> As for square roots, the reason why you can't use the underlying architecture is that it only works on the native i16 type.
My understanding of your code is that you've got `struct Number { int16 a,b,c,d; };` and the value of a number is equal to the floating point number 256.0a + b + c / 256.0 + d / 65536.0. (if the arch had floats, which it doesn't) If this assumption is wrong, my bad.
What I'm proposing is that you do `b = i16.sqrt(256a + b); a = 0;` then do 1-2 iterations of newton's method. For instance, if you have the value 1234.56789 then i16.sqrt(256*a+b) = i16.sqrt(1234) = 35. So your first approximation is x = 35.56789. Do x = (x + 1234.56789/x)/2, and with floats you get x = 35.139035. Do it again, you get x = 35.136418. The true value is also 35.136418, so there ya go.
> I'd be concerned about Newton's method (specifically the squaring of x_n) overflowing the fixed point.
I may have lost the plot. Are you calculating _inverse_ square root? x_n isn't squared for Newton's method of square root, but it is for inverse square root.
(Either way, the square of the square root of a number should be the same as the original number. So if you have overflow, you have other problems.)
Unrelated: What do you need pi and trig functions for? I wrote a ray tracer (actually a path tracer, same diff) about a year ago, and I only used trig/pi to set up the camera for the render. While the render was actually rendering, no trig was happening. It didn't matter for me, so I just used the standard library, but in your case it would probably be fine to use slow brutish methods.