min4

Min4 is a term used in mathematics and computer science to denote the minimum of four values. It is the four-argument extension of the standard minimum operator and is commonly implemented as a simple utility in algorithms and software.

Formally, for real numbers a, b, c, and d, min4(a, b, c, d) equals the smallest of the four inputs, i.e., min4(a, b, c, d) = min{a, b, c, d}. In practice, it can be computed with nested two-argument minima, for example min4(a, b, c, d) = min(min(a, b), min(c, d)) or min(min(a, b, c), d).

Key properties of min4 include commutativity and associativity: the result is independent of the order of the inputs and grouping does not affect the outcome. It is idempotent with respect to duplicates (min4(x, x, y, z) = min(x, y, z)), and it is monotone in each argument, meaning increasing any input cannot decrease the result.

Common applications involve situations where a small value must be selected among four candidates. This appears in thresholding, decision logic, or as a component in min-pooling operations in image processing and certain neural network architectures. In programming, min4 is often implemented by combining two-argument min operations since many languages provide a min function for two inputs.

Implementation notes include handling of special values: in floating-point arithmetic, the behavior when any argument is NaN can vary by language, and some environments propagate NaN to the result, while others select the minimum of the numeric inputs. min4 is a simple, widely portable building block for four-way comparisons.