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In 1980, Intel introduced the 8087 floating-point coprocessor chip. Plugging this chip into your IBM PC made math 100 times faster, good for CAD and spreadsheets. I opened up the chip to reverse-engineer exactly how it does complicated calculations. Let's take a look inside...

Under a microscope, you can see the circuitry of the 8087. The 8087 performs its calculations using low-level software called microcode, stored in the large ROM in the middle. Along with the "Opcode Collective", I'm trying to understand the algorithms in the microcode, from addition to arctangents.

Zooming in on the microcode storage ROM, you can see the individual transistors, the pinkish blobs. The 8087 is very unusual, using four transistor sizes, giving it double density: 2 bits per transistor. The Opcode Collective examined all 13184 transistors, revealing the 0s and 1s of the microcode.

I can now explain the microcode for an instruction called FSCALE that scales a number by a power of 2. It sounds simple, but the 8087 has an appalling number of special cases: positive and negative 0, two infinities, four rounding modes, three number sizes, six exceptions... so the code is complex.

The 8087's microcode is too complicated and low-level to explain here. For details, see my latest article: www.righto.com/2026/09/8087...