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.

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### Type Members

1. #### final class BigDecimal extends ScalaNumber with ScalaNumericConversions with Serializable

   `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 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.

   Version

     1.1

2. #### final class BigInt extends ScalaNumber with ScalaNumericConversions with Serializable

   Version

     1.0, 15/07/2003

3. #### 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 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`.
   Version

     1.0, 2008-04-03

   Since

     2.7

4. #### trait Fractional[T] extends Numeric[T]

   Since

     2.8

5. #### trait Integral[T] extends Numeric[T]

   Since

     2.8

6. #### trait LowPriorityEquiv extends AnyRef

7. #### trait LowPriorityOrderingImplicits extends AnyRef

8. #### trait Numeric[T] extends Ordering[T]

9. #### 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 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.

   Version

     1.1, 2006-07-24

   See also

     scala.math.Ordering, scala.math.PartiallyOrdered

10. #### 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 = ... )
    Version

      0.9.5, 2008-04-15

    Since

      2.7

    See also

      scala.math.Ordered, scala.util.Sorting

11. #### 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 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.

    Version

      1.0, 2008-04-0-3

    Since

      2.7

12. #### trait PartiallyOrdered[+A] extends AnyRef

    A class for partially ordered data.

    A class for partially ordered data.

    Version

      1.0, 23/04/2004

13. #### trait ScalaNumericAnyConversions extends Any

    Conversions which present a consistent conversion interface across all the numeric types, suitable for use in value classes.

14. #### trait ScalaNumericConversions extends ScalaNumber with ScalaNumericAnyConversions

    A slightly more specific conversion trait for classes which extend ScalaNumber (which excludes value classes.)

### Value Members

1. #### object BigDecimal extends Serializable

   Version

     1.1

   Since

     2.7

2. #### object BigInt extends Serializable

   Version

     1.0, 15/07/2003

   Since

     2.1

3. #### final val E: Double(2.718281828459045)

   The `double` value that is closer than any other to `e`, the base of the natural logarithms.

4. #### object Equiv extends LowPriorityEquiv with Serializable

5. #### object Fractional extends Serializable

6. #### def IEEEremainder(x: Double, y: Double): Double

7. #### object Integral extends Serializable

8. #### object Numeric extends Serializable

   Since

     2.8

9. #### object Ordered

10. #### object Ordering extends LowPriorityOrderingImplicits with 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.

11. #### final val Pi: Double(3.141592653589793)

    The `double` value that is closer than any other to `pi`, the ratio of the circumference of a circle to its diameter.

12. #### def abs(x: Double): Double

13. #### def abs(x: Float): Float

14. #### def abs(x: Long): Long

15. #### def abs(x: Int): Int

16. #### def acos(x: Double): Double

17. #### def asin(x: Double): Double

18. #### def atan(x: Double): Double

19. #### 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.

20. #### def cbrt(x: Double): Double

    Returns the cube root of the given `Double` value.

21. #### def ceil(x: Double): Double

22. #### def cos(x: Double): Double

23. #### def cosh(x: Double): Double

    Returns the hyperbolic cosine of the given `Double` value.

24. #### def exp(x: Double): Double

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

    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.

25. #### def expm1(x: Double): Double

    Returns `exp(x) - 1`.

26. #### def floor(x: Double): Double

27. #### 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.

28. #### def log(x: Double): Double

29. #### def log10(x: Double): Double

    Returns the base 10 logarithm of the given `Double` value.

30. #### def log1p(x: Double): Double

    Returns the natural logarithm of the sum of the given `Double` value and 1.

31. #### def max(x: Double, y: Double): Double

32. #### def max(x: Float, y: Float): Float

33. #### def max(x: Long, y: Long): Long

34. #### def max(x: Int, y: Int): Int

35. #### def min(x: Double, y: Double): Double

36. #### def min(x: Float, y: Float): Float

37. #### def min(x: Long, y: Long): Long

38. #### def min(x: Int, y: Int): Int

39. #### 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 `xy`.

40. #### def random: Double

    Returns a `double` value with a positive sign, greater than or equal to `0.0` and less than `1.0`.

41. #### 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.

42. #### 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.

43. #### 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.

44. #### def signum(x: Double): Double

45. #### def signum(x: Float): Float

46. #### def signum(x: Long): Long

47. #### def signum(x: Int): Int

    Note that these are not pure forwarders to the java versions.

    Note that these 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.

48. #### def sin(x: Double): Double

49. #### def sinh(x: Double): Double

    Returns the hyperbolic sine of the given `Double` value.

50. #### def sqrt(x: Double): Double

51. #### def tan(x: Double): Double

52. #### def tanh(x: Double): Double

    Returns the hyperbolic tangent of the given `Double` value.

53. #### 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.

54. #### 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.

55. #### def ulp(x: Float): Float

    Returns the size of an ulp of the given `Float` value.

56. #### def ulp(x: Double): Double

    Returns the size of an ulp of the given `Double` value.

### Deprecated Value Members

1. #### 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`.

   There is no reason to round a `Long`, but this method prevents unintended conversion to `Float` followed by rounding to `Int`.

   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?

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