I'm trying to find a good precise numeric solution for my problem.
Background:
I'm trying to create a trade simulation between cities. Each demands a certain amount of a resource and may have a certain number of importers cities that provide that resource. A city needs to take an equal fraction of each importer's resources, and the sum of the amounts taken must add up to the amount demanded. For example, if a city demands 2 bushels of grain, and has three importers, it will take 2/3 of the resources form each importer city, and the sum must add up to 2. Cities will always produce and demand an integer amount of goods, but a city may export to multiple places, so the amount of goods available may be a rational number. At no point are irrational numbers needed.
Limitations:
I'm working in C++ and emscripten. This means I cannot link any library to my project; I must include the whole source. For this reason, I'd prefer not to include any large library. I don't want to use boost. This is a closed source project, so I can't use anything GPL.
Options:
1) Use floating point with an epsilon. But I'm not sure how to pick the right epsilon here. This reproach has the advantage of being fast and simple though.
2) Use fixed point. If I use scaling factor that's a multiple or several lowest factors, it may be precise. But I need to ensure that any numerator of my fractions is a factor of the scaling factor. I'm not sure if I can ensure this. But if a city imports from at most N cites, and the scaling factor is N!, maybe this could work? or some version of it?
3) Use rational numbers. This ensure that calculations are precise all around. If I implement this myself, this is the most complex option.
The Ask:
I'm wondering if anyone here has any suggestions as to which is the best option for my use case, and if there are any libraries I might be able to use.
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