...the implementation was way too naive; in some cases we could go into an infinite loop. In the end, using Newton approximation was not necessary (and thus there is no loop anymore), but it helped me get at a much better solution with very small error margin on average case. All these corner cases are obviously "academic" to some degree, but it turns out there is no clear-cut point where you'd be able just so set a limit and be sure that fractional integer arithmetic works flawless in all cases. Thus the choice is - give up (fractional) integers and work with floats and have to deal with error accumulation - or do something as chosen here, namely add a boundary zone, where fractional integer arithmetic can be kept under control, while admitting small errors, and in turn get the absolutely precise integers in all everyday standard cases |
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| workflow.mm | ||