Mashimo Function (translation)

$Mashimo function$, or $M(x)$, is a function designed to make various sizes of large numbers. Its domain is real number and range is positive real number. It is a monotonically increasing function. There is an index of large numbers called Mashimo scale. Mashimo is a character in Sushi Kokuuhen.

If $x \geq 1$,

$M(x)=max(10^{10x}, ^{x/5}e, H(^{x/20}2,2), H(^{H(x-70,2)}3,3),$ $V(x-72), V(3^{x-80}), BHO(x-83), O(x-85), OF(x-86),$ $L(x-90), D(5(x-94),10), FC(x-80), RC(x-120))$

If $0 \leq x<1$, $M(x)=10^{10x}$

If $x<0$, $M(x)=M(-x)^{-1}$

Max function is a function which returns the biggest number in the argument. Sub functions H,V,BHO,O,OF,L,D,FC,RC are defined below. Generalization of tetration is like this:

$^x a=log_a(^{x+1} a) \,\, for x\leq -1$

$^x a=x+1 \,\,\,\,\, for -1 < x \leq 0$

$^x a= a^{(^{x-1} a)} \,\, for 0<x$