8087

4 Articles

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Reverse-Engineering The Intel 8087 Stack Circuitry

December 19, 2025 by 3 Comments

Although something that’s taken for granted these days, the ability to perform floating-point operations in hardware was, for the longest time, something reserved for people with big wallets. This began to change around the time that Intel released the 8087 FPU coprocessor in 1980, featuring hardware support for floating-point arithmetic at a blistering 50 KFLOPS. Notably, the 8087 uses a stack-based architecture, a major departure from existing FPUs. Recently [Ken Shirriff] took a literal closer look at this stack circuitry to see what it looks like and how it works.

Nearly half of the 8087’s die is taken up by the microcode frontend and bus controller, with a block containing constants like π alongside the FP calculation-processing datapath section taking up much of the rest. Nestled along the side are the eight registers and the stack controller. At 80 bits per FP number, the required registers and related were pretty sizeable for the era, especially when you consider that the roughly 60,000 transistors in the 8087 were paired alongside the 29,000 transistors in the 16-bit 8086.

Each of the 8087’s registers is selected by the decoded instructions via a lot of wiring that can still be fairly easily traced despite the FPU’s die being larger than the CPU it accompanied. As for the unique stack-based register approach, this turned out to be mostly a hindrance, and the reason why the x87 FP instructions in the x86 ISA are still quite maligned today. Yet with careful use, providing a big boost over traditional code, this made it a success by that benchmark, even if MMX, SSE, and others reverted to a stackless design.

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A Forgotten Consumer PC Becomes A Floating Point Powerhouse

February 17, 2025 by 24 Comments

[Michael Wessel] found some of his old DOS 3D graphics software and tried to run it on an 8088 PC. The tale of adding an 8087 co-processor to speed up the rendering was anything but straightforward, resulting in a useful little project.

There was a point around the end of the 1980s when the world of PCs had moved on to the 386, but the humble 8086 and 8088 hung around at the consumer end of the market. For Europeans that meant a variety of non-standard machines with brand names such as Amstrad and Schneider, and even surprisingly, later on Sinclair and Commodore too.

Of these the Schneider Euro PC was an all-in-one design reminiscent of an Amiga or Atari ST, packing a serviceable 8088 PC with a single 3.5″ floppy drive. A cheap machine like this was never thought to need an 8087, and lacked the usual socket on the motherboard, so he made a small PCB daughter board for the 8088 socket with space for both chips.

It’s a surprisingly simple circuit, as obviously the two chips were meant to exist together. It certainly had the desired effect on his frame rate, though we’re not sure how many other Euro PC users will need it. It does make us curious though, as to how quickly a modern microcontroller could emulate an 8087 for an even faster render time. Meanwhile if you’re curious about the 8087, of course [Ken Shirriff] has taken a look at it.

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Looking For Pi In The 8087 Math Coprocessor Chip

May 20, 2020 by 14 Comments

Even with ten fingers to work with, math can be hard. Microprocessors, with the silicon equivalent of just two fingers, can have an even harder time with calculations, often taking multiple machine cycles to figure out something as simple as pi. And so 40 years ago, Intel decided to give its fledgling microprocessors a break by introducing the 8087 floating-point coprocessor.

If you’ve ever wondered what was going on inside the 8087, wonder no more. [Ken Shirriff] has decapped an 8087 to reveal its inner structure, which turns out to be closely related to its function. After a quick tour of the general layout of the die, including locating the microcode engine and ROM, and a quick review of the NMOS architecture of the four-decade-old technology, [Ken] dug into the meat of the coprocessor and the reason it could speed up certain floating-point calculations by up to 100-fold. A generous portion of the complex die is devoted to a ROM that does nothing but store constants needed for its calculation algorithms. By carefully examining the pattern of NMOS transistors in the ROM area and making some educated guesses, he was able to see the binary representation of constants such as pi and the square root of two. There’s also an extensive series of arctangent and log2 constants, used for the CORDIC algorithm, which reduces otherwise complex transcendental calculations to a few quick and easy bitwise shifts and adds.

[Ken] has popped the hood on a lot of chips before, finding butterflies in an op-amp and reverse-engineering a Sinclair scientific calculator. But there’s something about seeing constants hard-coded in silicon that really fascinates us.

8087's -5V bias charge pump circuit

How The 8087 Coprocessor Got Its Bias

August 18, 2018 by 8 Comments

Most of us have been there. You build a device but realize you need two or more voltages. You could hook up multiple power supplies but that can be inconvenient and just not elegant. Alternatively, you can do something in the device itself to create the extra voltages starting with just one. When [Ken Shirriff] decapped an 8087 coprocessor to begin exploring it, he found it had that very problem. It needed: +5 V, a ground, and an additional -5 V.

His exploration starts with a smoking gun. After decapping the chip and counting out all the bond wires going to the various pads, he saw there was one too many. It wasn’t hard to see that the extra wire went to the chip’s substrate itself. This was for providing a negative bias to the substrate, something done in some high-performance chips to get increased speed, a more predictable transistor threshold voltage, and to reduce leakage current. Examining where the bond wire went to in the circuitry he found the two charge pump circuits shown in the banner image. Those worked in alternating fashion to supply a -5 V bias to the substrate, or rather around -3 V when you take into account voltage drops. Of course, he also explains the circuits and dives in deeper, including showing how the oscillations are provided to make the charge pumps work.

If this is anything like [Ken’s] previous explorations, it’ll be the first of a series of posts exploring the 8087. At least that’s what we hope given how he’d previously delighted us with a reverse engineering of the 76477 sound effects chip used in Space Invaders and then went deeper to talk about integrated injection logic (I2L) as used in parts of the chip.