Structs
Algebraic sigmoid.
f(x) = x / sqrt(1 + x^2).
Fitting the sigmoid-like function from the PoE whitepaper.
p and s are just equivalent to the Sigmoid parameters.
a is an adjustment / fitting parameter (1 <= a < 5), to better match the
two curves differing slopes.This takes a geometric mean of stake and engagement points using integer math
Sigmoid function.
f(x) = 1 / (1 + e^-x).
Fitting the sigmoid-like function from the PoE white-paper:
f(x) = r_max * (2 / (1 + e ^(-s * x^p) - 1)Sigmoid function.
f(x) = 1 / (1 + e^-x).
Fitting the sigmoid-like to a 1/2 (sqrt) exponent.
f(x) = r_max * (2 / (1 + e ^(-s * sqrt(x)) - 1)Traits
This defines the functions we can use for proof of engagement points.