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* ID :  [https://www.wikidata.org/wiki/Q117879 Q117879]

2020년 12월 26일 (토) 06:01 판

노트

  • Almost all modern systems use IEEE-754 floating point, and it is typically portable to assume IEEE-754 behavior these days.[1]
  • These floating point numbers therefore can use scientific notation like 1.0e-34 and -10e100 .[1]
  • In the JVM, floating-point arithmetic is performed on 32-bit floats and 64-bit doubles.[2]
  • The mantissa occupies the 23 least significant bits of a float and the 52 least significant bits of a double.[2]
  • The exponent, 8 bits in a float and 11 bits in a double, sits between the sign and mantissa.[2]
  • The format of a float is shown below.[2]
  • The ieee754 extension converts a floating point number between its binary64 representation and the M×2 E format.[3]
  • Except that the M and E are replaced by the mantissa and exponent of the floating point number.[3]
  • this makes floating point numbers an example of a leaky abstraction.[4]
  • For context, the basic idea of a floating point number is to use the binary-equivalent of scientific notation.[4]
  • The benefits of subnormal numbers are that, when you subtract two different normal floats, you are guaranteed to get a non-zero result.[4]
  • Okay, we spent all this time talking about floating point numbers.[4]
  • The IEEE standard specifies that 32-bit floats are represented with a sign bit, 8 bits for the exponent, and 23 bits for the significand.[5]
  • Infinite values result when performing computations like 1/0 in floating point, for example.[5]
  • We can see that the error introduced by rounding to the nearest float, δ, can be no more than half the spacing between floats.[5]
  • As a first application of these ideas, consider computing the sum of four numbers, a, b, c, and d, represented as floats.[5]
  • The float and double types also provide constants that represent not-a-number and infinity values.[6]
  • You can mix integral types and the float and double types in an expression.[6]
  • You cannot mix the decimal type with the float and double types in an expression.[6]
  • There is only one implicit conversion between floating-point numeric types: from float to double .[6]
  • In programming, a floating-point or float is a variable type that is used to store floating-point number values.[7]
  • Floating point numbers have limited precision.[8]
  • So never trust floating number results to the last digit, and do not compare floating point numbers directly for equality.[8]
  • Floating point numbers are represented, at the hardware level, as fractions of binary numbers (base 2).[9]
  • We assume that you are familiar with the binary representation of floating point numbers.[9]
  • However, all machines today (July 2010) follow the IEEE-754 standard for the arithmetic of floating point numbers.[9]
  • The "strange" features of floating point have a higher visibility in the language, improving the education of numerical programmers.[10]
  • The IEEE standard floating point types currently supported by D are float and double.[10]
  • On x87, 130 floats can be safely multiplied together in any order, and 16 doubles can similarly be multiplied together safely.[10]
  • There are two special categories of floating point numbers.[11]
  • NaN and Inf are only available if the compiler uses a specific format (IEEE 754) for floating point numbers.[11]
  • Floating point numbers often have small rounding errors, even when the number has fewer significant digits than the precision.[11]
  • However, comparisons of floating point numbers may not give the expected results.[11]
  • Compared to Floating Point numbers Integers are precise and there can never be any rounding errors.[12]
  • A Floating Point number usually has a decimal point.[12]
  • Floating Point numbers can’t be stored exactly like Integer numbers are.[12]
  • So clearly this isn’t the way that we store Floating Point numbers.[12]
  • Python provides tools that may help on those rare occasions when you really do want to know the exact value of a float.[13]
  • Deep learning models, such as the ResNet-50 convolutional neural network, are trained using floating point arithmetic.[14]
  • We have made radical changes to floating point to make it as much as 16 percent more efficient than int8/32 math.[14]
  • The neural networks that power many AI systems are usually trained using 32-bit IEEE 754 binary32 single precision floating point.[14]
  • But there are a variety of alternatives to integer, fixed point, or floating point for computer arithmetic as practiced today.[14]
  • In addition to the single precision floating point described here, there are also double precision floating point units.[15]
  • As an example, take the floating point number represented as 0x80280000.[15]
  • The exception is it reads in a floating point number.[15]
  • Just like and outputs the hexadecimal form plus the floating point number.[15]
  • This webpage is a tool to understand IEEE-754 floating point numbers.[16]
  • Rounding errors: Not every decimal number can be expressed exactly as a floating point number.[16]
  • Double-precision (64-bit) floats would work, but this too is some work to support alongside single precision floats.[16]
  • I've converted a number to floating point by hand/some other method, and I get a different result.[16]
  • Some simple rational numbers ( e.g. , 1/3 and 1/10) cannot be represented exactly in binary floating point, no matter what the precision is.[17]
  • , 1/3 and 1/10) cannot be represented exactly in binary floating point, no matter what the precision is.[17]
  • Single precision (binary32), usually used to represent the "float" type in the C language family (though this is not guaranteed).[17]
  • If that integer is negative, xor with its maximum positive, and the floats are sorted as integers.[17]
  • As the name implies, floating point numbers are numbers that contain floating decimal points.[18]
  • Computers recognize real numbers that contain fractions as floating point numbers.[18]
  • When a calculation includes a floating point number, it is called a "floating point calculation.[18]

소스

  1. ↑ 1.0 1.1 Floating point (GNU Coreutils)
  2. ↑ 2.0 2.1 2.2 2.3 Floating-point arithmetic
  3. ↑ 3.0 3.1 Floating Point Numbers
  4. ↑ 4.0 4.1 4.2 4.3 How Floating Point Numbers Work
  5. ↑ 5.0 5.1 5.2 5.3 Floating-Point Number - an overview
  6. ↑ 6.0 6.1 6.2 6.3 Floating-point numeric types - C# reference
  7. ↑ What is a Floating-point?
  8. ↑ 8.0 8.1 PHP: Floating point numbers
  9. ↑ 9.0 9.1 9.2 Is floating point math broken?
  10. ↑ 10.0 10.1 10.2 Real Close to the Machine: Floating Point in D
  11. ↑ 11.0 11.1 11.2 11.3 4.8 — Floating point numbers
  12. ↑ 12.0 12.1 12.2 12.3 What is a Floating Point Number?
  13. ↑ 15. Floating Point Arithmetic: Issues and Limitations — Python 3.9.1 documentation
  14. ↑ 14.0 14.1 14.2 14.3 Making floating point math highly efficient for AI hardware
  15. ↑ 15.0 15.1 15.2 15.3 Floating Point
  16. ↑ 16.0 16.1 16.2 16.3 IEEE-754 Floating Point Converter
  17. ↑ 17.0 17.1 17.2 17.3 Floating-point arithmetic
  18. ↑ 18.0 18.1 18.2 Floating Point Definition

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