Reverse-engineering the Intel 8087's tangent algorithm: more than CORDIC

The Intel 8087’s FPTAN instruction combines a CORDIC loop with a polynomial refinement to compute tangent values in 90 μs, compared with 13,000 μs on the 8086. The chip’s 1648-instruction microcode ROM drives a datapath that includes exponent and constant ROMs, a large shifter, an adder used for iterative calculations, and a shift register holding 16 CORDIC status bits. This hybrid algorithm delivers high accuracy while keeping hardware simple.