The Intel 8087, a floating-point chip introduced in 1980, significantly accelerated floating-point operations in the IBM PC and other systems. A recent analysis of the chip's circuitry and microcode has revealed the algorithm behind its tangent instruction, known as FPTAN, which combines the CORDIC algorithm and polynomial approximation to achieve high accuracy and performance. By reverse-engineering the chip, it was found that the FPTAN instruction computes a tangent in 90 microseconds, a substantial improvement over the 13,000 microseconds required by the 8086 microprocessor. The analysis involved creating a high-resolution image of the chip's die and examining its datapath, which consists of functional blocks that perform floating-point calculations on 80-bit values, to understand the algorithm's implementation and achieve a deeper understanding of the chip's architecture.