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0 pointsSolarNet9y ago0 comments

You aren't following the instructions. You have to rewrite all comparisons to use a small sigma.

`0.f == x` becomes `SIGMA > x`

`0.f == y` becomes `SIGMA > y`

`x == y` becomes `SIGMA > abs(x - y)`

All the expression work if written correctly.

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2 comments · 1 top-level

mauvehaus9y ago· 1 in thread

I probably should have given a better example instead of the hasty one. -sigma < x < 0 < y < sigma, abs(x - y) > sigma. I hope we can agree that this causes problems with transitivity :-)

There are also problems with granularity. Suppose x and y are both much, much larger than sigma, and the smallest representable difference between x and y is e.g. 1.0. Now there's no possible way that abs(x - y) < sigma.

I suspect that the resolution to this is to compare equality within some number of ULPs, but: 1) You still have the transitivity problem and 2) This is not my field of expertise, and there may be a more appropriate solution.

SolarNetOP9y ago

> -sigma < x < 0 < y < sigma, abs(x - y) > sigma

This statement works fine. If the numbers are farther than sigma apart then `abs(x - y) > sigma` is true as it should be. It's not distance to 0, it's distance from each other related to 0 that matters.

> There are also problems with granularity. Suppose x and y are both much, much larger than sigma

This is part of the same problem. You have to choose a maximum acceptable value. And ensure you don't overflow it, and then you can choose a sigma based on that maximum value such that the difference between any two numbers never exceeds sigma. In practice you already have a maximum value for your domain that the simulation should never exceed or it means it is incorrect anyway.

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