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16-bit computer number format
Half precision (sometimes called FP16 or float16) is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers)
Half-precision floating-point format
Half-precision_floating-point_format
32-bit computer number format
Single-precision floating-point format (sometimes called FP32, float32, or float) is a computer number format, usually occupying 32 bits in computer memory;
Single-precision floating-point format
Single-precision_floating-point_format
128-bit computer number format
quadruple precision (or quad precision) is a binary floating-point–based computer number format that occupies 16 bytes (128 bits) with precision at least
Quadruple-precision floating-point format
Quadruple-precision_floating-point_format
64-bit computer number format
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory;
Double-precision floating-point format
Double-precision_floating-point_format
Floating-point number format used in computer processors
by using a floating radix point. This format is a shortened (16-bit) version of the 32-bit IEEE 754 single-precision floating-point format (binary32)
Bfloat16 floating-point format
Bfloat16_floating-point_format
256-bit computer number format
In computing, octuple precision is a binary floating-point-based computer number format that occupies 32 bytes (256 bits) in computer memory. This 256-bit
Octuple-precision floating-point format
Octuple-precision_floating-point_format
Computer approximation for real numbers
mitigation Floating origin – a technique in 3D rendering to mitigate precision loss of floating-point formats FLOPS Gal's accurate tables GNU MPFR Half-precision
Floating-point_arithmetic
Measure of detail a quantity is expressed in
formats are: Half-precision floating-point format Single-precision floating-point format Double-precision floating-point format Quadruple-precision floating-point
Precision_(computer_science)
Floating-point number formats
Extended precision refers to floating-point number formats that provide greater precision than the basic floating-point formats. Extended-precision formats support
Extended_precision
Floating-point values coded as few bits
In computing, minifloats are floating-point values represented with very few bits. This reduced precision makes them ill-suited for general-purpose numerical
Minifloat
Number type in floating-point arithmetic
Half-precision floating-point format Single-precision floating-point format Double-precision floating-point format IEEE Standard for Floating-Point Arithmetic
Normal_number_(computing)
Method in computer arithmetic
formats are a type of Block Floating Point (BFP) data format specifically designed for AI and machine learning workloads. Very small floating-point numbers
Block_floating_point
Computer format for representing real numbers
value is greater than 224 (for binary single-precision IEEE floating point) or of 253 (for double-precision). Overflow or underflow may occur if |S| is
Fixed-point_arithmetic
to the largest value that can be represented in the IEEE half precision floating-point format. Computing - Fonts: The maximum possible number of glyphs
Orders_of_magnitude_(numbers)
Management of power supply
floating-point format, termed "Linear11". N = Signed Exponent Y = Signed Mantissa Value Represented = Y × 2N Unlike the half-precision floating-point
Power_Management_Bus
Topics referred to by the same term
16 catamaran design Volvo F16, a truck Half-precision floating-point format, a 16-bit computer number format Shibuya Station, a railway station in Tokyo
F16_(disambiguation)
Natural number
base 11 (4494411) 65,504 = largest representable value in half-precision floating-point format 65,535 = largest value for an unsigned 16-bit integer on
60,000
Decimal representation of real numbers in computing
Decimal floating-point (DFP) arithmetic refers to both a representation and operations on decimal floating-point numbers. Working directly with decimal
Decimal_floating_point
IEEE standard for floating-point arithmetic
IEEE 754 standard. The standard defines: arithmetic formats: sets of binary and decimal floating-point data, which consist of finite numbers (including signed
IEEE_754
128-bit computer number format
decimal floating-point number format defined by the IEEE 754 Standard for Floating-Point Arithmetic. It is one of the standard's basic interchange formats, designed
Decimal128 floating-point format
Decimal128_floating-point_format
Number representation
Hexadecimal floating-point (HFP) is a format for encoding floating-point numbers first introduced on the IBM System/360 computers, and supported on subsequent
IBM hexadecimal floating-point
IBM_hexadecimal_floating-point
64-bit computer number format
decimal64 is a decimal floating-point computer number format that occupies 8 bytes (64 bits) in computer memory. The format was formally introduced in
Decimal64 floating-point format
Decimal64_floating-point_format
Upper bound on rounding error in floating-point arithmetic
Machine epsilon or machine precision is an upper bound on the relative approximation error due to rounding in floating point number systems. This value
Machine_epsilon
Part of a number in scientific notation
Torres Quevedo introduced the idea of floating-point arithmetic in his Essays on Automatics, where he proposed the format n; m, showing the need for a fixed-sized
Significand
32-bit computer number format
decimal floating-point computer numbering format that occupies 4 bytes (32 bits) in computer memory. Like the binary16 and binary32 formats, decimal32
Decimal32 floating-point format
Decimal32_floating-point_format
Measure of computer performance
different measures of precision, for example, the TOP500 supercomputer list ranks computers by 64-bit (double-precision floating-point format) operations per
Floating point operations per second
Floating_point_operations_per_second
3D rendering technique
every power of two units away from the origin. With the single-precision floating-point format (32-bit IEEE 754), the accuracy reduces enough to not calculate
Floating_origin
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
Floating-point data type in C family languages
programming languages, long double refers to a floating-point data type that is often more precise than double precision though the language standard only requires
Long_double
Replacing a number with a simpler value
numbers into IEEE 754 double-precision floating-point values before exposing the computed digits with a limited precision (notably within standard JavaScript
Rounding
File format
precision or half-precision data in the IEEE floating-point format, and with a higher dynamic range than half-precision. An exponent value of 128 maps integer
RGBE_image_format
Internal representation of numeric values in a digital computer
greater range and precision of real numbers, we have to abandon signed integers and fixed-point numbers and go to a "floating-point" format. In the decimal
Computer_number_format
64-bit RISC instruction set architecture
two other floating-point data types are included: VAX G-floating point (double precision, 64-bit) VAX F-floating point (single precision, 32-bit) VAX
DEC_Alpha
IBM's 64-bit instruction set architecture implemented by its mainframe computers
supports Hexadecimal floating point, a format inherited from System/360 E Single precision, in half of a FP register D Double precision, a full FP register
Z/Architecture
Instructions for the x86 microprocessors
operations (math) on: eight 32-bit single-precision floating-point numbers or four 64-bit double-precision floating-point numbers. The width of the SIMD registers
Advanced_Vector_Extensions
Root-finding algorithm
inverse) of the square root of a 32-bit floating-point number x {\displaystyle x} in IEEE 754 floating-point format. The algorithm is best known for its
Fast_inverse_square_root
Floating-point accuracy metric
unit in the last place or unit of least precision (ulp) is the spacing between two consecutive floating-point numbers, i.e., the value the least significant
Unit_in_the_last_place
Intel SIMD processor supplementary instruction sets introduced by Intel
simultaneously. SSE2 introduced double-precision floating point instructions in addition to the single-precision floating point and integer instructions found
SSE2
Architectural instruction
provides support for converting between half-precision and standard IEEE single-precision floating-point formats. The CVT16 instruction set, announced by
F16C
Denormalized floating-point numbers near zero
in the IEEE binary floating-point formats, but they do exist in some other formats, including the IEEE decimal floating-point formats. Some systems handle
Subnormal_number
Instruction set extension by Intel
comprehensive support for the binary16 floating-point numbers (also known as FP16, float16 or half-precision floating-point numbers). The new instructions implement
AVX-512
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
RISC instruction set architecture
SPARC version 8, the floating-point register file has 16 double-precision registers. Each of them can be used as two single-precision registers, providing
SPARC
Set of x86 processor instructions
double-extended-precision floating-point format. All decimal integers are exactly representable in double extended-precision format. […] [1] Hyde, Randall
Intel_BCD_opcodes
The IEEE 754-2008 standard includes decimal floating-point number formats in which the significand and the exponent (and the payloads of NaNs) can be
Binary_integer_decimal
Interval of binary floating-point numbers with a common sign and exponent
and numerical analysis, a binade is a set of numbers in a binary floating-point format that all have the same sign and exponent. In other words, a binade
Binade
Offset of the exponent field of floating-point numbers
. When interpreting the floating-point number, the bias is subtracted to retrieve the actual exponent. For a half-precision number, the exponent is stored
Exponent_bias
Base-16 numeric representation
Hexadecimal time – Base 16 time format proposed in 1863 Hexspeak – Novelty form of variant English spelling IBM hexadecimal floating-point – Number representation
Hexadecimal
Second edition of the IEEE 754 floating-point standard
supporting other fixed-width floating-point formats, as well as arbitrary-precision formats (i.e., where the precision of representation and rounding
IEEE_754-2008_revision
Number of bits used to represent a color
file format OpenEXR which supported 16-bit-per-channel half-precision floating-point numbers. At values near 1.0, half precision floating point values
Color_depth
Value for unrepresentable data
two real numbers, or extended real numbers (as in the IEEE 754 floating-point formats), the first number may be either less than, equal to, or greater
NaN
Compressed image file format
higher-precision varieties of color representation known as deep color) 16 bits per component as integers, fixed-point numbers, or half-precision floating-point
JPEG_XR
Supercomputer designed by Tesla
more precision and range than needed for AI tasks, and FP16 does not have enough, Tesla has devised 8- and 16-bit configurable floating point formats (CFloat8
Tesla_Dojo
Instruction set architecture developed by Digital Equipment Corporation
than one format, including an unusual middle-endian format sometimes referred to as "PDP-endian". A 64-bit double-precision floating-point format is supported
PDP-11_architecture
computed to ±1/2000 bit of accuracy (which does not require extra floating-point precision as long as the correction is less than 1/2000 the magnitude of
Gal's_accurate_tables
Two raised to an integer power
fit in a 128-bit IEEE quadruple-precision floating-point format or the 80-bit x86 extended precision floating-point format 265536 = 200352993040684646497907
Power_of_two
64-bit extension of the ARM architecture
Optional half-precision floating-point data processing (half-precision was already supported, but not for processing, just as a storage format.) Memory
AArch64
System information, diagnostics, and auditing program
FPU Julia — tests the performance of the processor's floating-point units in 32-bit precision calculations. Models several fragments of the Julia fractal
AIDA64
VESA standard for metadata
pixel precision and only supports CVT-RB. Superseded by 0x24 Type IX formula-based timings. 0x13 Type VI Detailed timing block supports higher precision pixel
DisplayID
Lossy audio coding format
compiles on hardware architectures with or without a floating-point unit, although floating-point is currently required for audio bandwidth detection (dynamic
Opus_(audio_format)
Method for signed number representation
Standard for Floating-Point Arithmetic (IEEE 754) uses offset notation for the exponent part in each of its various formats of precision. Unusually however
Offset_binary
File format used in digital photography
software features native 32-bit floating-point processing and a plugin architecture. dcraw is a program which reads most raw formats and can be made to run on
Raw_image_format
Microprocessor produced by Western Digital
Floating point values are 48 bits long and can only be stored in memory. This format is half-way between single and double precision floating point formats
WD16
Measure of angles
(inclusive) and +0.5 (exclusive) in signed fixed-point format, with the same scaling factor; or a fraction of half-turn between −1.0 (inclusive) and +1.0 (exclusive)
Binary_angular_measurement
Floating-point microprocessor
was the first floating-point coprocessor for the 8086 line of microprocessors. The purpose of the chip was to speed up floating-point arithmetic operations
Intel_8087
IEEE standard for radix-independent floating-point arithmetic
formats for radix 10 floating-point values, and even more so with IEEE 754-2019. IEEE 754-2008 also had many other updates to the IEEE floating-point
IEEE_854-1987
Mainframe computer systems made by IBM through the 1950s and early 1960s
format. Single-precision floating-point numbers have a magnitude sign, an 8-bit excess-128 exponent and a 27-bit magnitude Double-precision floating-point
IBM_700/7000_series
Family of RISC-based computer architectures
VFPv3-F16 Uncommon; it supports IEEE754-2008 half-precision (16-bit) floating point as a storage format. VFPv4 or VFPv4-D32 Implemented on Cortex-A12
ARM_architecture_family
Toolkit for manipulation of images
(Portable Floatmap) is the unofficial four byte IEEE 754 single precision floating point extension. The first line is either the ASCII text "PF", for a
Netpbm
Mainframe computer, 1960s
described above. Data formats are Fixed-point numbers were stored in binary sign/magnitude format. Single-precision floating-point numbers had a magnitude
IBM_7090
Multi-core microprocessor microarchitecture
pipelined for single-precision floating point (AltiVec 1 does not support double-precision floating-point vectors) 32-bit fixed-point Unit (FXU) with 64-bit
Cell_(processor)
Family of instruction set architectures
is 80 bits wide and stores numbers in the IEEE floating-point standard double extended precision format. These registers are organized as a stack with
X86
Shading language for WebGPU
vec4) and matrices (up to 4×4) are available for floating-point element types. Optional f16 (half precision) may be enabled via a WebGPU feature; availability
WebGPU_Shading_Language
ITU-T recommendation
seen as a floating-point number with 4 bits of mantissa m (equivalent to a 5-bit precision), 3 bits of exponent e and 1 sign bit s, formatted as seeemmmm
G.711
Instruction set architecture
single-precision (32-bit) floating-point numbers stored in the existing 64-bit floating-point registers. Variants of existing floating-point instructions
MIPS_architecture
Fundamental trigonometric functions
double-precision floating-point format. Some software libraries provide implementations of sine and cosine using the input angle in half-turns, a half-turn
Sine_and_cosine
distinct types. Integers, floating point numbers, strings, etc. are all considered "scalars". ^e PHP has two arbitrary-precision libraries. The BCMath library
Comparison of programming languages (basic instructions)
Comparison_of_programming_languages_(basic_instructions)
Algorithms for calculating square roots
_{2}(m\times 2^{p})=p+\log _{2}(m)} So for a 32-bit single precision floating point number in IEEE format (where notably, the power has a bias of 127 added for
Square_root_algorithms
Open-source CPU instruction set architecture
additional set of 32 floating-point registers. These are separate from the integer registers. The double-precision floating point instructions (set D)
RISC-V
Rendering a computer graphics scene
lighting precision has a minimum of 32 bits as opposed to 2.0's 8-bit minimum. Also all lighting-precision calculations are now floating-point based. NVIDIA
High-dynamic-range_rendering
General-purpose programming language
uses arbitrary-precision arithmetic for all integer operations. The Decimal type/class in the decimal module provides decimal floating-point numbers to a
Python_(programming_language)
Librascope General Purpose computer (1956)
Precision, is an early off-the-shelf computer. It was manufactured by the Librascope company of Glendale, California (a division of General Precision
LGP-30
Model independent architecture for the S/360 line of mainframe computers
Floating point numbers are only stored as fullword or doubleword values on older models. On the 360/85 and 360/195 there are also extended precision floating
IBM_System/360_architecture
System of digitally encoding numbers
double-extended-precision floating-point format. All decimal integers are exactly representable in double extended-precision format. […] [13] Jones,
Binary-coded_decimal
(op1):(op2)) for minimum-value. For the SIMD floating-point compares, the imm8 argument has the following format: The basic comparison predicates are: A signalling
List_of_x86_SIMD_instructions
64-bit extension of x86 architecture
capable of storing two double-precision, or up to four single-precision floating-point numbers, along with various integer formats. In 64-bit mode, instructions
X86-64
Measure of a systems floating point architecture
world's most powerful computers. TOP500 measures these in double-precision floating-point format (FP64). The ratio Rmax/Rpeak is called parallel efficiency
LINPACK_benchmarks
version was not yet the long-rumoured "Cell+" with enhanced Double Precision floating point performance, which first saw the light of day mid-2008 in the Roadrunner
Cell microprocessor implementations
Cell_microprocessor_implementations
1970 mainframe computer
fraction rather than an integer. Binary floating-point data can be single precision (36 bits) or double precision (72 bits). In either case the exponent
Honeywell_6000_series
Series of video cards
double-precision floating-point format. Radeon HD 5770 and below products，have the capability to calculate only single-precision floating-point format. OpenGL
Radeon_HD_5000_series
Series of microarchitectures and instruction set architecture by AMD
full fixed-function VP9 decode. Picasso Renoir Cezanne Double-precision floating-point (FP64) performance of all GCN 5th generation GPUs, except for Vega
Graphics_Core_Next
Spreadsheet editor by Microsoft
unintentionally changed to a standard date format. A similar problem occurs when a text happens to be in the form of a floating-point notation of a number. In these
Microsoft_Excel
GPU microarchitecture designed by Nvidia
community-defined MXFP6 and MXFP4 microscaling formats to improve efficiency and accuracy in low-precision computations. The previous Hopper architecture
Blackwell_(microarchitecture)
Subset of the OpenGL API for embedded systems
efficiently process complex scenes on the GPU. Floating point render targets for increased flexibility in higher precision compute operations. ASTC compression
OpenGL_ES
General-purpose programming language
a floating-point number occupying ten spaces along the line of output and showing 2 digits after the decimal point, the .2 in F10.2 of the FORMAT statement
Fortran
Microprocessor
Digital's 1.0-micrometre (μm) CMOS-3 process. The test chip lacked a floating point unit and only had 1 KB caches. The test chip was used to confirm the
Alpha_21064
List of x86 microprocessor instructions
of control and status registers, including "PC" (precision control, to control whether floating-point operations should be rounded to 24, 53 or 64 mantissa
List_of_x86_instructions
General Electric mainframe computers
fraction rather than an integer. Binary floating-point data could be single precision (36 bits) or double precision (72 bits). In either case the exponent
GE-600_series
Method for division with remainder
formats. The following computes the quotient of N and D with a precision of P binary places: Express D as M × 2e where 1 ≤ M < 2 (standard floating point
Division_algorithm
Data organization and storage formats
false. Character Floating-point representation of a finite subset of the rationals. Including single-precision and double-precision IEEE 754 floats, among
List_of_data_structures
HALF PRECISION-FLOATING-POINT-FORMAT
HALF PRECISION-FLOATING-POINT-FORMAT
HALF PRECISION-FLOATING-POINT-FORMAT
HALF PRECISION-FLOATING-POINT-FORMAT
HALF PRECISION-FLOATING-POINT-FORMAT
HALF PRECISION-FLOATING-POINT-FORMAT
HALF PRECISION-FLOATING-POINT-FORMAT
HALF PRECISION-FLOATING-POINT-FORMAT
HALF PRECISION-FLOATING-POINT-FORMAT