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Real floating-point type, usually mapped to an extended precision floating-point number format. Actual properties unspecified. Actual properties unspecified. It can be either x86 extended-precision floating-point format (80 bits, but typically 96 bits or 128 bits in memory with padding bytes ), the non-IEEE " double-double " (128 bits), IEEE ...
This means that numbers that appear to be short and exact when written in decimal format may need to be approximated when converted to binary floating-point. For example, the decimal number 0.1 is not representable in binary floating-point of any finite precision; the exact binary representation would have a "1100" sequence continuing endlessly:
To approximate the 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 system, we are familiar with floating-point numbers of the form (scientific notation): 1.1030402 × 10 5 = 1.1030402 × 100000 = 110304.02. or, more compactly: 1.1030402E5
Decimal [Zairean 1] floating-point (DFP) arithmetic refers to both a representation and operations on decimal floating-point numbers. Working directly with decimal (base-10) fractions can avoid the rounding errors that otherwise typically occur when converting between decimal fractions (common in human-entered data, such as measurements or ...
A decimal data type could be implemented as either a floating-point number or as a fixed-point number. In the fixed-point case, the denominator would be set to a fixed power of ten. In the floating-point case, a variable exponent would represent the power of ten to which the mantissa of the number is multiplied.
For other binary formats, the required number of decimal digits is [h] + ⌈ ⌉, where p is the number of significant bits in the binary format, e.g. 237 bits for binary256. When using a decimal floating-point format, the decimal representation will be preserved using:
These numbers are stored internally in a format equivalent to scientific notation, typically in binary but sometimes in decimal. Because floating-point numbers have limited precision, only a subset of real or rational numbers are exactly representable; other numbers can be represented only approximately.
The 2008 revision extended the previous standard where it was necessary, added decimal arithmetic and formats, tightened up certain areas of the original standard which were left undefined, and merged in IEEE 854 (the radix-independent floating-point standard). In a few cases, where stricter definitions of binary floating-point arithmetic might ...