I've always thought the 8087 was a marvelous bit of engineering. I never understood why it didn't get much respect in the software business.
For example, when Microsoft was making Win64, I caught wind that they were not going to save the x87 state during a context switch, which would have made use of the x87 impractical with Win64. I got upset about that, and contacted Microsoft and convinced them to support it.
But the deprecation of the x87 continued, as Microsoft C did not provide an 80 bit real type.
Back in the late 80's, Zortech C/C++ was the first compiler to fully implement NaN in the C math library.
Excel needed the x87 as well as they cared about maintaining the 80-bit precision in some places to get exactly the same recalc results. So they would have fixed it eventually most likely.
I’d agree that the engineering was brilliant (but 68882 gang represent!). Its ISA was so un-x86-like, though, as it was basically an RPN calculator. X86 had devs manipulating registers. X87 had them pushing operands and running ops that implicitly popped them and pushed the result back on the stack.
That’s not better or worse, just different. However, I can imagine devs of the days saying hey, uh, Intel, can we do math the same way we do everything else? (Which TBH is how you’d end up with an opcode for a hardware-accelerated bubble sort or something, because Intel sure does love them some baroque ISAs.)
> Its ISA was so un-x86-like, though, as it was basically an RPN calculator
Yeah I remember when I first came across floating point stuff when trying to reverse engineer some assembly - I wasn't expecting something stack-based.
Eh, as far as compiler backends go, the RPN stack was worse.
I thought the X86_64 instruction set was a giant kludge-fest, so I was looking forward to implement the AArch64 code generator. Turns out it is just as kludgy, but at right angles. For example, all the wacky ways of simply loading a constant into a register!
What do you mean by respect? Here's a layperson's perspective, at least.
Up through the 486 (with its built in x87), the x87 was always a niche product. You had to know about it, need it, buy it, and install it. This is over and on top of buying a PC in the first place. So definitionally, it was relegated it to the peripheries of the industry. Most people didn't even know x87 was a possibility. (I remember distinctly a PC World article having to explain why there was an empty socket next to the 8088 socket in the IBM PC.)
However, in the periphery where it mattered, it gained acceptance within a matter of a few years of being available. Lotus 1-2-3, AutoCAD, and many compilers (including yours, IIRC) had support for x87 early on. I would argue that this is one of the better examples of marginal hardware being appropriately supported.
The other argument I'd make is that (thanks to William Kahan), the 8087 was the first real attempt at IEEE-754 support in hardware. Given that IEEE-754 is still the standard, I'd suggest that x87's place in history is secure. While we may not be executing x87 opcodes, our floating point data is still in a format first used in the x87. (Not the 80-bit type, but do we really care? If the 80-bit type was truly important, I'd have thought that in the intervening 45 years, there'd be a material attempt to bring it back. Instead, what we have are a push towards narrower floating point types used in GPGPU, etc.... fp8 and f16, sure... fp80, not so much.)
The disinterest programmers have in using 80 bit arithmetic.
A bit of background - I wrote my one numerical analysis programs when I worked at Boeing. The biggest issue I had was accumulation of rounding errors. More bits would put off the cliff where the results turned into gibberish.
I know there are techniques to minimize this problem. But they aren't simple or obvious. It's easier to go to higher precision. After all, you have the chip in your computer.
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 :-)
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
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.
I've always thought the 8087 was a marvelous bit of engineering. I never understood why it didn't get much respect in the software business.
For example, when Microsoft was making Win64, I caught wind that they were not going to save the x87 state during a context switch, which would have made use of the x87 impractical with Win64. I got upset about that, and contacted Microsoft and convinced them to support it.
But the deprecation of the x87 continued, as Microsoft C did not provide an 80 bit real type.
Back in the late 80's, Zortech C/C++ was the first compiler to fully implement NaN in the C math library.
Excel needed the x87 as well as they cared about maintaining the 80-bit precision in some places to get exactly the same recalc results. So they would have fixed it eventually most likely.
I’d agree that the engineering was brilliant (but 68882 gang represent!). Its ISA was so un-x86-like, though, as it was basically an RPN calculator. X86 had devs manipulating registers. X87 had them pushing operands and running ops that implicitly popped them and pushed the result back on the stack.
That’s not better or worse, just different. However, I can imagine devs of the days saying hey, uh, Intel, can we do math the same way we do everything else? (Which TBH is how you’d end up with an opcode for a hardware-accelerated bubble sort or something, because Intel sure does love them some baroque ISAs.)
> Its ISA was so un-x86-like, though, as it was basically an RPN calculator
Yeah I remember when I first came across floating point stuff when trying to reverse engineer some assembly - I wasn't expecting something stack-based.
Eh, as far as compiler backends go, the RPN stack was worse.
I thought the X86_64 instruction set was a giant kludge-fest, so I was looking forward to implement the AArch64 code generator. Turns out it is just as kludgy, but at right angles. For example, all the wacky ways of simply loading a constant into a register!
What do you mean by respect? Here's a layperson's perspective, at least.
Up through the 486 (with its built in x87), the x87 was always a niche product. You had to know about it, need it, buy it, and install it. This is over and on top of buying a PC in the first place. So definitionally, it was relegated it to the peripheries of the industry. Most people didn't even know x87 was a possibility. (I remember distinctly a PC World article having to explain why there was an empty socket next to the 8088 socket in the IBM PC.)
However, in the periphery where it mattered, it gained acceptance within a matter of a few years of being available. Lotus 1-2-3, AutoCAD, and many compilers (including yours, IIRC) had support for x87 early on. I would argue that this is one of the better examples of marginal hardware being appropriately supported.
The other argument I'd make is that (thanks to William Kahan), the 8087 was the first real attempt at IEEE-754 support in hardware. Given that IEEE-754 is still the standard, I'd suggest that x87's place in history is secure. While we may not be executing x87 opcodes, our floating point data is still in a format first used in the x87. (Not the 80-bit type, but do we really care? If the 80-bit type was truly important, I'd have thought that in the intervening 45 years, there'd be a material attempt to bring it back. Instead, what we have are a push towards narrower floating point types used in GPGPU, etc.... fp8 and f16, sure... fp80, not so much.)
> What do you mean by respect?
The disinterest programmers have in using 80 bit arithmetic.
A bit of background - I wrote my one numerical analysis programs when I worked at Boeing. The biggest issue I had was accumulation of rounding errors. More bits would put off the cliff where the results turned into gibberish.
I know there are techniques to minimize this problem. But they aren't simple or obvious. It's easier to go to higher precision. After all, you have the chip in your computer.
x87 should have been killed off. It would have forced lazy game developers to use SSE around the 2005 era.
Game floating point precision doesn't matter much - speed does. But if you're doing numerical analysis, it does matter.
Author here if anyone has questions...
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 :-)
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Is there 8087 IP available in verilog etc?
As far as I know, you can't get the 8087 itself as an IP block. You can get generic IEEE-754 floating-point as an IP block, e.g. from AMD: https://www.amd.com/en/products/adaptive-socs-and-fpgas/inte...
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Thank you. As always.
Thank you for the deep dive.
super cool! i wonder how difficult it would be to recreate the entire chip at logic gate level in, say, VHDL or Verilog
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
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Noob here,
does VH have options for encoding working with both clock edges?
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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.
How do you think the EXX and EX AF,AF' instructions work on the Z80?
And EX DE, HL
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If you feel cheated now, wait until you find out that the ALU in the 8-bit Z80 was just 4 bits. :-)
Does this have any similarities at all to the fact that the Pentium 4 used a 16-bit ALU?