In computer science and numerical analysis, unit in the last place or unit of least precision (ULP) is the spacing between floating-point numbers, i.e., the value the least significant bit (lsb) represents if it is 1. It is used as a measure of precision in numeric calculations. If x has exponent E, then ULP(x) = machine epsilon x 2^E.
The IEEE 754 specification—followed by all modern floating-point hardware—requires that the result of an elementary arithmetic operation (addition, subtraction, multiplication, division, and square root) be within 0.5 ULP of the mathematically exact result—that is, that it be the best possible result. Reputable numeric libraries compute the basic transcendental functions to between 0.5 and about 1 ULP, as it is computationally expensive to guarantee 0.5 ULP precision.
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