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/* __ *\
** ________ ___ / / ___ Scala API **
** / __/ __// _ | / / / _ | (c) 2006-2013, LAMP/EPFL **
** __\ \/ /__/ __ |/ /__/ __ | http://scala-lang.org/ **
** /____/\___/_/ |_/____/_/ | | **
** |/ **
\* */
package scala.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)
@deprecated("Use Long.MinValue", "2.9.0")
val MinLong = BigInt(Long.MinValue)
@deprecated("Use Long.MaxValue", "2.9.0")
val MaxLong = BigInt(Long.MaxValue)
/** 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)); cache(offset) = n }
n
} else new BigInt(BigInteger.valueOf(i))
/** 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
*/
@deprecatedInheritance("This class will me made final.", "2.10.0")
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.toBigIntExact exists (this equals _)
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 m).
* 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()
@deprecated("Use ~bigInt (the unary_~ method) instead", "2.10.0")
def ~ : BigInt = ~this
/** 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 a 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()
}
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