Some overlap within:If you like reading about math approximations and “theoretical vs. actual” algorithms, there’s a fascinating series of presentations by Robin Green. I don’t know if videos exist anywhere, but the slides come with plenty of notes
- Faster Math Functions (2016)
- Even Faster Math Functions (2020)
- Even Faster Math Functions, 2021 Edition
If you analyze the maximal error of an interpolated sin table you can show that a 33-entry table is sufficient to reconstruct a 32-bit floating point sine and cosine at the same time.
[I think Sophie referred to this work, in reference to BBC Basic's maths routines]The code mentions “Cody & Waite” in many places – a title so out of print that many people work from their own photocopied version of the title, copies of copies that are handed down between researchers
The dramatic story of how IEEE754 was created is a story of David vs. Goliath. ... There was a standoff between Digital Equipment’s VAX- format that had worked well in the minicomputer world for a decade, and the Kahan-Coonen-Stone (K-C-S) proposal from Intel.
(Emphasis added!)On the web there are a lot of presentations on “advanced” computer math that end up using Taylor series to generate polynomial approximations for famous math functions. You’ve seen them in your Calculus textbook, they’re the definitions for Exp, Tan, Sin that you leaned at school so clearly that must be how they are calculated on computers. Truncate the series, generate a remainder and voila, you’re golden. Wrong.
via which links to How do calculators compute sine?