Author here for your 8087 questions...

This is cool, but the renormalization and (Programmable and bidirectional) barrel shifter are of much more interest.

I had a 10Mhz XT, and ran a 8087-8 at a bit higher clock rate. I used it both for Lotus 1-2-3 and Turbo Pascal-87. It made Turbo Pascal significantly faster.

The 2-bit-per-transistor ROM using four transistor sizes is wild. Were there other chips from this era experimenting with semi-analog storage, or was the 8087 unusually aggressive here?

Looking at the complexity and area of hardware floating point, I often wonder why we don't see more unified combined integer+floating point units, like done in the R4200 [1], which reused most of the integer datapath while just adding a smaller extra smaller 12-bit datapath for the exponent.

[1] https://en.wikipedia.org/wiki/R4200

Very cool.

It's all about that 80-bit/82-bit floating point format with the explicit mantissa bit just to be extra different. ;) Not only is it a 1:15:1:63, it's (2(tag)):1:15:1:63, whereas binary64 is 1:11:0:52. (sign:exponent [biased]:explicit leading mantissa bit stored?:manitissa remaining)

Other pre-P5 ISA idiosyncrasies: Only the 8087 has FDISI/FNDISI, FENI/FNENI. Only the plain 287 has a functional FSETPM. Most everything else looks like a 387 ISA-wise, more or less until MMX arrived. That's all I know.

I'm curious what the CX-83D87 and Weiteks look like.

Keep up the good work!

PS: Perhaps sometime in the (near) future we might get almost 1:1 silicon "OCR" transcription of die scans to FPGA RTL with bugs and all?

Sometime in the 80s, I implemented the core of the Mandelbrot Set calculation using assembly on an 8087. As the article mentions, the compilers did math very inefficiently on this stack architecture. For example, if you multiplied two numbers together and then added a third, they would push the first two numbers, multiply, pop the result, push the result back onto the stack (perhaps clearing the stack? after 40 years I don't remember), push the third number, add, pop the result. For the Mandelbrot loop this was even worse, as it never kept the results of the loop. My assembly kept all the intermediate results on the stack for a 100x speed up.

Running this code, the 8087 emitted a high-pitched whine. I could tell when my code was broken and it had gone into an infinite loop by the sound. Which was convenient because, of course, there was no debugger.

Thanks for bringing back this memory.