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# Integral

### Companion object Integral

#### traitIntegral[T] extends Numeric[T]

Source
Integral.scala
Since

2.8

Linear Supertypes
Numeric[T], Ordering[T], PartialOrdering[T], Equiv[T], java.io.Serializable, Comparator[T], AnyRef, Any
Type Hierarchy
Ordering
1. Alphabetic
2. By Inheritance
Inherited
1. Integral
2. Numeric
3. Ordering
4. PartialOrdering
5. Equiv
6. Serializable
7. Comparator
8. AnyRef
9. Any
Implicitly
2. by StringFormat
3. by Ensuring
4. by ArrowAssoc
1. Hide All
2. Show All
Visibility
1. Public
2. All

### Type Members

1. class IntegralOps extends NumericOps
2. class NumericOps extends AnyRef
Definition Classes
Numeric
3. class OrderingOps extends AnyRef

This inner class defines comparison operators available for `T`.

This inner class defines comparison operators available for `T`.

Definition Classes
Ordering

### Abstract Value Members

1. abstract def compare(x: T, y: T): Int

Returns an integer whose sign communicates how x compares to y.

Returns an integer whose sign communicates how x compares to y.

The result sign has the following meaning:

• negative if x < y
• positive if x > y
• zero otherwise (if x == y)
Definition Classes
Ordering → Comparator
2. abstract def fromInt(x: Int): T
Definition Classes
Numeric
3. abstract def minus(x: T, y: T): T
Definition Classes
Numeric
4. abstract def negate(x: T): T
Definition Classes
Numeric
5. abstract def parseString(str: String): Option[T]
Definition Classes
Numeric
6. abstract def plus(x: T, y: T): T
Definition Classes
Numeric
7. abstract def quot(x: T, y: T): T
8. abstract def rem(x: T, y: T): T
9. abstract def times(x: T, y: T): T
Definition Classes
Numeric
10. abstract def toDouble(x: T)
Definition Classes
Numeric
11. abstract def toFloat(x: T)
Definition Classes
Numeric
12. abstract def toInt(x: T): Int
Definition Classes
Numeric
13. abstract def toLong(x: T): Long
Definition Classes
Numeric

### Concrete Value Members

1. final def !=(arg0: Any)

Test two objects for inequality.

Test two objects for inequality.

returns

`true` if !(this == that), false otherwise.

Definition Classes
AnyRef → Any
2. final def ##(): Int

Equivalent to `x.hashCode` except for boxed numeric types and `null`.

Equivalent to `x.hashCode` except for boxed numeric types and `null`. For numerics, it returns a hash value which is consistent with value equality: if two value type instances compare as true, then ## will produce the same hash value for each of them. For `null` returns a hashcode where `null.hashCode` throws a `NullPointerException`.

returns

a hash value consistent with ==

Definition Classes
AnyRef → Any
3. def +(other: String)
Implicit
This member is added by an implicit conversion from Integral[T] toany2stringadd[Integral[T]] performed by method any2stringadd in scala.Predef.
Definition Classes
4. def ->[B](y: B): (Integral[T], B)
Implicit
This member is added by an implicit conversion from Integral[T] toArrowAssoc[Integral[T]] performed by method ArrowAssoc in scala.Predef.
Definition Classes
ArrowAssoc
Annotations
()
5. final def ==(arg0: Any)

The expression `x == that` is equivalent to `if (x eq null) that eq null else x.equals(that)`.

The expression `x == that` is equivalent to `if (x eq null) that eq null else x.equals(that)`.

returns

`true` if the receiver object is equivalent to the argument; `false` otherwise.

Definition Classes
AnyRef → Any
6. def abs(x: T): T
Definition Classes
Numeric
7. final def asInstanceOf[T0]: T0

Cast the receiver object to be of type `T0`.

Cast the receiver object to be of type `T0`.

Note that the success of a cast at runtime is modulo Scala's erasure semantics. Therefore the expression `1.asInstanceOf[String]` will throw a `ClassCastException` at runtime, while the expression `List(1).asInstanceOf[List[String]]` will not. In the latter example, because the type argument is erased as part of compilation it is not possible to check whether the contents of the list are of the requested type.

returns

Definition Classes
Any
Exceptions thrown

`ClassCastException` if the receiver object is not an instance of the erasure of type `T0`.

8. def clone()

Create a copy of the receiver object.

Create a copy of the receiver object.

The default implementation of the `clone` method is platform dependent.

returns

a copy of the receiver object.

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
(classOf[java.lang.CloneNotSupportedException]) ()
Note

not specified by SLS as a member of AnyRef

9. def ensuring(cond: (Integral[T]) => Boolean, msg: => Any): Integral[T]
Implicit
This member is added by an implicit conversion from Integral[T] toEnsuring[Integral[T]] performed by method Ensuring in scala.Predef.
Definition Classes
Ensuring
10. def ensuring(cond: (Integral[T]) => Boolean): Integral[T]
Implicit
This member is added by an implicit conversion from Integral[T] toEnsuring[Integral[T]] performed by method Ensuring in scala.Predef.
Definition Classes
Ensuring
11. def ensuring(cond: Boolean, msg: => Any): Integral[T]
Implicit
This member is added by an implicit conversion from Integral[T] toEnsuring[Integral[T]] performed by method Ensuring in scala.Predef.
Definition Classes
Ensuring
12. def ensuring(cond: Boolean): Integral[T]
Implicit
This member is added by an implicit conversion from Integral[T] toEnsuring[Integral[T]] performed by method Ensuring in scala.Predef.
Definition Classes
Ensuring
13. final def eq(arg0: AnyRef)

Tests whether the argument (`that`) is a reference to the receiver object (`this`).

Tests whether the argument (`that`) is a reference to the receiver object (`this`).

The `eq` method implements an equivalence relation on non-null instances of `AnyRef`, and has three additional properties:

• It is consistent: for any non-null instances `x` and `y` of type `AnyRef`, multiple invocations of `x.eq(y)` consistently returns `true` or consistently returns `false`.
• For any non-null instance `x` of type `AnyRef`, `x.eq(null)` and `null.eq(x)` returns `false`.
• `null.eq(null)` returns `true`.

When overriding the `equals` or `hashCode` methods, it is important to ensure that their behavior is consistent with reference equality. Therefore, if two objects are references to each other (`o1 eq o2`), they should be equal to each other (`o1 == o2`) and they should hash to the same value (`o1.hashCode == o2.hashCode`).

returns

`true` if the argument is a reference to the receiver object; `false` otherwise.

Definition Classes
AnyRef
14. def equals(arg0: AnyRef)

The equality method for reference types.

The equality method for reference types. Default implementation delegates to `eq`.

See also `equals` in scala.Any.

returns

`true` if the receiver object is equivalent to the argument; `false` otherwise.

Definition Classes
AnyRef → Any
15. def equiv(x: T, y: T)

Return true if `x` == `y` in the ordering.

Return true if `x` == `y` in the ordering.

Definition Classes
OrderingPartialOrderingEquiv
16. def finalize(): Unit

Called by the garbage collector on the receiver object when there are no more references to the object.

Called by the garbage collector on the receiver object when there are no more references to the object.

The details of when and if the `finalize` method is invoked, as well as the interaction between `finalize` and non-local returns and exceptions, are all platform dependent.

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
(classOf[java.lang.Throwable])
Note

not specified by SLS as a member of AnyRef

17. def formatted(fmtstr: String)

Returns string formatted according to given `format` string.

Returns string formatted according to given `format` string. Format strings are as for `String.format` (@see java.lang.String.format).

Implicit
This member is added by an implicit conversion from Integral[T] toStringFormat[Integral[T]] performed by method StringFormat in scala.Predef.
Definition Classes
StringFormat
Annotations
()
18. final def getClass(): Class[_ <: AnyRef]

Returns the runtime class representation of the object.

Returns the runtime class representation of the object.

returns

a class object corresponding to the runtime type of the receiver.

Definition Classes
AnyRef → Any
Annotations
()
19. def gt(x: T, y: T)

Return true if `x` > `y` in the ordering.

Return true if `x` > `y` in the ordering.

Definition Classes
OrderingPartialOrdering
20. def gteq(x: T, y: T)

Return true if `x` >= `y` in the ordering.

Return true if `x` >= `y` in the ordering.

Definition Classes
OrderingPartialOrdering
21. def hashCode(): Int

The hashCode method for reference types.

The hashCode method for reference types. See hashCode in scala.Any.

returns

the hash code value for this object.

Definition Classes
AnyRef → Any
Annotations
()
22. final def isInstanceOf[T0]

Test whether the dynamic type of the receiver object is `T0`.

Test whether the dynamic type of the receiver object is `T0`.

Note that the result of the test is modulo Scala's erasure semantics. Therefore the expression `1.isInstanceOf[String]` will return `false`, while the expression `List(1).isInstanceOf[List[String]]` will return `true`. In the latter example, because the type argument is erased as part of compilation it is not possible to check whether the contents of the list are of the specified type.

returns

`true` if the receiver object is an instance of erasure of type `T0`; `false` otherwise.

Definition Classes
Any
23. def isReverseOf(other: Ordering[_])

Returns whether or not the other ordering is the opposite ordering of this one.

Returns whether or not the other ordering is the opposite ordering of this one.

Equivalent to `other == this.reverse`.

Implementations should only override this method if they are overriding reverse as well.

Definition Classes
Ordering
24. def lt(x: T, y: T)

Return true if `x` < `y` in the ordering.

Return true if `x` < `y` in the ordering.

Definition Classes
OrderingPartialOrdering
25. def lteq(x: T, y: T)

Return true if `x` <= `y` in the ordering.

Return true if `x` <= `y` in the ordering.

Definition Classes
OrderingPartialOrdering
26. def max[U <: T](x: U, y: U): U

Return `x` if `x` >= `y`, otherwise `y`.

Return `x` if `x` >= `y`, otherwise `y`.

Definition Classes
Ordering
27. def min[U <: T](x: U, y: U): U

Return `x` if `x` <= `y`, otherwise `y`.

Return `x` if `x` <= `y`, otherwise `y`.

Definition Classes
Ordering
28. implicit def mkNumericOps(lhs: T)
Definition Classes
IntegralNumeric
29. implicit def mkOrderingOps(lhs: T)

This implicit method augments `T` with the comparison operators defined in `scala.math.Ordering.Ops`.

This implicit method augments `T` with the comparison operators defined in `scala.math.Ordering.Ops`.

Definition Classes
Ordering
30. final def ne(arg0: AnyRef)

Equivalent to `!(this eq that)`.

Equivalent to `!(this eq that)`.

returns

`true` if the argument is not a reference to the receiver object; `false` otherwise.

Definition Classes
AnyRef
31. final def notify(): Unit

Wakes up a single thread that is waiting on the receiver object's monitor.

Wakes up a single thread that is waiting on the receiver object's monitor.

Definition Classes
AnyRef
Annotations
()
Note

not specified by SLS as a member of AnyRef

32. final def notifyAll(): Unit

Wakes up all threads that are waiting on the receiver object's monitor.

Wakes up all threads that are waiting on the receiver object's monitor.

Definition Classes
AnyRef
Annotations
()
Note

not specified by SLS as a member of AnyRef

33. def on[U](f: (U) => T): Ordering[U]

Given f, a function from U into T, creates an Ordering[U] whose compare function is equivalent to:

Given f, a function from U into T, creates an Ordering[U] whose compare function is equivalent to:

`def compare(x:U, y:U) = Ordering[T].compare(f(x), f(y))`
Definition Classes
Ordering
34. def one: T
Definition Classes
Numeric
35. def orElse(other: Ordering[T]): Ordering[T]

Creates an Ordering[T] whose compare function returns the result of this Ordering's compare function, if it is non-zero, or else the result of `other`s compare function.

Creates an Ordering[T] whose compare function returns the result of this Ordering's compare function, if it is non-zero, or else the result of `other`s compare function.

other

an Ordering to use if this Ordering returns zero

Definition Classes
Ordering
Example:
1. ```case class Pair(a: Int, b: Int)

val pairOrdering = Ordering.by[Pair, Int](_.a)
.orElse(Ordering.by[Pair, Int](_.b))```
36. def orElseBy[S](f: (T) => S)(implicit ord: Ordering[S]): Ordering[T]

Given f, a function from T into S, creates an Ordering[T] whose compare function returns the result of this Ordering's compare function, if it is non-zero, or else a result equivalent to:

Given f, a function from T into S, creates an Ordering[T] whose compare function returns the result of this Ordering's compare function, if it is non-zero, or else a result equivalent to:

`Ordering[S].compare(f(x), f(y))`

This function is equivalent to passing the result of `Ordering.by(f)` to `orElse`.

Definition Classes
Ordering
Example:
1. ```case class Pair(a: Int, b: Int)

val pairOrdering = Ordering.by[Pair, Int](_.a)
.orElseBy[Int](_.b)```
37. def reverse: Ordering[T]

Return the opposite ordering of this one.

Return the opposite ordering of this one.

Implementations overriding this method MUST override isReverseOf as well if they change the behavior at all (for example, caching does not require overriding it).

Definition Classes
OrderingPartialOrdering
38. def reversed(): Comparator[T]
Definition Classes
Comparator
39. def sign(x: T): T
Definition Classes
Numeric
40. final def synchronized[T0](arg0: => T0): T0
Definition Classes
AnyRef
41. def thenComparing[U <: Comparable[_ >: U <: AnyRef]](arg0: java.util.function.Function[_ >: T <: AnyRef, _ <: U]): Comparator[T]
Definition Classes
Comparator
42. def thenComparing[U <: AnyRef](arg0: java.util.function.Function[_ >: T <: AnyRef, _ <: U], arg1: Comparator[_ >: U <: AnyRef]): Comparator[T]
Definition Classes
Comparator
43. def thenComparing(arg0: Comparator[_ >: T <: AnyRef]): Comparator[T]
Definition Classes
Comparator
44. def thenComparingDouble(arg0: ToDoubleFunction[_ >: T <: AnyRef]): Comparator[T]
Definition Classes
Comparator
45. def thenComparingInt(arg0: ToIntFunction[_ >: T <: AnyRef]): Comparator[T]
Definition Classes
Comparator
46. def thenComparingLong(arg0: ToLongFunction[_ >: T <: AnyRef]): Comparator[T]
Definition Classes
Comparator
47. def toString(): String

Creates a String representation of this object.

Creates a String representation of this object. The default representation is platform dependent. On the java platform it is the concatenation of the class name, "@", and the object's hashcode in hexadecimal.

returns

a String representation of the object.

Definition Classes
AnyRef → Any
48. def tryCompare(x: T, y: T): Some[Int]

Returns whether a comparison between `x` and `y` is defined, and if so the result of `compare(x, y)`.

Returns whether a comparison between `x` and `y` is defined, and if so the result of `compare(x, y)`.

Definition Classes
OrderingPartialOrdering
49. final def wait(): Unit
Definition Classes
AnyRef
Annotations
(classOf[java.lang.InterruptedException])
50. final def wait(arg0: Long, arg1: Int): Unit
Definition Classes
AnyRef
Annotations
(classOf[java.lang.InterruptedException])
51. final def wait(arg0: Long): Unit
Definition Classes
AnyRef
Annotations
(classOf[java.lang.InterruptedException]) ()
52. def zero: T
Definition Classes
Numeric

### Deprecated Value Members

1. def signum(x: T): Int
Definition Classes
Numeric
Annotations
Deprecated

(Since version 2.13.0) use `sign` method instead

2. def [B](y: B): (Integral[T], B)
Implicit
This member is added by an implicit conversion from Integral[T] toArrowAssoc[Integral[T]] performed by method ArrowAssoc in scala.Predef.
Definition Classes
ArrowAssoc
Annotations
Deprecated

(Since version 2.13.0) Use `->` instead. If you still wish to display it as one character, consider using a font with programming ligatures such as Fira Code.