Signed zero is zero with an associated sign. In ordinary arithmetic, the number 0 does not have a sign, so that −0, +0 and 0 are equivalent. However, in computing, some number representations allow for the existence of two zeros, often denoted by −0 (negative zero) and +0 (positive zero), regarded as equal by the numerical comparison operations but with possible different behaviors in particular operations. This occurs in the sign-magnitude and ones' complement signed number representations for integers, and in most floating-point number representations. The number 0 is usually encoded as +0, but can still be represented by +0, −0, or 0.
The IEEE 754 standard for floating-point arithmetic (presently used by most computers and programming languages that support floating-point numbers) requires both +0 and −0. Real arithmetic with signed zeros can be considered a variant of the extended real number line such that 1/−0 = −∞ and 1/+0 = +∞; division is undefined only for ±0/±0 and ±∞/±∞.
Negatively signed zero echoes the mathematical analysis concept of approaching 0 from below as a one-sided limit, which may be denoted by x → 0−, x → 0−, or x → ↑0. The notation "−0" may be used informally to denote a negative number that has been rounded to zero. The concept of negative zero also has some theoretical applications in statistical mechanics and other disciplines.
It is claimed that the inclusion of signed zero in IEEE 754 makes it much easier to achieve numerical accuracy in some critical problems,[1] in particular when computing with complex elementary functions.[2] On the other hand, the concept of signed zero runs contrary to the usual assumption made in mathematics that negative zero is the same value as zero. Representations that allow negative zero can be a source of errors in programs, if software developers do not take into account that while the two zero representations behave as equal under numeric comparisons, they yield different results in some operations.
^William Kahan, "Branch Cuts for Complex Elementary Functions, or Much Ado About Nothing's Sign Bit", in The State of the Art in Numerical Analysis (eds. Iserles and Powell), Clarendon Press, Oxford, 1987.
^William Kahan, Derivatives in the Complex z-plane, p. 10.
Signedzero is zero with an associated sign. In ordinary arithmetic, the number 0 does not have a sign, so that −0, +0 and 0 are equivalent. However, in...
representation is known as signedzero, with the latter form sometimes called negative zero. These representations include the signed magnitude and ones' complement...
Formats other than two's complement integers allow a signedzero: distinct "positive zero" and "negative zero" representations, the latter of which does not...
Moreover, there are two zero values, called signedzeros: the sign bit specifies whether a zero is +0 (positive zero) or −0 (negative zero). Two infinities:...
result in signed infinity, with positive or negative sign depending on the sign of the dividend. In these number systems division by zero is no longer...
zero extension is usually the correct way to move it to a larger field while preserving its numeric value, while sign extension is correct for signed...
Zero Hedge (or ZeroHedge) is a far-right libertarian financial blog and news aggregator. Zero Hedge is bearish in its investment outlook and analysis...
The dotted or slashed zero 0̷ is a representation of the Arabic digit "0" (zero) with a slash or a dot through it. This variant zero glyph is often used...
always define atan2(0, 0). On implementations without signedzero, or when given positive zero arguments, it is normally defined as 0. It will always...
ternary Binary-coded decimal Computer number format Method of complements Signedness Choo, Hunsoo; Muhammad, K.; Roy, K. (February 2003). "Two's complement...
Jude Kinkade and Zero are fictional characters from the VH1 series Hit the Floor, which chronicles the off-the-court drama surrounding a fictional professional...
nonsensical. Signedzero Additive inverse History of zero Integers Positive and negative parts Rational numbers Real numbers Sign function Sign (mathematics)...
Zero to the power of zero, denoted by 00, is a mathematical expression that is either defined as 1 or left undefined, depending on context. In algebra...
{\displaystyle 0.000_{2}\times 2^{-6}=0} . Floating point numbers use a signedzero, so − 0 {\displaystyle -0} is also available and is equal to positive...
The percent sign % (sometimes per cent sign in British English) is the symbol used to indicate a percentage, a number or ratio as a fraction of 100. Related...
xxxx xxxx where s is the sign (most often ignored in applications) and the x sequence represents a non-zero number (the value zero encodes infinities). In...
titled Size Zero, to be directed by Prakash Kovelamudi, which would star Arya and Anushka Shetty. Nirav Shah and M. M. Keeravani were signed on as cinematographer...
Global net zero emissions describes the state where emissions of carbon dioxide due to human activities and removals of these gases are in balance over...
A zero-crossing is a point where the sign of a mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis...
decreases in value as x approaches the boundary of Ω where the signed distance function is zero, and it takes negative values outside of Ω. However, the alternative...
of the Month: 'ZeroZeroZero' Star Harold Torres". Collider. Retrieved November 9, 2023. Gaydos, Steven (April 10, 2020). "'ZeroZeroZero' Star Harold Torres...
announced". Sify. Archived from the original on 3 July 2017. "Shivada signs 'zero', a supernatural thriller". Sify. Archived from the original on 26 April...
Global Information