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.
1.1
1.0, 15/07/2003
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:
equiv(x, x) == true
for any x of type T
.equiv(x, y) == equiv(y, x)
for any x
and y
of type T
.equiv(x, y) == true
and equiv(y, z) == true
, then
equiv(x, z) == true
for any x
, y
, and z
of type T
.
1.0, 2008-04-03
2.7
2.8
2.8
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.
1.1, 2006-07-24
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.
0.9.5, 2008-04-15
2.7
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:
lteq(x, x) == true
, for any x
of type T
.lteq(x, y) == true
and
lteq(y, x) == true
then equiv(x, y) == true
, for any x
and y
of type T
.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.
1.0, 2008-04-0-3
2.7
A class for partially ordered data.
A class for partially ordered data.
1.0, 23/04/2004
Conversions which present a consistent conversion interface across all the numeric types, suitable for use in value classes.
A slightly more specific conversion trait for classes which extend ScalaNumber (which excludes value classes.)
1.1
2.7
1.0, 15/07/2003
2.1
The double
value that is closer than any other to e
, the base of
the natural logarithms.
2.8
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.
The double
value that is closer than any other to pi
, the ratio of
the circumference of a circle to its diameter.
Converts rectangular coordinates (x, y)
to polar (r, theta)
.
Converts rectangular coordinates (x, y)
to polar (r, theta)
.
the abscissa coordinate
the ordinate coordinate
the theta component of the point (r, theta)
in polar
coordinates that corresponds to the point (x, y)
in
Cartesian coordinates.
Returns the cube root of the given Double
value.
Returns the hyperbolic cosine of the given Double
value.
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.
the exponent to raise e
to.
the value e^{a}
, where e
is the base of the natural
logarithms.
Returns exp(x) - 1
.
Returns the square root of the sum of the squares of both given Double
values without intermediate underflow or overflow.
Returns the natural logarithm of a double
value.
Returns the natural logarithm of a double
value.
the number to take the natural logarithm of
the value logₑ(x)
where e
is Eulers number
Returns the base 10 logarithm of the given Double
value.
Returns the natural logarithm of the sum of the given Double
value and 1.
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.
the base.
the exponent.
the value x^{y}
.
Returns a double
value with a positive sign, greater than or equal
to 0.0
and less than 1.0
.
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.
a double
value
the closest floating-point value to a that is equal to a mathematical integer.
Returns the closest Long
to the argument.
Returns the closest Long
to the argument.
a floating-point value to be rounded to a Long
.
the value of the argument rounded to the nearestlong
value.
Returns the closest Int
to the argument.
Returns the closest Int
to the argument.
a floating-point value to be rounded to a Int
.
the value of the argument rounded to the nearest Int
value.
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.
Returns the hyperbolic sine of the given Double
value.
Returns the square root of a double
value.
Returns the square root of a double
value.
the number to take the square root of
the value √x
Returns the hyperbolic tangent of the given Double
value.
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.
angle, in radians
the measurement of the angle x
in degrees.
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.
an angle, in degrees
the measurement of the angle x
in radians.
Returns the size of an ulp of the given Float
value.
Returns the size of an ulp of the given Double
value.
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
.
(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?
The package object
scala.math
contains methods for performing basic numeric operations such as elementary exponential, logarithmic, root and trigonometric functions.