Floating-point arithmetic

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History

Leonardo Torres Quevedo Charles Babbage Analytical engine Digits Typewriter

36 related topics

IEEE 754: floating point in modern computers

IEEE Revised in 2008 Cray T90 SV1 32-bit floating point

23 related topics

Other notable floating-point formats

Microsoft Binary Format Altair BASIC TRS-80 LEVEL II CP/M MBASIC

30 related topics

Accuracy problems

Precision Commutative Associativity Distributive Derivative

25 related topics

Topics to explore

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Overview

Computing
Arithmetic
Real numbers Real number
Significand
Signed Sign (mathematics)
Radix
Integer power
Base two Binary number
Decimal floating point
Specific rules for halfway values Rounding
Radix point
Significant digits
Scientific notation
Orders of magnitude Orders of magnitude (numbers)
Between protons in an atom Orders of magnitude (length)
Dynamic range
IEEE 754
FLOPS
Computer system
Floating-point units Floating-point unit
Coprocessors Coprocessor
Number representation
"point" character Decimal separator
Integer
Fixed-point Fixed-point arithmetic
Power of 10
Jupiter
Io Io (moon)
Exponent
Decimal Decimal representation

History

Leonardo Torres Quevedo
Charles Babbage
Analytical engine
Digits Numerical digit
Typewriter
Electromechanical Arithmometer Leonardo Torres y Quevedo
Konrad Zuse
Z1 Z1 (computer)
Mechanical computer
Relay
Z3 Z3 (computer)
Division by infinity
Von Neumann John von Neumann
IAS machine
Z4 Z4 (computer)
Model V
Pilot ACE
National Physical Laboratory, UK
English Electric DEUCE
IBM 704
Biased exponent Exponent bias
Scientific computation
Extensions for Scientific Computation
UNIVAC 1100/2200 series
IBM 7094
Hexadecimal floating-point representations IBM hexadecimal floating-point
System/360
Z/Architecture
Word Word (computer architecture)
I8087 Intel 8087

Range of floating-point numbers

Double-precision Double-precision floating-point format
Positive and negative zeros Signed zero
Subnormal numbers Subnormal number

IEEE 754: floating point in modern computers

IEEE Institute of Electrical and Electronics Engineers
Revised in 2008 IEEE 754-2008 revision
Cray T90
SV1 Cray SV1
32-bit floating point Single-precision floating-point format
Type in the C language C data types
Double extended Extended precision
C99
C11 C11 (C standard revision)
Long double
X86
Alignment Data structure alignment
Round-off error
Decimal64 Decimal64 floating-point format
Decimal128 Decimal128 floating-point format
Decimal32 Decimal32 floating-point format
Quadruple precision Quadruple-precision floating-point format
Half precision Half-precision floating-point format
Cg Cg (programming language)
Infinity
Negative zero
NaNs NaN
Hexadecimal

Dealing with exceptional cases

Square root
Complex numbers Complex number
Underflow Arithmetic underflow
Trap Trap (computing)
Portable Porting
Exception Exception handling
Means Concurrency (computer science)
Thread-local storage
IEEE 754 design rationale Floating point
Root-finding Zero of a function

Accuracy problems

Precision Precision (computer science)
Commutative
Associativity Associative property
Distributive Distributive property
Derivative
Floor and ceiling functions
Loss of significance
Prevented it from intercepting MIM-104 Patriot
Scud Al Hussein (missile)
Dhahran
Saudi Arabia
14th Quartermaster Detachment
Salami slicing Salami slicing tactics
Backward error analysis Error analysis (mathematics)
Relative error
James H. Wilkinson
Numerically unstable Numerical stability
Ill-conditioned Condition number
Numerical linear algebra
Compilers
Common subexpression elimination
Vectorization Single instruction, multiple data
Library Library (computing)
Fortran
Intel Fortran Compiler

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Map overview Semantic statistics

Nodes227

Edges226

Triples150

Avg. degree1.99

Density0.008811

Components1

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Floating-point arithmetic

Top relations

related to Further reading · 91

Floating-point arithmetic → Addison-Wesley, Algebraic Processes, Arithmetic, Automatic Computation, Birkhäuser, Blaauw, Brian, Brooks, Brunie, Cambridge University Press, CD-ROM, Charles, Clarendon Press, Classic, Claude-Pierre, Computer Architecture, Computer Programming, Concepts, Date, David

related to Alternatives to floating-point numbers · 25

Floating-point arithmetic → Binary, Charles Clenshaw, Computer, Conversely, Fixed-point, Frank Olver, However, Interval, It, LI, LNSs, Logarithmic, Maple, Mathematica, Maxima, Peter Turner, Posit, SLI, Software, Some

see also · 13

Floating-point arithmetic → Apple Numerics Environment, Arbitrary-precision, Binary Floating-Point ArithmeticIBM Floating, Binary Format, Computable, IEEE, MBF, MinifloatQ, MPFRHalf-precision, Point ArchitectureKahan, SANE, Significant, Standard

Important terminology Word statistics

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Important terminology

floating-point precision number numbers ieee significand digits binary exponent decimal arithmetic format used bits example result 754 point rounding value

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Mathematica	instance of	in particular floating point.Computer algebra systems	0.80	text
Maxima	instance of	in particular floating point.Computer algebra systems	0.80	text
and Maple can often handle irrational numbers like π	instance of	in particular floating point.Computer algebra systems	0.80	text
cosine	instance of	functions	0.80	text
log are not mandated	instance of	functions	0.80	text
a C	instance of	and is a different usage to that typically defined in programming languages	0.80	text
π	instance of	inability to represent numbers	0.80	text
0.1 exactly	instance of	inability to represent numbers	0.80	text
and other slight inaccuracies	instance of	inability to represent numbers	0.80	text
the following phenomena may occur	instance of	inability to represent numbers	0.80	text
iterative refinement	instance of	using numerical approaches	0.80	text
if they are to work well.Summation of a vector of floating-point values is a basic algorithm in scientific computing	instance of	using numerical approaches	0.80	text

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Research this topic

Explore this topic

History

IEEE 754: floating point in modern computers

Other notable floating-point formats

Accuracy problems

Key facts & relationships

Topics to explore

Overview

History

Range of floating-point numbers

IEEE 754: floating point in modern computers

Other notable floating-point formats

Representable numbers, conversion and rounding

Floating-point operations

Dealing with exceptional cases

Accuracy problems

Advanced semantic analysis

Map overview Semantic statistics

Floating-point arithmetic

How this topic connects Entity context

Floating-point arithmetic

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges