Computer arithmetic is the scientific field that deals with representation of

number A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...

s on

computer A computer is a machine that can be Computer programming, programmed to automatically Execution (computing), carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic set ...

s and corresponding implementations of the arithmetic operations. It includes: *

Fixed-point arithmetic In computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, represen ...

Floating-point arithmetic In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a Sign (mathematics), signed sequence of a fixed number of digits in some Radix, base) multiplied by an integer power of that ba ...

Interval arithmetic Interval arithmetic (also known as interval mathematics; interval analysis or interval computation) is a mathematical technique used to mitigate rounding and measurement errors in mathematical computation by computing function bounds. Numeri ...

Arbitrary-precision arithmetic In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are po ...

Modular arithmetic In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to mo ...

** Multi-modular arithmetic ** ''p''-adic arithmetic, consisting of computing modulo a single

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

and retrieving the

integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

rational Rationality is the quality of being guided by or based on reason. In this regard, a person acts rationally if they have a good reason for what they do, or a belief is rational if it is based on strong evidence. This quality can apply to an ...

result by using Hensel lifting **

Finite field arithmetic In mathematics, finite field arithmetic is arithmetic in a finite field (a field containing a finite number of elements) contrary to arithmetic in a field with an infinite number of elements, like the field of rational numbers. There are infinit ...

* Matrix arithmetic In the cases where the size of the representation of a number is fixed (fixed-point, floating-point and interval arithmetic), the main concern is to control the computational error, as far as possible; see, for example

IEEE 754 The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard #Design rationale, add ...

. In the other cases, where an exact result should be provided, the main concern is the practical efficiency, which is optimized by combining improvements of

computational complexity In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations ...

with hardware specificities. ARITH Symposium on Computer Arithmetic is an international symposium devoted to computer arithmetic.

References

Computer arithmetic {{compu-stub