How to do floating point calculations with integers

Question

I have a coprocessor attached to the main processor. Some floating point calculations needs to be done in the coprocessor, but it does not support hardware floating point instructions, and emulation is too slow.

Now one way is to have the main processor to scale the floating point values so that they can be represented as integers, send them to the co processor, who performs some calculations, and scale back those values on return. However, that wouldn't work most of the time, as the numbers would eventually become too big or small to be out of range of those integers. So my question is, what is the fastest way of doing this properly.

Answer 1

You are saying emulation is too slow. I guess you mean emulation of floating point. The only remaining alternative if scaled integers are not sufficient, is fixed point math but it's not exactly fast either, even though it's much faster than emulated float.

Also, you are never going to escape the fact that with both scaled integers, and fixed point math, you are going to get less dynamic range than with floating point.

However, if your range is known in advance, the fixed point math implementation can be tuned for the range you need.

Here is an article on fixed point. The gist of the trick is deciding how to split the variable, how many bits for the low and high part of the number.

A full implementation of fixed point for C can be found here. (BSD license.) There are others.

Answer 2

In addition to @Amigable Clark Kant's suggestion, Anthony Williams' fixed point math library provides a C++ fixed class that can be use almost interchangeably with float or double and on ARM gives a 5x performance improvement over software floating point. It includes a complete fixed point version of the standard math library including trig and log functions etc. using the CORDIC algorithm.