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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.
Real floating-point type, usually referred to as a double-precision floating-point type. Actual properties unspecified (except minimum limits); however, on most systems, this is the IEEE 754 double-precision binary floating-point format (64 bits). This format is required by the optional Annex F "IEC 60559 floating-point arithmetic".
An extended precision format extends a basic format by using more precision and more exponent range. An extendable precision format allows the user to specify the precision and exponent range. An implementation may use whatever internal representation it chooses for such formats; all that needs to be defined are its parameters (b, p, and emax ...
The bfloat16 format, being a shortened IEEE 754 single-precision 32-bit float, allows for fast conversion to and from an IEEE 754 single-precision 32-bit float; in conversion to the bfloat16 format, the exponent bits are preserved while the significand field can be reduced by truncation (thus corresponding to round toward 0) or other rounding ...
It returns the exact value of x–(round(x/y)·y). Round to nearest integer. For undirected rounding when halfway between two integers the even integer is chosen. Comparison operations. Besides the more obvious results, IEEE 754 defines that −∞ = −∞, +∞ = +∞ and x ≠ NaN for any x (including NaN).
In the example from "Double rounding" section, rounding 9.46 to one decimal gives 9.4, which rounding to integer in turn gives 9. With binary arithmetic, this rounding is also called "round to odd" (not to be confused with "round half to odd"). For example, when rounding to 1/4 (0.01 in binary), x = 2.0 ⇒ result is 2 (10.00 in binary)
In these languages, conversion refers to either implicitly or explicitly changing a value from one data type storage format to another, e.g. a 16-bit integer to a 32-bit integer. The storage needs may change as a result of the conversion, including a possible loss of precision or truncation.
These operations may be translated by the compiler into a sequence of integer machine instructions, or into library calls. Support may also extend to other operations, such as formatting, rounding to an integer or floating point value, etc.. An example of this is 123.456 [clarification needed]