what mathematical model can I use for this and how to implement it in c++/c#

Question

I want to write a function that gets up to six parameter and an array of input values and map inputs value to output based on the following conditions:

1. we know min and max of input values.
2. The output min and max should be a constant value (say -10,100).
3. Based on parameters, it amplify small input values more than input values which are near inputmax.
4. after mapping, the output min and max should be the constant values.

I think I need some sort of logarithmic amplification. But I am not sure how to define it so that it match the above mentioned conditions.

What mathematical formula can I use for this?

I need to implement it both in c++ and c#. If I know how to implement it in one of them, I can convert it to other one.

Answer 1

I don't really understand where is the problem; am I missing something? What you say seems to require a simple component-wise operation, something of the form:

forall x in range
    out[x] = ((in[x]-in_min)/(in_max-in_min))^gamma * (out_max-out_min)+out_min

where gamma is some constant, probably smaller than 1 if you want low values to be amplified more than high values. Think of it like a "gamma correction".

I do not however see how your "6 parameters" come into play?