Aaron VanderGraaff
3/26/20

This is intended as a cubic spline library for Arduino. It's written in pure
C, so it will run on any architecture compiled with gcc or g++ as long as 
there are stdlib functions. 
The:
    #ifndef NUMBER_POINTS
    #define NUMBER_POINTS 20
    #endif
lines in spline.h set the maxiumum size for the initital value arrays. 
This has to do with the calling mechanics for 2-D arrays and could be
solved using pointers instead, but it works for me so I'm leaving it. It also
defines the size of the arrays in the initial S struct. The value can be 
adjusted to fit different needs to save memory or for bigger data sets.

There are several functions defined in spline.h; however, you only need 2:
        S *nat_cubic_spline(int num_points, S* output) and
        int evaluate(S *function, float val, float *result)

Before calling nat_cubic_spline, arrays of initial x and y values must be
created and put inside of an S struct. x and y must be the same length, x must
be sorted in increasing order, and each x,y pair must have the same index in
their respective arrays. Take a look at the "examples" directory for a few 
examples.

nat_cubic_spline takes the number of points in the x and y arrays and an S
struct to store all results in. 
The function returns an S struct pointer, which holds the interpolation 
parameters. The output is also stored in the original S struct passed to 
the funciton.
nat_cubic_spline performs a natural cubic spline of the given data points,
as its name suggests.

evaluate takes an S struct pointer, an x value to interpolate at and an
int pointer to store the result. This function returns 0 on success, and 
either -1, -2, or -3 on failure. A return value of -1 or -2 indicates the 
val passed does not fit in the domain of the initial x values (-1 for too
small and -2 for too big), and -3 indicates a total failure for some unknown
reason (this shouldn't happen. If it does, it's a bug). 

The other functions aren't static so you can use them, but their intended
purpose is as helper functions to nat_cubic_spline and evaluate. Only 
nat_cubic_spline and evaluate are setup to be run in a C++ program, so if 
you want to use the other functions in a C++ program, look in spline.h to 
see how to do that, then alter it.