Call from Mobile Phone to another phone through Asterisk?

I would like to know if the following is possible with Asterisk and if yes, how to setup?
With my mobile phone (GSM) I call my home phone (it is VOIP phone). Asterisk knows my mobile number and asks me to give the final number which I want to call. I do it and the final number I want to call is connected to my mobile phone.
The deal is that I can call my home from my mob free (the same French operator) and also all my calls from home are free (except mobile phones)
It is the only option I would like to setup with Asterisk (which I have not yet installed)
May I install Asterisk not having Linux installed?
I would appreciate if somebody can explain how to do it.

should be doable lots of info here