Signed
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object Signed
| package algebra
An idempotent function that ensures an object has a non-negative sign.
Returns 0 if a is 0, 1 if a is positive, and -1 is a is negative.
Returns Zero if a is 0, Positive if a is positive, and Negative is a is negative.
A trait for linearly ordered additive commutative monoid. The following laws holds:
(1) if
a <= bthena + c <= b + c(linear order), (2)signum(x) = -1ifx < 0,signum(x) = 1ifx > 0,signum(x) = 0otherwise,Negative elements only appear when
scalaris a additive abelian group, and then (3)abs(x) = -xifx < 0, orxotherwise,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?).