ceilmax2

ceilmax2 is a mathematical function that returns the smallest integer greater than or equal to the maximum of two input real numbers. Formally, ceilmax2(a, b) = ceil(max(a, b)).

A useful equivalent form is ceilmax2(a, b) = max(ceil(a), ceil(b)) for all real a and b. This follows from the monotonicity of the ceiling function and the fact that the maximum of the two inputs governs the ceiling value.

Key properties include commutativity, since ceilmax2(a, b) = ceilmax2(b, a), and its behavior for integers: if a and b are both integers, ceilmax2(a, b) equals max(a, b). The function is defined for real numbers; if either input is NaN, the result is typically NaN in most programming contexts, while infinities are treated according to the usual rules for max and ceil.

In computation, ceilmax2 can be implemented directly as ceil(max(a, b)) in most languages. An equivalent expression is max(ceil(a), ceil(b)). Both forms are mathematically identical for finite real inputs.

Examples: ceilmax2(3.2, 4.7) = ceil(4.7) = 5. ceilmax2(-1.1, -2.9) = ceil(-1.1) = -1. If a = 2 and b = 5, ceilmax2(2, 5) = 5.

Extensions of the concept include ceilmax_n for n inputs, defined as ceil(max(x1, x2, ..., xn)).

See also: ceiling function, maximum function, integer rounding.