Hi kens, thanks for the knowledge sharing all these years. Can you please confirm this one? From Wikipedia, it says that 8087 uses CORDIC algorithm. Does that mean that it's the same (but different speed) as what I'd implement the functions in software, except in microcode (which has more granularity than usual assembly code)?
I found it a bit surprising that as a 45-year old chip, there is no public information of its microcode. I guess hardware is indeed much more secret than software.
Yes, the 8087 uses CORDIC. I extracted the constants from the 8087's internal constant ROM and they are arctangent and log values for the CORDIC algorithm. You can implement the same functions in software, which is what floating-point emulation libraries did back then.
There's almost no public information on the 8087 microcode, but I'm working on that :-)
Until I read this I did not know that 1970s microprocessors had register renaming. Feel a little cheated, thinking for all those years that they were actually moving the bits.
If you work through a math problem with pen and paper or nand2tetris or nandgame.com then it becomes obvious that changing indexes into a register file (a.k.a. pointers) are way faster and easier than wires to move stuff around.
It would be difficult, but not impossible. The main problem is tracing out all the circuitry, which is very time-consuming and error-prone. Trust me on this :-)
The second problem is that converting the circuitry to Verilog is straightforward, but converting it to usable Verilog is considerably more difficult. If you model the circuit at the transistor level in Verilog, you won't be able to do much with the model. You want a higher-level model, which requires converting the transistors into gates, registers, and so forth. Most of this is easy, but some conversions require a lot of thought.
The next issue is that you would probably want to use the Verilog in an FPGA. A lot of the 8087's circuitry isn't a good match for an FPGA. The 8087 uses a lot of dynamic logic and pass transistors. Things happen on both clock edges, so it will take some work to map it onto edge-trigger flip-flops. Moreover, a key part of the 8087 is the 64-bit shifter, built from bidirectional pass transistors, which would need to be redesigned, probably with a bunch of logic gates.
The result is that you'd end up more-or-less reimplementing the 8087 rather than simply translating it to Verilog.
ah, i see, thanks for the insight! do you have any advice on how one might get started with IC reverse-engineering? i think it would be interesting to reimplement these chips in a way that's at least inspired by the original design
How to get started reverse engineering? That's a big topic for a HN comment, but in brief... Either get a metallurgical microscope and start opening up chips, or look at chip photos from a site like Zeptobars. Then start tracing out simple chips and see how transistors are constructed, and then learn how larger circuits are built up. This works well for chips from the 1970s, but due to Moore's Law, it gets exponentially more difficult for newer chips.
Do you have any good tips on what to look out for when buying a used metallurgical microscope for looking at decapped chips? Even if not a complete set constraints, I'd appreciate some off the cuff thoughts if you have the time.
I use a basic metallurgical microscope (AmScope ME300TZB). An X-Y stage is very useful for taking photos of chips and stitching them together. A camera is also important; my scope has a 10MP camera. I'm not into optics, so I don't know what lens characteristics to look for.
I found it a bit surprising that as a 45-year old chip, there is no public information of its microcode. I guess hardware is indeed much more secret than software.
There's almost no public information on the 8087 microcode, but I'm working on that :-)
The second problem is that converting the circuitry to Verilog is straightforward, but converting it to usable Verilog is considerably more difficult. If you model the circuit at the transistor level in Verilog, you won't be able to do much with the model. You want a higher-level model, which requires converting the transistors into gates, registers, and so forth. Most of this is easy, but some conversions require a lot of thought.
The next issue is that you would probably want to use the Verilog in an FPGA. A lot of the 8087's circuitry isn't a good match for an FPGA. The 8087 uses a lot of dynamic logic and pass transistors. Things happen on both clock edges, so it will take some work to map it onto edge-trigger flip-flops. Moreover, a key part of the 8087 is the 64-bit shifter, built from bidirectional pass transistors, which would need to be redesigned, probably with a bunch of logic gates.
The result is that you'd end up more-or-less reimplementing the 8087 rather than simply translating it to Verilog.
does VH have options for encoding working with both clock edges?
I also have a video from Hackaday Supercon on reverse engineering chips: https://www.youtube.com/watch?v=TKi1xX7KKOI