Maya Posch writes about the reverse-engineering of the Intel 8087 FPU, specifically focusing on how it implements trigonometric functions like `FPTAN`. To achieve high accuracy for 64-bit values efficiently, the hardware uses a hybrid approach that combines the CORDIC algorithm with Padé approximants. The system first performs most calculations using CORDIC and then switches to polynomial approximation once the remaining value is small enough, allowing it to avoid large look-up tables or excessive processing time.
- For one calculated value of `FPTAN`, CORDIC pseudo-division takes 33% of the time, while pseudo-multiplication takes 47%.
- The polynomial approximation stage accounts for only about 15% of the execution time with a 5% overhead.
- Later CPUs like the Pentium series moved away from CORDIC because it is difficult to scale for high bit-accuracy without significant performance penalties.
- For one calculated value of `FPTAN`, CORDIC pseudo-division takes 33% of the time, while pseudo-multiplication takes 47%.
- The polynomial approximation stage accounts for only about 15% of the execution time with a 5% overhead.
- Later CPUs like the Pentium series moved away from CORDIC because it is difficult to scale for high bit-accuracy without significant performance penalties.
