In 1980, Intel introduced the 8087, a floating-point chip that dramatically accelerated trigonometric calculations in systems like the IBM PC. This article explores the algorithm behind its tangent instruction, FPT AN, which cleverly combines CORDIC with polynomial approximation to achieve both speed and precision. The 8087 computed a tangent in 90 microseconds, a massive improvement over the 13,000 microseconds required by the 8086 microprocessor.

By examining the chip’s microcode ROM and datapath—revealed through microscopic imaging—the author details how the B-58 Hustler bomber’s legacy influenced the design. Engineer Jack Volder originally developed CORDIC in 1956 for the Convair B-58A Hustler, using shift-and-add operations to compute trig functions without multiplication. The algorithm breaks an angle into precomputed rotations, converging rapidly with each iteration.

The 8087’s datapath includes functional blocks like the constant ROM, shifter, and adder, all optimized for efficient transcendental computation.