Roundoff is the bane of numerical computing. Floating point operations can produce arbitrarily inaccurate values. When these values are then used to perform even more calculations, the round-off error will be magnified, creating misleading and unreliable results. Imagine a physicist performing a series of operations on the data she collected. At the end of the […]

In the blissful days of today, virtually every computer capable of performing floating point arithmetic implements the IEEE 754 standard. In your numerical analysis class, you have likely been told that “This is how floating point works,” upon which you were introduced to the IEEE 754 standard — as if there couldn’t possibly be an […]

In scientific computing, units give a valuable check to make sure that all calculations were valid. For example, adding meters to seconds is a nonsensical operation, and should thus be reported as an error. Mathematica allows for unit checking with its Units package. However, few general purpose programming provide this functionality. In some languages, such […]