Signed

A trait for linearly ordered additive commutative monoid. The following laws holds:

(1) if a <= b then a + c <= b + c (linear order), (2) signum(x) = -1 if x < 0, signum(x) = 1 if x > 0, signum(x) = 0 otherwise,

Negative elements only appear when scalar is a additive abelian group, and then (3) abs(x) = -x if x < 0, or x otherwise,

Laws (1) and (2) lead to the triange inequality:

(4) abs(a + b) <= abs(a) + abs(b)

Signed should never be extended in implementations, rather the AdditiveCMonoid and AdditiveAbGroup subtraits. We cannot use self-types to express the constraint self: AdditiveCMonoid => (interaction with specialization?).

Linear Supertypes

cats.kernel.Order[A], cats.kernel.PartialOrder[A], cats.kernel.Eq[A], Serializable, Serializable, Any

Known Subclasses

BigDecimalAlgebra, BigDecimalIsReal, BigDecimalSigned, BigDecimalTruncatedDivision, BigIntAlgebra, BigIntIsReal, BigIntSigned, BigIntTruncatedDivision, BigIntegerAlgebra, BigIntegerIsReal, BigIntegerSigned, BigIntegerTruncatedDivision, ByteAlgebra, ByteIsReal, ByteSigned, ByteTruncatedDivision, DoubleAlgebra, DoubleIsReal, DoubleSigned, DoubleTruncatedDivision, FloatAlgebra, FloatIsReal, FloatSigned, FloatTruncatedDivision, Fractional, IntAlgebra, IntIsReal, IntSigned, IntTruncatedDivision, Integral, IsAlgebraic, IsIntegral, IsRational, IsReal, LongAlgebra, LongIsReal, LongSigned, LongTruncatedDivision, Numeric, RealAlgebra, RealIsFractional, ShortAlgebra, ShortIsReal, ShortSigned, ShortTruncatedDivision, SignAlgebra, SignedAdditiveAbGroup, SignedAdditiveCMonoid, TruncatedDivision, TruncatedDivisionCRing

Abstract Value Members

abstract def abs(a: A): A

An idempotent function that ensures an object has a non-negative sign.
abstract def compare(x: A, y: A): Int

Definition Classes
Order
abstract def getClass(): Class[_]

Definition Classes
Any
abstract def signum(a: A): Int

Returns 0 if a is 0, 1 if a is positive, and -1 is a is negative.

Concrete Value Members

final def !=(arg0: Any): Boolean

Definition Classes
Any
final def ##(): Int

Definition Classes
Any
final def ==(arg0: Any): Boolean

Definition Classes
Any
final def asInstanceOf[T0]: T0

Definition Classes
Any
def comparison(x: A, y: A): Comparison

Definition Classes
Order
def equals(arg0: Any): Boolean

Definition Classes
Any
def eqv(x: A, y: A): Boolean

Definition Classes
Order → PartialOrder → Eq
def gt(x: A, y: A): Boolean

Definition Classes
Order → PartialOrder
def gteqv(x: A, y: A): Boolean

Definition Classes
Order → PartialOrder
def hashCode(): Int

Definition Classes
Any
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def isSignNegative(a: A): Boolean
def isSignNonNegative(a: A): Boolean
def isSignNonPositive(a: A): Boolean
def isSignNonZero(a: A): Boolean
def isSignPositive(a: A): Boolean
def isSignZero(a: A): Boolean
def lt(x: A, y: A): Boolean

Definition Classes
Order → PartialOrder
def lteqv(x: A, y: A): Boolean

Definition Classes
Order → PartialOrder
def max(x: A, y: A): A

Definition Classes
Order
def min(x: A, y: A): A

Definition Classes
Order
def neqv(x: A, y: A): Boolean

Definition Classes
Order → Eq
def partialCompare(x: A, y: A): Double

Definition Classes
Order → PartialOrder
def partialComparison(x: A, y: A): Option[Comparison]

Definition Classes
PartialOrder
def pmax(x: A, y: A): Option[A]

Definition Classes
PartialOrder
def pmin(x: A, y: A): Option[A]

Definition Classes
PartialOrder
def sign(a: A): Sign

Returns Zero if a is 0, Positive if a is positive, and Negative is a is negative.
def toOrdering: Ordering[A]

Definition Classes
Order
def toString(): String

Definition Classes
Any
def tryCompare(x: A, y: A): Option[Int]

Definition Classes
PartialOrder

Related Docs: object Signed | package algebra

trait Signed[A] extends Order[A]

Abstract Value Members

abstract def abs(a: A): A

abstract def compare(x: A, y: A): Int

abstract def getClass(): Class[_]

abstract def signum(a: A): Int

Concrete Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

final def asInstanceOf[T0]: T0

def comparison(x: A, y: A): Comparison

def equals(arg0: Any): Boolean

def eqv(x: A, y: A): Boolean

def gt(x: A, y: A): Boolean

def gteqv(x: A, y: A): Boolean

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

def isSignNegative(a: A): Boolean

def isSignNonNegative(a: A): Boolean

def isSignNonPositive(a: A): Boolean

def isSignNonZero(a: A): Boolean

def isSignPositive(a: A): Boolean

def isSignZero(a: A): Boolean

def lt(x: A, y: A): Boolean

def lteqv(x: A, y: A): Boolean

def max(x: A, y: A): A

def min(x: A, y: A): A

def neqv(x: A, y: A): Boolean

def partialCompare(x: A, y: A): Double

def partialComparison(x: A, y: A): Option[Comparison]

def pmax(x: A, y: A): Option[A]

def pmin(x: A, y: A): Option[A]

def sign(a: A): Sign

def toOrdering: Ordering[A]

def toString(): String

def tryCompare(x: A, y: A): Option[Int]

Inherited from cats.kernel.Order[A]

Inherited from cats.kernel.PartialOrder[A]

Inherited from cats.kernel.Eq[A]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

Ungrouped