How Can Floating Point Rounding Errors Impact Calculations and Data Analysis?

Uncovering Floating Point Rounding Errors

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.

A Simple Example

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.

Error Accumulation

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.

Impact on Floating-Point Operations

In general, operations involving floating-point variables can introduce errors due to rounding. Specifically, the following factors can contribute to floating-point errors:

• Limited precision of floating-point representation
• Accumulation of rounding errors in calculations
• Loss of precision when converting between different floating-point formats

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