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In section 6.2 of the old IEEE 754-2008 standard, there are two anomalous functions (the maxNum and minNum functions, which return the maximum and the minimum, respectively, of two operands that are expected to be numbers) that favor numbers — if just one of the operands is a NaN then the value of the other operand is returned.
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
Riemann's prime-power counting function is usually denoted as Π 0 (x) or J 0 (x). It has jumps of 1 / n at prime powers p n and it takes a value halfway between the two sides at the discontinuities of π(x). That added detail is used because the function may then be defined by an inverse Mellin transform. Formally, we may define Π 0 ...
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