Scala example source code file (BigDecimal.scala)

This example Scala source code file (BigDecimal.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

bigdec, bigdecimal, bigint, boolean, collection, double, float, immutable, int, long, mathcontext, use

The BigDecimal.scala Scala example source code

/*                     __                                               *\
**     ________ ___   / /  ___     Scala API                            **
**    / __/ __// _ | / /  / _ |    (c) 2007-2013, LAMP/EPFL             **
**  __\ \/ /__/ __ |/ /__/ __ |    http://scala-lang.org/               **
** /____/\___/_/ |_/____/_/ | |                                         **
**                          |/                                          **
\*                                                                      */


package scala
package math

import java.{ lang => jl }
import java.math.{ MathContext, BigDecimal => BigDec }
import scala.collection.immutable.NumericRange
import scala.language.implicitConversions


/** 
 *  @author  Stephane Micheloud
 *  @author  Rex Kerr
 *  @version 1.1
 *  @since 2.7
 */
object BigDecimal {
  private final val maximumHashScale = 4934           // Quit maintaining hash identity with BigInt beyond this scale
  private final val hashCodeNotComputed = 0x5D50690F  // Magic value (happens to be "BigDecimal" old MurmurHash3 value)
  private final val deci2binary = 3.3219280948873626  // Ratio of log(10) to log(2)
  private val minCached = -512
  private val maxCached = 512
  val defaultMathContext = MathContext.DECIMAL128

  /** Cache only for defaultMathContext using BigDecimals in a small range. */
  private lazy val cache = new Array[BigDecimal](maxCached - minCached + 1)

  object RoundingMode extends Enumeration {
    // Annoying boilerplate to ensure consistency with java.math.RoundingMode
    import java.math.{RoundingMode => RM}
    type RoundingMode = Value
    val UP          = Value(RM.UP.ordinal)
    val DOWN        = Value(RM.DOWN.ordinal)
    val CEILING     = Value(RM.CEILING.ordinal)
    val FLOOR       = Value(RM.FLOOR.ordinal)
    val HALF_UP     = Value(RM.HALF_UP.ordinal)
    val HALF_DOWN   = Value(RM.HALF_DOWN.ordinal)
    val HALF_EVEN   = Value(RM.HALF_EVEN.ordinal)
    val UNNECESSARY = Value(RM.UNNECESSARY.ordinal) 
  }
  
  /** Constructs a `BigDecimal` using the decimal text representation of `Double` value `d`, rounding if necessary. */
  def decimal(d: Double, mc: MathContext): BigDecimal =
    new BigDecimal(new BigDec(java.lang.Double.toString(d), mc))

  /** Constructs a `BigDecimal` using the decimal text representation of `Double` value `d`. */
  def decimal(d: Double): BigDecimal = decimal(d, defaultMathContext)
  
  /** Constructs a `BigDecimal` using the decimal text representation of `Float` value `f`, rounding if necessary. 
   *  Note that `BigDecimal.decimal(0.1f) != 0.1f` since equality agrees with the `Double` representation, and
   *  `0.1 != 0.1f`.
   */
  def decimal(f: Float, mc: MathContext): BigDecimal =
    new BigDecimal(new BigDec(java.lang.Float.toString(f), mc))

  /** Constructs a `BigDecimal` using the decimal text representation of `Float` value `f`.
   *  Note that `BigDecimal.decimal(0.1f) != 0.1f` since equality agrees with the `Double` representation, and
   *  `0.1 != 0.1f`.
   */
  def decimal(f: Float): BigDecimal = decimal(f, defaultMathContext)
  
  // This exists solely to avoid conversion from Int/Long to Float, screwing everything up.
  /** Constructs a `BigDecimal` from a `Long`, rounding if necessary.  This is identical to `BigDecimal(l, mc)`. */
  def decimal(l: Long, mc: MathContext): BigDecimal = apply(l, mc)
  
  // This exists solely to avoid conversion from Int/Long to Float, screwing everything up.
  /** Constructs a `BigDecimal` from a `Long`.  This is identical to `BigDecimal(l)`. */
  def decimal(l: Long): BigDecimal = apply(l)
  
  /** Constructs a `BigDecimal` using a `java.math.BigDecimal`, rounding if necessary. */
  def decimal(bd: BigDec, mc: MathContext): BigDecimal = new BigDecimal(bd.round(mc), mc)
  
  /** Constructs a `BigDecimal` by expanding the binary fraction
   *  contained by `Double` value `d` into a decimal representation,
   *  rounding if necessary.  When a `Float` is converted to a
   *  `Double`, the binary fraction is preserved, so this method
   *  also works for converted `Float`s.
   */
  def binary(d: Double, mc: MathContext): BigDecimal = new BigDecimal(new BigDec(d, mc), mc)
  
  /** Constructs a `BigDecimal` by expanding the binary fraction
   *  contained by `Double` value `d` into a decimal representation.
   *  Note: this also works correctly on converted `Float`s.
   */
  def binary(d: Double): BigDecimal = binary(d, defaultMathContext)
  
  /** Constructs a `BigDecimal` from a `java.math.BigDecimal`.  The
   *  precision is the default for `BigDecimal` or enough to represent
   *  the `java.math.BigDecimal` exactly, whichever is greater.
   */
  def exact(repr: BigDec): BigDecimal = {
    val mc = 
      if (repr.precision <= defaultMathContext.getPrecision) defaultMathContext
      else new MathContext(repr.precision, java.math.RoundingMode.HALF_EVEN)
    new BigDecimal(repr, mc)
  }
  
  /** Constructs a `BigDecimal` by fully expanding the binary fraction
   *  contained by `Double` value `d`, adjusting the precision as
   *  necessary.  Note: this works correctly on converted `Float`s also.
   */
  def exact(d: Double): BigDecimal = exact(new BigDec(d))
  
  /** Constructs a `BigDecimal` that exactly represents a `BigInt`.
   */
  def exact(bi: BigInt): BigDecimal = exact(new BigDec(bi.bigInteger))
  
  /** Constructs a `BigDecimal` that exactly represents a `Long`.  Note that
   *  all creation methods for `BigDecimal` that do not take a `MathContext`
   *  represent a `Long`; this is equivalent to `apply`, `valueOf`, etc..
   */
  def exact(l: Long): BigDecimal = apply(l)
  
  /** Constructs a `BigDecimal` that exactly represents the number
   *  specified in a `String`.
   */
  def exact(s: String): BigDecimal = exact(new BigDec(s))
  
  /** Constructs a 'BigDecimal` that exactly represents the number
   *  specified in base 10 in a character array.
   */
 def exact(cs: Array[Char]): BigDecimal = exact(new BigDec(cs))
  

  /** Constructs a `BigDecimal` using the java BigDecimal static
   *  valueOf constructor.  Equivalent to `BigDecimal.decimal`.
   *
   *  @param  d the specified double value
   *  @return the constructed `BigDecimal`
   */
  def valueOf(d: Double): BigDecimal = apply(BigDec valueOf d)
  
  /** Constructs a `BigDecimal` using the java BigDecimal static
   *  valueOf constructor, specifying a `MathContext` that is
   *  used for computations but isn't used for rounding.  Use
   *  `BigDecimal.decimal` to use `MathContext` for rounding,
   *  or `BigDecimal(java.math.BigDecimal.valueOf(d), mc)` for
   *  no rounding.
   *
   *  @param  d the specified double value
   *  @param  mc the `MathContext` used for future computations
   *  @return the constructed `BigDecimal`
   */
  @deprecated("MathContext is not applied to Doubles in valueOf.  Use BigDecimal.decimal to use rounding, or java.math.BigDecimal.valueOf to avoid it.","2.11")
  def valueOf(d: Double, mc: MathContext): BigDecimal = apply(BigDec valueOf d, mc)
  
  /** Constructs a `BigDecimal` using the java BigDecimal static
   *  valueOf constructor.
   *
   *  @param  x the specified `Long` value
   *  @return the constructed `BigDecimal`
   */
  def valueOf(x: Long): BigDecimal = apply(x)
  
  /** Constructs a `BigDecimal` using the java BigDecimal static
   *  valueOf constructor.  This is unlikely to do what you want;
   *  use `valueOf(f.toDouble)` or `decimal(f)` instead.
   */
  @deprecated("Float arguments to valueOf may not do what you wish.  Use decimal or valueOf(f.toDouble).","2.11")
  def valueOf(f: Float): BigDecimal = valueOf(f.toDouble)
  
  /** Constructs a `BigDecimal` using the java BigDecimal static
   *  valueOf constructor.  This is unlikely to do what you want;
   *  use `valueOf(f.toDouble)` or `decimal(f)` instead.
   */
  @deprecated("Float arguments to valueOf may not do what you wish.  Use decimal or valueOf(f.toDouble).","2.11")
  def valueOf(f: Float, mc: MathContext): BigDecimal = valueOf(f.toDouble, mc)

  
  /** Constructs a `BigDecimal` whose value is equal to that of the
   *  specified `Integer` value.
   *
   *  @param i the specified integer value
   *  @return  the constructed `BigDecimal`
   */
  def apply(i: Int): BigDecimal = apply(i, defaultMathContext)

  /** Constructs a `BigDecimal` whose value is equal to that of the
   *  specified `Integer` value, rounding if necessary.
   *
   *  @param i the specified integer value
   *  @param mc the precision and rounding mode for creation of this value and future operations on it
   *  @return  the constructed `BigDecimal`
   */
  def apply(i: Int, mc: MathContext): BigDecimal =
    if (mc == defaultMathContext && minCached <= i && i <= maxCached) {
      val offset = i - minCached
      var n = cache(offset)
      if (n eq null) { n = new BigDecimal(BigDec.valueOf(i.toLong), mc); cache(offset) = n }
      n
    }
    else apply(i.toLong, mc)

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

  /** Constructs a `BigDecimal` whose value is equal to that of the
   *  specified long value, but rounded if necessary.
   *
   *  @param l the specified long value
   *  @param mc the precision and rounding mode for creation of this value and future operations on it
   *  @return  the constructed `BigDecimal`
   */
  def apply(l: Long, mc: MathContext): BigDecimal =
    new BigDecimal(new BigDec(l, mc), mc)

  /** Constructs a `BigDecimal` whose unscaled value is equal to that
   *  of the specified long value.
   *
   *  @param  unscaledVal the value
   *  @param  scale       the scale
   *  @return the constructed `BigDecimal`
   */
  def apply(unscaledVal: Long, scale: Int): BigDecimal =
    apply(BigInt(unscaledVal), scale)

  /** Constructs a `BigDecimal` whose unscaled value is equal to that
   *  of the specified long value, but rounded if necessary.
   *
   *  @param  unscaledVal the value
   *  @param  scale       the scale
   *  @param mc the precision and rounding mode for creation of this value and future operations on it
   *  @return the constructed `BigDecimal`
   */
  def apply(unscaledVal: Long, scale: Int, mc: MathContext): BigDecimal =
    apply(BigInt(unscaledVal), scale, mc)

  /** Constructs a `BigDecimal` whose value is equal to that of the
   *  specified double value.  Equivalent to `BigDecimal.decimal`.
   *
   *  @param d the specified `Double` value
   *  @return  the constructed `BigDecimal`
   */
  def apply(d: Double): BigDecimal = decimal(d, defaultMathContext)
  
  // note we don't use the static valueOf because it doesn't let us supply
  // a MathContext, but we should be duplicating its logic, modulo caching.
  /** Constructs a `BigDecimal` whose value is equal to that of the
   *  specified double value, but rounded if necessary.  Equivalent to
   *  `BigDecimal.decimal`.
   *
   *  @param d the specified `Double` value
   *  @param mc the precision and rounding mode for creation of this value and future operations on it
   *  @return  the constructed `BigDecimal`
   */
  def apply(d: Double, mc: MathContext): BigDecimal = decimal(d, mc)

  @deprecated("The default conversion from Float may not do what you want.  Use BigDecimal.decimal for a String representation, or explicitly convert the Float with .toDouble.", "2.11")
  def apply(x: Float): BigDecimal = apply(x.toDouble)

  @deprecated("The default conversion from Float may not do what you want.  Use BigDecimal.decimal for a String representation, or explicitly convert the Float with .toDouble.", "2.11")
  def apply(x: Float, mc: MathContext): BigDecimal = apply(x.toDouble, mc)

  /** Translates a character array representation of a `BigDecimal`
   *  into a `BigDecimal`.
   */
  def apply(x: Array[Char]): BigDecimal = exact(x)

  /** Translates a character array representation of a `BigDecimal`
   *  into a `BigDecimal`, rounding if necessary.
   */
  def apply(x: Array[Char], mc: MathContext): BigDecimal =
    new BigDecimal(new BigDec(x, mc), mc)

  /** Translates the decimal String representation of a `BigDecimal`
   *  into a `BigDecimal`.
   */
  def apply(x: String): BigDecimal = exact(x)
  
  /** Translates the decimal String representation of a `BigDecimal`
   *  into a `BigDecimal`, rounding if necessary.
   */
  def apply(x: String, mc: MathContext): BigDecimal =
    new BigDecimal(new BigDec(x, mc), mc)

  /** Constructs a `BigDecimal` whose value is equal to that of the
   *  specified `BigInt` value.
   *
   *  @param x the specified `BigInt` value
   *  @return  the constructed `BigDecimal`
   */
  def apply(x: BigInt): BigDecimal = exact(x)
  
  /** Constructs a `BigDecimal` whose value is equal to that of the
   *  specified `BigInt` value, rounding if necessary.
   *
   *  @param x  the specified `BigInt` value
   *  @param mc the precision and rounding mode for creation of this value and future operations on it   
   *  @return   the constructed `BigDecimal`
   */
  def apply(x: BigInt, mc: MathContext): BigDecimal =
    new BigDecimal(new BigDec(x.bigInteger, mc), mc)

  /** Constructs a `BigDecimal` whose unscaled value is equal to that
   *  of the specified `BigInt` value.
   *
   *  @param unscaledVal the specified `BigInt` value
   *  @param scale       the scale
   *  @return  the constructed `BigDecimal`
   */
  def apply(unscaledVal: BigInt, scale: Int): BigDecimal =
    exact(new BigDec(unscaledVal.bigInteger, scale))
  
  /** Constructs a `BigDecimal` whose unscaled value is equal to that
   *  of the specified `BigInt` value.
   *
   *  @param unscaledVal the specified `BigInt` value
   *  @param scale       the scale
   *  @param mc          the precision and rounding mode for creation of this value and future operations on it   
   *  @return  the constructed `BigDecimal`
   */
  def apply(unscaledVal: BigInt, scale: Int, mc: MathContext): BigDecimal =
    new BigDecimal(new BigDec(unscaledVal.bigInteger, scale, mc), mc)

  /** Constructs a `BigDecimal` from a `java.math.BigDecimal`. */
  def apply(bd: BigDec): BigDecimal = apply(bd, defaultMathContext)
  
  @deprecated("This method appears to round a java.math.BigDecimal but actually doesn't.  Use new BigDecimal(bd, mc) instead for no rounding, or BigDecimal.decimal(bd, mc) for rounding.", "2.11")
  def apply(bd: BigDec, mc: MathContext): BigDecimal = new BigDecimal(bd, mc)

  /** Implicit conversion from `Int` to `BigDecimal`. */
  implicit def int2bigDecimal(i: Int): BigDecimal = apply(i)

  /** Implicit conversion from `Long` to `BigDecimal`. */
  implicit def long2bigDecimal(l: Long): BigDecimal = apply(l)

  /** Implicit conversion from `Double` to `BigDecimal`. */
  implicit def double2bigDecimal(d: Double): BigDecimal = decimal(d)

  /** Implicit conversion from `java.math.BigDecimal` to `scala.BigDecimal`. */
  implicit def javaBigDecimal2bigDecimal(x: BigDec): BigDecimal = apply(x)
}

/**
 *  `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 corrsponding 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.
 *
 *  @author  Stephane Micheloud
 *  @author  Rex Kerr
 *  @version 1.1
 */
final class BigDecimal(val bigDecimal: BigDec, val mc: MathContext)
extends ScalaNumber with ScalaNumericConversions with Serializable {
  def this(bigDecimal: BigDec) = this(bigDecimal, BigDecimal.defaultMathContext)
  import BigDecimal.RoundingMode._
  import BigDecimal.{decimal, binary, exact}
  
  if (bigDecimal eq null) throw new IllegalArgumentException("null value for BigDecimal")
  if (mc eq null) throw new IllegalArgumentException("null MathContext for BigDecimal")

  // There was an implicit to cut down on the wrapper noise for BigDec -> BigDecimal.
  // However, this may mask introduction of surprising behavior (e.g. lack of rounding
  // where one might expect it).  Wrappers should be applied explicitly with an
  // eye to correctness.

  // Sane hash code computation (which is surprisingly hard).
  // Note--not lazy val because we can't afford the extra space.
  private final var computedHashCode: Int = BigDecimal.hashCodeNotComputed
  private final def computeHashCode(): Unit = {
    computedHashCode =
      if (isWhole && (precision - scale) < BigDecimal.maximumHashScale) toBigInt.hashCode
      else if (isValidDouble) doubleValue.##
      else {
        val temp = bigDecimal.stripTrailingZeros
        scala.util.hashing.MurmurHash3.mixLast( temp.scaleByPowerOfTen(temp.scale).toBigInteger.hashCode, temp.scale )
      }
  }
  
  /** Returns the hash code for this BigDecimal.
   *  Note that this does not merely use the underlying java object's
   *  `hashCode` because we compare `BigDecimal`s with `compareTo`
   *  which deems 2 == 2.00, whereas in java these are unequal
   *  with unequal `hashCode`s.  These hash codes agree with `BigInt`
   *  for whole numbers up ~4934 digits (the range of IEEE 128 bit floating
   *  point).  Beyond this, hash codes will disagree; this prevents the
   *  explicit represention of the `BigInt` form for `BigDecimal` values
   *  with large exponents.
   */
  override def hashCode(): Int = {
    if (computedHashCode == BigDecimal.hashCodeNotComputed) computeHashCode
    computedHashCode
  }

  /** Compares this BigDecimal with the specified value for equality.  Where `Float` and `Double`
   *  disagree, `BigDecimal` will agree with the `Double` value
   */
  override def equals (that: Any): Boolean = that match {
    case that: BigDecimal     => this equals that
    case that: BigInt         => 
      that.bitLength > (precision-scale-2)*BigDecimal.deci2binary && 
      this.toBigIntExact.exists(that equals _)
    case that: Double         => 
      !that.isInfinity && {
        val d = toDouble
        !d.isInfinity && d == that && equals(decimal(d))
      }
    case that: Float          => 
      !that.isInfinity && {
        val f = toFloat
        !f.isInfinity && f == that && equals(decimal(f.toDouble))
      }
    case _                    => isValidLong && unifiedPrimitiveEquals(that)
  }
  override def isValidByte  = noArithmeticException(toByteExact)
  override def isValidShort = noArithmeticException(toShortExact)
  override def isValidChar  = isValidInt && toIntExact >= Char.MinValue && toIntExact <= Char.MaxValue
  override def isValidInt   = noArithmeticException(toIntExact)
  def isValidLong  = noArithmeticException(toLongExact)
  /** Tests whether the value is a valid Float.  "Valid" has several distinct meanings, however.  Use
    * `isExactFloat`, `isBinaryFloat`, or `isDecimalFloat`, depending on the intended meaning.
    * By default, `decimal` creation is used, so `isDecimalFloat` is probably what you want.
    */
  @deprecated("What constitutes validity is unclear.  Use `isExactFloat`, `isBinaryFloat`, or `isDecimalFloat` instead.", "2.11")
  def isValidFloat = {
    val f = toFloat
    !f.isInfinity && bigDecimal.compareTo(new BigDec(f.toDouble)) == 0
  }
  /** Tests whether the value is a valid Double.  "Valid" has several distinct meanings, however.  Use
    * `isExactDouble`, `isBinaryDouble`, or `isDecimalDouble`, depending on the intended meaning.
    * By default, `decimal` creation is used, so `isDecimalDouble` is probably what you want.
    */
  @deprecated("Validity has two distinct meanings.  Use `isExactBinaryDouble` or `equivalentToDouble` instead.", "2.11")
  def isValidDouble = {
    val d = toDouble
    !d.isInfinity && bigDecimal.compareTo(new BigDec(d)) == 0
  }
  
  /** Tests whether this `BigDecimal` holds the decimal representation of a `Double`. */
  def isDecimalDouble = {
    val d = toDouble
    !d.isInfinity && equals(decimal(d))
  }
  
  /** Tests whether this `BigDecimal` holds the decimal representation of a `Float`. */
  def isDecimalFloat = {
    val f = toFloat
    !f.isInfinity && equals(decimal(f))
  }
  
  /** Tests whether this `BigDecimal` holds, to within precision, the binary representation of a `Double`. */
  def isBinaryDouble = {
    val d = toDouble
    !d.isInfinity && equals(binary(d,mc))
  }
  
  /** Tests whether this `BigDecimal` holds, to within precision, the binary representation of a `Float`. */
  def isBinaryFloat = {
    val f = toFloat
    !f.isInfinity && equals(binary(f,mc))
  }
  
  /** Tests whether this `BigDecimal` holds the exact expansion of a `Double`'s binary fractional form into base 10. */
  def isExactDouble = {
    val d = toDouble
    !d.isInfinity && equals(exact(d))
  }
  
  /** Tests whether this `BigDecimal` holds the exact expansion of a `Float`'s binary fractional form into base 10. */
  def isExactFloat = {
    val f = toFloat
    !f.isInfinity && equals(exact(f.toDouble))
  }
  

  private def noArithmeticException(body: => Unit): Boolean = {
    try   { body ; true }
    catch { case _: ArithmeticException => false }
  }

  def isWhole() = scale <= 0 || bigDecimal.stripTrailingZeros.scale <= 0
  
  def underlying = bigDecimal
  

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

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

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

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

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

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

  /** Addition of BigDecimals
   */
  def +  (that: BigDecimal): BigDecimal = new BigDecimal(this.bigDecimal add that.bigDecimal, mc)

  /** Subtraction of BigDecimals
   */
  def -  (that: BigDecimal): BigDecimal = new BigDecimal(this.bigDecimal subtract that.bigDecimal, mc)

  /** Multiplication of BigDecimals
   */
  def *  (that: BigDecimal): BigDecimal = new BigDecimal(this.bigDecimal.multiply(that.bigDecimal, mc), mc)

  /** Division of BigDecimals
   */
  def /  (that: BigDecimal): BigDecimal = new BigDecimal(this.bigDecimal.divide(that.bigDecimal, mc), mc)

  /** Division and Remainder - returns tuple containing the result of
   *  divideToIntegralValue and the remainder.  The computation is exact: no rounding is applied.
   */
  def /% (that: BigDecimal): (BigDecimal, BigDecimal) =
    this.bigDecimal.divideAndRemainder(that.bigDecimal) match {
      case Array(q, r)  => (new BigDecimal(q, mc), new BigDecimal(r, mc))
    }

  /** Divide to Integral value.
   */
  def quot (that: BigDecimal): BigDecimal =
    new BigDecimal(this.bigDecimal divideToIntegralValue that.bigDecimal, mc)

  /** Returns the minimum of this and that, or this if the two are equal
   */
  def min (that: BigDecimal): BigDecimal = (this compare that) match {
    case x if x <= 0 => this
    case _           => that
  }
  
  /** Returns the maximum of this and that, or this if the two are equal
   */
  def max (that: BigDecimal): BigDecimal = (this compare that) match {
    case x if x >= 0 => this
    case _           => that
  }
  
  /** Remainder after dividing this by that.
   */
  def remainder (that: BigDecimal): BigDecimal = new BigDecimal(this.bigDecimal remainder that.bigDecimal, mc)

  /** Remainder after dividing this by that.
   */
  def % (that: BigDecimal): BigDecimal = this remainder that

  /** Returns a BigDecimal whose value is this ** n.
   */
  def pow (n: Int): BigDecimal = new BigDecimal(this.bigDecimal.pow(n, mc), mc)

  /** Returns a BigDecimal whose value is the negation of this BigDecimal
   */
  def unary_- : BigDecimal = new BigDecimal(this.bigDecimal.negate(), mc)

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

  /** Returns the sign of this BigDecimal, 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.bigDecimal.signum()

  /** Returns the precision of this `BigDecimal`.
   */
  def precision: Int = this.bigDecimal.precision()

  /** Returns a BigDecimal rounded according to the supplied MathContext settings, but
   *  preserving its own MathContext for future operations.
   */
  def round(mc: MathContext): BigDecimal = {
    val r = this.bigDecimal round mc
    if (r eq bigDecimal) this else new BigDecimal(r, this.mc)
  }
  
  /** Returns a `BigDecimal` rounded according to its own `MathContext` */
  def rounded: BigDecimal = {
    val r = bigDecimal round mc
    if (r eq bigDecimal) this else new BigDecimal(r, mc)
  }

  /** Returns the scale of this `BigDecimal`.
   */
  def scale: Int = this.bigDecimal.scale()

  /** Returns the size of an ulp, a unit in the last place, of this BigDecimal.
   */
  def ulp: BigDecimal = new BigDecimal(this.bigDecimal.ulp, mc)

  /** Returns a new BigDecimal based on the supplied MathContext, rounded as needed.
   */
  def apply(mc: MathContext): BigDecimal = new BigDecimal(this.bigDecimal round mc, mc)

  /** Returns a `BigDecimal` whose scale is the specified value, and whose value is
   *  numerically equal to this BigDecimal's.
   */
  def setScale(scale: Int): BigDecimal = 
    if (this.scale == scale) this
    else new BigDecimal(this.bigDecimal setScale scale, mc)

  def setScale(scale: Int, mode: RoundingMode): BigDecimal =
    if (this.scale == scale) this
    else new BigDecimal(this.bigDecimal.setScale(scale, mode.id), mc)

  /** Converts this BigDecimal to a Byte.
   *  If the BigDecimal 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
   *  BigDecimal value as well as return a result with the opposite sign.
   */
  override def byteValue   = intValue.toByte

  /** Converts this BigDecimal to a Short.
   *  If the BigDecimal 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
   *  BigDecimal value as well as return a result with the opposite sign.
   */
  override def shortValue  = intValue.toShort

  /** Converts this BigDecimal to a Char.
   *  If the BigDecimal 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
   *  BigDecimal value and that it always returns a positive result.
   */
  def charValue   = intValue.toChar

  /** Converts this BigDecimal to an Int.
   *  If the BigDecimal 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 BigDecimal value as well as return a result with
   *  the opposite sign.
   */
  def intValue    = this.bigDecimal.intValue

  /** Converts this BigDecimal to a Long.
   *  If the BigDecimal 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 BigDecimal value as well as return a result with
   *  the opposite sign.
   */
  def longValue   = this.bigDecimal.longValue

  /** Converts this BigDecimal to a Float.
   *  if this BigDecimal 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.bigDecimal.floatValue

  /** Converts this BigDecimal to a Double.
   *  if this BigDecimal 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.bigDecimal.doubleValue

  /** Converts this `BigDecimal` to a [[scala.Byte]], checking for lost information.
    * If this `BigDecimal` has a nonzero fractional part, or is out of the possible
    * range for a [[scala.Byte]] result, then a `java.lang.ArithmeticException` is
    * thrown.
    */
  def toByteExact = bigDecimal.byteValueExact

  /** Converts this `BigDecimal` to a [[scala.Short]], checking for lost information.
    * If this `BigDecimal` has a nonzero fractional part, or is out of the possible
    * range for a [[scala.Short]] result, then a `java.lang.ArithmeticException` is
    * thrown.
    */
  def toShortExact = bigDecimal.shortValueExact

  /** Converts this `BigDecimal` to a [[scala.Int]], checking for lost information.
    * If this `BigDecimal` has a nonzero fractional part, or is out of the possible
    * range for an [[scala.Int]] result, then a `java.lang.ArithmeticException` is
    * thrown.
    */
  def toIntExact = bigDecimal.intValueExact

  /** Converts this `BigDecimal` to a [[scala.Long]], checking for lost information.
    * If this `BigDecimal` has a nonzero fractional part, or is out of the possible
    * range for a [[scala.Long]] result, then a `java.lang.ArithmeticException` is
    * thrown.
    */
  def toLongExact = bigDecimal.longValueExact

  /** Creates a partially constructed NumericRange[BigDecimal] in range
   *  `[start;end)`, where start is the target BigDecimal.  The step
   *  must be supplied via the "by" method of the returned object in order
   *  to receive the fully constructed range.  For example:
   * {{{
   * val partial = BigDecimal(1.0) to 2.0       // not usable yet
   * val range = partial by 0.01                // now a NumericRange
   * val range2 = BigDecimal(0) to 1.0 by 0.01  // all at once of course is fine too
   * }}}
   *
   *  @param end    the end value of the range (exclusive)
   *  @return       the partially constructed NumericRange
   */
  def until(end: BigDecimal): Range.Partial[BigDecimal, NumericRange.Exclusive[BigDecimal]] =
    new Range.Partial(until(end, _))

  /** Same as the one-argument `until`, but creates the range immediately. */
  def until(end: BigDecimal, step: BigDecimal) = Range.BigDecimal(this, end, step)

  /** Like `until`, but inclusive of the end value. */
  def to(end: BigDecimal): Range.Partial[BigDecimal, NumericRange.Inclusive[BigDecimal]] =
    new Range.Partial(to(end, _))

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

  /** Converts this `BigDecimal` to a scala.BigInt.
   */
  def toBigInt(): BigInt = new BigInt(this.bigDecimal.toBigInteger())

  /** Converts this `BigDecimal` to a scala.BigInt if it
   *  can be done losslessly, returning Some(BigInt) or None.
   */
  def toBigIntExact(): Option[BigInt] =
    if (isWhole()) {
      try Some(new BigInt(this.bigDecimal.toBigIntegerExact()))
      catch { case _: ArithmeticException => None }
    }
    else None

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

}