Is Javascript multiplying these values wrong?

Question

Allright, I know what machine precision is, but this, I can't understand...

Code:

 console.log("meanX",meanX);
 meanX2 = meanX * meanX;           //squared
 console.log("meanX2",meanX2);

Console output:

meanX 300.3
meanX2 28493.4400000000002

In case you are wondering, the correct value for meanX2 would be 90180.09 And this is only one of the many examples visible in the screenshot..

.toFixed(6) seems to fix this... But I have no idea why it doesn't work without it.

Edit

Ok, I don't want to post the whole program code here because in first place I'm not the only author, and second, I also wouldn't like this to be copied without our permission. But I'll gladly explain how I get this error and will post the whole method/function code here.

This code belongs, as you may have guessed from the window title, to a lane detection algorithm. We use Three.js/webgl to run some pre processing shaders on each frame of a video and then we analyze the resulting image. The method/function you see on the screenshot is a perpendicular line fitting algorithm and is part of the whole thing. I can see the algorithm running nicely because I have the lane being drawn on top of the video, and It is well placed. Until suddenly the lane turns into an horizontal bar. This unexpected behavior happens exactly because of the phenomenon I described here, since it's from that moment that I start to see wrong math in the console.

Also, because the video and algorithm run at slightly different fps everytime, the problem doesn't always happen in the same moment of the video, and sometimes It doesn't happen at all.

Here is the code (it has some alterations because I was trying to isolate the issue):

this.perpendicularLineFit = function (points, slopeSign) {
    var count = points.length;
    var sumX = 0,
        sumY = 0;
    var sumX2 = 0,
        sumY2 = 0,
        sumXY = 0;
    var meanX, meanY;
    var i, lowp = {}, highp = {};
    var B;
    var slope;
    var originY;

    for (i = 0; i < count; i++) {
        sumX += points[i].x;
        sumY += points[i].y;
        sumX2 += points[i].x * points[i].x;
        sumY2 += points[i].y * points[i].y;
        sumXY += points[i].y * points[i].x;
    }

    meanX = sumX / count;
    meanY = sumY / count;

    //If you uncoment this, problem reappears: 
    //var numeratorLeft = meanY * meanY;
    console.log("meanX",meanX);
    var meanX2 = meanX*meanX;
    console.log("meanX2",meanX2);

    var numerator = (sumY2 - count * (meanY * meanY)) - (sumX2 - count * meanX2);
    var denominator = (count * meanX * meanY - sumXY);  
    B = 0.5 * (numerator / denominator);


    slope = -B + slopeSign * Math.sqrt(B * B + 1);
    originY = meanY - slope * meanX;

    slope = isNaN(slope) ? slopeSign : slope;
    originY = isNaN(originY) ? originY : originY;

    lowp.y = this.lowY;
    lowp.x = (this.lowY - originY) / slope;
    highp.y = this.highY;
    highp.x = (this.highY - originY) / slope;

    return {
        low: lowp,
        high: highp
    };
};

Now, I was trying to understand what was causing this, and the most bizarre thing is that it seems that when I place a statement of this form

var x = ... meanY * meanY ...;

before the meanX2 attribution, the issue happens. Otherwise it doesn't.

Also, I tried to catch this anomaly in the debugger but just when I enter the debugging tab, the problem disapears. And the values turn correct again.

I certainly don't believe in black magic, and I know that you are probably skeptic to this. I would be too. But here is a link to a video showing it happening: The video

Edit2:

I managed to reproduce this issue in another computer.. Both having ubuntu and using firefox (versions 20 and 21).

Edit3:

I'm sorry it took so much time! Here is a zip containing the issue. Just run it in any webserver. The code mentioned is in LaneDetection.js. Search for "HERE" in the file to find it.

https://docs.google.com/file/d/0B7y9wWiGlcYnYlo1S2pBelR1cHM/edit?usp=sharing

The problem might not happen in the first attempts. If that's the case refresh the page and try again. When the lines get horizontal you know it's there. As I said, I saw this problem happening in firefox versions 20 and 21 on ubuntu. In chrome it never happened.

By the way, I noticed that changing javascript.options.typeinference flag in firefox seems to stop the problem... I don't know exactly what that flag does, but maybe this optimization is not correctly implemented in firefox?

Answer 1

I can't say for sure that I actually have an answer but I think that I have confirmed that basilikum was correct to suggest a memory problem. Here's what I did: I took the first ten entries from your screenshot and calculated the correct answer. I then converted the correct answer and the wrong answer into the hexidecimal representation of the double-precision float. What I ended up with was the following:

292.416^2 = 85507.506 = 40F4E0381C71C71E
 changed to 27583.373 = 40DAEFEB1C71C722

293.166^2 = 85946.694 = 40F4FBAB1C71C72A
 changed to 27583.373 = 40DAEFEB1C71C722

295.818^2 = 87508.396 = 40F55D4658DC0876
 changed to 28041.024 = 40DB62419637021F

294.500^2 = 86730.250 = 40F52CA400000000
 changed to 27583.373 = 40DAEFEB1C71C722

297.000^2 = 88290.000 = 40F58E2000000000
 changed to 28041.024 = 40DB62419637021F

221.750^2 = 49173.062 = 40E802A200000000
 changed to 24964.000 = 40D8610000000000

300.300^2 = 90180.090 = 40F6044170A3D70A
 changed to 28493.440 = 40DBD35C28F5C290

220.200^2 = 48488.040 = 40E7AD0147AE147B
 changed to 25408.360 = 40D8D0170A3D70A4

300.600^2 = 90360.360 = 40F60F85C28F5C29
 changed to 28493.440 = 40DBD35C28F5C290

213.000^2 = 45369.000 = 40E6272000000000
 changed to 28032.326 = 40DB6014E5E0A72E

There's no persistent pattern to the change but there are a couple instances that are very telling of a memory issue. In the first two entries you can see that bytes 1, 2 and 3 were unchanged. In the 9th entry there's something even more odd. It would appear that bytes 0 - 3 were shifted left by exactly 4 bits! Upon considering the statement that the problem doesn't arise until after some time has passed and in light of these two anomalies, I'm fairly confident that you're encountering some sort of memory issue. Could it be, dare I say, a stack overflow?