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

The Intel 8087 floating-point chip used a hybrid algorithm combining CORDIC and polynomial approximation to compute the tangent function, achieving a 144x speedup over software implementations on the 8086 microprocessor. By reverse-engineering the chip's circuitry and microcode, researchers discovered that the FPTAN instruction leveraged specialized hardware components including a constant ROM for CORDIC values, a shifter, and an adder to balance both accuracy and performance. The CORDIC algorithm itself, originally developed in 1956 for aircraft navigation computers, uses only shift and add operations with table lookups, avoiding the need for multiplication or division.