scala.math (original) (raw)

Mathematical Constants

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

Attributes

Source

package.scala

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

Attributes

Source

package.scala

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

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

Value parameters

a Double value

Attributes

Returns

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

Source

package.scala

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

Attributes

Note

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?

Source

package.scala

Returns the closest Int to the argument.

Value parameters

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

Attributes

Returns

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

Source

package.scala

Returns the closest Long to the argument.

Value parameters

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

Attributes

Returns

the value of the argument rounded to the nearestlong value.

Source

package.scala

Scaling

Scaling with rounding guarantees

Exponential and Logarithmic

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

Value parameters

the exponent to raise e to.

Attributes

Returns

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

Source

package.scala

Returns the natural logarithm of a Double value.

Value parameters

the number to take the natural logarithm of

Attributes

Returns

the value logₑ(x) where e is Eulers number

Source

package.scala

Returns the base 10 logarithm of the given Double value.

Attributes

Source

package.scala

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

Attributes

Source

package.scala

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

Value parameters

the base.

the exponent.

Attributes

Returns

the value xy.

Source

package.scala

Trigonometric

Arguments in radians

Angular Measurement Conversion

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

Value parameters

angle, in radians

Attributes

Returns

the measurement of the angle x in degrees.

Source

package.scala

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

Value parameters

an angle, in degrees

Attributes

Returns

the measurement of the angle x in radians.

Source

package.scala

Hyperbolic

Returns the hyperbolic cosine of the given Double value.

Attributes

Source

package.scala

Returns the hyperbolic sine of the given Double value.

Attributes

Source

package.scala

Returns the hyperbolic tangent of the given Double value.

Attributes

Source

package.scala

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

Returns the cube root of the given Double value.

Value parameters

the number to take the cube root of

Attributes

Returns

the value ∛x

Source

package.scala

Returns the square root of a Double value.

Value parameters

the number to take the square root of

Attributes

Returns

the value √x

Source

package.scala

Polar Coordinates

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

Value parameters

the ordinate coordinate

the abscissa coordinate

Attributes

Returns

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

Source

package.scala

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.

Attributes

Source

package.scala

Unit of Least Precision

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

Attributes

Source

package.scala

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

Attributes

Source

package.scala

Pseudo Random Number Generation

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

Attributes

Source

package.scala

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

Adjacent Floats

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.

Attributes

Companion

object

Source

BigDecimal.scala

Supertypes

class ScalaNumber

Show all

A type with efficient encoding of arbitrary integers.

It wraps java.math.BigInteger, with optimization for small values that can be encoded in a Long.

Attributes

Companion

object

Source

BigInt.scala

Supertypes

class ScalaNumber

Show all

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:

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.

Attributes

Companion

object

Source

Equiv.scala

Supertypes

Known subtypes

Attributes

Source

Equiv.scala

Supertypes

Known subtypes

Self type

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.

Attributes

Companion

trait

Source

Ordering.scala

Supertypes

Self type

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.