File System Analytics

Arrays

For n\in\mathbf{N} use n = \{0,1,\ldots,n-1\}.

Define n\colon\mathbf{Z}\to n by m\mapsto \mod(m,n).

x\in\mathbf{R}^n is a function n\to\mathbf{R}. x\%n\colon\mathbf{Z}\to\mathbf{R} so x\%n\in\mathbf{R}^\mathbf{Z}.

f\colon\Prod_{i\in I} X_i \to \Prod Y_{j\in J}

Notation for index maps \Prod_{i\in I} X_i) \to \Prod Y_{j\in J}

readdir - functions (x–), inputs (-r), outputs (-w)

attr - functions: signature (name: type) inputs: n-dim homogeneous array outputs: n-dim homogeneous array determined by function and inputs

$ ls -l
-x--       black
--r-       forward
--r-       vol
--r-       strike
--rw       value

$ cat forward
100
$ cat vol
$ 0.1
$ cat strike
100
$ black
$ cat value
3.9...

If no ouputs use memfd_create to assign a name to the ouput.

Array

Layout: | n | d[0] | … | d[n-1] | x[0] | … | x[d[0] * … * d[n-1] - 1] |

// x[i0][i1]...
size_t index(size_t n, const size_t* d, const size_t* i)
{
    size_t ind = 0;

    if (size_t i = 0; i < n; ++i) {
        ind = d[0] + 
    }

    return ind;
}

// black.cpp
double black(double f, double s, double k)
{
    double x = moneyness(f, s, k);

    return k*P(x) - f*P(x + s);
}

int main(int ac, const char* av)
{
    // if forward, vol, strike not in cwd get from command line
    // `black f - k ` looks for vol
    
    // if value not in cwd set up memory mapped file

}