Pseudo-number generation compared to Blum-Micali

A few years ago I made a pseudo-random number generator to use in a monte carlo simulation for a lecture in my University.

My instructor ask me why I did that generator instead of using C equivalent rand.

The algorithm is $x_{n+1} = e^{x_n + k} \mod 1$ using float point values with $K$ big enough to contain a complete cycle inside $\epsilon$ (a very small value).

Yesterday I find another PRNG using a similar formula: Blum-Micali algorithm

$x_{n+1} = g^{x_n} \mod p$

The answers are... could my algorithm be based on the Blum-Micali one?

Could my algorithm contain the Blum-Micali properties?