Incorrect output when calculating magnitude of 3 vectors in Atmel Studio

Question

I'm having some trouble trying to get a floating point output. What I'm trying to do is take the output of an accelerometer on 3 axes. The output from each axis has a high and low byte that are combined into a single variable. The magnitude of these three variables is then computed thusly: mag = sqrt(x*x + y*y + z*z). The output from each axis is output as a 16-bit signed integer.

At least, that's how it should work, but I can't even manage to multiply two large numbers together to produce the correct value in my program, and I see no reason for it as the variables should all be plenty large to hold any results. Here's the code:

    double xAccel = 0;              // 16 bit X acceleration value
    double accelSum = 0;
    xAccel = xAccelRead();

    accelSum = 10000*10000;
    char aMag[64];
    sprintf(aMag, "Accel Mag: %.2f", accelSum);

    clearDisplay();
    writeText(aMag,0,0,WHITE,BLACK,1);
    OLED_buffer();

The output of xAccelRead() is a 16 bit int. Normally, "accelSum" would be set equal to the magnitude equation given above, but for now the static numbers aren't even working. If I set the equation to 100^2, it works. But 10000 * 10000 doesn't work. The result of that should be 100,000,000. But the output I get is:

Accel Mag: -7936.00

I can't understand why this is. I've tried setting the types to int32, int64, and now floating point. Same problem with all of them. I set the correct linker options in Atmel Studio to allow floating point sprintf support, so that's not the problem. I'm guessing there is an overflow somewhere but I can't figure out where. All variables involved have types that are more than large enough to accommodate max values in the hundreds of billions, which is far more than I need anyway.

Say I set accelSum = 1000 * 1000. That's a mere million. Plenty small for an int32 to hold. But my output is:

Accel Mag: 16960.00

Even with 200 * 200, the output is -25536.00.

This has to be some stupid simple problem. If anybody can help me out I'd really appreciate it!

Answer 1

You have answered most of your question in your comment.

Your problem is similar to the surprise some programmers have with float f = 5 / 3; that the division is computed as an integer division, although it is destined to be assigned to a float. The solution in their case is to use float f = 5.0 / 3.0; instead.

If the expressions being divided or, in your case, multiplied, are not constants, you can convert them to a wider type with a cast: float f = (float)int_var1 / (float)int_var2; or, in your case, unsigned long foo = (unsigned long)int_var1 * (unsigned long)int_var2;. You could also convert to double so that the computed multiplication is a double multiplication: accelSum = (double)int_var1 * (double)int_var2;.

Only one of the casts is actually necessary because of “promotion rules”, but it is just as clear to write both.

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If you are interested in the details, the C standard mandates that the type of an integer constant is selected as the first type that can represent the constant in a list. In C99(*), the list is int, long, long long. In your case, a 16-bit int is enough to contain 10000 or 200, so int is picked as the type of these constants.

(*) The idea was the same but the list was different in C90.