Floor takes a single numeric argument x and returns a numeric vector containing the largest integers not greater than the corresponding elements of x.
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Fortran was defined to require this behavior and thus almost all processors implement.
Ceiling takes a single numeric argument x and returns a numeric vector containing the smallest integers not less than the corresponding elements of x.
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In most programming languages the simplest method to convert a floating point number to an integer does not do floor or ceiling but truncation the reason for this is historical as the first machines used ones complement and truncation was simpler to implement floor is simpler in two s complement.
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