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/Scala 2.13 Library

Package scala.math

package math

The package object scala.math contains methods for performing basic numeric operations such as elementary exponential, logarithmic, root and trigonometric functions.

All methods forward to java.lang.Math unless otherwise noted.

Source
package.scala
See also

java.lang.Math

Linear Supertypes
AnyRef, Any

Type Members

final class BigDecimal 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.

final class BigInt extends ScalaNumber with ScalaNumericConversions with Serializable with Ordered[BigInt]

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:

    reflexive: equiv(x, x) == true for any x of type T.symmetric: equiv(x, y) == equiv(y, x) for any x and y of type T.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.
Since

2.7

trait Fractional[T] extends Numeric[T]

Since

2.8

trait Integral[T] extends Numeric[T]

Since

2.8

trait LowPriorityEquiv extends AnyRef

trait LowPriorityOrderingImplicits extends AnyRef

trait Numeric[T] extends Ordering[T]

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

scala.math.Ordering, scala.math.PartiallyOrdered

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.

Annotations
@implicitNotFound("No implicit Ordering defined for ${T}.")
Since

2.7

See also

scala.math.Ordered, scala.util.Sorting

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.

Since

2.7

trait PartiallyOrdered[+A] extends Any

trait ScalaNumericAnyConversions extends Any

trait ScalaNumericConversions extends ScalaNumber with ScalaNumericAnyConversions

Value Members

final val E: Double(2.718281828459045)

def IEEEremainder(x: Double, y: Double): Double

final val Pi: Double(3.141592653589793)

def abs(x: Double): Double

def abs(x: Float): Float

def abs(x: Long): Long

def abs(x: Int): Int

def acos(x: Double): Double

def addExact(x: Long, y: Long): Long

def addExact(x: Int, y: Int): Int

def asin(x: Double): Double

def atan(x: Double): Double

def atan2(y: Double, x: Double): Double

Converts rectangular coordinates (x, y) to polar (r, theta).

y

the abscissa coordinate

x

the ordinate coordinate

returns

the theta component of the point (r, theta) in polar coordinates that corresponds to the point (x, y) in Cartesian coordinates.

def cbrt(x: Double): Double

Returns the cube root of the given Double value.

x

the number to take the cube root of

returns

the value ∛x

def ceil(x: Double): Double

def copySign(magnitude: Float, sign: Float): Float

def copySign(magnitude: Double, sign: Double): Double

def cos(x: Double): Double

def cosh(x: Double): Double

def decrementExact(x: Long): Long

def decrementExact(x: Int): Int

def exp(x: Double): Double

Returns Euler's number e raised to the power of a Double value.

x

the exponent to raise e to.

returns

the value ea, where e is the base of the natural logarithms.

def expm1(x: Double): Double

def floor(x: Double): Double

def floorDiv(x: Long, y: Long): Long

def floorDiv(x: Int, y: Int): Int

def floorMod(x: Long, y: Long): Long

def floorMod(x: Int, y: Int): Int

def getExponent(d: Double): Int

def getExponent(f: Float): Int

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.

def incrementExact(x: Long): Long

def incrementExact(x: Int): Int

def log(x: Double): Double

Returns the natural logarithm of a Double value.

x

the number to take the natural logarithm of

returns

the value logₑ(x) where e is Eulers number

def log10(x: Double): Double

def log1p(x: Double): Double

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

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

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

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

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

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

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

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

def multiplyExact(x: Long, y: Long): Long

def multiplyExact(x: Int, y: Int): Int

def negateExact(x: Long): Long

def negateExact(x: Int): Int

def nextAfter(start: Float, direction: Double): Float

def nextAfter(start: Double, direction: Double): Double

def nextDown(f: Float): Float

def nextDown(d: Double): Double

def nextUp(f: Float): Float

def nextUp(d: Double): Double

def pow(x: Double, y: Double): Double

Returns the value of the first argument raised to the power of the second argument.

x

the base.

y

the exponent.

returns

the value xy.

def random(): Double

def rint(x: Double): Double

Returns the Double value that is closest in value to the argument and is equal to a mathematical integer.

x

a Double value

returns

the closest floating-point value to a that is equal to a mathematical integer.

def round(x: Double): Long

Returns the closest Long to the argument.

x

a floating-point value to be rounded to a Long.

returns

the value of the argument rounded to the nearestlong value.

def round(x: Float): Int

Returns the closest Int to the argument.

x

a floating-point value to be rounded to a Int.

returns

the value of the argument rounded to the nearest Int value.

def scalb(f: Float, scaleFactor: Int): Float

def scalb(d: Double, scaleFactor: Int): Double

def signum(x: Double): Double

def signum(x: Float): Float

def signum(x: Long): Long

Note

Forwards to java.lang.Long

def signum(x: Int): Int

Note

Forwards to java.lang.Integer

def sin(x: Double): Double

def sinh(x: Double): Double

def sqrt(x: Double): Double

Returns the square root of a Double value.

x

the number to take the square root of

returns

the value √x

def subtractExact(x: Long, y: Long): Long

def subtractExact(x: Int, y: Int): Int

def tan(x: Double): Double

def tanh(x: Double): Double

def toDegrees(x: Double): Double

Converts an angle measured in radians to an approximately equivalent angle measured in degrees.

x

angle, in radians

returns

the measurement of the angle x in degrees.

def toIntExact(x: Long): Int

def toRadians(x: Double): Double

Converts an angle measured in degrees to an approximately equivalent angle measured in radians.

x

an angle, in degrees

returns

the measurement of the angle x in radians.

def ulp(x: Float): Float

def ulp(x: Double): Double

object BigDecimal extends java.io.Serializable

Since

2.7

object BigInt extends java.io.Serializable

Since

2.1

object Equiv extends LowPriorityEquiv with java.io.Serializable

object Fractional extends java.io.Serializable

object Integral extends java.io.Serializable

object Numeric extends java.io.Serializable

Since

2.8

object Ordered

object Ordering extends LowPriorityOrderingImplicits with java.io.Serializable

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.

object PartialOrdering extends java.io.Serializable

© 2002-2019 EPFL, with contributions from Lightbend.
Licensed under the Apache License, Version 2.0.
https://www.scala-lang.org/api/2.13.0/scala/math/index.html