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A bit of a story time! As part of my high school math program, I must write a paper on a topic related to math. I've chosen the implementation of a scientific calculator. I've created my own using an Arduino. The internal numbers are BCD and it uses CORDIC algorithms for trig plus constant subtraction methods for exp and ln.

I used this page that details the HP-35's (the first ever pocket scientific calculator!) implementation of the algorithms. I want to say that the TI-84 and its ilk still use the same algorithms even in the present day, but in the annoying world of academia I need a source to back me up. I've been told about the CORDIC implementation but something more presentable and about the other algorithms would be excellent! Thanks for your help, and I'll be happy to post my paper and details about my calculator once I have finished.
I have been Googling trying to find an article that I believe I once saw on TI's website about how a few of the functions are computed. Unfortunately, I cannot find anything other than the the link in your post :/ It is very likely that TI uses almost exactly the same algorithms as they are fairly standard on simple processors.

You may find some calculators that use the BKM algorithm to compute trig functions, exponential, and logarithm. It is similar to CORDIC, and depending on how it is implemented, is probably a little slower than CORDIC.
I believe that this document from TI's website might be what you're looking for. In particular, it indicates that:
Texas Instruments wrote:
How does TI graphing calculators compute values for sine, cosine and tangent?

Texas Instruments uses the CORDIC algorithm method to compute trigonometric and other transcendental functions. A recent thread on Graph-TI asks about the internal methods used to compute trigonometric and other transcendental functions.

Most practical algorithms in use for transcendental functions are either polynomial approximations or the CORDIC method. TI calculators have almost always used CORDIC, the exceptions being the CC-40, TI-74 and TI-95 which used polynomial approximations.
Quote:
The polynomial approximations, however, are not usually familiar ones like a Taylor's series, but more related to Chebyshev polynomials. Early work on this topic was done by Hastings (ref 3) which is a fascinating book that represents a lot of tedious work in an age when "computers" were still likely to be people!

Edit: Since you asked, the File Format and Link Protocol Guide has the most easy-to-understand explanation of the TI-OS real number format. If you want a more "official" source, the TI-83+ SDK PDF from http://education.ti.com also documents the format, albeit less clearly.

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