pete-8.c is one of the nine entries an anonymous "Pete" submitted to Bignum Bakeoff.[1] It was a failed attempt at improving upon Pete's largest entry, pete-7.c, and it produces a much smaller number than pete-7.c because the f(n) function Pete defines in this program has a bug which causes f(n), no matter what n equals, to equal the square of a previously defined number. It is almost identical to it successor, pete-9.c.
The output of pete-8.c can be precisely expressed as \(z^{16\cdot17^6}(999)\), where \(z(n) = 9\cdot 2^n\).
Approximations in other notations[]
| Notation | Approximation |
|---|---|
| Up-arrow notation | \(2 \uparrow\uparrow 386,201,107\) |
| Hyper-E notation | \(E301.16181795010226\#386,201,104\) |
| Chained arrow notation | \(2 \rightarrow 386,201,107 \rightarrow 2\) |
| Hyperfactorial array notation | \(386,201,107!1\) |
| Fast-growing hierarchy | \(f_3(386,201,107)\) |
| Hardy hierarchy | \(H_{\omega^3}(386,201,107)\) |
| Slow-growing hierarchy | \(g_{\varepsilon_0}(386,201,107)\) |
Code[]
#define Z (9<<(9<<
#define Y Z Z Z Z Z Z Z Z
#define W ))))))))))))))))
#define Q Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y
#define O W W W W W W W W W W W W W W W W W
#define P Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q
#define M O O O O O O O O O O O O O O O O O
#define L P P P P P P P P P P P P P P P P P
#define K M M M M M M M M M M M M M M M M M
#define H L L L L L L L L L L L L L L L L L
#define J K K K K K K K K K K K K K K K K K
#define A H H H H H H H H H H H H H H H H H
#define D J J J J J J J J J J J J J J J J J
#define X A A A A A A A A A A A A A A A A A 999 D D D D D D D D D D D D D D D D D
int B = X;
f(int* a)
{
int C = B, b[X], n = X;
while(n--)
b[n] = a[n];
if(b[n = X - 1]--)
while(C--)
B = f(b);
while(n && !(b[n] = B, b[--n]--))
;
return n ? f(b) : B * B;
}
main()
{
int a[X] = {X};
return f(a);
}
Sources[]
See also[]
Large numbers in computers
Main article: Numbers in computer arithmetic
127 · 128 · 256 · 32767 · 32768 · 65536 · 2147483647 · 4294967296 · 9007199254740991 · 9223372036854775807 · FRACTRAN catalogue numbersBignum 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