Turbocharging BASIC programs with native procedure calls

To demonstrate the benefit of having a built-in C compiler to the common BASIC programmer, here's a quick rundown of how to speed up @SanguineBrah's brotexplorer by a factor of 5 with these steps:

1. Replace this BASIC code:

   iteration=0
   WHILE x*x+y*y<=(2*2) AND iteration<maxiteration
       xtemp=x*x-y*y+x0
       y=2*x*y+y0
       x=xtemp
       iteration=iteration+1
   WEND 
   IF iteration<>maxiteration THEN c=iteration ELSE c=0 

   with this native procedure call:

   c = |iterbrot(#x0, #y0, #x, #y, maxiteration)

2. Write a 1:1 translation of the BASIC code into C and save it in a file, say "bexturbo.c":

   int iterbrot(double x0, double y0, double x, double y, int maxiteration)
   {
       int iteration = 0;
       double xtemp;
       while (x*x + y*y <= 4 && iteration < maxiteration) {
           xtemp = x*x - y*y + x0;
           y = 2 * x * y + y0;
           x = xtemp;
           ++iteration;
       }
       if (iteration >= maxiteration)
           return 0;
       else
           return iteration;
   }

3. Write a loader. This is required because native calls like |iterbrot ... can only be tokenized correctly when the symbol that is called already exists.

   TCC "bexturbo.c"
   TCCLINK "bexturbo"
   CHAIN "bexturbo_imp.bas"

4. Done.

You can find both the interpreted and the sped-up version in the basicengine-demos repo. (@SanguineBrah: please shout if you don't approve of this)
I have also modified it to do incremental rendering for increased responsiveness.