scala.math.Numeric

trait Numeric[T] extends Ordering[T]

Type Members

class Ops extends AnyRef

Concrete Value Members From java.util.Comparator

def reversed(): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

def thenComparing(arg0: Comparator[_ >: T]): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

def thenComparingDouble(arg0: ToDoubleFunction[_ >: T]): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

def thenComparingInt(arg0: ToIntFunction[_ >: T]): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

def thenComparingLong(arg0: ToLongFunction[_ >: T]): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

def thenComparing[U <: Comparable[_ >: U]](arg0: java.util.function.Function[_ >: T, _ <: U]): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

def thenComparing[U](arg0: java.util.function.Function[_ >: T, _ <: U], arg1: Comparator[_ >: U]): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

Abstract Value Members From scala.math.Numeric

abstract def fromInt(x: Int): T

(defined at scala.math.Numeric)

abstract def minus(x: T, y: T): T

(defined at scala.math.Numeric)

abstract def negate(x: T): T

(defined at scala.math.Numeric)

abstract def plus(x: T, y: T): T

(defined at scala.math.Numeric)

abstract def times(x: T, y: T): T

(defined at scala.math.Numeric)

abstract def toDouble(x: T): Double

(defined at scala.math.Numeric)

abstract def toFloat(x: T): Float

(defined at scala.math.Numeric)

abstract def toInt(x: T): Int

(defined at scala.math.Numeric)

abstract def toLong(x: T): Long

(defined at scala.math.Numeric)

Concrete Value Members From scala.math.Numeric

def abs(x: T): T

(defined at scala.math.Numeric)

implicit def mkNumericOps(lhs: T): Ops

(defined at scala.math.Numeric)

def signum(x: T): Int

(defined at scala.math.Numeric)

Abstract Value Members From scala.math.Ordering

abstract def compare(x: T, y: T): Int

Returns an integer whose sign communicates how x compares to y.

The result sign has the following meaning:

  • negative if x < y
  • positive if x > y

  • zero otherwise (if x == y)

  • Definition Classes
    • Ordering → Comparator

(defined at scala.math.Ordering)

Concrete Value Members From scala.math.Ordering

def equiv(x: T, y: T): Boolean

Return true if x == y in the ordering.

  • Definition Classes
    • Ordering → PartialOrdering → Equiv

(defined at scala.math.Ordering)

def gt(x: T, y: T): Boolean

Return true if x > y in the ordering.

  • Definition Classes
    • Ordering → PartialOrdering

(defined at scala.math.Ordering)

def gteq(x: T, y: T): Boolean

Return true if x >= y in the ordering.

  • Definition Classes
    • Ordering → PartialOrdering

(defined at scala.math.Ordering)

def lt(x: T, y: T): Boolean

Return true if x < y in the ordering.

  • Definition Classes
    • Ordering → PartialOrdering

(defined at scala.math.Ordering)

def lteq(x: T, y: T): Boolean

Return true if x <= y in the ordering.

  • Definition Classes
    • Ordering → PartialOrdering

(defined at scala.math.Ordering)

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

Return x if x >= y , otherwise y .

  • Definition Classes
    • Ordering

(defined at scala.math.Ordering)

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

Return x if x <= y , otherwise y .

  • Definition Classes
    • Ordering

(defined at scala.math.Ordering)

implicit def mkOrderingOps(lhs: T): Numeric.Ops

This implicit method augments T with the comparison operators defined in scala.math.Ordering.Ops .

  • Definition Classes
    • Ordering

(defined at scala.math.Ordering)

def on[U](f: (U) ⇒ T): Ordering[U]

Given f, a function from U into T, creates an Ordering[U] whose compare function is equivalent to:

def compare(x:U, y:U) = Ordering[T].compare(f(x), f(y))
  • Definition Classes
    • Ordering

(defined at scala.math.Ordering)

def reverse: Ordering[T]

Return the opposite ordering of this one.

  • Definition Classes
    • Ordering → PartialOrdering

(defined at scala.math.Ordering)

def tryCompare(x: T, y: T): Some[Int]

Returns whether a comparison between x and y is defined, and if so the result of compare(x, y) .

  • Definition Classes
    • Ordering → PartialOrdering (defined at scala.math.Ordering)

Full Source:

/*                     __                                               *\
**     ________ ___   / /  ___     Scala API                            **
**    / __/ __// _ | / /  / _ |    (c) 2003-2013, LAMP/EPFL             **
**  __\ \/ /__/ __ |/ /__/ __ |    http://scala-lang.org/               **
** /____/\___/_/ |_/____/_/ | |                                         **
**                          |/                                          **
\*                                                                      */

package scala
package math

import scala.language.implicitConversions

/**
 * @since 2.8
 */
object Numeric {
  trait ExtraImplicits {
    /** These implicits create conversions from a value for which an implicit Numeric
     *  exists to the inner class which creates infix operations.  Once imported, you
     *  can write methods as follows:
     *  {{{
     *  def plus[T: Numeric](x: T, y: T) = x + y
     *  }}}
     */
    implicit def infixNumericOps[T](x: T)(implicit num: Numeric[T]): Numeric[T]#Ops = new num.Ops(x)
  }
  object Implicits extends ExtraImplicits { }

  trait BigIntIsIntegral extends Integral[BigInt] {
    def plus(x: BigInt, y: BigInt): BigInt = x + y
    def minus(x: BigInt, y: BigInt): BigInt = x - y
    def times(x: BigInt, y: BigInt): BigInt = x * y
    def quot(x: BigInt, y: BigInt): BigInt = x / y
    def rem(x: BigInt, y: BigInt): BigInt = x % y
    def negate(x: BigInt): BigInt = -x
    def fromInt(x: Int): BigInt = BigInt(x)
    def toInt(x: BigInt): Int = x.intValue
    def toLong(x: BigInt): Long = x.longValue
    def toFloat(x: BigInt): Float = x.floatValue
    def toDouble(x: BigInt): Double = x.doubleValue
  }
  implicit object BigIntIsIntegral extends BigIntIsIntegral with Ordering.BigIntOrdering

  trait IntIsIntegral extends Integral[Int] {
    def plus(x: Int, y: Int): Int = x + y
    def minus(x: Int, y: Int): Int = x - y
    def times(x: Int, y: Int): Int = x * y
    def quot(x: Int, y: Int): Int = x / y
    def rem(x: Int, y: Int): Int = x % y
    def negate(x: Int): Int = -x
    def fromInt(x: Int): Int = x
    def toInt(x: Int): Int = x
    def toLong(x: Int): Long = x.toLong
    def toFloat(x: Int): Float = x.toFloat
    def toDouble(x: Int): Double = x.toDouble
  }
  implicit object IntIsIntegral extends IntIsIntegral with Ordering.IntOrdering

  trait ShortIsIntegral extends Integral[Short] {
    def plus(x: Short, y: Short): Short = (x + y).toShort
    def minus(x: Short, y: Short): Short = (x - y).toShort
    def times(x: Short, y: Short): Short = (x * y).toShort
    def quot(x: Short, y: Short): Short = (x / y).toShort
    def rem(x: Short, y: Short): Short = (x % y).toShort
    def negate(x: Short): Short = (-x).toShort
    def fromInt(x: Int): Short = x.toShort
    def toInt(x: Short): Int = x.toInt
    def toLong(x: Short): Long = x.toLong
    def toFloat(x: Short): Float = x.toFloat
    def toDouble(x: Short): Double = x.toDouble
  }
  implicit object ShortIsIntegral extends ShortIsIntegral with Ordering.ShortOrdering

  trait ByteIsIntegral extends Integral[Byte] {
    def plus(x: Byte, y: Byte): Byte = (x + y).toByte
    def minus(x: Byte, y: Byte): Byte = (x - y).toByte
    def times(x: Byte, y: Byte): Byte = (x * y).toByte
    def quot(x: Byte, y: Byte): Byte = (x / y).toByte
    def rem(x: Byte, y: Byte): Byte = (x % y).toByte
    def negate(x: Byte): Byte = (-x).toByte
    def fromInt(x: Int): Byte = x.toByte
    def toInt(x: Byte): Int = x.toInt
    def toLong(x: Byte): Long = x.toLong
    def toFloat(x: Byte): Float = x.toFloat
    def toDouble(x: Byte): Double = x.toDouble
  }
  implicit object ByteIsIntegral extends ByteIsIntegral with Ordering.ByteOrdering

  trait CharIsIntegral extends Integral[Char] {
    def plus(x: Char, y: Char): Char = (x + y).toChar
    def minus(x: Char, y: Char): Char = (x - y).toChar
    def times(x: Char, y: Char): Char = (x * y).toChar
    def quot(x: Char, y: Char): Char = (x / y).toChar
    def rem(x: Char, y: Char): Char = (x % y).toChar
    def negate(x: Char): Char = (-x).toChar
    def fromInt(x: Int): Char = x.toChar
    def toInt(x: Char): Int = x.toInt
    def toLong(x: Char): Long = x.toLong
    def toFloat(x: Char): Float = x.toFloat
    def toDouble(x: Char): Double = x.toDouble
  }
  implicit object CharIsIntegral extends CharIsIntegral with Ordering.CharOrdering

  trait LongIsIntegral extends Integral[Long] {
    def plus(x: Long, y: Long): Long = x + y
    def minus(x: Long, y: Long): Long = x - y
    def times(x: Long, y: Long): Long = x * y
    def quot(x: Long, y: Long): Long = x / y
    def rem(x: Long, y: Long): Long = x % y
    def negate(x: Long): Long = -x
    def fromInt(x: Int): Long = x.toLong
    def toInt(x: Long): Int = x.toInt
    def toLong(x: Long): Long = x
    def toFloat(x: Long): Float = x.toFloat
    def toDouble(x: Long): Double = x.toDouble
  }
  implicit object LongIsIntegral extends LongIsIntegral with Ordering.LongOrdering

  trait FloatIsConflicted extends Numeric[Float] {
    def plus(x: Float, y: Float): Float = x + y
    def minus(x: Float, y: Float): Float = x - y
    def times(x: Float, y: Float): Float = x * y
    def negate(x: Float): Float = -x
    def fromInt(x: Int): Float = x.toFloat
    def toInt(x: Float): Int = x.toInt
    def toLong(x: Float): Long = x.toLong
    def toFloat(x: Float): Float = x
    def toDouble(x: Float): Double = x.toDouble
    // logic in Numeric base trait mishandles abs(-0.0f)
    override def abs(x: Float): Float = math.abs(x)
  }
  trait FloatIsFractional extends FloatIsConflicted with Fractional[Float] {
    def div(x: Float, y: Float): Float = x / y
  }
  trait FloatAsIfIntegral extends FloatIsConflicted with Integral[Float] {
    def quot(x: Float, y: Float): Float = (BigDecimal(x) quot BigDecimal(y)).floatValue
    def rem(x: Float, y: Float): Float = (BigDecimal(x) remainder BigDecimal(y)).floatValue
  }
  implicit object FloatIsFractional extends FloatIsFractional with Ordering.FloatOrdering
  object FloatAsIfIntegral extends FloatAsIfIntegral with Ordering.FloatOrdering {
  }

  trait DoubleIsConflicted extends Numeric[Double] {
    def plus(x: Double, y: Double): Double = x + y
    def minus(x: Double, y: Double): Double = x - y
    def times(x: Double, y: Double): Double = x * y
    def negate(x: Double): Double = -x
    def fromInt(x: Int): Double = x.toDouble
    def toInt(x: Double): Int = x.toInt
    def toLong(x: Double): Long = x.toLong
    def toFloat(x: Double): Float = x.toFloat
    def toDouble(x: Double): Double = x
    // logic in Numeric base trait mishandles abs(-0.0)
    override def abs(x: Double): Double = math.abs(x)
  }
  trait DoubleIsFractional extends DoubleIsConflicted with Fractional[Double] {
    def div(x: Double, y: Double): Double = x / y
  }
  trait DoubleAsIfIntegral extends DoubleIsConflicted with Integral[Double] {
    def quot(x: Double, y: Double): Double = (BigDecimal(x) quot BigDecimal(y)).doubleValue
    def rem(x: Double, y: Double): Double = (BigDecimal(x) remainder BigDecimal(y)).doubleValue
  }

  trait BigDecimalIsConflicted extends Numeric[BigDecimal] {
    def plus(x: BigDecimal, y: BigDecimal): BigDecimal = x + y
    def minus(x: BigDecimal, y: BigDecimal): BigDecimal = x - y
    def times(x: BigDecimal, y: BigDecimal): BigDecimal = x * y
    def negate(x: BigDecimal): BigDecimal = -x
    def fromInt(x: Int): BigDecimal = BigDecimal(x)
    def toInt(x: BigDecimal): Int = x.intValue
    def toLong(x: BigDecimal): Long = x.longValue
    def toFloat(x: BigDecimal): Float = x.floatValue
    def toDouble(x: BigDecimal): Double = x.doubleValue
  }

  trait BigDecimalIsFractional extends BigDecimalIsConflicted with Fractional[BigDecimal] {
    def div(x: BigDecimal, y: BigDecimal): BigDecimal = x / y
  }
  trait BigDecimalAsIfIntegral extends BigDecimalIsConflicted with Integral[BigDecimal] {
    def quot(x: BigDecimal, y: BigDecimal): BigDecimal = x quot y
    def rem(x: BigDecimal, y: BigDecimal): BigDecimal = x remainder y
  }

  // For Double and BigDecimal we offer implicit Fractional objects, but also one
  // which acts like an Integral type, which is useful in NumericRange.
  implicit object BigDecimalIsFractional extends BigDecimalIsFractional with Ordering.BigDecimalOrdering
  object BigDecimalAsIfIntegral extends BigDecimalAsIfIntegral with Ordering.BigDecimalOrdering

  implicit object DoubleIsFractional extends DoubleIsFractional with Ordering.DoubleOrdering
  object DoubleAsIfIntegral extends DoubleAsIfIntegral with Ordering.DoubleOrdering
}

trait Numeric[T] extends Ordering[T] {
  def plus(x: T, y: T): T
  def minus(x: T, y: T): T
  def times(x: T, y: T): T
  def negate(x: T): T
  def fromInt(x: Int): T
  def toInt(x: T): Int
  def toLong(x: T): Long
  def toFloat(x: T): Float
  def toDouble(x: T): Double

  def zero = fromInt(0)
  def one = fromInt(1)

  def abs(x: T): T = if (lt(x, zero)) negate(x) else x
  def signum(x: T): Int =
    if (lt(x, zero)) -1
    else if (gt(x, zero)) 1
    else 0

  class Ops(lhs: T) {
    def +(rhs: T) = plus(lhs, rhs)
    def -(rhs: T) = minus(lhs, rhs)
    def *(rhs: T) = times(lhs, rhs)
    def unary_-() = negate(lhs)
    def abs(): T = Numeric.this.abs(lhs)
    def signum(): Int = Numeric.this.signum(lhs)
    def toInt(): Int = Numeric.this.toInt(lhs)
    def toLong(): Long = Numeric.this.toLong(lhs)
    def toFloat(): Float = Numeric.this.toFloat(lhs)
    def toDouble(): Double = Numeric.this.toDouble(lhs)
  }
  implicit def mkNumericOps(lhs: T): Ops = new Ops(lhs)
}