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A range check is a check to make sure a number is within a certain range; for example, to ensure that a value about to be assigned to a 16-bit integer is within the capacity of a 16-bit integer (i.e. checking against wrap-around).
One can encode the numbers so that encoded 0 corresponds to 0, 1 to −1, 10 to 1, 11 to −2, 100 to 2, etc.: counting up alternates between nonnegative (starting at 0) and negative (since each step changes the least-significant bit, hence the sign), whence the name "zigzag encoding".
"subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence.
In computer science, an integer literal is a kind of literal for an integer whose value is directly represented in source code.For example, in the assignment statement x = 1, the string 1 is an integer literal indicating the value 1, while in the statement x = 0x10 the string 0x10 is an integer literal indicating the value 16, which is represented by 10 in hexadecimal (indicated by the 0x prefix).
Given real numbers x and y, integers m and n and the set of integers, floor and ceiling may be defined by the equations ⌊ ⌋ = {}, ⌈ ⌉ = {}. Since there is exactly one integer in a half-open interval of length one, for any real number x, there are unique integers m and n satisfying the equation
For the case n = 2, an extension of the Euclidean algorithm can find any integer relation that exists between any two real numbers x 1 and x 2.The algorithm generates successive terms of the continued fraction expansion of x 1 /x 2; if there is an integer relation between the numbers, then their ratio is rational and the algorithm eventually terminates.
An integer is even if it is divisible by 2, and odd if it is not. [1] For example, −4, 0, and 82 are even numbers, while −3, 5, 7, and 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201.
Typically, it is assumed that w ≥ log 2 (max(n, K)); that is, that machine words are large enough to represent an index into the sequence of input data, and also large enough to represent a single key. [2] Integer sorting algorithms are usually designed to work in either the pointer machine or random access machine models of computing. The ...