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
- Grouped
- Alphabetic
- By Inheritance
- math
- AnyRef
- Any
- Hide All
- Show All
- Public
- Protected
Type Members
- final class BigDecimal extends ScalaNumber with ScalaNumericConversions with Serializable with Ordered[BigDecimal]
BigDecimal
represents decimal floating-point numbers of arbitrary precision.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 withBigInt
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--thehashCode
ofBigInt
andBigDecimal
is allowed to diverge due to difficulty in efficiently computing both the decimal representation inBigDecimal
and the binary representation inBigInt
.When creating a
BigDecimal
from aDouble
orFloat
, care must be taken as the binary fraction representation ofDouble
andFloat
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 aBigDecimal
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 ofDouble
:BigDecimal.decimal(0.1) == 0.1
. Note that since0.1f != 0.1
, the same is not true forFloat
. Instead,0.1f == BigDecimal.decimal((0.1f).toDouble)
.To test whether a
BigDecimal
number can be converted to aDouble
orFloat
and then back without loss of information by using one of these methods, test withisDecimalDouble
,isBinaryDouble
, orisExactDouble
or the correspondingFloat
versions. Note thatBigInt
'sisValidDouble
will agree withisExactDouble
, not theisDecimalDouble
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 betweenLong
andDouble
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 aMathContext
that determines the rounding that is applied to certain calculations. In most cases, the value of theBigDecimal
is also rounded to the precision specified by theMathContext
. To create aBigDecimal
with a different precision than itsMathContext
, usenew 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'sMathContext
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.
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 theEquiv
trait. The relation must be:- reflexive:
equiv(x, x) == true
for any x of typeT
. - symmetric:
equiv(x, y) == equiv(y, x)
for anyx
andy
of typeT
. - transitive: if
equiv(x, y) == true
andequiv(y, z) == true
, thenequiv(x, z) == true
for anyx
,y
, andz
of typeT
.
- reflexive:
- trait Fractional[T] extends Numeric[T]
- trait Integral[T] extends Numeric[T]
- 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.
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 ofOrdered[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 ofOrdered[A]
. Therefore, if you need to be able to use equality on an instance ofOrdered[A]
you must provide it yourself either when inheriting or instantiating.It is important that the
hashCode
method for an instance ofOrdered[A]
be consistent with thecompare
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 ofOrdered[A]
you must provide it yourself either when inheriting or instantiating. - 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 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(msg = "No implicit Ordering defined for ${T}.")
- See also
- trait PartialOrdering[T] extends Equiv[T]
A trait for representing partial orderings.
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 thelteq
method of this trait. This relation must be:- reflexive:
lteq(x, x) == true
, for anyx
of typeT
. - anti-symmetric: if
lteq(x, y) == true
andlteq(y, x) == true
thenequiv(x, y) == true
, for anyx
andy
of typeT
. - transitive: if
lteq(x, y) == true
andlteq(y, z) == true
thenlteq(x, z) == true
, for anyx
,y
, andz
of typeT
.
Additionally, a partial ordering induces an equivalence relation on a type
T
:x
andy
of typeT
are equivalent if and only iflteq(x, y) && lteq(y, x) == true
. This equivalence relation is exposed as theequiv
method, inherited from the Equiv trait. - reflexive:
- trait PartiallyOrdered[+A] extends Any
A class for partially ordered data.
- trait ScalaNumericAnyConversions extends Any
Conversions which present a consistent conversion interface across all the numeric types, suitable for use in value classes.
- trait ScalaNumericConversions extends ScalaNumber with ScalaNumericAnyConversions
A slightly more specific conversion trait for classes which extend ScalaNumber (which excludes value classes.)
Value Members
- final val E: Double(2.718281828459045)
The
Double
value that is closer than any other toe
, the base of the natural logarithms. - def IEEEremainder(x: Double, y: Double): Double
- final val Pi: Double(3.141592653589793)
The
Double
value that is closer than any other topi
, the ratio of the circumference of a circle to its diameter. - 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)
.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.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
Returns the hyperbolic cosine of the given
Double
value. - 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 aDouble
value.Returns Euler's number
e
raised to the power of aDouble
value.- x
the exponent to raise
e
to.- returns
the value
e^{a}
, wheree
is the base of the natural logarithms.
- def expm1(x: Double): Double
Returns
exp(x) - 1
. - 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.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.Returns the natural logarithm of a
Double
value.- x
the number to take the natural logarithm of
- returns
the value
logₑ(x)
wheree
is Eulers number
- def log10(x: Double): Double
Returns the base 10 logarithm of the given
Double
value. - def log1p(x: Double): Double
Returns the natural logarithm of the sum of the given
Double
value and 1. - 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.
Returns the value of the first argument raised to the power of the second argument.
- x
the base.
- y
the exponent.
- returns
the value
x^{y}
.
- def random(): Double
Returns a
Double
value with a positive sign, greater than or equal to0.0
and less than1.0
. - def rint(x: Double): Double
Returns the
Double
value that is closest in value to the argument and is equal to a mathematical integer.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.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 nearest
long
value.
- def round(x: Float): Int
Returns the closest
Int
to the argument.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
Returns the hyperbolic sine of the given
Double
value. - def sqrt(x: Double): Double
Returns the square root of a
Double
value.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
Returns the hyperbolic tangent of the given
Double
value. - def toDegrees(x: Double): Double
Converts an angle measured in radians to an approximately equivalent angle measured in degrees.
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.
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
Returns the size of an ulp of the given
Float
value. - def ulp(x: Double): Double
Returns the size of an ulp of the given
Double
value. - object BigDecimal extends java.io.Serializable
- object BigInt extends java.io.Serializable
- 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
- object Ordered
- object Ordering extends LowPriorityOrderingImplicits with java.io.Serializable
This is the companion object for the scala.math.Ordering trait.
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
Deprecated Value Members
- def round(x: Long): Long
There is no reason to round a
Long
, but this method prevents unintended conversion toFloat
followed by rounding toInt
.There is no reason to round a
Long
, but this method prevents unintended conversion toFloat
followed by rounding toInt
.- Annotations
- @deprecated
- Deprecated
(Since version 2.11.0) This is an integer type; there is no reason to round it. Perhaps you meant to call this with a floating-point value?
- Note
Does not forward to java.lang.Math
Mathematical Constants
Minimum and Maximum
Find the min or max of two numbers. Note: scala.collection.IterableOnceOps has min and max methods which determine the min or max of a collection.
Rounding
Scaling
Scaling with rounding guarantees
Exponential and Logarithmic
Trigonometric
Arguments in radians
Angular Measurement Conversion
Hyperbolic
Absolute Values
Determine the magnitude of a value by discarding the sign. Results are >= 0.
Signs
For signum
extract the sign of a value. Results are -1, 0 or 1.
Note the signum
methods are not pure forwarders to the Java versions.
In particular, the return type of java.lang.Long.signum
is Int
,
but here it is widened to Long
so that each overloaded variant
will return the same numeric type it is passed.
Root Extraction
Polar Coordinates
Unit of Least Precision
Pseudo Random Number Generation
Exact Arithmetic
Integral addition, multiplication, stepping and conversion throwing ArithmeticException instead of underflowing or overflowing
Modulus and Quotient
Calculate quotient values by rounding to negative infinity
This is the documentation for the Scala standard library.
Package structure
The scala package contains core types like
Int
,Float
,Array
orOption
which are accessible in all Scala compilation units without explicit qualification or imports.Notable packages include:
scala.collection
and its sub-packages contain Scala's collections frameworkscala.collection.immutable
- Immutable, sequential data-structures such asVector
,List
,Range
,HashMap
orHashSet
scala.collection.mutable
- Mutable, sequential data-structures such asArrayBuffer
,StringBuilder
,HashMap
orHashSet
scala.collection.concurrent
- Mutable, concurrent data-structures such asTrieMap
scala.concurrent
- Primitives for concurrent programming such asFutures
andPromises
scala.io
- Input and output operationsscala.math
- Basic math functions and additional numeric types likeBigInt
andBigDecimal
scala.sys
- Interaction with other processes and the operating systemscala.util.matching
- Regular expressionsOther packages exist. See the complete list on the right.
Additional parts of the standard library are shipped as separate libraries. These include:
scala.reflect
- Scala's reflection API (scala-reflect.jar)scala.xml
- XML parsing, manipulation, and serialization (scala-xml.jar)scala.collection.parallel
- Parallel collections (scala-parallel-collections.jar)scala.util.parsing
- Parser combinators (scala-parser-combinators.jar)scala.swing
- A convenient wrapper around Java's GUI framework called Swing (scala-swing.jar)Automatic imports
Identifiers in the scala package and the
scala.Predef
object are always in scope by default.Some of these identifiers are type aliases provided as shortcuts to commonly used classes. For example,
List
is an alias forscala.collection.immutable.List
.Other aliases refer to classes provided by the underlying platform. For example, on the JVM,
String
is an alias forjava.lang.String
.