Microcode inside the Intel 8087 floating-point chip: register exchange

In 1980, Intel introduced the 8087 floating-point chip, a co-processor that made floating-point operations up to 100 times faster. This chip was highly influential, and today most processors use the floating-point standard introduced by the 8087. The 8087 uses complicated algorithms to accurately compute functions such as square roots, tangents, and exponentials. These algorithms are implemented inside the chip in low-level code called microcode. I'm part of a group, the Opcode Collective, that is reverse-engineering this microcode. In this post, I take a close look at the microcode for one of the 8087's instructions—FXCH—and explain how the microcode works. The FXCH (Floating-point Exchange) instruction exchanges two floating-point registers. You might expect this instruction to be trivial, but there's more going on than you might expect; the microcode uses 14 micro-instructions to implement the exchange instruction. The Intel 8087 chip is packaged in a 40-pin DIP (dual in-line…