CORDIC, or Coordinate Rotation Digital Computer, is a venerable algorithm used by calculators to calculate trigonometric and logarithmic functions and their inverses:
sin, cos, tan, sinh, cosh, tanh, ln, exp.
Rather than give an explanation here, I know of no better explanation than that given by Richard Parris.
The CORDIC algorithm uses some number of constants, and then successive additions or subtractions and shifts, followed by one multiplication at the end to give the answer. Since it consists of two of the simplest possible mathematical operations, it is fast enough and simple enough to be implemented by quite limited processors.
Now, since my calculator is meant to be able to represent the magnitude of any number up to
100 to an accuracy of
-100, I decided to use 200 digits (or so) to represent any number using the
100.100 format, or 100 digits for the integer part, and 100 digits for the fractional part.
This meant that I needed all the CORDIC constants, to at least 200 digits, in this format. I wrote a Mathematica notebook which does this for me, which you can see in PDF format.