scala.math

package scala.math

randomisation

def random(): Double
Returns a Double value with a positive sign, greater than or equal to 0.0 and less than 1.0.
Source
(source)

exact

def addExact(x: Int, y: Int): Int
Source
(source)
def addExact(x: Long, y: Long): Long
Source
(source)
Source
(source)
Source
(source)
def multiplyExact(x: Int, y: Int): Int
Source
(source)
def multiplyExact(x: Long, y: Long): Long
Source
(source)
def negateExact(x: Int): Int
Source
(source)
Source
(source)
def subtractExact(x: Int, y: Int): Int
Source
(source)
def subtractExact(x: Long, y: Long): Long
Source
(source)
def toIntExact(x: Long): Int
Source
(source)

abs

def abs(x: Int): Int
Source
(source)
def abs(x: Long): Long
Source
(source)
def abs(x: Float): Float
Source
(source)
def abs(x: Double): Double
Source
(source)

hyperbolic

def cosh(x: Double): Double
Returns the hyperbolic cosine of the given Double value.
Source
(source)
def sinh(x: Double): Double
Returns the hyperbolic sine of the given Double value.
Source
(source)
def tanh(x: Double): Double
Returns the hyperbolic tangent of the given Double value.
Source
(source)

modquo

def floorDiv(x: Int, y: Int): Int
Source
(source)
def floorDiv(x: Long, y: Long): Long
Source
(source)
def floorMod(x: Int, y: Int): Int
Source
(source)
def floorMod(x: Long, y: Long): Long
Source
(source)

ulp

def ulp(x: Double): Double
Returns the size of an ulp of the given Double value.
Source
(source)
def ulp(x: Float): Float
Returns the size of an ulp of the given Float value.
Source
(source)

minmax

def max(x: Int, y: Int): Int
Source
(source)
def max(x: Long, y: Long): Long
Source
(source)
def max(x: Float, y: Float): Float
Source
(source)
def max(x: Double, y: Double): Double
Source
(source)
def min(x: Int, y: Int): Int
Source
(source)
def min(x: Long, y: Long): Long
Source
(source)
def min(x: Float, y: Float): Float
Source
(source)
def min(x: Double, y: Double): Double
Source
(source)

signs

def copySign(magnitude: Double, sign: Double): Double
Source
(source)
def copySign(magnitude: Float, sign: Float): Float
Source
(source)
def signum(x: Int): Int
Note
Forwards to java.lang.Integer
Source
(source)
def signum(x: Long): Long
Note
Forwards to java.lang.Long
Source
(source)
def signum(x: Float): Float
Source
(source)
def signum(x: Double): Double
Source
(source)

math-const

final val E: 2.718281828459045
The Double value that is closer than any other to e, the base of the natural logarithms.
Source
(source)
final val Pi: 3.141592653589793
The Double value that is closer than any other to pi, the ratio of the circumference of a circle to its diameter.
Source
(source)

adjacent-float

def nextAfter(start: Double, direction: Double): Double
Source
(source)
def nextAfter(start: Float, direction: Double): Float
Source
(source)
Source
(source)
def nextDown(f: Float): Float
Source
(source)
def nextUp(d: Double): Double
Source
(source)
def nextUp(f: Float): Float
Source
(source)

explog

def exp(x: Double): Double
Returns Euler's number e raised to the power of a Double value.
Value Params
x
the exponent to raise e to.
Returns
the value ea, where e is the base of the natural logarithms.
Source
(source)
def expm1(x: Double): Double
Returns exp(x) - 1.
Source
(source)
Source
(source)
Source
(source)
def log(x: Double): Double
Returns the natural logarithm of a Double value.
Value Params
x
the number to take the natural logarithm of
Returns
the value logₑ(x) where e is Eulers number
Source
(source)
def log10(x: Double): Double
Returns the base 10 logarithm of the given Double value.
Source
(source)
def log1p(x: Double): Double
Returns the natural logarithm of the sum of the given Double value and 1.
Source
(source)
def pow(x: Double, y: Double): Double
Returns the value of the first argument raised to the power of the second argument.
Value Params
x
the base.
y
the exponent.
Returns
the value xy.
Source
(source)

angle-conversion

Converts an angle measured in radians to an approximately equivalent angle measured in degrees.
Value Params
x
angle, in radians
Returns
the measurement of the angle x in degrees.
Source
(source)
Converts an angle measured in degrees to an approximately equivalent angle measured in radians.
Value Params
x
an angle, in degrees
Returns
the measurement of the angle x in radians.
Source
(source)

root-extraction

def cbrt(x: Double): Double
Returns the cube root of the given Double value.
Value Params
x
the number to take the cube root of
Returns
the value ∛x
Source
(source)
def sqrt(x: Double): Double
Returns the square root of a Double value.
Value Params
x
the number to take the square root of
Returns
the value √x
Source
(source)

scaling

def scalb(d: Double, scaleFactor: Int): Double
Source
(source)
def scalb(f: Float, scaleFactor: Int): Float
Source
(source)

rounding

def ceil(x: Double): Double
Source
(source)
def floor(x: Double): Double
Source
(source)
def rint(x: Double): Double
Returns the Double value that is closest in value to the argument and is equal to a mathematical integer.
Value Params
x
a Double value
Returns
the closest floating-point value to a that is equal to a mathematical integer.
Source
(source)
@deprecated("This is an integer type; there is no reason to round it. Perhaps you meant to call this with a floating-point value?", "2.11.0")
def round(x: Long): Long
There is no reason to round a Long, but this method prevents unintended conversion to Float followed by rounding to Int.
Note
Does not forward to java.lang.Math
Source
(source)
def round(x: Float): Int
Returns the closest Int to the argument.
Value Params
x
a floating-point value to be rounded to a Int.
Returns
the value of the argument rounded to the nearest Int value.
Source
(source)
def round(x: Double): Long
Returns the closest Long to the argument.
Value Params
x
a floating-point value to be rounded to a Long.
Returns
the value of the argument rounded to the nearestlong value.
Source
(source)

polar-coords

def atan2(y: Double, x: Double): Double
Converts rectangular coordinates (x, y) to polar (r, theta).
Value Params
x
the ordinate coordinate
y
the abscissa coordinate
Returns
the theta component of the point (r, theta) in polar coordinates that corresponds to the point (x, y) in Cartesian coordinates.
Source
(source)
def hypot(x: Double, y: Double): Double
Returns the square root of the sum of the squares of both given Double values without intermediate underflow or overflow.
The r component of the point (r, theta) in polar coordinates that corresponds to the point (x, y) in Cartesian coordinates.
Source
(source)

trig

def acos(x: Double): Double
Source
(source)
def asin(x: Double): Double
Source
(source)
def atan(x: Double): Double
Source
(source)
def cos(x: Double): Double
Source
(source)
def sin(x: Double): Double
Source
(source)
def tan(x: Double): Double
Source
(source)

Type members

Classlikes

object BigDecimal
Companion
class
Source
(source)
final class BigDecimal(val bigDecimal: BigDecimal, val mc: MathContext) extends ScalaNumber with ScalaNumericConversions with Serializable with Ordered[BigDecimal]
BigDecimal represents decimal floating-point numbers of arbitrary precision. By default, the precision approximately matches that of IEEE 128-bit floating point numbers (34 decimal digits, HALF_EVEN rounding mode). Within the range of IEEE binary128 numbers, BigDecimal will agree with BigInt for both equality and hash codes (and will agree with primitive types as well). Beyond that range--numbers with more than 4934 digits when written out in full--the hashCode of BigInt and BigDecimal is allowed to diverge due to difficulty in efficiently computing both the decimal representation in BigDecimal and the binary representation in BigInt.
When creating a BigDecimal from a Double or Float, care must be taken as the binary fraction representation of Double and Float does not easily convert into a decimal representation. Three explicit schemes are available for conversion. BigDecimal.decimal will convert the floating-point number to a decimal text representation, and build a BigDecimal based on that. BigDecimal.binary will expand the binary fraction to the requested or default precision. BigDecimal.exact will expand the binary fraction to the full number of digits, thus producing the exact decimal value corresponding to the binary fraction of that floating-point number. BigDecimal equality matches the decimal expansion of Double: BigDecimal.decimal(0.1) == 0.1. Note that since 0.1f != 0.1, the same is not true for Float. Instead, 0.1f == BigDecimal.decimal((0.1f).toDouble).
To test whether a BigDecimal number can be converted to a Double or Float and then back without loss of information by using one of these methods, test with isDecimalDouble, isBinaryDouble, or isExactDouble or the corresponding Float versions. Note that BigInt's isValidDouble will agree with isExactDouble, not the isDecimalDouble used by default.
BigDecimal uses the decimal representation of binary floating-point numbers to determine equality and hash codes. This yields different answers than conversion between Long and Double values, where the exact form is used. As always, since floating-point is a lossy representation, it is advisable to take care when assuming identity will be maintained across multiple conversions.
BigDecimal maintains a MathContext that determines the rounding that is applied to certain calculations. In most cases, the value of the BigDecimal is also rounded to the precision specified by the MathContext. To create a BigDecimal with a different precision than its MathContext, use new BigDecimal(new java.math.BigDecimal(...), mc). Rounding will be applied on those mathematical operations that can dramatically change the number of digits in a full representation, namely multiplication, division, and powers. The left-hand argument's MathContext always determines the degree of rounding, if any, and is the one propagated through arithmetic operations that do not apply rounding themselves.
Companion
object
Source
(source)
object BigInt
Companion
class
Source
(source)
final class BigInt(val bigInteger: BigInteger) extends ScalaNumber with ScalaNumericConversions with Serializable with Ordered[BigInt]
Companion
object
Source
(source)
trait Equiv[T] extends Serializable
A trait for representing equivalence relations. It is important to distinguish between a type that can be compared for equality or equivalence and a representation of equivalence on some type. This trait is for representing the latter.
An equivalence relation is a binary relation on a type. This relation is exposed as the equiv method of the Equiv trait. The relation must be:
  1. reflexive: equiv(x, x) == true for any x of type T.
  2. symmetric: equiv(x, y) == equiv(y, x) for any x and y of type T.
  3. transitive: if equiv(x, y) == true and equiv(y, z) == true, then equiv(x, z) == true for any x, y, and z of type T.
Companion
object
Source
(source)
object Equiv extends LowPriorityEquiv
Companion
class
Source
(source)
trait Fractional[T] extends Numeric[T]
Companion
object
Source
(source)
object Fractional
Companion
class
Source
(source)
trait Integral[T] extends Numeric[T]
Companion
object
Source
(source)
object Integral
Companion
class
Source
(source)
object Numeric
Companion
class
Source
(source)
trait Numeric[T] extends Ordering[T]
Companion
object
Source
(source)
trait Ordered[A] extends Comparable[A]
A trait for data that have a single, natural ordering. See scala.math.Ordering before using this trait for more information about whether to use scala.math.Ordering instead.
Classes that implement this trait can be sorted with scala.util.Sorting and can be compared with standard comparison operators (e.g. > and <).
Ordered should be used for data with a single, natural ordering (like integers) while Ordering allows for multiple ordering implementations. An Ordering instance will be implicitly created if necessary.
scala.math.Ordering is an alternative to this trait that allows multiple orderings to be defined for the same type.
scala.math.PartiallyOrdered is an alternative to this trait for partially ordered data.
For example, create a simple class that implements Ordered and then sort it with scala.util.Sorting:
case class OrderedClass(n:Int) extends Ordered[OrderedClass] {
	def compare(that: OrderedClass) =  this.n - that.n
}

val x = Array(OrderedClass(1), OrderedClass(5), OrderedClass(3))
scala.util.Sorting.quickSort(x)
x
It is important that the equals method for an instance of Ordered[A] be consistent with the compare method. However, due to limitations inherent in the type erasure semantics, there is no reasonable way to provide a default implementation of equality for instances of Ordered[A]. Therefore, if you need to be able to use equality on an instance of Ordered[A] you must provide it yourself either when inheriting or instantiating.
It is important that the hashCode method for an instance of Ordered[A] be consistent with the compare method. However, it is not possible to provide a sensible default implementation. Therefore, if you need to be able compute the hash of an instance of Ordered[A] you must provide it yourself either when inheriting or instantiating.
See also
Companion
object
Source
(source)
object Ordered
Companion
class
Source
(source)
@implicitNotFound(msg = "No implicit Ordering defined for ${T}.")
trait Ordering[T] extends Comparator[T] with PartialOrdering[T] with Serializable
Ordering is a trait whose instances each represent a strategy for sorting instances of a type.
Ordering's companion object defines many implicit objects to deal with subtypes of AnyVal (e.g. Int, Double), String, and others.
To sort instances by one or more member variables, you can take advantage of these built-in orderings using Ordering.by and Ordering.on:
import scala.util.Sorting
val pairs = Array(("a", 5, 2), ("c", 3, 1), ("b", 1, 3))

// sort by 2nd element
Sorting.quickSort(pairs)(Ordering.by[(String, Int, Int), Int](_._2))

// sort by the 3rd element, then 1st
Sorting.quickSort(pairs)(Ordering[(Int, String)].on(x => (x._3, x._1)))
An Ordering[T] is implemented by specifying compare(a:T, b:T), which decides how to order two instances a and b. Instances of Ordering[T] can be used by things like scala.util.Sorting to sort collections like Array[T].
For example:
import scala.util.Sorting

case class Person(name:String, age:Int)
val people = Array(Person("bob", 30), Person("ann", 32), Person("carl", 19))

// sort by age
object AgeOrdering extends Ordering[Person] {
 def compare(a:Person, b:Person) = a.age compare b.age
}
Sorting.quickSort(people)(AgeOrdering)
This trait and scala.math.Ordered both provide this same functionality, but in different ways. A type T can be given a single way to order itself by extending Ordered. Using Ordering, this same type may be sorted in many other ways. Ordered and Ordering both provide implicits allowing them to be used interchangeably.
You can import scala.math.Ordering.Implicits to gain access to other implicit orderings.
See also
scala.math.Ordered, scala.util.Sorting
Companion
object
Source
(source)
This is the companion object for the scala.math.Ordering trait.
It contains many implicit orderings as well as well as methods to construct new orderings.
Companion
class
Source
(source)
trait PartialOrdering[T] extends Equiv[T]
A trait for representing partial orderings. It is important to distinguish between a type that has a partial order and a representation of partial ordering on some type. This trait is for representing the latter.
A partial ordering is a binary relation on a type T, exposed as the lteq method of this trait. This relation must be:
- reflexive: lteq(x, x) == true, for any x of type T. - anti-symmetric: if lteq(x, y) == true and lteq(y, x) == true then equiv(x, y) == true, for any x and y of type T. - transitive: if lteq(x, y) == true and lteq(y, z) == true then lteq(x, z) == true, for any x, y, and z of type T.
Additionally, a partial ordering induces an equivalence relation on a type T: x and y of type T are equivalent if and only if lteq(x, y) && lteq(y, x) == true. This equivalence relation is exposed as the equiv method, inherited from the Equiv trait.
Companion
object
Source
(source)
Companion
class
Source
(source)
trait PartiallyOrdered[+A]
A class for partially ordered data.
Source
(source)
Conversions which present a consistent conversion interface across all the numeric types, suitable for use in value classes.
Source
(source)
trait ScalaNumericConversions extends ScalaNumber with ScalaNumericAnyConversions
A slightly more specific conversion trait for classes which extend ScalaNumber (which excludes value classes.)
Source
(source)