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Что (кто) такое floating-point - определение
COMPUTER FORMAT FOR REPRESENTING RATIONAL NUMBERS
Floating-point; Floating-point number; Floating point number; Hidden bit; Floating point type; Floating point numbers; Floating point arithmetic; Floating-point error; Floating point value; Numeric (data type); Floating point error; Floating-point math; Float (computing); Floating point exception; Floating-Point; Finite precision arithmetics; Floating-point numbers; Floating decimal point; Floating point format; Floating-point format; Floating point representation; Floating-point representation; Floating-point arithmetics; Floating point arithmetics; Floating point; Binary floating point; Assumed bit; Implicit bit; Assumed bit (floating point); Hidden bit (floating point); Implicit bit (floating point); Leading bit (floating point); Implicit leading bit (floating point); Implicit leading bit; Implicit leading bit convention; Assumed bit convention; Leading bit convention; Implicit bit convention; Hidden bit convention; Hidden bit rule; Implicit bit rule; Implicit leading bit rule; Assumed bit rule; Leading bit rule; Binary floating-point; Octal floating point; Octal floating-point; Binary floating-point arithmetic; Binary floating-point number; Octal floating-point number; Octal floating-point arithmetic; Base 2 floating point; Base-2 floating point; Radix-2 floating point; Radix 2 floating point; Base 8 floating point; Base-8 floating point; Radix-8 floating point; Radix 8 floating point; Binary512; Radix 65536 floating point; Radix-65536 floating point; Base 65536 floating point; Base-65536 floating point; Base-256 floating point; Quaternary floating point; Base 256 floating point; Radix 256 floating point; Radix-256 floating point; Base 4 floating point; Base-4 floating point; Radix 4 floating point; Radix-4 floating point; Binary floating point number; Representable floating-point number; Fast math; Floating point math; Binary floating-point number system; Binary floating point number system; Binary floating point numbering system; Binary floating-point numbering system
![Single-precision floating-point numbers on a [[number line]]: the green lines mark representable values.](https://commons.wikimedia.org/wiki/Special:FilePath/A number line representing single-precision floating point's numbers and numbers that it cannot display.png?width=200 "Single-precision floating-point numbers on a [[number line]]: the green lines mark representable values.")
![signs]] of representable values](https://commons.wikimedia.org/wiki/Special:FilePath/FloatingPointPrecisionAugmented.png?width=200 "signs]] of representable values")
![Z3]] computer, which uses a 22-bit binary floating-point representation](https://commons.wikimedia.org/wiki/Special:FilePath/Konrad Zuse (1992).jpg?width=200 "Z3]] computer, which uses a 22-bit binary floating-point representation")
![[[Leonardo Torres y Quevedo]], who proposed a form of floating point in 1914](https://commons.wikimedia.org/wiki/Special:FilePath/Quevedo 1917.jpg?width=200 "[[Leonardo Torres y Quevedo]], who proposed a form of floating point in 1914")
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floating-point
¦ noun [as modifier] Computing denoting a mode of representing numbers as two sequences of bits, one representing the digits in the number and the other an exponent which determines the position of the radix point.
floating-point
<programming, mathematics> A number representation consisting
of a mantissa, M, an exponent, E, and a radix (or
"base"). The number represented is M*R^E where R is the
radix.
In science and engineering, exponential notation or
scientific notation uses a radix of ten so, for example, the
number 93,000,000 might be written 9.3 x 10^7 (where ^7 is
superscript 7).
In computer hardware, floating point numbers are usually
represented with a radix of two since the mantissa and
exponent are stored in binary, though many different
representations could be used. The IEEE specify a
standard representation which is used by many hardware
floating-point systems. Non-zero numbers are normalised so
that the binary point is immediately before the most
significant bit of the mantissa. Since the number is
non-zero, this bit must be a one so it need not be stored. A
fixed "bias" is added to the exponent so that positive and
negative exponents can be represented without a sign bit.
Finally, extreme values of exponent (all zeros and all ones)
are used to represent special numbers like zero and positive
and negative infinity.
In programming languages with explicit typing,
floating-point types are introduced with the keyword "float"
or sometimes "double" for a higher precision type.
See also floating-point accelerator, floating-point unit.
Opposite: fixed-point.
(2008-06-13)
Floating-point arithmetic
In computing, floating-point arithmetic (FP) is arithmetic using formulaic representation of real numbers as an approximation to support a trade-off between range and precision. For this reason, floating-point computation is often used in systems with very small and very large real numbers that require fast processing times.
Floating-point unit
COPROCESSOR FOR FLOATING POINT ARITHMETIC
Floating Point Unit; Floating-Point Processor; Math coprocessor; Floating point processor; Floating-Point Unit; Floating point unit; Floating-point emulation; Floating point emulation; FP emulation; FP emulator; FPU emulation; FPU emulator; Floating-point emulator; Floating point emulator; Floating-point unit emulator; Floating point unit emulator; Floating-point unit emulation; Floating point unit emulation; Floating point software emulation; Floating-point software emulation; Floating point software emulator; Floating-point software emulator; FP software emulation; FP software emulator; Floating-point emulation software; Floating point emulation software; FP emulation software; Floating-point emulation software routine; Floating point emulation software routine; FP emulation software routine
A floating-point unit (FPU, colloquially a math coprocessor) is a part of a computer system specially designed to carry out operations on floating-point numbers. Typical operations are addition, subtraction, multiplication, division, and square root.
Floating-Point Unit
COPROCESSOR FOR FLOATING POINT ARITHMETIC
Floating Point Unit; Floating-Point Processor; Math coprocessor; Floating point processor; Floating-Point Unit; Floating point unit; Floating-point emulation; Floating point emulation; FP emulation; FP emulator; FPU emulation; FPU emulator; Floating-point emulator; Floating point emulator; Floating-point unit emulator; Floating point unit emulator; Floating-point unit emulation; Floating point unit emulation; Floating point software emulation; Floating-point software emulation; Floating point software emulator; Floating-point software emulator; FP software emulation; FP software emulator; Floating-point emulation software; Floating point emulation software; FP emulation software; Floating-point emulation software routine; Floating point emulation software routine; FP emulation software routine
<hardware> (FPU) A floating-point accelerator, usually in a
single integrated circuit, possible on the same IC as the
central processing unit.
(1994-10-27)
IBM hexadecimal floating-point
NUMBER REPRESENTATION
IBM Floating Point Standard; IBM floating point architecture; IBM floating-point architecture; IBM Floating Point Architecture; Hexadecimal floating point (IBM); IBM Hexadecimal Floating Point; IBM hexadecimal floating point
Hexadecimal floating point (now called HFP by IBM) is a format for encoding floating-point numbers first introduced on the IBM System/360 computers, and supported on subsequent machines based on that architecture,IBM System/360 Principles of Operation, IBM Publication A22-6821-6, Seventh Edition (January 13, 1967), pp.41-50IBM System/370 Principles of Operation, IBM Publication GA22-7000-4, Fifth Edition (September 1, 1975), pp.
Block floating point
METHOD USED TO PROVIDE AN ARITHMETIC APPROACHING FLOATING POINT WHILE USING A FIXED-POINT PROCESSOR; IN WHICH AN EXPONENT IS ASSIGNED TO AN ENTIRE BLOCK OF MANTISSAS
Block Floating Point; BFP (floating point format); Block-floating-point; BFP algorithm; Block floating-point algorithm; Block floating point algorithm; Block floating-point scaling; Block floating point scaling; BFP scaling; Block Floating Point Scaling; Block floating-point
Block floating point (BFP) is a method used to provide an arithmetic approaching floating point while using a fixed-point processor. BFP assigns a group of significands (the non-exponent part of the floating-point number) to a single exponent, rather than single significand being assigned its own exponent.
Tapered floating point
FORMAT SIMILAR TO FLOATING POINT, BUT WITH VARIABLE-SIZED ENTRIES FOR THE SIGNIFICAND AND EXPONENT INSTEAD OF THE FIXED-LENGTH ENTRIES FOUND IN NORMAL FLOATING-POINT FORMATS, AND A FIXED-SIZE POINTER INDICATING THE NUMBER OF DIGITS IN THE EXPONENT
Tapered floating-point; Tapered floating point format; Tapered floating-point format; Tapered floating point arithmetic; Tapered floating-point arithmetic; Tapered floating point scheme; Tapered floating-point scheme; Tapered floating point representation; Tapered floating-point representation; Tapered accuracy; Tapered overflow; Tapered underflow; Leveling (tapered floating point); Level (tapered floating point); Tapered arithmetic
In computing, tapered floating point (TFP) is a format similar to floating point, but with variable-sized entries for the significand and exponent instead of the fixed-length entries found in normal floating-point formats. In addition to this, tapered floating-point formats provide a fixed-size pointer entry indicating the number of digits in the exponent entry.
Floating-point error mitigation
STRATEGIES TO MAKE SURE APPROXIMATE CALCULATIONS STAY CLOSE TO ACCURATE
Floating point error mitigation
Floating-point error mitigation is the minimization of errors caused by the fact that real numbers cannot, in general, be accurately represented in a fixed space. By definition, floating-point error cannot be eliminated, and, at best, can only be managed.
Quadruple-precision floating-point format
128-BIT COMPUTER NUMBER FORMAT
Quad precision; Quadruple precision; Binary128; Double-double (arithmetic); Double-double arithmetic; Quadruple precision floating-point format; Double double arithmetic; Double-double (computing); IEEE 754 quadruple-precision floating-point format; Float128; IEEE quad precision; IEEE quadruple precision; 128-bit floating point format; 128-bit floating-point format; 128-bit floating point; 128-bit floating-point; 128-bit binary floating point format; 128-bit binary floating-point format; Quad-precision floating-point format; Quad-precision floating point format; Quad precision floating-point format; Quad precision floating point format; Quadruple-precision floating-point; Quadruple-precision floating point; Quadruple precision floating-point; Quadruple precision floating point; Quad-precision floating-point; Quad-precision floating point; Quad precision floating-point; Quad precision floating point; Quadruple-precision floating point format; Quadruple precision floating point format; Quad-precision
In computing, quadruple precision (or quad precision) is a binary floating point–based computer number format that occupies 16 bytes (128 bits) with precision at least twice the 53-bit double precision.
Википедия
Floating-point arithmetic
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be represented as a base-ten floating-point number:
In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common.
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. This position is indicated by the exponent, so floating point can be considered a form of scientific notation.
A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-point arithmetic is often used to allow very small and very large real numbers that require fast processing times. The result of this dynamic range is that the numbers that can be represented are not uniformly spaced; the difference between two consecutive representable numbers varies with their exponent.
Over the years, a variety of floating-point representations have been used in computers. In 1985, the IEEE 754 Standard for Floating-Point Arithmetic was established, and since the 1990s, the most commonly encountered representations are those defined by the IEEE.
The speed of floating-point operations, commonly measured in terms of FLOPS, is an important characteristic of a computer system, especially for applications that involve intensive mathematical calculations.
A floating-point unit (FPU, colloquially a math coprocessor) is a part of a computer system specially designed to carry out operations on floating-point numbers.
