Ken Shirriff
LightNews LightNews
banner
righto.com
Ken Shirriff
@righto.com
5.8K followers 290 following 360 posts
Computer history. Reverse-engineering old chips. Restored Apollo Guidance Computer, Alto. Ex-Google, Sun, Msft. So-called boffin.
Posts Replies Media Videos
righto.com
The 8087 was much more advanced than previous floating point. In particular, it was designed by Prof. Kahan, a floating-point expert, and was much more rigorous and accurate. It became the IEEE 754 standard, which almost all computers now use.
ieeemilestones.ethw.org/Milestone-Pr...
Milestone-Proposal:Intel 8087 Math Coprocessor
ieeemilestones.ethw.org
December 11, 2025 at 8:17 PM
righto.com
I looked at the AM9511 datasheet. It's similar to the 8087 in that they are both floating-point chips that do arithmetic as well as transcendental functions, and both use a stack. However, the 9511 uses 16/32-bit floats, while the 8087 uses much larger floats, up to 80 digits.
December 11, 2025 at 8:15 PM
righto.com
No, I haven't looked at that chip yet.
December 9, 2025 at 7:11 PM
righto.com
For more on the stack circuitry in the 8087, see my blog post: www.righto.com/2025/12/8087...
The stack circuitry of the Intel 8087 floating point chip, reverse-engineered
Early microprocessors were very slow when operating with floating-point numbers. But in 1980, Intel introduced the 8087 floating-point copro...
www.righto.com
December 9, 2025 at 6:38 PM
righto.com
Intel was hesitant to produce the 8087 chip, considering it complex, risky, and with an unknown market. Intel's Israel site took on the project; the die is marked "i/IL". The chip was a highly profitable success. Now, almost all computers use floating-point systems based on the 8087.
A close-up of the 8087 die. There are white horizontal and vertical lines of various widths, the chip's metal wiring. Text in metal is also visible: "8087", "i/IL", and a maskwork/copyright marking: "(m) (c) intel 1980".
December 9, 2025 at 6:38 PM
righto.com
This diagram, based on the 8087 patent, shows the implementation of the stack. You saw the registers (yellow) earlier. This photo shows the three-bit circuitry that controls the stack (purple, green, and blue). The schematic shows one bit in detail.
A block diagram from the patent. It shows the top-of-stack pointer (TOS) with controls to increment and decrement when pushing or popping values. A subtractor circuit computes offsets into the stack. A multiplexer selects either the top-of-stack or the offset value. A decoder selects one entry in the stack based on this value. The value in the stack is split across the fraction bus, exponent bus, and tag bus. The stack control circuitry on the die. It consists of complex silicon structures forming tan patterns. I've labeled regions of the circuitry. Circuitry blocks handle increment/decrement and latching of the three bits. Underneath, blocks compute the sum and multiplex the two values. There are irregular regions of deep blue at the right. These are not significant, just oxide that didn't get completely removed when I dissolved the metal layer with acid. A complicated schematic showing one bit of the stack register control. The left half is a flip-flop that can hold a bit or toggle the bit (for incrementing or decrementing). The right half is a multiplexer to select either the top-of-stack from the flip-flop or the sum. The summing circuitry is not shown, but uses a carry-lookahead adder.
December 9, 2025 at 6:38 PM
righto.com
Each bit is stored in a "static RAM" cell, consisting of two inverters in a loop. This circuit has two stable states, holding a 0 or a 1. The implementation is complicated: silicon with polysilicon lines on top to make transistors. Horizontal metal wires connect everything.
A diagram showing two inverters in a loop. On the left, the first inverter has a 0 and the second has a 1. On the right, the values are switched. Thus, the circuit can hold a 0 or a 1. A close-up of the silicon showing the circuitry for one storage cell. Each cell has two inverters. Each inverter has a transistor and a weak pull-up transistor. A transistor is formed when polysilicon crosses over doped silicon. The two inverters are connected to bit lines to read and write the cell. This connection is through two selection transistors, controlled by a vertical word line.
December 9, 2025 at 6:38 PM
righto.com
Unlike most processors, the 8087 organizes its registers into a "stack", pushing numbers onto the top of the stack and popping them off. Here's a close-up of the eight registers, organized in a grid of cells. Each register holds an 80-bit number, so the registers are very tall.
The registers in the 8087 chip form a tall, skinny rectangle. The storage cells are arranged in eight columns for the eight registers. At the top are two tag bits, then 16 bits for sign and exponent, and then 64 bits for the fraction part of the number. The image zooms in on an 8 by 8 block of storage cells. For this image, I removed the metal layer with acid, so you can see the silicon structures underneath. The silicon appears pinkish-tan.
December 9, 2025 at 6:38 PM
righto.com
Not yet...
November 22, 2025 at 7:14 PM
righto.com
My latest blog post describes the wayward transistor and two other curiosities in the 386 processor's standard cell logic, so read it for details.

www.righto.com/2025/11/unus...
Unusual circuits in the Intel 386's standard cell logic
I've been studying the standard cell circuitry in the Intel 386 processor recently. The 386, introduced in 1985, was Intel's most complex pr...
www.righto.com
November 22, 2025 at 4:56 PM
righto.com
Standard cells sped up the design of the 386 and the chip was completed ahead of schedule. Pat Gelsinger was one of the key people behind the use of standard cells in the 386 processor. Decades later, he became CEO of Intel.
A standard-cell inverter as it appears on the die, along with a diagram explaining the layout. The die image has green lines of polysilicon over grayish rectangles of silicon that look a bit like Lego bricks. The diagram shows how the inverter is constructed from a PMOS transistor and an NMOS transistor
November 22, 2025 at 4:56 PM
righto.com
In standard cell logic, all the transistors are in orderly stripes. Except one that's out of place below, in the middle of the wiring region. What's going on? I think it's a bug fix. Instead of redoing all the circuitry, someone realized they could patch an extra transistor into an empty spot!
A close-up of two columns of standard cell logic. I dissolved the metal layers with acid for this photo, so you can see the silicon. Each transistor has a dark outline around it. The transistors are all in columns except for one lone transistor between the columns; it is marked with a red arrow. The photo also has a few large greenish regions. These are areas where I couldn't remove the oxide layer completely, so they can be ignored.
November 22, 2025 at 4:56 PM
righto.com
It's much easier to build circuits with standard cells. Instead of manually arranging each transistor, you feed a description of the logic into a computer. It places the cells into rows, and then routes the wires to connect the cells. In 1985, this took many hours on an IBM mainframe computer.
A close-up of two standard cells in the 386. The cells are outlined with green boxes. The photo looks like dark brown horizontal and vertical lines on a tan background, with large and small circles in the boxes. The photo is mostly incomprehensible because of the density of wiring in the 386, but what it shows is a layer of horizontal wiring and a layer of vertical wiring (the stripes between the dark lines). The larger circles connect the two metal layers, while the small dots connect the metal layer to the silicon or polysilicon underneath,
November 22, 2025 at 4:56 PM
righto.com
The previous photo shows the 386 processor under a microscope. I've highlighted the regions that use standard cells and the layout was automated. Simple logic blocks (the "standard cells") are arranged in rows, with wiring between the rows. This creates a distinctive striped pattern.
A close-up of standard cell logic in the 386 processor. The circuitry appears as four irregular dark bands, with horizontal and vertical connections in the regions between the dark bands.
November 22, 2025 at 4:56 PM
righto.com
MiniZinc solver page: www.minizinc.org
Link to Pips: www.nytimes.com/games/pips
The article on HN that inspired me to investigate constraint solvers: buttondown.com/hillelwayne/...
Play Pips, our new dominoes game for all skill levels.
Every domino has a spot. Can you find where each belongs?
www.nytimes.com
October 18, 2025 at 4:20 PM
righto.com
If you're a programmer, I recommend looking at constraint solvers. This different paradigm will broaden your horizons. It's also much easier than I expected. See my blog for details: www.righto.com/2025/10/solv...
Solving the NYTimes Pips puzzle with a constraint solver
The New York Times recently introduced a new daily puzzle called Pips . The idea is to place a set of dominoes on a grid, satisfying variou...
www.righto.com
October 18, 2025 at 4:20 PM
righto.com
MiniZinc gave me a solution to the Pips puzzle in 100 milliseconds. Admittedly, this puzzle is rated "easy", but MiniZinc quickly solves hard puzzles too. Internally, MiniZinc uses complicated algorithms such as backjumping and constraint propagation, but I don't need to worry about that.
A Pips problem with the solution. It has numbers in the cells, corresponding to dominoes. A much larger Pips puzzle, a 6 by 6 grid in an octagonal shape. It has 12 dominoes and many constraints. The image shows the solution.
October 18, 2025 at 4:20 PM
righto.com
I used a constraint solver called MiniZinc. I wrote constraints for the problem: the conditions on the grid, the shape of the grid, and the values of the dominoes. A few more constraints defined how the problem works. I didn't need to write algorithms because MiniZinc solves automatically.
The same three-by-three grid of squares with four dominoes below it. Two squares are labeled with "8", indicating that the numbers in that region must sum to eight. Another square is labeled "<5", indicating that the number in that square must be less than 5. The three bottom squares are labeled with an equals sign, indicating that the three numbers must be the same. The upper-right square is missing so there are 8 squares in total, able to hold four dominoes. Code: constraint pips[1,1] + pips[2,1] == 8; constraint pips[2,3] < 5; constraint all_equal([pips[3,1], pips[3,2], pips[3,3]]); Code: grid = [| 1,1,0| 1,1,1| 1,1,1|]; Code: spots = [|5,1| 1,4| 4,2| 1,3|];
October 18, 2025 at 4:20 PM
righto.com
If you want to know more about the IBM 1403 printer, I wrote about how we played music on it:
www.righto.com/2019/09/risk...
I also made an animation to explain the extraordinarily complicated timing between the hammers and the chain to print characters: static.righto.com/ibm1401/prin...
Risky line printer music on a vintage IBM mainframe
At the Computer History Museum , we recently obtained card decks for a 50-year-old computer music program. Back then, most computers didn't...
www.righto.com
October 2, 2025 at 9:54 PM
righto.com
The hammers looked okay, but @tubetime.bsky.social found that hammer #83 was sticky. He cleaned it and then the printer worked, just in time for the demo. (Stop by the museum on Wednesdays or Saturdays to see the system in operation.) Photo shows a hammer from an earlier repair.
A hammer assemblly with the coil attached. It is an irregularly-shaped metal unit that is kind of grungy. It looks vaguely like an elephant with a long, straight trunk forming the part that hits the paper.
October 2, 2025 at 9:54 PM
righto.com
We took the hammer unit out of the printer. Fortunately, IBM designed the printer for (relatively) easy maintenance. Inside the printer are two rails that can be attached to the back. The hammer unit slides out and tilts for access. You can see some hammers and coils; more are underneath.
The back side of the printer after removing the cover, paper guides, and cooling air hose. The hammer unit is a big gray unit in the middle. On either side, metal guide rails have been attached to the printer and stick out horizontally. The hammer unit has been slid out along the guide rails and tilted up. With the cover removed, you can see 33 electromagnetic coils in a row with a jumble of wiring behind. Each coil has a hammer, a gray rectangle of metal. At the bottom of the photo is a row of 132 small rectangles. These are the ends of the hammer that hit the paper to print characters.
October 2, 2025 at 9:54 PM