Scala example source code file (BigInt.scala)

This example Scala source code file (BigInt.scala) is included in my "Source Code Warehouse" project. The intent of this project is to help you more easily find Scala source code examples by using tags.

All credit for the original source code belongs to scala-lang.org; I'm just trying to make examples easier to find. (For my Scala work, see my Scala examples and tutorials.)

Scala tags/keywords

array, bigint, biginteger, boolean, double, int, long, scalanumericconversions, serializable, string

The BigInt.scala Scala example source code

/*                     __                                               *\
**     ________ ___   / /  ___     Scala API                            **
**    / __/ __// _ | / /  / _ |    (c) 2006-2013, LAMP/EPFL             **
**  __\ \/ /__/ __ |/ /__/ __ |    http://scala-lang.org/               **
** /____/\___/_/ |_/____/_/ | |                                         **
**                          |/                                          **
\*                                                                      */

package scala
package math

import java.math.BigInteger
import scala.language.implicitConversions

/**
 *  @author  Martin Odersky
 *  @version 1.0, 15/07/2003
 *  @since 2.1
 */
object BigInt {

  private val minCached = -1024
  private val maxCached = 1024
  private val cache = new Array[BigInt](maxCached - minCached + 1)
  private val minusOne = BigInteger.valueOf(-1)

  /** Constructs a `BigInt` whose value is equal to that of the
   *  specified integer value.
   *
   *  @param i the specified integer value
   *  @return  the constructed `BigInt`
   */
  def apply(i: Int): BigInt =
    if (minCached <= i && i <= maxCached) {
      val offset = i - minCached
      var n = cache(offset)
      if (n eq null) { n = new BigInt(BigInteger.valueOf(i.toLong)); cache(offset) = n }
      n
    } else new BigInt(BigInteger.valueOf(i.toLong))

  /** Constructs a `BigInt` whose value is equal to that of the
   *  specified long value.
   *
   *  @param l the specified long value
   *  @return  the constructed `BigInt`
   */
  def apply(l: Long): BigInt =
    if (minCached <= l && l <= maxCached) apply(l.toInt)
    else new BigInt(BigInteger.valueOf(l))

  /** Translates a byte array containing the two's-complement binary
   *  representation of a BigInt into a BigInt.
   */
  def apply(x: Array[Byte]): BigInt =
    new BigInt(new BigInteger(x))

  /** Translates the sign-magnitude representation of a BigInt into a BigInt.
   */
  def apply(signum: Int, magnitude: Array[Byte]): BigInt =
    new BigInt(new BigInteger(signum, magnitude))

  /** Constructs a randomly generated positive BigInt that is probably prime,
   *  with the specified bitLength.
   */
  def apply(bitlength: Int, certainty: Int, rnd: scala.util.Random): BigInt =
    new BigInt(new BigInteger(bitlength, certainty, rnd.self))

  /** Constructs a randomly generated BigInt, uniformly distributed over the
   *  range `0` to `(2 ^ numBits - 1)`, inclusive.
   */
  def apply(numbits: Int, rnd: scala.util.Random): BigInt =
    new BigInt(new BigInteger(numbits, rnd.self))

  /** Translates the decimal String representation of a BigInt into a BigInt.
   */
  def apply(x: String): BigInt =
    new BigInt(new BigInteger(x))

  /** Translates the string representation of a `BigInt` in the
   *  specified `radix` into a BigInt.
   */
  def apply(x: String, radix: Int): BigInt =
    new BigInt(new BigInteger(x, radix))

  /** Translates a `java.math.BigInteger` into a BigInt.
   */
  def apply(x: BigInteger): BigInt =
    new BigInt(x)

  /** Returns a positive BigInt that is probably prime, with the specified bitLength.
   */
  def probablePrime(bitLength: Int, rnd: scala.util.Random): BigInt =
    new BigInt(BigInteger.probablePrime(bitLength, rnd.self))

  /** Implicit conversion from `Int` to `BigInt`.
   */
  implicit def int2bigInt(i: Int): BigInt = apply(i)

  /** Implicit conversion from `Long` to `BigInt`.
   */
  implicit def long2bigInt(l: Long): BigInt = apply(l)

  /** Implicit conversion from `java.math.BigInteger` to `scala.BigInt`.
   */
  implicit def javaBigInteger2bigInt(x: BigInteger): BigInt = apply(x)
}

/**
 *  @author  Martin Odersky
 *  @version 1.0, 15/07/2003
 */
final class BigInt(val bigInteger: BigInteger) extends ScalaNumber with ScalaNumericConversions with Serializable {
  /** Returns the hash code for this BigInt. */
  override def hashCode(): Int =
    if (isValidLong) unifiedPrimitiveHashcode()
    else bigInteger.##

  /** Compares this BigInt with the specified value for equality.
   */
  override def equals(that: Any): Boolean = that match {
    case that: BigInt     => this equals that
    case that: BigDecimal => that equals this
    case that: Double     => isValidDouble && toDouble == that
    case that: Float      => isValidFloat && toFloat == that
    case x                => isValidLong && unifiedPrimitiveEquals(x)
  }
  override def isValidByte  = this >= Byte.MinValue && this <= Byte.MaxValue
  override def isValidShort = this >= Short.MinValue && this <= Short.MaxValue
  override def isValidChar  = this >= Char.MinValue && this <= Char.MaxValue
  override def isValidInt   = this >= Int.MinValue && this <= Int.MaxValue
           def isValidLong  = this >= Long.MinValue && this <= Long.MaxValue
  /** Returns `true` iff this can be represented exactly by [[scala.Float]]; otherwise returns `false`.
    */
  def isValidFloat = {
    val bitLen = bitLength
    (bitLen <= 24 ||
      {
        val lowest = lowestSetBit
        bitLen <= java.lang.Float.MAX_EXPONENT + 1 && // exclude this < -2^128 && this >= 2^128
        lowest >= bitLen - 24 &&
        lowest < java.lang.Float.MAX_EXPONENT + 1 // exclude this == -2^128
      }
    ) && !bitLengthOverflow
  }
  /** Returns `true` iff this can be represented exactly by [[scala.Double]]; otherwise returns `false`.
    */
  def isValidDouble = {
    val bitLen = bitLength
    (bitLen <= 53 ||
      {
        val lowest = lowestSetBit
        bitLen <= java.lang.Double.MAX_EXPONENT + 1 && // exclude this < -2^1024 && this >= 2^1024
        lowest >= bitLen - 53 &&
        lowest < java.lang.Double.MAX_EXPONENT + 1 // exclude this == -2^1024
      }
    ) && !bitLengthOverflow
  }
  /** Some implementations of java.math.BigInteger allow huge values with bit length greater than Int.MaxValue .
   * The BigInteger.bitLength method returns truncated bit length in this case .
   * This method tests if result of bitLength is valid.
   * This method will become unnecessary if BigInt constructors reject huge BigIntegers.
   */
  private def bitLengthOverflow = {
    val shifted = bigInteger.shiftRight(Int.MaxValue)
    (shifted.signum != 0) && !(shifted equals BigInt.minusOne)
  }

  def isWhole() = true
  def underlying = bigInteger

  /** Compares this BigInt with the specified BigInt for equality.
   */
  def equals (that: BigInt): Boolean = compare(that) == 0

  /** Compares this BigInt with the specified BigInt
   */
  def compare (that: BigInt): Int = this.bigInteger.compareTo(that.bigInteger)

  /** Less-than-or-equals comparison of BigInts
   */
  def <= (that: BigInt): Boolean = compare(that) <= 0

  /** Greater-than-or-equals comparison of BigInts
   */
  def >= (that: BigInt): Boolean = compare(that) >= 0

  /** Less-than of BigInts
   */
  def <  (that: BigInt): Boolean = compare(that) <  0

  /** Greater-than comparison of BigInts
   */
  def >  (that: BigInt): Boolean = compare(that) > 0

  /** Addition of BigInts
   */
  def +  (that: BigInt): BigInt = new BigInt(this.bigInteger.add(that.bigInteger))

  /** Subtraction of BigInts
   */
  def -  (that: BigInt): BigInt = new BigInt(this.bigInteger.subtract(that.bigInteger))

  /** Multiplication of BigInts
   */
  def *  (that: BigInt): BigInt = new BigInt(this.bigInteger.multiply(that.bigInteger))

  /** Division of BigInts
   */
  def /  (that: BigInt): BigInt = new BigInt(this.bigInteger.divide(that.bigInteger))

  /** Remainder of BigInts
   */
  def %  (that: BigInt): BigInt = new BigInt(this.bigInteger.remainder(that.bigInteger))

  /** Returns a pair of two BigInts containing (this / that) and (this % that).
   */
  def /% (that: BigInt): (BigInt, BigInt) = {
    val dr = this.bigInteger.divideAndRemainder(that.bigInteger)
    (new BigInt(dr(0)), new BigInt(dr(1)))
  }

  /** Leftshift of BigInt
   */
  def << (n: Int): BigInt = new BigInt(this.bigInteger.shiftLeft(n))

  /** (Signed) rightshift of BigInt
   */
  def >> (n: Int): BigInt = new BigInt(this.bigInteger.shiftRight(n))

  /** Bitwise and of BigInts
   */
  def &  (that: BigInt): BigInt = new BigInt(this.bigInteger.and(that.bigInteger))

  /** Bitwise or of BigInts
   */
  def |  (that: BigInt): BigInt = new BigInt(this.bigInteger.or (that.bigInteger))

  /** Bitwise exclusive-or of BigInts
   */
  def ^  (that: BigInt): BigInt = new BigInt(this.bigInteger.xor(that.bigInteger))

  /** Bitwise and-not of BigInts. Returns a BigInt whose value is (this & ~that).
   */
  def &~ (that: BigInt): BigInt = new BigInt(this.bigInteger.andNot(that.bigInteger))

  /** Returns the greatest common divisor of abs(this) and abs(that)
   */
  def gcd (that: BigInt): BigInt = new BigInt(this.bigInteger.gcd(that.bigInteger))

  /** Returns a BigInt whose value is (this mod that).
   *  This method differs from `%` in that it always returns a non-negative BigInt.
   */
  def mod (that: BigInt): BigInt = new BigInt(this.bigInteger.mod(that.bigInteger))

  /** Returns the minimum of this and that
   */
  def min (that: BigInt): BigInt = new BigInt(this.bigInteger.min(that.bigInteger))

  /** Returns the maximum of this and that
   */
  def max (that: BigInt): BigInt = new BigInt(this.bigInteger.max(that.bigInteger))

  /** Returns a BigInt whose value is (<tt>this</tt> raised to the power of <tt>exp</tt>).
   */
  def pow (exp: Int): BigInt = new BigInt(this.bigInteger.pow(exp))

  /** Returns a BigInt whose value is
   *  (<tt>this</tt> raised to the power of <tt>exp</tt> modulo <tt>m</tt>).
   */
  def modPow (exp: BigInt, m: BigInt): BigInt =
    new BigInt(this.bigInteger.modPow(exp.bigInteger, m.bigInteger))

  /** Returns a BigInt whose value is (the inverse of <tt>this</tt> modulo <tt>m</tt>).
   */
  def modInverse (m: BigInt): BigInt = new BigInt(this.bigInteger.modInverse(m.bigInteger))

  /** Returns a BigInt whose value is the negation of this BigInt
   */
  def unary_- : BigInt   = new BigInt(this.bigInteger.negate())

  /** Returns the absolute value of this BigInt
   */
  def abs: BigInt = new BigInt(this.bigInteger.abs())

  /** Returns the sign of this BigInt, i.e.
   *   -1 if it is less than 0,
   *   +1 if it is greater than 0
   *   0  if it is equal to 0
   */
  def signum: Int = this.bigInteger.signum()

  /** Returns the bitwise complement of this BigInt
   */
  def unary_~ : BigInt = new BigInt(this.bigInteger.not())

  /** Returns true if and only if the designated bit is set.
   */
  def testBit (n: Int): Boolean = this.bigInteger.testBit(n)

  /** Returns a BigInt whose value is equivalent to this BigInt with the designated bit set.
   */
  def setBit  (n: Int): BigInt  = new BigInt(this.bigInteger.setBit(n))

  /** Returns a BigInt whose value is equivalent to this BigInt with the designated bit cleared.
   */
  def clearBit(n: Int): BigInt  = new BigInt(this.bigInteger.clearBit(n))

  /** Returns a BigInt whose value is equivalent to this BigInt with the designated bit flipped.
   */
  def flipBit (n: Int): BigInt  = new BigInt(this.bigInteger.flipBit(n))

  /** Returns the index of the rightmost (lowest-order) one bit in this BigInt
   * (the number of zero bits to the right of the rightmost one bit).
   */
  def lowestSetBit: Int         = this.bigInteger.getLowestSetBit()

  /** Returns the number of bits in the minimal two's-complement representation of this BigInt,
   *  excluding a sign bit.
   */
  def bitLength: Int            = this.bigInteger.bitLength()

  /** Returns the number of bits in the two's complement representation of this BigInt
   *  that differ from its sign bit.
   */
  def bitCount: Int             = this.bigInteger.bitCount()

  /** Returns true if this BigInt is probably prime, false if it's definitely composite.
   *  @param certainty  a measure of the uncertainty that the caller is willing to tolerate:
   *                    if the call returns true the probability that this BigInt is prime
   *                    exceeds (1 - 1/2 ^ certainty).
   *                    The execution time of this method is proportional to the value of
   *                    this parameter.
   */
  def isProbablePrime(certainty: Int) = this.bigInteger.isProbablePrime(certainty)

  /** Converts this BigInt to a <tt>byte</tt>.
   *  If the BigInt is too big to fit in a byte, only the low-order 8 bits are returned.
   *  Note that this conversion can lose information about the overall magnitude of the
   *  BigInt value as well as return a result with the opposite sign.
   */
  override def byteValue   = intValue.toByte

  /** Converts this BigInt to a <tt>short</tt>.
   *  If the BigInt is too big to fit in a short, only the low-order 16 bits are returned.
   *  Note that this conversion can lose information about the overall magnitude of the
   *  BigInt value as well as return a result with the opposite sign.
   */
  override def shortValue  = intValue.toShort

  /** Converts this BigInt to a <tt>char</tt>.
   *  If the BigInt is too big to fit in a char, only the low-order 16 bits are returned.
   *  Note that this conversion can lose information about the overall magnitude of the
   *  BigInt value and that it always returns a positive result.
   */
  def charValue   = intValue.toChar

  /** Converts this BigInt to an <tt>int</tt>.
   *  If the BigInt is too big to fit in an int, only the low-order 32 bits
   *  are returned. Note that this conversion can lose information about the
   *  overall magnitude of the BigInt value as well as return a result with
   *  the opposite sign.
   */
  def intValue    = this.bigInteger.intValue

  /** Converts this BigInt to a <tt>long</tt>.
   *  If the BigInt is too big to fit in a long, only the low-order 64 bits
   *  are returned. Note that this conversion can lose information about the
   *  overall magnitude of the BigInt value as well as return a result with
   *  the opposite sign.
   */
  def longValue   = this.bigInteger.longValue

  /** Converts this `BigInt` to a `float`.
   *  If this `BigInt` has too great a magnitude to represent as a float,
   *  it will be converted to `Float.NEGATIVE_INFINITY` or
   *  `Float.POSITIVE_INFINITY` as appropriate.
   */
  def floatValue  = this.bigInteger.floatValue

  /** Converts this `BigInt` to a `double`.
   *  if this `BigInt` has too great a magnitude to represent as a double,
   *  it will be converted to `Double.NEGATIVE_INFINITY` or
   *  `Double.POSITIVE_INFINITY` as appropriate.
   */
  def doubleValue = this.bigInteger.doubleValue

  /** Create a `NumericRange[BigInt]` in range `[start;end)`
   *  with the specified step, where start is the target BigInt.
   *
   *  @param end    the end value of the range (exclusive)
   *  @param step   the distance between elements (defaults to 1)
   *  @return       the range
   */
  def until(end: BigInt, step: BigInt = BigInt(1)) = Range.BigInt(this, end, step)

  /** Like until, but inclusive of the end value.
   */
  def to(end: BigInt, step: BigInt = BigInt(1)) = Range.BigInt.inclusive(this, end, step)

  /** Returns the decimal String representation of this BigInt.
   */
  override def toString(): String = this.bigInteger.toString()

  /** Returns the String representation in the specified radix of this BigInt.
   */
  def toString(radix: Int): String = this.bigInteger.toString(radix)

  /** Returns a byte array containing the two's-complement representation of
   *  this BigInt. The byte array will be in big-endian byte-order: the most
   *  significant byte is in the zeroth element. The array will contain the
   *  minimum number of bytes required to represent this BigInt, including at
   *  least one sign bit.
   */
  def toByteArray: Array[Byte] = this.bigInteger.toByteArray()
}