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IEEE Std 754-2019
IEEE Standard for Floating-Point Arithmetic
exponent: The component of a finite floating-point representation that signifies the integer power to which
the radix is raised in determining the value of that floating-point representation. The exponent e is used
when the significand is regarded as an integer digit and fraction field, and the exponent q is used when the
significand is regarded as an integer; e
=
q
+
p
−
1 where p is the precision of the format in digits.
extendable precision format: A format with precision and range that are defined under user control.
extended precision format: A format that extends a supported basic format by providing wider precision
and range.
external character sequence: A representation of a floating-point datum as a sequence of characters,
including the character sequences in floating-point literals in program text.
flag: See: status flag.
floating-point datum: A floating-point number or non-number (NaN) that is representable in a floating-
point format. In this standard, a floating-point datum is not always distinguished from its representation or
encoding.
floating-point number: A finite or infinite number that is representable in a floating-point format. A
floating-point datum that is not a NaN. All floating-point numbers, including zeros and infinities, are
signed.
floating-point operation: An operation where an operand or result is a floating-point datum.
floating-point representation: An unencoded member of a floating-point format, representing a finite
number, a signed infinity, a quiet NaN, or a signaling NaN. A representation of a finite number has three
components: a sign, an exponent, and a significand; its numerical value is the signed product of its
significand and its radix raised to the power of its exponent.
format: A set of representations of numerical values and symbols, perhaps accompanied by an encoding.
fusedMultiplyAdd: The operation fusedMultiplyAdd(x, y, z) computes (x
×
y
)
+
z as if with unbounded
range and precision, rounding only once to the destination format.
generic operation: An operation of this standard that can take operands of various formats, for which the
formats of the results might depend on the formats of the operands.
homogeneous operation: An operation of this standard that takes operands and returns results all in the
same format.
implementation-defined: Behavior defined by a specific implementation of a specific programming
environment conforming to this standard.
integer format: A format not defined in this standard that represents a subset of the integers and perhaps
additional values representing infinities, NaNs, or negative zeros.
interchange format: A format that has a specific fixed-width encoding defined in this standard.
language-defined: Behavior defined by a programming language standard supporting this standard.
NaN: not a number
—
a symbolic floating-point datum. There are two kinds of NaN representations: quiet
and signaling. Most operations propagate quiet NaNs without signaling exceptions, and signal the invalid
operation exception when given a signaling NaN operand.
narrower/wider format: If the set of floating-point numbers of one format is a proper subset of another
format, the first is called narrower and the second wider. The wider format might have greater precision,
range, or (usually) both.
non-computational operation: An operation that is not computational.
normal number: For a particular format, a finite non-zero floating-point number with magnitude greater
than or equal to a minimum b
emin
value, where b is the radix. Normal numbers can use the full precision
available in a format. In this standard, zero is neither normal nor subnormal.
not a number: See: NaN.
operation: this standard defines required and recommended operations which operate on zero or more
operands and produce results or side effects, such as changes in dynamic modes or flags or control flow, or
both. In this standard, operations are written as named functions; in a specific programming environment
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