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0 pointsbsder3y ago0 comments

> Can you explain why such large numbers are required?

Absolutely.

Even if you start with 32 bits, you often have polygons with many sides. In the worst case, you are modeling a "circle" and have to increase your precision to enough level to be accurate (please note that nobody in the right mind in VLSI would ever draw a "circle"--however, you wind up with an "implied" one due to DRC, more down below ...)

The problem is that line sweep intersection checks in DRC require approximately 3n+a couple bits to differentiate intersections that may be close to degenerate or have multple intersections near to each other. So, if you start with 32-bit numbers, you require approximately 96 bits plus a little for your intermediate calculations. (See: Hobby -- "Practical segment intersection with finite precision output" -- I'll let people find their own copy of the paper so HN doesn't splatter some poor site that I link)

You would think that doesn't matter since VLSI tends to limit itself to rectilinear and 45 degree angles. Unfortunately life isn't that simple.

If you take a simple rectangle and say "Nothing can be within distance x", you get a slightly larger rectangle parallel to the sides. Easy. The problem is that you also wind up with an implied quarter circle (told you this would come back) near each corner. Not so easy.

Put those circles such that they overlap only very slightly and you may have segments that are pretty close to tangent. Super not easy. Unfortunately, VLSI design often consists of putting those metals such that they are riiiight at the limit of spacing. Consequently, your super-not-easy case also becomes a very common case. Ouch.

Of course, you could just move the rectangle completely outward so that you have squares at the corners. However, that gives up a non-trivial amount of area that most places aren't willing to concede.

There is a reason why Siemens (nee Mentor) Calibre is so egregiously expensive.

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jiggawatts3y ago

Disclaimer: I have zero silicon design experience.

However, I have designed computer game engines that use 32-bit floats throughout and encountered rounding errors in practice.

I’ve found that there’s always a solution that avoids the need to go past 64 bits, and even that is a last resort.

So for example the circle could be approximated with a polygon. Or fixed-point arithmetic can be used. Or simply use a quad-tree or related space partitioning algorithms to check for intersections.

There are literally thousands of algorithms that sidestep these issues and are used extensively in computer games, typically at 32-bit precision exclusively.

For example “back in the day” you would often see shimmering due to “z-fighting”. You would also often see white pixels due to “cracks” between adjacent polygons.

All of these are largely gone now. The problems have been solved without the enormous performance hit of 64-bit doubles, let alone 128!

Meanwhile contemporary CAD programs would insist on using 64-bit doubles, even through the OpenGL pipeline out to the screen.

But if you sit down for a second and just divide your screen (or wafer mask) by the range of your chosen numbers you’ll instantly see that you have thousands of steps per pixel (or atom!) to work with.

Any visible noise is your fault for choosing the wrong algorithm, not the fault of the hardware for not providing enough bits.

q3k3y ago

Please keep in mind that even the slightest error in a silicon mask is likely to cause hundreds of millions of dollars of losses and months of delay in time to market for a modern chip.

With that in mind, does it make more sense to come up with new, experimental, untested algorithms... or just use wider numbers and slowly iterate on well known algorithms? Especially with LVS/DRC you really want the dumbest, easiest to reason about thing that is most likely to catch design issues no matter what. Even if it's excruciatingly slow, it's your last line of defense against writing off a set of masks as a hundreds of millions of dollars loss.

EDA / silicon CAD is a totally different world of design requirements compared to video games or even MCAD software.

EDIT: and just for context, here's a DRC set for the (very much not modern) SKY130 process: https://github.com/RTimothyEdwards/open_pdks/blob/master/sky...

jiggawatts3y ago

The exact same arguments were made by CAD people insisting on 64-bit maths for OpenGL. They were wrong. They too were working on projects worth billions of dollars, over decades, where mistakes were very costly.

Your link to a "DRC set" doesn't mean much to me out of context. I see some basic looking code with small-ish numeric constants in it. So what? This is not that different to the input to a simple physics simulation or a computer game.

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jiggawatts3y ago

Replying to myself to add:

Here's a Design Rule Checking (DRC) paper that mentions using 32-bit floats for things like checking distances between polygonal traces: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.49...

If 32-bit is sufficient, then 64-bit definitely is, even for the latest & greatest silicon processes...

gchadwick3y ago

Of course when you're doing such intersection calculations you know the things you're intersecting are very close. You don't need a general method that can test arbitrarily sized and spaced polygons against each other. You need a method to determine what is sufficiently close to each other to be worthy of a more detailed check. Then a more specific method to do this check.

You could use 32 bit integers with all shapes specified vs say a 0.1 nm grid giving you around a maximum 0.4m x 0.4m chip size which seems ample. Then when you want to check for rules violations in the cases like you specify with very fine precision use a dedicated check that can assume the relevant geometry is within a small number of grid points of each other. For example the check could work using relative coordinates rather than absolute so say switch to a grid on a 0.00001nm basis (to pull an arbitrary precision out of a hat) and convert the 32-bit absolute 0.1nm coords to relative 32-bit 0.00001nm coords.

Easier said then done to be sure (as you say the tools are egregiously expensive!) but just saying I need a 64-bit or a 128-bit float isn't trying to get to the grips with the problem, just hoping you wave it away with more bits.

bsderOP3y ago

> You need a method to determine what is sufficiently close to each other to be worthy of a more detailed check.

Your line sweep data structure effectively already does that. I recommend reading the Hobby paper and thinking about how it works. And then you should think about how you differentiate inside from outside when you union/difference your polygons.

Any segments in the line sweep data structure simultaneously have already demonstrated that they need the detailed check.

If you want to argue this, you're going to need to study up on about 40 years of prior art. Given how much money this is worth and how many really smart people went after it (it basically drove the field of Computational Geometry for decades), the probability of you contributing something new to the current algorithms is basically zero.

However, the probability of you contributing something new to parallel DRC algorithms is really quite decent. Nobody I know of has yet come up with "good" parallel algorithms for DRC--most of them are hacks that quite often break down when they hit even common cases.

Being able to handle DRC on a billion VLSI polygons/10 billion line segments in a parallel fashion would be quite an advance, and the field is waiting for it.

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