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Branch of elementary mathematics
of binary arithmetic on computers. Some arithmetic systems operate on mathematical objects other than numbers, such as interval arithmetic and matrix
Arithmetic
Implementation of arithmetic operations
Computer arithmetic is the scientific field that deals with representation of numbers on computers and corresponding implementations of the arithmetic
Computer_arithmetic
Computer approximation for real numbers
In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a significand (a signed sequence of a fixed number of
Floating-point_arithmetic
Computer science conference
The IEEE International Symposium on Computer Arithmetic (ARITH) is a conference in the area of computer arithmetic. The symposium was established in 1969
ARITH Symposium on Computer Arithmetic
ARITH_Symposium_on_Computer_Arithmetic
Combinational digital circuit
In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers
Arithmetic_logic_unit
IEEE standard for floating-point arithmetic
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the
IEEE_754
Calculations where numbers' precision is only limited by computer memory
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic
Arbitrary-precision arithmetic
Arbitrary-precision_arithmetic
Method for bounding the errors of numerical computations
Interval arithmetic (also known as interval mathematics, interval analysis or interval computation) is a mathematical technique used to mitigate rounding
Interval_arithmetic
Digit transferred from one column to another
In elementary arithmetic, a carry is a digit that is transferred from one column of digits to another column of more significant digits. It is part of
Carry_(arithmetic)
Computer format for representing real numbers
do not have specific support for fixed-point arithmetic. However, most computers with binary arithmetic have fast bit shift instructions that can multiply
Fixed-point_arithmetic
Computer arithmetic error
In computer programming, an integer overflow occurs when an arithmetic operation on integers attempts to create a numeric value that is outside of the
Integer_overflow
Computer programming condition
The term arithmetic underflow (also floating-point underflow, or just underflow) is a condition in a computer program where the result of a calculation
Arithmetic_underflow
Type of arithmetic where output is limited to a fixed range of values
Saturation arithmetic is a version of arithmetic in which all operations, such as addition and multiplication, are limited to a fixed range between a
Saturation_arithmetic
Binary representation for signed numbers
Israel (2002). Computer Arithmetic Algorithms. A. K. Peters. ISBN 1-56881-160-8. Flores, Ivan (1963). The Logic of Computer Arithmetic. Prentice-Hall
Two's_complement
Number expressed in the base-2 numeral system
] + [ 1 × 4 ] + [ 0 × 2 ] + [ 1 × 1 ] 1001012 = 3710 Arithmetic in binary is much like arithmetic in other numeral systems using positional notation. Addition
Binary_number
Storage of digital data readable by computers
unit and the arithmetic logic unit (ALU). The former controls the flow of data between the CPU and memory, while the latter performs arithmetic and logical
Computer_data_storage
Datum of integral data type
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
Integer_(computer_science)
Number format for specifying provision
the multiplication can be implemented as an arithmetic shift to the left and the division as an arithmetic shift to the right; on many processors shifts
Q_(number_format)
N-th root of the product of n numbers
real numbers by using the product of their values (as opposed to the arithmetic mean, which uses their sum). The geometric mean of n {\displaystyle
Geometric_mean
Programmable machine that processes data
A computer is a machine that can be programmed to automatically carry out sequences of arithmetic or logical operations (computation). Modern digital
Computer
Strategies to make sure approximate calculations stay close to accurate
in 1936, was the first computer with floating-point arithmetic and was thus susceptible to floating-point error. Early computers, however, with operation
Floating-point error mitigation
Floating-point_error_mitigation
Arithmetic operation
denoted with the plus sign +, is one of the four basic operations of arithmetic, the other three being subtraction, multiplication, and division. The
Addition
Decidable first-order theory of the natural numbers with addition
Presburger arithmetic is the first-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who introduced it in 1929.
Presburger_arithmetic
French computer scientist (born 1961)
mathematician and computer scientist working in the field of computer arithmetic. He is known for his early work on online arithmetic, in particular the
Jean-Michel_Muller
Books about algorithms by Donald Knuth
The Art of Computer Programming (TAOCP) is a comprehensive multi-volume monograph (Volumes 1–7) written by the computer scientist Donald Knuth presenting
The Art of Computer Programming
The_Art_of_Computer_Programming
Affine arithmetic (AA) is a model for self-validated numerical analysis. In AA, the quantities of interest are represented as affine combinations (affine
Affine_arithmetic
Algorithm in numerical analysis
radix, only for the arithmetic to "normalize floating-point sums before rounding or truncating". Computers typically use binary arithmetic, but to make the
Kahan_summation_algorithm
Free software
security applications, and computer algebra systems. GMP aims to be faster than any other arbitrary-precision arithmetic (big number) library for all
GNU Multiple Precision Arithmetic Library
GNU_Multiple_Precision_Arithmetic_Library
Computation modulo a fixed integer
In mathematics, modular arithmetic is a system of arithmetic operations for integers, differing from the usual ones in that numbers "wrap around" when
Modular_arithmetic
Mathematical expression with disputed status
Nathalie; Stehlé, Damien; Torres, Serge (2010). Handbook of Floating-Point Arithmetic (1 ed.). Birkhäuser. p. 216. doi:10.1007/978-0-8176-4705-6. ISBN 978-0-8176-4704-9
Zero_to_the_power_of_zero
Shift operator in computer programming
In computer programming, an arithmetic shift is a shift operator, sometimes termed a signed shift (though it is not restricted to signed operands). The
Arithmetic_shift
Arithmetic logic circuit
Technology", Proceedings of the 7th Symposium on Computer Arithmetic ARITH-7, pp. 2-8. Reprinted in Computer Arithmetic, E. E. Swartzlander, (editor), Vol. II,
Carry-skip_adder
Class of mathematical expression
dividend (numerator). The usual definition of the quotient in elementary arithmetic is the number which yields the dividend when multiplied by the divisor
Division_by_zero
Type of computer arithmetic
algorithms for arithmetic operations, were introduced by Charles Clenshaw and Frank Olver in 1984. The symmetric form of the LI system and its arithmetic operations
Symmetric level-index arithmetic
Symmetric_level-index_arithmetic
Algorithm for fast modular multiplication
In modular arithmetic computation, Montgomery modular multiplication, more commonly referred to as Montgomery multiplication, is a method for performing
Montgomery modular multiplication
Montgomery_modular_multiplication
Computational operation
signs): bool is_odd(int n) { return n % 2 != 0; } Or with the binary arithmetic: bool is_odd(int n) { return n & 1; } Modulo operations might be implemented
Modulo
32-bit computer number format
Integer arithmetic and bit-shifting can yield an approximation to reciprocal square root (fast inverse square root), commonly required in computer graphics
Single-precision floating-point format
Single-precision_floating-point_format
bigfloats. Maple, Mathematica, and several other computer algebra software include arbitrary-precision arithmetic. Mathematica employs GMP for approximate number
List of arbitrary-precision arithmetic software
List_of_arbitrary-precision_arithmetic_software
Base-3 numeral system
logarithmic time. A library of C code supporting BCT arithmetic is available. Qutrit Setun, a ternary computer Ternary logic Taixuanjing Kindra, Vladimir; Rogalev
Ternary_numeral_system
Mixed-precision arithmetic is a form of floating-point arithmetic that uses numbers with varying widths in a single operation. A common usage of mixed-precision
Mixed-precision_arithmetic
Mathematical proof at least partially generated by computer
conjecture in non-linear dynamics. Proven by O. E. Lanford using rigorous computer arithmetic, 1982 Connect Four, 1988 – a solved game Non-existence of a finite
Computer-assisted_proof
Concise notation for large or small numbers
significand m is at least 1 but less than 10. Decimal floating point is a computer arithmetic system closely related to scientific notation. For performing calculations
Scientific_notation
64-bit computer number format
float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating
Double-precision floating-point format
Double-precision_floating-point_format
Floating-point accuracy metric
error Goldberg, David (March 1991). "What Every Computer Scientist Should Know About Floating-Point Arithmetic". ACM Computing Surveys. 23 (1): 5–48. doi:10
Unit_in_the_last_place
Data type approximating a real number
type used in a computer program to represent an approximation of a real number. Because the real numbers are not countable, computers cannot represent
Real_data_type
Fixed-precision arithmetic, also referred to as finite-precision arithmetic, is arithmetic on numbers that are represented in a fixed number of digits
Fixed-precision_arithmetic
Central computer component that executes instructions
primary processor in a given computer. Its electronic circuitry executes instructions of a computer program, such as arithmetic, logic, controlling, and input/output
Central_processing_unit
Replacing a number with a simpler value
removing bias. A rounding method should have utility in computer science or human arithmetic where finite precision is used, and speed is a consideration
Rounding
Digital circuit implementation method
Technology", Proceedings of the 7th Symposium on Computer Arithmetic ARITH-7, pp. 2-8. Reprinted in Computer Arithmetic, E. E. Swartzlander, (editor), Vol. II,
Carry-select_adder
Mathematical software library
der 4361 realisiert" [Computers don't deliver exact results - Karlsruhe research team Kulisch implements new computer arithmetic for the IBM 4361]. Computerwoche
Karlsruhe_Accurate_Arithmetic
Denormalized floating-point numbers near zero
Proceedings 16th IEEE Symposium on Computer Arithmetic (Arith16). 16th IEEE Symposium on Computer Arithmetic. IEEE Computer Society. pp. 104–111. ISBN 0-7695-1894-X
Subnormal_number
Encoding for a sequence of byte values using 36 printable characters
Base36 is a binary-to-text encoding that represents binary data in an ASCII string format by translating it into a radix-36 representation. The choice
Base36
Computer scientist, author and university professor
of computer science, with emphasis on computer arithmetic, digital design, vector computers and computer system architecture. Lang's legacy was celebrated
Tomás_Lang
Property of a numeric data type in computing
language. Nevertheless, arithmetic instructions usually set different CPU flags such as the carry flag for unsigned arithmetic and the overflow flag for
Signedness
System of digitally encoding numbers
needed to implement basic arithmetic as well as slightly less dense storage. BCD was used in many early decimal computers, and is implemented in the
Binary-coded_decimal
Operation in computer arithmetic
abbreviated as sext, particularly in mnemonics) is the operation, in computer arithmetic, of increasing the number of bits of a binary number while preserving
Sign_extension
Part of a number in scientific notation
Frank H. (ed.). Design of Arithmetic Units for Digital Computers. Macmillan Computer Science Series (1 ed.). Department of Computer Science, University of
Significand
Interval of binary floating-point numbers with a common sign and exponent
elementary functions in double precision" (PDF). 15th IEEE Symposium on Computer Arithmetic. ARITH 2001. IEEE. pp. 111–118. doi:10.1109/ARITH.2001.930110. ISSN 1063-6889
Binade
Arithmetic logic circuit
"Fast area-efficient VLSI adders". Proceedings 8th Symposium on Computer Arithmetic. IEEE: 49–56. Lynch, Thomas Walker; Swartzlander, Jr., Earl E. (August
Kogge–Stone_adder
Arithmetic operation
Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is
Division_(mathematics)
Computer arithmetic standards
ISO/IEC 10967, Language independent arithmetic (LIA), is a series of standards on computer arithmetic. It is compatible with IEEE 754 (also published
ISO/IEC_10967
Algorithm that multiplies two signed binary numbers in two's complement notation
Booth Encoding Radix-8 Booth Encoding in A Formal Theory of RTL and Computer Arithmetic Booth's Algorithm JavaScript Simulator Implementation in Python Implementation
Booth's multiplication algorithm
Booth's_multiplication_algorithm
Hardware multiplier design
The Dadda multiplier is a hardware binary multiplier design invented by computer scientist Luigi Dadda in 1965. It uses a selection of full and half adders
Dadda_multiplier
Variant of floating-point numbers in computers
(universal numbers) are a family of number formats and arithmetic for implementing real numbers on a computer, proposed by John L. Gustafson in 2015. They are
Unum_(number_format)
Mathematical problem
is division where the divisor (denominator) is infinity. In ordinary arithmetic, this does not have a well-defined meaning, since ∞ is a mathematical
Division_by_infinity
Calculating tool
completed a cycle and approximated one year. When translated into modern computer arithmetic, the Nepōhualtzintzin amounted to the rank from 10 to 18 in floating
Abacus
Differentiating positive and negative zero
arithmetic (presently used by most computers and programming languages that support floating-point numbers) requires both +0 and −0. Its arithmetic can
Signed_zero
Internal representation of numeric values in a digital computer
A computer number format is the internal representation of numeric values in digital device hardware and software, such as in programmable computers and
Computer_number_format
Upper bound on rounding error in floating-point arithmetic
rounding in floating point number systems. This value characterizes computer arithmetic in the field of numerical analysis, and by extension in the subject
Machine_epsilon
Algorithm in modular arithmetic
In modular arithmetic, Barrett reduction is an algorithm designed to optimize the calculation of a mod n {\displaystyle a\,{\bmod {\,}}n\,} without needing
Barrett_reduction
Encoding of negative numbers in binary number systems
Signed Integers Ivan Flores, The Logic of Computer Arithmetic, Prentice-Hall (1963) Israel Koren, Computer Arithmetic Algorithms, A.K. Peters (2002), ISBN 1-56881-160-8
Signed_number_representations
Algorithm for fast exponentiation
exponentiation. These can be of quite general use, for example in modular arithmetic or powering of matrices. For semigroups for which additive notation is
Exponentiation_by_squaring
Early electronic digital computing device
vacuum tubes to do arithmetic calculations. Prior to this, slower electro-mechanical methods were used by Konrad Zuse's Z1 computer, and the simultaneously
Atanasoff–Berry_computer
Operation common in numerical signal processing
That is, digital floating-point arithmetic is generally not associative or distributive. (See Floating-point arithmetic § Accuracy problems.) Therefore
Multiply–accumulate_operation
Electronic circuit used to multiply binary numbers
used in digital electronics, such as a computer, to multiply two binary numbers. A variety of computer arithmetic techniques can be used to implement a
Binary_multiplier
Number in base-10 numeral system
revisions of the IEEE 754 Standard for Floating-Point Arithmetic). Decimal arithmetic is used in computers so that decimal fractional results of adding (or
Decimal
Algorithm to compute rounding error
Fast2Sum was later factored out of it by Dekker in 1971 for double-double arithmetic algorithms. The names 2Sum and Fast2Sum appear to have been applied retroactively
2Sum
Computer representation of real numbers
A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal
Logarithmic_number_system
Efficient hardware implementation of a digital multiplier
the original on 2011-02-06. Savard, John J. G. (2018) [2006]. "Advanced Arithmetic Techniques". quadibloc. Archived from the original on 2018-07-03. Retrieved
Wallace_tree
University Professor
computer arithmetic, digital design, and computer system architecture. Ercegovac is Distinguished Professor Emeritus and former Chair in the Computer
Milos_Ercegovac
2.71828...; base of natural logarithms
Symposium on Computer Arithmetic (ARITH 2024). Porto, Portugal: IEEE. Retrieved 2025-07-21. Goldberg, David (March 1991). "What Every Computer Scientist
E_(mathematical_constant)
piecewise step-polynomials. All computations are performed in exact integer arithmetic using GMP or imath. Many program analysis techniques are based on integer
Integer_set_library
Method for division with remainder
Press. ISBN 978-1-351-83197-0. Shaw, Robert F. (1950). "Arithmetic Operations in a Binary Computer". Review of Scientific Instruments. 21 (8): 690. Bibcode:1950RScI
Division_algorithm
Number type in floating-point arithmetic
Double-precision floating-point format IEEE Standard for Floating-Point Arithmetic, 2008-08-29, doi:10.1109/IEEESTD.2008.4610935, ISBN 978-0-7381-5752-8
Normal_number_(computing)
Algorithm for integer multiplication
numbers are so small that they can (or must) be computed directly. In a computer with a full 32-bit by 32-bit multiplier, for example, one could choose
Karatsuba_algorithm
Multi-modular arithmetic
{\displaystyle m_{i}} . RNS have applications in the field of digital computer arithmetic. By decomposing in this a large integer into a set of smaller integers
Residue_number_system
Multiprecision integer software library
multiprecision integer library forked from the GNU Multiple Precision Arithmetic Library (GMP) project. It consists of much code from past GMP releases
MPIR_(mathematics_software)
Annual conference
The Conference on Computer Vision and Pattern Recognition is an annual conference on computer vision and pattern recognition. The conference was first
Conference on Computer Vision and Pattern Recognition
Conference_on_Computer_Vision_and_Pattern_Recognition
Algorithmic runtime requirements for common math procedures
Modern Computer Arithmetic. Cambridge University Press. ISBN 978-0-521-19469-3. Knuth, Donald Ervin (1997). Seminumerical Algorithms. The Art of Computer Programming
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
to limitations in representing real numbers and performing arithmetic operation on computers. These errors commonly appear in software engineering and
Numerical_error
Second edition of the IEEE 754 floating-point standard
IEEE 754r) is a revision of the IEEE 754 standard for floating-point arithmetic. It was published in August 2008 and is a significant revision to, and
IEEE_754-2008_revision
IEEE standard for radix-independent floating-point arithmetic
floating-point standardisation. IEEE 854 arithmetic was first commercially implemented in the HP-71B handheld computer, which used decimal floating point with
IEEE_854-1987
Numbering format in Nvidia hardware
TensorFloat-32 (TF32) is a numeric floating point format designed for Tensor Core running on certain Nvidia GPUs. It was first implemented in the Ampere
TensorFloat-32
Part of a computer system
microcontroller units (MCUs/μCs)/single-board computer (SBCs), which serve to provide floating-point arithmetic capability. These add-on FPUs are host-processor-independent
Floating-point_unit
Algorithmic runtime requirements for matrix multiplication
problem in computer science What is the fastest algorithm for matrix multiplication? More unsolved problems in computer science In theoretical computer science
Computational complexity of matrix multiplication
Computational_complexity_of_matrix_multiplication
Fast method for calculating the digits of π
14.18} . Brent, Richard P.; Zimmermann, Paul (2010). Modern Computer Arithmetic. Vol. 18. Cambridge University Press. doi:10.1017/CBO9780511921698
Chudnovsky_algorithm
value problems. Computer arithmetic, 225–286. L.B. Rall: Automatic Differentiation: Techniques and Applications, Lecture Notes in Computer Science 120, Springer
INTLAB
Offset of the exponent field of floating-point numbers
Frank H. (ed.). Design of Arithmetic Units for Digital Computers. Macmillan Computer Science Series (1 ed.). Department of Computer Science, University of
Exponent_bias
{\displaystyle (X^{7}\cdot X^{2})+(X^{5}\cdot X^{4})\equiv 0} thanks to the arithmetic in GF(2). This corresponds to the columns marked ^ in the example. The
Carry-less_product
while right-associative operators are the other way round. The basic arithmetic operators are normally all left-associative, which means that 1-2-3 =
Common_operator_notation
COMPUTER ARITHMETIC
COMPUTER ARITHMETIC
Boy/Male
Indian, Sanskrit
Unattained; Cannot be Competed with
Boy/Male
Hindu
Computer
Boy/Male
Muslim
Compiler of Hadith
Girl/Female
Muslim
To compete with pride
Male
German
Middle High German byname HEIDEN means "heathen." The composer Josef Haydn's surname was a respelling of this name.
Boy/Male
Arabic, Muslim
Abu Isa Muhammad Al-tirmidhi; Compiler of the One Collection of Prophet Muhammad
Boy/Male
Arabic, Muslim
Compiler of Hadith
Boy/Male
Irish
From an Irish name meaning “â€one who aids or assists.â€â€ It is usually translated as Terence and Terry, two names that have become strongly associated with Ireland. Turlough O’Carolan was a 17th century blind harpist and composer who wrote one of the most haunting pieces of Irish music, “â€O’Carolan’s Concerto.â€â€
Boy/Male
Latin
He who loves God. Famous Bearer: late composer Wolfgang Amadeus Mozart.
Boy/Male
Irish
From an Irish name meaning “â€one who aids or assists.â€â€ It is usually translated as Terence and Terry, two names that have become strongly associated with Ireland. Turlough O’Carolan was a 17th century blind harpist and composer who wrote one of the most haunting pieces of Irish music, “â€O’Carolan’s Concerto.â€â€
Boy/Male
Irish
From an Irish name meaning “â€one who aids or assists.â€â€ It is usually translated as Terence and Terry, two names that have become strongly associated with Ireland. Turlough O’Carolan was a 17th century blind harpist and composer who wrote one of the most haunting pieces of Irish music, “â€O’Carolan’s Concerto.â€â€
Boy/Male
Latin
He who loves God. Famous Bearer: late composer Wolfgang Amadeus Mozart.
Girl/Female
Arabic, Muslim
To Compete with Pride
Boy/Male
Hindu, Indian, Sanskrit
Compiler of the Vedas
Boy/Male
Tamil
Computer
COMPUTER ARITHMETIC
COMPUTER ARITHMETIC
Boy/Male
Tamil
Devarshi | தேவரà¯à®·à®¿Â
Teacher of the God, Sage of the devas
Girl/Female
Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Goddess Durga
Girl/Female
American, British, English, French, German, Hebrew, Latin
Joyous; Medieval Male Name Adopted as a Feminine Name; Tribal Name of the Gauts; Supplanter; God is My Salvation; Cheerful
Biblical
my son; my corn
Girl/Female
Hindu
Good picture, Beautiful
Boy/Male
Gujarati, Hindu, Indian
Power of Intellect
Girl/Female
Indian
She who fulfills
Boy/Male
Indian
The best, The chosen
Boy/Male
Tamil
Kesarisuta | கேஸரீஸà¯à®¤à®¾
(Son of Kesari)
Boy/Male
Hindu, Indian
God; Famous; Like Helping Nature
COMPUTER ARITHMETIC
COMPUTER ARITHMETIC
COMPUTER ARITHMETIC
COMPUTER ARITHMETIC
COMPUTER ARITHMETIC
imp. & p. p.
of Commute
imp. & p. p.
of Compute
p. pr. & vb. n.
of Commute
v. i.
To pay, or arrange to pay, in gross instead of part by part; as, to commute for a year's travel over a route.
v. t.
To compute or rate too high.
n.
A preparation of fruit in sirup in such a manner as to preserve its form, either whole, halved, or quartered; as, a compote of pears.
n.
One who composes or writes a book; a composer, as distinguished from an editor, translator, or compiler.
n.
One who computes.
imp. & p. p.
of Compete
n.
A composer or compiler of hymns; one versed in hymnology.
n.
One who commutes; especially, one who commutes in traveling.
p. pr. & vb. n.
of Compete
n.
A computer.
v. i.
To calculate; to compute.
v. i.
To contend emulously; to seek or strive for the same thing, position, or reward for which another is striving; to contend in rivalry, as for a prize or in business; as, tradesmen compete with one another.
v. t.
To compute erroneously.
v. t.
To compute; to count.
p. pr. & vb. n.
of Compute
v. t.
To exchange; to put or substitute something else in place of, as a smaller penalty, obligation, or payment, for a greater, or a single thing for an aggregate; hence, to lessen; to diminish; as, to commute a sentence of death to one of imprisonment for life; to commute tithes; to commute charges for fares.
n.
Compiler.