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Floating point errors occur when dealing with floating-point variables, which store decimal numbers using a limited number of bits. As a result, operations involving floating-point values may lead to rounding and precision issues.
Consider the following C code snippet:
double p_2x_success = pow(1 - p, (double)8) * pow(p, (double)2) * (double)choose(8, 2);
This code calculates the probability of exactly two successful trials in a scenario with a probability p for success and 10 independent trials. However, due to floating-point limitations, the result may not be exact.
Imagine a function f(k) that calculates the probabilities of having a certain number of successes out of k trials, where p is a constant probability of success. If we plot f(k) on a logarithmic scale for both the X and Y axes, we would ideally get a line at zero (meaning no error).
However, due to floating-point rounding, the errors accumulate, leading to noticeable deviations from zero for larger values of k. This highlights the issue of floating-point error accumulation.
In general, operations involving floating-point variables can introduce errors due to rounding. Specifically, the following factors can contribute to floating-point errors:
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