D and math, can you isolate this ?

[Basile B. via Digitalmars-d-learn]

On Wednesday, 21 September 2016 at 01:34:06 UTC, Nicholas Wilson 
wrote:
> On Tuesday, 20 September 2016 at 12:35:18 UTC, Basile B. wrote:
>> I've recently started an easing/interpolation family of 
>> function in my D user library. It's based on something I know 
>> well since I've already used them in 2012 in a VST plugin 
>> called GrainPlot (RIP).
>>
>> However for one of the function, I can't manage to get the 
>> inverse.
>>
>> A function that's fully implemented:
>> https://github.com/BBasile/iz/blob/master/import/iz/math.d#L598
>> - f(x,c) = x*x*x - x*x*c + x*c;
>> - c(f(0.5)) = 4 * (y - 0.125));
>>
>> Another:
>> https://github.com/BBasile/iz/blob/master/import/iz/math.d#L749
>> - f(x,c) = pow(x, c);
>> - c(f(0.5)) = log(y) / log(0.5));
>>
>> The problem is here:
>> https://github.com/BBasile/iz/blob/master/import/iz/math.d#L849
>> - f(x,c) = 1.0 - pow(1.0 - pow(x, 2.0/c), c * 0.5);
>> - c(f0.5)) = ?
>>
>> Which means that I ask you if you can isolate c for
>>
>> y = 1.0 - pow(1.0 - pow(0.5, 2.0/c), c * 0.5);
>>
>> y is always f(0.5,c)
>
> So if we rearrange and take the logs of both sides and divide 
> by c we get
>
> 2*log(1-y)/c = log(1-2^(-2/c))
>
> and then that we have one occurrence of c on each side do an 
> iterative back substitution to find the intersection given that 
> you know for y=0.5 ,c = 2.
> We used this method for finding voltages and currents in 
> circuits with semiconductors.

Y is a floating point value. I think I'm gonna make a LUT for 
let's say 100 values to find the initial range where the result 
stands.