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In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values.
Variable-length representations of integers, such as bignums, can store any integer that fits in the computer's memory. Other integer data types are implemented with a fixed size, usually a number of bits which is a power of 2 (4, 8, 16, etc.) or a memorable number of decimal digits (e.g., 9 or 10).
Bit length or bit width is the number of binary digits, called bits, necessary to represent an unsigned integer [1] as a binary number. Formally, the bit length of a natural number n ≥ 0 {\displaystyle n\geq 0} is
The number of digits in the binary representation of a positive integer n is the integral part of 1 + log 2 n, i.e. [12] ⌊ log 2 n ⌋ + 1. {\displaystyle \lfloor \log _{2}n\rfloor +1.} In information theory, the definition of the amount of self-information and information entropy is often expressed with the binary logarithm ...
Fastest integer types that are guaranteed to be the fastest integer type available in the implementation, that has at least specified number n of bits. Guaranteed to be specified for at least N=8,16,32,64. Pointer integer types that are guaranteed to be able to hold a pointer. Included only if it is available in the implementation.
The n th term describes the length of the n th run A000002: Euler's totient function ... Number of triangles with integer sides and perimeter n. A005044:
In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.)
If, for example, the output is constrained to 32-bit integer values, then the hash values can be used to index into an array. Such hashing is commonly used to accelerate data searches. [10] Producing fixed-length output from variable-length input can be accomplished by breaking the input data into chunks of specific size.