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I've heard of "error" when using floating point variables. Now I'm trying to solve this puzzle and I think I'm getting some rounding/floating point error. So I'm finally going to figure out the basics of floating point error.
What is a simple example of floating point/rounding error (preferably in C++) ?
Edit: For example say I have an event that has probability p of succeeding. I do this event 10 times (p does not change and all trials are independent). What is the probability of exactly 2 successful trials? I have this coded as:
double p_2x_success = pow(1-p, (double)8) * pow(p, (double)2) * (double)choose(8, 2); Is this an opportunity for floating point error?
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For example, the irrational number pi equals approximately 3.14, rounded to two decimal places or three significant digits. As an example of rounding error, consider the speed of light in a vacuum. The official value is 299,792,458 meters per second.
A floating point number, is a positive or negative whole number with a decimal point. For example, 5.5, 0.25, and -103.342 are all floating point numbers, while 91, and 0 are not. Floating point numbers get their name from the way the decimal point can "float" to any position necessary.
Even if some numbers can be represented exactly by floating-point numbers and such numbers are called machine numbers, performing floating-point arithmetic may lead to roundoff error in the final result.
Floating-point error mitigation is the minimization of errors caused by the fact that real numbers cannot, in general, be accurately represented in a fixed space. By definition, floating-point error cannot be eliminated, and, at best, can only be managed.
Picture is worth a thousand words - try to draw equation f(k) :
and you will get such XY graph (X and Y are in logarithmic scale).
If computer could represent 32-bit floats without rounding error then for every k we should get zero. But instead error increases with bigger values of k because of floating point error accumulation.
hth!
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