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Editorial Team
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Asked: 2026-06-03T12:05:33+00:00

I’m trying to diagnose and fix a bug which boils down to X/Y yielding

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I’m trying to diagnose and fix a bug which boils down to X/Y yielding an unstable result when X and Y are small:

enter image description here

In this case, both cx and patharea increase smoothly. Their ratio is a smooth asymptote at high numbers, but erratic for “small” numbers. The obvious first thought is that we’re reaching the limit of floating point accuracy, but the actual numbers themselves are nowhere near it. ActionScript “Number” types are IEE 754 double-precision floats, so should have 15 decimal digits of precision (if I read it right).

Some typical values of the denominator (patharea):

0.0000000002119123
0.0000000002137313
0.0000000002137313
0.0000000002155502
0.0000000002182787
0.0000000002200977
0.0000000002210072

And the numerator (cx):

0.0000000922932995
0.0000000930474444
0.0000000930582124
0.0000000938123574
0.0000000950458711
0.0000000958000159
0.0000000962901528
0.0000000970442977
0.0000000977984426

Each of these increases monotonically, but the ratio is chaotic as seen above.

At larger numbers it settles down to a smooth hyperbola.

So, my question: what’s the correct way to deal with very small numbers when you need to divide one by another?

I thought of multiplying numerator and/or denominator by 1000 in advance, but couldn’t quite work it out.

The actual code in question is the recalculate() function here. It computes the centroid of a polygon, but when the polygon is tiny, the centroid jumps erratically around the place, and can end up a long distance from the polygon. The data series above are the result of moving one node of the polygon in a consistent direction (by hand, which is why it’s not perfectly smooth).

This is Adobe Flex 4.5.

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1 Answer

  1. Editorial Team

    I believe the problem most likely is caused by the following line in your code:

    sc = (lx*latp-lon*ly)*paint.map.scalefactor;

    If your polygon is very small, then lx and lon are almost the same, as are ly and latp. They are both very large compared to the result, so you are subtracting two numbers that are almost equal.

    To get around this, we can make use of the fact that:

    x1*y2-x2*y1 = (x2+(x1-x2))*y2 - x2*(y2+(y1-y2))
            = x2*y2 + (x1-x2)*y2 - x2*y2 - x2*(y2-y1)
            = (x1-x2)*y2 - x2*(y2-y1)

    So, try this:

    dlon = lx - lon
dlat = ly - latp
sc = (dlon*latp-lon*dlat)*paint.map.scalefactor;

    The value is mathematically the same, but the terms are an order of magnitude smaller, so the error should be an order of magnitude smaller as well.

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