> 100x speed improvement ...

Vs. Ken's Blog says "up to 100 times", and Wikipedia gives a lower estimate.

Theory: Your 100X experience compared Intel's "exact emulation" code (noted in the article) with native x87. That emulation would have to cover the myriad x87 oddities and corner cases which Ken describes. Vs. Ken's & Wikipedia's are comparing x87 to various "good enough" 8088 floating point libraries - so naturally much faster than Intel's exact code.

(And yes, speed might have been a low priority for the team writing Intel's emulator.)

Any modern processor has different execution ports specialized in different things and replicated a different number of times, and all of them can execute instructions in parallel.

It schedules to these transparently for you, that's known as superscalar execution. To maximize occupation, out-of-order execution and simultaneous multithreading are used.

I remember getting a 80387 (coprocessor for the 80386) and POVRAY renders going from running for days to still many minutes but you could sit and watch it.

> But for a compiler to target, it's just so painful. It's so different from almost all other ways CPUs work. There's a reason both CPU and compilers prefer to avoid x87 when possible and use regular SIMD (SSE/AVX) instead.

The x87 ISA is essentially a one-address stack-based ISA (so unlike a pure stack ISA, you can reference another value on the stack without having to introduce something like a dup instruction). Which honestly isn't particularly painful to work with for a compiler; it's not usual, but there are other ISAs that are also stack-based (the JVM bytecode is the one that most immediately comes to mind).

The actual weirdness of x87, what makes all the compilers run away from it, is that the only values you can have on the stack are 80-bit extended-precision types. But people don't use those types in their code, they use 32-bit and 64-bit single and double precision, and compilers largely implemented these types by pretending that the x87 just used those value sizes in the first type (the only ones to actually get it correct that I'm aware of are Java's strictfp and Intel's icc, although the latter is merely just correctly implementing FLT_EVAL_METHOD==2). The end result is that compilers caused code to have essentially random and largely uncontrollable precision changes, which pissed a lot of users off, and the SSE units having regular scalar proper single and double precision types made it easier for compilers to switch to that rather than introducing the proper sequences to compile for x87.

> Also, the arbitrary "Oh, and the registers are 80 bits wide" is also just one of those weird "Where did that number come from?".

One of the features that was advertised (mentioned in the iAPX 86, 88, 186 Microprocessors Part II book (July 1984)) was the ability to do exact arithmetic on integers up to 2^64, which is possible due to the 64-bit mantissa used in the 80-bit format.

80-bit wide registers isn't really arbitrary if you consider that the bulk of the floating point number is a 64-bit significand (and the signifiand ALU makes sense as power-of two) and that you don't need as many bits for exponent (it would be wasteful to go to the next power of two up). Memory is stored as 8-bit bytes as the lowest addressable unit, and so the question would be how many extra bytes the number should take, and 80 bits is a nice integer number of 10 bytes.

For compilers yes, but if you look at the 8086 demoscene where presumably most things are hand-coded, 8087 instructions allow incredible code compression. eg https://www.pouet.net/prod.php?which=78045

It may have designed as a stack to better decoding math expressions. Or they may have used stacks because Intel liked stacks at the time.

It's known that the 8087 was designed to attach to either the 8087 or Intel's 32-bit chip the 432. The contemporary rumor is it is in fact the floating point unit FROM the 432, a money-is-no-object project to make the "ultimate" 32-bit chips. The 432 itself had only stack-based registers, had all kinds of weird-length instructions, had to be split across multiple chips, and locked those registers away from programmers who were only allowed a slow high-level language to program it. Only when 432 was clearly failing was also paired to the 8086/88--a chip that itself was a crash project because of delays in the 432. Adding the very different 8087 to the 8088 was described as pairing a race car engine into a poky Volksagen bug.

Rumors mongered in 1982 by Hal Hardenburgh: http://www.easy68k.com/paulrsm/dg/dg06.htm, "Page 4" section.

On the other hand, getting floating point right in the 8087 was absolutely worth the effort. You can see the comparisons in a 1983 issue of Hal's newsletter on the Savage benchmark: http://www.easy68k.com/paulrsm/dg/dg26.htm. Go to "Timing Conclusions" and particularly "Error Conclusions" and beyond.

It only has 2048 opcodes available. A one-operand register or memory operand operation takes 32, while two register operands would take twice as many. Loads and stores have to specify the memory format (three floating point formats, BCD, word, 64-bit integer), so each instruction used 120 encodings or so even with a single operand; loads and stores alone would use almost all the opcode space if they also had to include the destination register.

In other words there simply isn't room in the encoding to specify two operands, so they went for the stack model.

There's also the fact that for all intents and purposes, the real floating-point unit of any x86 in the last 20 years is the SIMD unit, and legacy x87 instructions are emulated on top of that.

> But for a compiler to target...

To what degree did Intel assume their target market was either using hand-coded assembly, or written-for-x87 code with x87-specific compilers? Memory was not cheap in 1980, ditto 8087 chips, and oddities like the x86's 64K segments would discourage anyone trying to "just recompile" existing programs for x86/x87.

I've looked at some early calculators and they are a whole different world of weirdness. They used decimal arithmetic (BCD) because it's a lot easier than converting between binary and decimal. The first calculators were serial, with a 1-bit adder and shift registers and bits constantly in motion. The Sinclair Scientific calculator used TI's strange 4-bit architecture along with terrible algorithms.

That's a really vertical microcode. It looks more like a specialized assembly than microcode. I guess it makes sense, since the algorithms are so complex and executing one microinstruction per cycle (is that correct?) already provides almost an order of magnitude performance improvement.

Great work! I love to read your articles.

I'm curious to know - you say Intel's 8087 emulation code was a bit of a lump at 16KB, do you know if it emulated the 8087 microcode state machine or did it use a different strategy?

no questions, just thanks