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Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient.
In computer science and numerical analysis, 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 digit (rightmost digit) represents if it is 1.
Converting a double-precision binary floating-point number to a decimal string is a common operation, but an algorithm producing results that are both accurate and minimal did not appear in print until 1990, with Steele and White's Dragon4. Some of the improvements since then include:
It is related to precision in mathematics, which describes the number of digits that are used to express a value. Some of the standardized precision formats are Half-precision floating-point format; Single-precision floating-point format; Double-precision floating-point format; Quadruple-precision floating-point format
This standard defines the format for 32-bit numbers called single precision, as well as 64-bit numbers called double precision and longer numbers called extended precision (used for intermediate results). Floating-point representations can support a much wider range of values than fixed-point, with the ability to represent very small numbers ...
The IEEE standard stores the sign, exponent, and significand in separate fields of a floating point word, each of which has a fixed width (number of bits). The two most commonly used levels of precision for floating-point numbers are single precision and double precision.
Thus the 're-subtracting' of 1 leaves a mantissa ending in '100000000000000' instead of '010111000110010', representing a value of '1.1111111111117289E-4' rounded by Excel to 15 significant digits: '1.11111111111173E-4'. Of course mathematical 1 + x − 1 = x, 'floating point math' is sometimes a little different, that is not to be blamed on ...
The number 0.15625 represented as a single-precision IEEE 754-1985 floating-point number. See text for explanation. The three fields in a 64bit IEEE 754 float. Floating-point numbers in IEEE 754 format consist of three fields: a sign bit, a biased exponent, and a fraction. The following example illustrates the meaning of each.