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A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation. Specifically, for functions, a fixed point is an element that is mapped to itself by the function. Any set of fixed points of a transformation is also an invariant set.
[1]: 22 [2]: 10 For example, in a floating-point arithmetic with five base-ten digits, the sum 12.345 + 1.0001 = 13.3451 might be rounded to 13.345. The term floating point refers to the fact that the number's radix point can "float" anywhere to the left, right, or between the significant digits of the number.
Compared with the fixed-point number system, the floating-point number system is more efficient in representing real numbers so it is widely used in modern computers. While the real numbers R {\displaystyle \mathbb {R} } are infinite and continuous, a floating-point number system F {\displaystyle F} is finite and discrete.
Variable-length arithmetic operations are considerably slower than fixed-length format floating-point instructions. When high performance is not a requirement, but high precision is, variable length arithmetic can prove useful, though the actual accuracy of the result may not be known.
Arbitrary-precision arithmetic can also be used to avoid overflow, which is an inherent limitation of fixed-precision arithmetic. Similar to an automobile's odometer display which may change from 99999 to 00000, a fixed-precision integer may exhibit wraparound if numbers grow too large to represent at the fixed level of precision.
Floating point operations per second (FLOPS, flops or flop/s) is a measure of computer performance in computing, useful in fields of scientific computations that require floating-point calculations. [1] For such cases, it is a more accurate measure than measuring instructions per second. [citation needed]
Computer arithmetic is the scientific field that deals with representation of numbers on computers and corresponding implementations of the arithmetic operations. [1] [2] It includes: Fixed-point arithmetic; Floating-point arithmetic; Interval arithmetic; Arbitrary-precision arithmetic; Modular arithmetic. Multi-modular arithmetic