MedianFAME.h

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#pragma once 


template<typename T>
class MedianFAME {
public:

    T M;
    size_t n;
    T step;
    
    MedianFAME() : M(0.0), n(0), step(NaN) {
    }   
        
    T median() const { 
        if(n == 0) 
            return NaN;
        else
            return M;
    }
    
    void add(T x) {
        
        if(n == 0) {
            M = x;
            step = sqrt(abs(x)); // seems bad to initialize at x b/c then we start with giant sign swings; sqrt has a nice aesthetic
        }
        else {
            
            if(x > M) {
                M += step;
            }
            else if(x <= M) {
                M -= step;
            }
            
            if(abs(x-M) < step) {
                step = step/2.0;
            }
        }
        ++n;
    }
    void operator<<(T x) {  add(x);}

    
};