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In computing, a roundoff error, [ 1] also called rounding error, [ 2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [ 3] Rounding errors are due to inexactness in the representation of real numbers and the ...
In computing, half precision (sometimes called FP16 or float16) is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers) in computer memory. It is intended for storage of floating-point values in applications where higher precision is not essential, in particular image processing and neural networks .
When using a decimal floating-point format, the decimal representation will be preserved using: 7 decimal digits for decimal32, 16 decimal digits for decimal64, 34 decimal digits for decimal128. Algorithms, with code, for correctly rounded conversion from binary to decimal and decimal to binary are discussed by Gay, [59] and for testing – by ...
Variable length arithmetic represents numbers as a string of digits of variable length limited only by the memory available. Variable length arithmetic operations are considerably slower than fixed length format floating-point instructions.
In computing, floating-point arithmetic ( FP) is arithmetic that represents subsets of real numbers using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. Numbers of this form are called floating-point numbers. [ 1]: 3 [ 2]: 10 For example, 12.345 is a floating-point number in base ten ...
Double dabble. In computer science, the double dabble algorithm is used to convert binary numbers into binary-coded decimal (BCD) notation. [ 1][ 2] It is also known as the shift-and-add -3 algorithm, and can be implemented using a small number of gates in computer hardware, but at the expense of high latency. [ 3]
Catastrophic cancellation. In numerical analysis, catastrophic cancellation[ 1][ 2] is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbers. For example, if there are two studs, one long and the other long, and they are measured with a ruler that ...
Rounding to a specified multiple. The most common type of rounding is to round to an integer; or, more generally, to an integer multiple of some increment – such as rounding to whole tenths of seconds, hundredths of a dollar, to whole multiples of 1/2 or 1/8 inch, to whole dozens or thousands, etc.