pete.c numbers

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The Pete.c numbers were a series of seven numbers made by Bignum Bakeoff contestant Pete.

Programs

pete-4.c

pete-4.c's program is as follows:

#define F(Q,R,P) Q(int x){int i=x;while(i--)x=R(x,x);return x;}\
P(int L,int x){int i=x;if(L--)while(i--)x=P(L,x);return Q(x);}
#define Y(A,z,B,C,D,E,G,H,I,J,K,M,N,O,S,T,U,V,W)\
F(A,z,B)F(C,B,D)F(E,D,G)F(H,G,I)F(J,I,K)F(M,K,N)F(O,N,S)F(T,S,U)F(V,U,W)
Z(int L,int x)
{
    int i = x;
    if(L--)
        while(i--)
            x = Z(L,x);
    return x << x;
}
Y(a,Z,b,c,d,e,g,h,X,j,k,m,n,o,s,t,u,v,w)
Y(Aa,w,Ba,Ca,Da,Ea,Ga,Ha,Ia,Ja,Ka,Ma,Na,Oa,Sa,Ta,Ua,Va,Wa)
Y(Ab,Wa,Bb,Cb,Db,Eb,Gb,Hb,Ib,Jb,Kb,V,U,W,T,S,O,N,M)
F(A,M,B)
F(C,B,D)
F(E,D,G)
F(H,G,I)
F(J,I,K)
int main()
{
    return K(99999,9);
}

Its lower bound is \(f_{\omega32+10^5}(9)\) and its upper bound is \(f_{\omega32+10^5}(11)\).

pete-5.c

pete-5.c's program is as follows:

int C = 999;
A(int S,int R,int P,int O,int N,int M,int L,int K,int J,int F,int E)
{
    int D = C; 
    if(E--)
        while(D--)
            C = A(S,R,P,O,N,M,L,K,J,F,E);
    return 
          F-- ? A(S,R,P,O,N,M,L,K,J,F,C)
        : J-- ? A(S,R,P,O,N,M,L,K,J,C,C)
        : K-- ? A(S,R,P,O,N,M,L,K,C,C,C)
        : L-- ? A(S,R,P,O,N,M,L,C,C,C,C)
        : M-- ? A(S,R,P,O,N,M,C,C,C,C,C)
        : N-- ? A(S,R,P,O,N,C,C,C,C,C,C)
        : O-- ? A(S,R,P,O,C,C,C,C,C,C,C)
        : P-- ? A(S,R,P,C,C,C,C,C,C,C,C)
        : R-- ? A(S,R,C,C,C,C,C,C,C,C,C)
        : S-- ? A(S,C,C,C,C,C,C,C,C,C,C)
        : C * C;
}
#define Q ,C,C,C,C,C,C,C,C,C,C)
main()
{return A(A(A(A(A(A(A(A(A(A(A(A(A(A(A(A(C Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q;}

Its lower bound is \(f_{\omega^{11}}^{16}(999)\) and its upper bound is \(f_{\omega^{11}}^{16}(1031)\).

pete-6.c

pete-6.c's program is as follows:

#define M E H,h,g,f
#define L E G,p,o,n
#define K E w,v
#define J ,B,B
#define I J J
#define H G,p,o,n,m,l,k,j,i
#define G w,v,u,t,s,r,q
#define F I I
#define E --?A(
#define D ,B):
#define C ,int
int B = 9 << 9999;
A(int w C v C u C t C s C r C q C p C o C n C m C l
        C k C j C i C h C g C f C e C d C c C b C a)
{
    int y = B;
    if(a--)
        while(y--)
            B = A(H,h,g,f,e,d,c,b,a);
        return 
            b M,e,d,c,b D
            c M,e,d,c,B D
            d M,e,d J D
            e M,e J,B D
            f M I D
            g E H,h,g I,B D
            h E H,h I J D
            i E H I J,B D
            j L,m,l,k,j F D
            k L,m,l,k F,B D
            l L,m,l F J D
            m L,m F J,B D
            n L F I D
            o E G,p,o F I,B D
            p E G,p F I J D
            q E G F I J,B D
            r K,u,t,s,r F F D
            s K,u,t,s F F,B D
            t K,u,t F F J D
            u K,u F F J,B D
            v K F F I D
            w E w F F I,B D
            B * B;
}
main(){return A(B I F F J);}

Its lower bound is \(f_{\omega^{23}}(2^{9999}\cdot 9)\) while its upper bound is \(f_{\omega^{23}}(2^{9999}\cdot 9+2)\).

See also

Large numbers in computers

Main article: Numbers in computer arithmetic

127 · 128 · 256 · 32767 · 32768 · 65536 · 2147483647 · 4294967296 · 9007199254740991 · 9223372036854775807 · FRACTRAN catalogue numbers
Bignum Bakeoff contestants: pete-3.c · pete-9.c · pete-8.c · harper.c · ioannis.c · chan-2.c · chan-3.c · pete-4.c · chan.c · pete-5.c · pete-6.c · pete-7.c · marxen.c · loader.c
Channel systems: lossy channel system · priority channel system
Concepts: Recursion