BigInt.scala

/*
 * Scala (https://www.scala-lang.org)
 *
 * Copyright EPFL and Lightbend, Inc.
 *
 * Licensed under Apache License 2.0
 * (http://www.apache.org/licenses/LICENSE-2.0).
 *
 * See the NOTICE file distributed with this work for
 * additional information regarding copyright ownership.
 */

package scala
package math

import java.math.BigInteger

import scala.annotation.nowarn
import scala.language.implicitConversions
import scala.collection.immutable.NumericRange

object BigInt {

  private val longMinValueBigInteger = BigInteger.valueOf(Long.MinValue)
  private val longMinValue = new BigInt(longMinValueBigInteger, Long.MinValue)

  private[this] val minCached = -1024
  private[this] val maxCached = 1024
  private[this] val cache = new Array[BigInt](maxCached - minCached + 1)

  private[this] def getCached(i: Int): BigInt = {
    val offset = i - minCached
    var n = cache(offset)
    if (n eq null) {
      n = new BigInt(null, i.toLong)
      cache(offset) = n
    }
    n
  }

  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) getCached(i) else apply(i: Long)

  /** 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) getCached(l.toInt)
    else if (l == Long.MinValue) longMinValue
    else new BigInt(null, l)

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

  /** Translates the sign-magnitude representation of a BigInt into a BigInt.
   *
   * @param  signum    signum of the number (-1 for negative, 0 for zero, 1
   *                   for positive).
   * @param  magnitude big-endian binary representation of the magnitude of
   *                   the number.
   */
  def apply(signum: Int, magnitude: Array[Byte]): BigInt =
    apply(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 =
    apply(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 =
    apply(new BigInteger(numbits, rnd.self))

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

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

  /** Translates a `java.math.BigInteger` into a BigInt.
   */
  def apply(x: BigInteger): BigInt = {
    if (x.bitLength <= 63) {
      val l = x.longValue
      if (minCached <= l && l <= maxCached) getCached(l.toInt) else new BigInt(x, l)
    } else new BigInt(x, Long.MinValue)
  }

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

  // this method is adapted from Google Guava's version at
  //   https://github.com/google/guava/blob/master/guava/src/com/google/common/math/LongMath.java
  // that code carries the following notice:
  //   * Copyright (C) 2011 The Guava Authors
  //   *
  //   * Licensed under the Apache License, Version 2.0 (the "License")
  /**
   * Returns the greatest common divisor of a and b. Returns 0 if a == 0 && b == 0.
   */
  private def longGcd(a: Long, b: Long): Long = {
    // both a and b must be >= 0
    if (a == 0) { // 0 % b == 0, so b divides a, but the converse doesn't hold.
      // BigInteger.gcd is consistent with this decision.
      return b
    }
    else if (b == 0) return a // similar logic
    /*
     * Uses the binary GCD algorithm; see http://en.wikipedia.org/wiki/Binary_GCD_algorithm. This is
     * >60% faster than the Euclidean algorithm in benchmarks.
     */
    val aTwos = java.lang.Long.numberOfTrailingZeros(a)
    var a1 = a >> aTwos // divide out all 2s

    val bTwos = java.lang.Long.numberOfTrailingZeros(b)
    var b1 = b >> bTwos
    while (a1 != b1) { // both a, b are odd
      // The key to the binary GCD algorithm is as follows:
      // Both a1 and b1 are odd. Assume a1 > b1; then gcd(a1 - b1, b1) = gcd(a1, b1).
      // But in gcd(a1 - b1, b1), a1 - b1 is even and b1 is odd, so we can divide out powers of two.
      // We bend over backwards to avoid branching, adapting a technique from
      // http://graphics.stanford.edu/~seander/bithacks.html#IntegerMinOrMax
      val delta          = a1 - b1 // can't overflow, since a1 and b1 are nonnegative
      val minDeltaOrZero = delta & (delta >> (java.lang.Long.SIZE - 1))
      // equivalent to Math.min(delta, 0)
      a1 = delta - minDeltaOrZero - minDeltaOrZero // sets a to Math.abs(a - b)

      // a is now nonnegative and even
      b1 += minDeltaOrZero // sets b to min(old a, b)

      a1 >>= java.lang.Long.numberOfTrailingZeros(a1) // divide out all 2s, since 2 doesn't divide b

    }
    a1 << scala.math.min(aTwos, bTwos)
  }

}

/** 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`.
 */
final class BigInt private (private var _bigInteger: BigInteger, private val _long: Long)
  extends ScalaNumber
    with ScalaNumericConversions
    with Serializable
    with Ordered[BigInt]
{
  // The class has a special encoding for integer that fit in a Long *and* are not equal to Long.MinValue.
  //
  // The Long value Long.MinValue is a tag specifying that the integer is encoded in the BigInteger field.
  //
  // There are three possible states for the class fields (_bigInteger, _long)
  // 1. (null, l) where l != Long.MinValue, encodes the integer "l"
  // 2. (b, l) where l != Long.MinValue; then b is a BigInteger with value l, encodes "l" == "b"
  // 3a. (b, Long.MinValue) where b == Long.MinValue, encodes Long.MinValue
  // 3b. (b, Long.MinValue) where b does not fit in a Long, encodes "b"
  //
  // There is only one possible transition 1. -> 2., when the method .bigInteger is called, then the field
  // _bigInteger caches the result.
  //
  // The case 3a. is the only one where the BigInteger could actually fit in a Long, but as its value is used as a
  // tag, we'll take the slow path instead.
  //
  // Additionally, we know that if this.isValidLong is true, then _long is the encoded value.

  /** Public constructor present for compatibility. Use the BigInt.apply companion object method instead. */
  def this(bigInteger: BigInteger) = this(
    bigInteger, // even if it is a short BigInteger, we cache the instance
    if (bigInteger.bitLength <= 63)
      bigInteger.longValue // if _bigInteger is actually equal to Long.MinValue, no big deal, its value acts as a tag
    else Long.MinValue
  )

  /** Returns whether the integer is encoded in the Long. Returns true for all values fitting in a Long except
   *  Long.MinValue. */
  private def longEncoding: Boolean = _long != Long.MinValue

  def bigInteger: BigInteger = {
    val read = _bigInteger
    if (read ne null) read else {
      val write = BigInteger.valueOf(_long)
      _bigInteger = write // reference assignment is atomic; this is multi-thread safe (if possibly wasteful)
      write
    }
  }

  /** 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. */
  @nowarn("cat=other-non-cooperative-equals")
  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: Boolean = _long >= Byte.MinValue && _long <= Byte.MaxValue /* && longEncoding */
  override def isValidShort: Boolean = _long >= Short.MinValue && _long <= Short.MaxValue /* && longEncoding */
  override def isValidChar: Boolean = _long >= Char.MinValue && _long <= Char.MaxValue /* && longEncoding */
  override def isValidInt: Boolean = _long >= Int.MinValue && _long <= Int.MaxValue /* && longEncoding */
           def isValidLong: Boolean = longEncoding || _bigInteger == BigInt.longMinValueBigInteger // rhs of || tests == Long.MinValue

  /** Returns `true` iff this can be represented exactly by [[scala.Float]]; otherwise returns `false`.
    */
  def isValidFloat: Boolean = {
    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: Boolean = {
    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)
  }

  @deprecated("isWhole on an integer type is always true", "2.12.15")
  def isWhole: Boolean = true
  def underlying: BigInteger = bigInteger

  /** Compares this BigInt with the specified BigInt for equality.
   */
  def equals(that: BigInt): Boolean =
    if (this.longEncoding)
      that.longEncoding && (this._long == that._long)
    else
      !that.longEncoding && (this._bigInteger == that._bigInteger)

  /** Compares this BigInt with the specified BigInt
   */
  def compare(that: BigInt): Int =
    if (this.longEncoding) {
      if (that.longEncoding) java.lang.Long.compare(this._long, that._long) else -that._bigInteger.signum()
    } else {
      if (that.longEncoding) _bigInteger.signum() else this._bigInteger.compareTo(that._bigInteger)
    }

  /** Addition of BigInts
   */
  def +(that: BigInt): BigInt = {
    if (this.longEncoding && that.longEncoding) { // fast path
      val x = this._long
      val y = that._long
      val z = x + y
      if ((~(x ^ y) & (x ^ z)) >= 0L) return BigInt(z)
    }
    BigInt(this.bigInteger.add(that.bigInteger))
  }

  /** Subtraction of BigInts
   */
  def -(that: BigInt): BigInt = {
    if (this.longEncoding && that.longEncoding) { // fast path
      val x = this._long
      val y = that._long
      val z = x - y
      if (((x ^ y) & (x ^ z)) >= 0L) return BigInt(z)
    }
    BigInt(this.bigInteger.subtract(that.bigInteger))
  }

  /** Multiplication of BigInts
   */
  def *(that: BigInt): BigInt = {
    if (this.longEncoding && that.longEncoding) { // fast path
      val x = this._long
      val y = that._long
      val z = x * y
      // original code checks the y != Long.MinValue, but when longEncoding is true, that is never the case
      // if (x == 0 || (y == z / x && !(x == -1 && y == Long.MinValue))) return BigInt(z)
      if (x == 0 || y == z / x) return BigInt(z)
    }
    BigInt(this.bigInteger.multiply(that.bigInteger))
  }

  /** Division of BigInts
   */
  def /(that: BigInt): BigInt =
  // in the fast path, note that the original code avoided storing -Long.MinValue in a long:
  //    if (this._long != Long.MinValue || that._long != -1) return BigInt(this._long / that._long)
  // but we know this._long cannot be Long.MinValue, because Long.MinValue is the tag for bigger integers
    if (this.longEncoding && that.longEncoding) BigInt(this._long / that._long)
    else BigInt(this.bigInteger.divide(that.bigInteger))

  /** Remainder of BigInts
   */
  def %(that: BigInt): BigInt =
  // see / for the original logic regarding Long.MinValue
    if (this.longEncoding && that.longEncoding) BigInt(this._long % that._long)
    else BigInt(this.bigInteger.remainder(that.bigInteger))

  /** Returns a pair of two BigInts containing (this / that) and (this % that).
   */
  def /%(that: BigInt): (BigInt, BigInt) =
    if (this.longEncoding && that.longEncoding) {
      val x = this._long
      val y = that._long
      // original line: if (x != Long.MinValue || y != -1) return (BigInt(x / y), BigInt(x % y))
      (BigInt(x / y), BigInt(x % y))
    } else {
      val dr = this.bigInteger.divideAndRemainder(that.bigInteger)
      (BigInt(dr(0)), BigInt(dr(1)))
    }

  /** Leftshift of BigInt
   */
  def <<(n: Int): BigInt =
    if (longEncoding && n <= 0) (this >> (-n)) else BigInt(this.bigInteger.shiftLeft(n))

  /** (Signed) rightshift of BigInt
   */
  def >>(n: Int): BigInt =
    if (longEncoding && n >= 0) {
      if (n < 64) BigInt(_long >> n)
      else if (_long < 0) BigInt(-1)
      else BigInt(0) // for _long >= 0
    } else BigInt(this.bigInteger.shiftRight(n))
  
  /** Bitwise and of BigInts
   */
  def &(that: BigInt): BigInt =
    if (this.longEncoding && that.longEncoding)
      BigInt(this._long & that._long)
    else BigInt(this.bigInteger.and(that.bigInteger))

  /** Bitwise or of BigInts
   */
  def |(that: BigInt): BigInt =
    if (this.longEncoding && that.longEncoding)
      BigInt(this._long | that._long)
    else BigInt(this.bigInteger.or(that.bigInteger))

  /** Bitwise exclusive-or of BigInts
   */
  def ^(that: BigInt): BigInt =
    if (this.longEncoding && that.longEncoding)
      BigInt(this._long ^ that._long)
    else BigInt(this.bigInteger.xor(that.bigInteger))

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

  /** Returns the greatest common divisor of abs(this) and abs(that)
   */
  def gcd(that: BigInt): BigInt =
    if (this.longEncoding) {
      if (this._long == 0) return that.abs
      // if (this._long == Long.MinValue) return (-this) gcd that
      // this != 0 && this != Long.MinValue
      if (that.longEncoding) {
        if (that._long == 0) return this.abs
        // if (that._long == Long.MinValue) return this gcd (-that)
        BigInt(BigInt.longGcd(this._long.abs, that._long.abs))
      } else that gcd this // force the BigInteger on the left
    } else {
      // this is not a valid long
      if (that.longEncoding) {
        if (that._long == 0) return this.abs
        // if (that._long == Long.MinValue) return this gcd (-that)
        val red = (this._bigInteger mod BigInteger.valueOf(that._long.abs)).longValue()
        if (red == 0) return that.abs
        BigInt(BigInt.longGcd(that._long.abs, red))
      } else 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.
   *  @param that A positive number
   */
  def mod(that: BigInt): BigInt =
    if (this.longEncoding && that.longEncoding && that._long > 0) {
      val res = this._long % that._long
      if (res >= 0) BigInt(res) else BigInt(res + that._long)
    } else BigInt(this.bigInteger.mod(that.bigInteger))

  /** Returns the minimum of this and that
   */
  def min(that: BigInt): BigInt =
    if (this <= that) this else that

  /** Returns the maximum of this and that
   */
  def max(that: BigInt): BigInt =
    if (this >= that) this else that

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

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

  /** Returns the absolute value of this BigInt
   */
  def abs: BigInt = if (signum < 0) -this else this

  /** Returns the sign of this BigInt;
   *   -1 if it is less than 0,
   *   +1 if it is greater than 0,
   *   0  if it is equal to 0.
   */
  def signum: Int = if (longEncoding) java.lang.Long.signum(_long) else _bigInteger.signum()

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

  /** Returns the bitwise complement of this BigInt
   */
  def unary_~ : BigInt =
    // it is equal to -(this + 1)
    if (longEncoding && _long != Long.MaxValue) BigInt(-(_long + 1)) else BigInt(this.bigInteger.not())

  /** Returns true if and only if the designated bit is set.
   */
  def testBit(n: Int): Boolean =
    if (longEncoding && n >= 0) {
      if (n <= 63)
        (_long & (1L << n)) != 0
      else
        _long < 0 // give the sign bit
    } else _bigInteger.testBit(n)

  /** Returns a BigInt whose value is equivalent to this BigInt with the designated bit set.
   */
  def setBit(n: Int): BigInt  = // note that we do not operate on the Long sign bit #63
    if (longEncoding && n <= 62 && n >= 0) BigInt(_long | (1L << n)) else 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  = // note that we do not operate on the Long sign bit #63
    if (longEncoding && n <= 62 && n >= 0) BigInt(_long & ~(1L << n)) else 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  = // note that we do not operate on the Long sign bit #63
    if (longEncoding && n <= 62 && n >= 0) BigInt(_long ^ (1L << n)) else 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 =
    if (longEncoding) {
      if (_long == 0) -1 else java.lang.Long.numberOfTrailingZeros(_long)
    } else 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 =
  // bitLength is defined as ceil(log2(this < 0 ? -this : this + 1)))
  // where ceil(log2(x)) = 64 - numberOfLeadingZeros(x - 1)
    if (longEncoding) {
      if (_long < 0) 64 - java.lang.Long.numberOfLeadingZeros(-(_long + 1)) // takes care of Long.MinValue
      else 64 - java.lang.Long.numberOfLeadingZeros(_long)
    } else _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 =
    if (longEncoding) {
      if (_long < 0) java.lang.Long.bitCount(-(_long + 1)) else java.lang.Long.bitCount(_long)
    } else 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): Boolean = 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: Byte = 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: Short = 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: Char = 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: Int = if (longEncoding) _long.toInt else 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: Long = if (longEncoding) _long else _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: Float = 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: Double =
    if (isValidLong && (-(1L << 53) <= _long && _long <= (1L << 53))) _long.toDouble
    else 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)): NumericRange.Exclusive[BigInt] = Range.BigInt(this, end, step)

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

  /** Returns the decimal String representation of this BigInt.
   */
  override def toString(): String = if (longEncoding) _long.toString() else _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()
}