Package org.apache.commons.math.dfp

Class Dfp

java.lang.Object
org.apache.commons.math.dfp.Dfp
All Implemented Interfaces:
FieldElement<Dfp>
Direct Known Subclasses:
DfpDec
public class Dfp extends Object implements FieldElement<Dfp>
Decimal floating point library for Java

Another floating point class. This one is built using radix 10000 which is 104, so its almost decimal.

The design goals here are:

  1. Decimal math, or close to it
  2. Settable precision (but no mix between numbers using different settings)
  3. Portability. Code should be keep as portable as possible.
  4. Performance
  5. Accuracy - Results should always be +/- 1 ULP for basic algebraic operation
  6. Comply with IEEE 854-1987 as much as possible. (See IEEE 854-1987 notes below)

Trade offs:

  1. Memory foot print. I'm using more memory than necessary to represent numbers to get better performance.
  2. Digits are bigger, so rounding is a greater loss. So, if you really need 12 decimal digits, better use 4 base 10000 digits there can be one partially filled.

Numbers are represented in the following form: 

  n  =  sign × mant × (radix)exp;
where sign is ±1, mantissa represents a fractional number between zero and one. mant[0] is the least significant digit. exp is in the range of -32767 to 32768

IEEE 854-1987 Notes and differences

IEEE 854 requires the radix to be either 2 or 10. The radix here is 10000, so that requirement is not met, but it is possible that a subclassed can be made to make it behave as a radix 10 number. It is my opinion that if it looks and behaves as a radix 10 number then it is one and that requirement would be met.

The radix of 10000 was chosen because it should be faster to operate on 4 decimal digits at once instead of one at a time. Radix 10 behavior can be realized by add an additional rounding step to ensure that the number of decimal digits represented is constant.

The IEEE standard specifically leaves out internal data encoding, so it is reasonable to conclude that such a subclass of this radix 10000 system is merely an encoding of a radix 10 system.

IEEE 854 also specifies the existence of "sub-normal" numbers. This class does not contain any such entities. The most significant radix 10000 digit is always non-zero. Instead, we support "gradual underflow" by raising the underflow flag for numbers less with exponent less than expMin, but don't flush to zero until the exponent reaches MIN_EXP-digits. Thus the smallest number we can represent would be: 1E(-(MIN_EXP-digits-1)*4), eg, for digits=5, MIN_EXP=-32767, that would be 1e-131092.

IEEE 854 defines that the implied radix point lies just to the right of the most significant digit and to the left of the remaining digits. This implementation puts the implied radix point to the left of all digits including the most significant one. The most significant digit here is the one just to the right of the radix point. This is a fine detail and is really only a matter of definition. Any side effects of this can be rendered invisible by a subclass.

Since:
2.2
Version:
$Revision: 1003889 $ $Date: 2010-10-02 23:11:55 +0200 (sam. 02 oct. 2010) $
See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    static final int
    ERR_SCALE
    The amount under/overflows are scaled by before going to trap handler
    protected int
    exp
    Exponent.
    static final byte
    FINITE
    Indicator value for normal finite numbers.
    static final byte
    INFINITE
    Indicator value for Infinity.
    protected int[]
    mant
    Mantissa.
    static final int
    MAX_EXP
    The maximum exponent before overflow is signaled and results flushed to infinity
    static final int
    MIN_EXP
    The minimum exponent before underflow is signaled.
    protected byte
    nans
    Indicator for non-finite / non-number values.
    static final byte
    QNAN
    Indicator value for quiet NaN.
    static final int
    RADIX
    The radix, or base of this system.
    protected byte
    sign
    Sign bit: invalid input: '&' for positive, -1 for negative.
    static final byte
    SNAN
    Indicator value for signaling NaN.

  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
     
    Dfp(Dfp d)
    Copy constructor.
    protected
    Dfp(DfpField field)
    Makes an instance with a value of zero.
    protected
    Dfp(DfpField field, byte x)
    Create an instance from a byte value.
    protected
    Dfp(DfpField field, byte sign, byte nans)
    Creates an instance with a non-finite value.
    protected
    Dfp(DfpField field, double x)
    Create an instance from a double value.
    protected
    Dfp(DfpField field, int x)
    Create an instance from an int value.
    protected
    Dfp(DfpField field, long x)
    Create an instance from a long value.
    protected
    Dfp(DfpField field, String s)
    Create an instance from a String representation.

  • Method Summary

    Modifier and Type
    Method
    Description
    Dfp
    add(Dfp x)
    Add x to this.
    protected int
    align(int e)
    Make our exp equal to the supplied one, this may cause rounding.
    Dfp
    ceil()
    Round to an integer using the round ceil mode.
    int
    classify()
    Returns the type - one of FINITE, INFINITE, SNAN, QNAN.
    protected int
    complement(int extra)
    Negate the mantissa of this by computing the complement.
    static Dfp
    copysign(Dfp x, Dfp y)
    Creates an instance that is the same as x except that it has the sign of y.
    protected String
    dfp2sci()
    Convert an instance to a string using scientific notation.
    protected String
    dfp2string()
    Convert an instance to a string using normal notation.
    Dfp
    divide(int divisor)
    Divide by a single digit less than radix.
    Dfp
    divide(Dfp divisor)
    Divide this by divisor.
    Dfp
    dotrap(int type, String what, Dfp oper, Dfp result)
    Raises a trap.
    boolean
    equals(Object other)
    Check if instance is equal to x.
    Dfp
    floor()
    Round to an integer using the round floor mode.
    DfpField
    getField()
    Get the Field (really a DfpField) to which the instance belongs.
    Dfp
    getOne()
    Get the constant 1.
    int
    getRadixDigits()
    Get the number of radix digits of the instance.
    Dfp
    getTwo()
    Get the constant 2.
    Dfp
    getZero()
    Get the constant 0.
    boolean
    greaterThan(Dfp x)
    Check if instance is greater than x.
    int
    hashCode()
    Gets a hashCode for the instance.
    int
    intValue()
    Convert this to an integer.
    boolean
    isInfinite()
    Check if instance is infinite.
    boolean
    isNaN()
    Check if instance is not a number.
    boolean
    lessThan(Dfp x)
    Check if instance is less than x.
    int
    log10()
    Get the exponent of the greatest power of 10 that is less than or equal to abs(this).
    int
    log10K()
    Get the exponent of the greatest power of 10000 that is less than or equal to the absolute value of this.
    Dfp
    multiply(int x)
    Multiply this by a single digit 0<=x<radix.
    Dfp
    multiply(Dfp x)
    Multiply this by x.
    Dfp
    negate()
    Returns a number that is this number with the sign bit reversed.
    Dfp
    newInstance()
    Create an instance with a value of 0.
    Dfp
    newInstance(byte x)
    Create an instance from a byte value.
    Dfp
    newInstance(byte sig, byte code)
    Creates an instance with a non-finite value.
    Dfp
    newInstance(double x)
    Create an instance from a double value.
    Dfp
    newInstance(int x)
    Create an instance from an int value.
    Dfp
    newInstance(long x)
    Create an instance from a long value.
    Dfp
    newInstance(String s)
    Create an instance from a String representation.
    Dfp
    newInstance(Dfp d)
    Create an instance by copying an existing one.
    Dfp
    nextAfter(Dfp x)
    Returns the next number greater than this one in the direction of x.
    Dfp
    power10(int e)
    Return the specified power of 10.
    Dfp
    power10K(int e)
    Get the specified power of 10000.
    Dfp
    remainder(Dfp d)
    Returns the IEEE remainder.
    Dfp
    rint()
    Round to nearest integer using the round-half-even method.
    protected int
    round(int n)
    Round this given the next digit n using the current rounding mode.
    protected void
    shiftLeft()
    Shift the mantissa left, and adjust the exponent to compensate.
    protected void
    shiftRight()
    Shift the mantissa right, and adjust the exponent to compensate.
    Dfp
    sqrt()
    Compute the square root.
    Dfp
    subtract(Dfp x)
    Subtract x from this.
    double
    toDouble()
    Convert the instance into a double.
    double[]
    toSplitDouble()
    Convert the instance into a split double.
    String
    toString()
    Get a string representation of the instance.
    protected Dfp
    trap(int type, String what, Dfp oper, Dfp def, Dfp result)
    Trap handler.
    protected Dfp
    trunc(DfpField.RoundingMode rmode)
    Does the integer conversions with the specified rounding.
    boolean
    unequal(Dfp x)
    Check if instance is not equal to x.

    Methods inherited from class java.lang.Object

    clone, finalize, getClass, notify, notifyAll, wait, wait, wait

  • Field Details

    • RADIX

      public static final int RADIX
      The radix, or base of this system. Set to 10000
      See Also:

    • MIN_EXP

      public static final int MIN_EXP
      The minimum exponent before underflow is signaled. Flush to zero occurs at minExp-DIGITS
      See Also:

    • MAX_EXP

      public static final int MAX_EXP
      The maximum exponent before overflow is signaled and results flushed to infinity
      See Also:

    • ERR_SCALE

      public static final int ERR_SCALE
      The amount under/overflows are scaled by before going to trap handler
      See Also:

    • FINITE

      public static final byte FINITE
      Indicator value for normal finite numbers.
      See Also:

    • INFINITE

      public static final byte INFINITE
      Indicator value for Infinity.
      See Also:

    • SNAN

      public static final byte SNAN
      Indicator value for signaling NaN.
      See Also:

    • QNAN

      public static final byte QNAN
      Indicator value for quiet NaN.
      See Also:

    • mant

      protected int[] mant
      Mantissa.

    • sign

      protected byte sign
      Sign bit: invalid input: '&' for positive, -1 for negative.

    • exp

      protected int exp
      Exponent.

    • nans

      protected byte nans
      Indicator for non-finite / non-number values.

  • Constructor Details

    • Dfp

      protected Dfp(DfpField field)
      Makes an instance with a value of zero.
      Parameters:
      field - field to which this instance belongs

    • Dfp

      protected Dfp(DfpField field, byte x)
      Create an instance from a byte value.
      Parameters:
      field - field to which this instance belongs
      x - value to convert to an instance

    • Dfp

      protected Dfp(DfpField field, int x)
      Create an instance from an int value.
      Parameters:
      field - field to which this instance belongs
      x - value to convert to an instance

    • Dfp

      protected Dfp(DfpField field, long x)
      Create an instance from a long value.
      Parameters:
      field - field to which this instance belongs
      x - value to convert to an instance

    • Dfp

      protected Dfp(DfpField field, double x)
      Create an instance from a double value.
      Parameters:
      field - field to which this instance belongs
      x - value to convert to an instance

    • Dfp

      public Dfp(Dfp d)
      Copy constructor.
      Parameters:
      d - instance to copy

    • Dfp

      protected Dfp(DfpField field, String s)
      Create an instance from a String representation.
      Parameters:
      field - field to which this instance belongs
      s - string representation of the instance

    • Dfp

      protected Dfp(DfpField field, byte sign, byte nans)
      Creates an instance with a non-finite value.
      Parameters:
      field - field to which this instance belongs
      sign - sign of the Dfp to create
      nans - code of the value, must be one of INFINITE, SNAN, QNAN

  • Method Details

    • newInstance

      public Dfp newInstance()
      Create an instance with a value of 0. Use this internally in preference to constructors to facilitate subclasses
      Returns:
      a new instance with a value of 0

    • newInstance

      public Dfp newInstance(byte x)
      Create an instance from a byte value.
      Parameters:
      x - value to convert to an instance
      Returns:
      a new instance with value x

    • newInstance

      public Dfp newInstance(int x)
      Create an instance from an int value.
      Parameters:
      x - value to convert to an instance
      Returns:
      a new instance with value x

    • newInstance

      public Dfp newInstance(long x)
      Create an instance from a long value.
      Parameters:
      x - value to convert to an instance
      Returns:
      a new instance with value x

    • newInstance

      public Dfp newInstance(double x)
      Create an instance from a double value.
      Parameters:
      x - value to convert to an instance
      Returns:
      a new instance with value x

    • newInstance

      public Dfp newInstance(Dfp d)
      Create an instance by copying an existing one. Use this internally in preference to constructors to facilitate subclasses.
      Parameters:
      d - instance to copy
      Returns:
      a new instance with the same value as d

    • newInstance

      public Dfp newInstance(String s)
      Create an instance from a String representation. Use this internally in preference to constructors to facilitate subclasses.
      Parameters:
      s - string representation of the instance
      Returns:
      a new instance parsed from specified string

    • newInstance

      public Dfp newInstance(byte sig, byte code)
      Creates an instance with a non-finite value.
      Parameters:
      sig - sign of the Dfp to create
      code - code of the value, must be one of INFINITE, SNAN, QNAN
      Returns:
      a new instance with a non-finite value

    • getField

      public DfpField getField()
      Get the Field (really a DfpField) to which the instance belongs.

      The field is linked to the number of digits and acts as a factory for Dfp instances.

      Specified by:
      getField in interface FieldElement<Dfp>
      Returns:
      Field (really a DfpField) to which the instance belongs

    • getRadixDigits

      public int getRadixDigits()
      Get the number of radix digits of the instance.
      Returns:
      number of radix digits

    • getZero

      public Dfp getZero()
      Get the constant 0.
      Returns:
      a Dfp with value zero

    • getOne

      public Dfp getOne()
      Get the constant 1.
      Returns:
      a Dfp with value one

    • getTwo

      public Dfp getTwo()
      Get the constant 2.
      Returns:
      a Dfp with value two

    • shiftLeft

      protected void shiftLeft()
      Shift the mantissa left, and adjust the exponent to compensate.

    • shiftRight

      protected void shiftRight()
      Shift the mantissa right, and adjust the exponent to compensate.

    • align

      protected int align(int e)
      Make our exp equal to the supplied one, this may cause rounding. Also causes de-normalized numbers. These numbers are generally dangerous because most routines assume normalized numbers. Align doesn't round, so it will return the last digit destroyed by shifting right.
      Parameters:
      e - desired exponent
      Returns:
      last digit destroyed by shifting right

    • lessThan

      public boolean lessThan(Dfp x)
      Check if instance is less than x.
      Parameters:
      x - number to check instance against
      Returns:
      true if instance is less than x and neither are NaN, false otherwise

    • greaterThan

      public boolean greaterThan(Dfp x)
      Check if instance is greater than x.
      Parameters:
      x - number to check instance against
      Returns:
      true if instance is greater than x and neither are NaN, false otherwise

    • isInfinite

      public boolean isInfinite()
      Check if instance is infinite.
      Returns:
      true if instance is infinite

    • isNaN

      public boolean isNaN()
      Check if instance is not a number.
      Returns:
      true if instance is not a number

    • equals

      public boolean equals(Object other)
      Check if instance is equal to x.
      Overrides:
      equals in class Object
      Parameters:
      other - object to check instance against
      Returns:
      true if instance is equal to x and neither are NaN, false otherwise

    • hashCode

      public int hashCode()
      Gets a hashCode for the instance.
      Overrides:
      hashCode in class Object
      Returns:
      a hash code value for this object

    • unequal

      public boolean unequal(Dfp x)
      Check if instance is not equal to x.
      Parameters:
      x - number to check instance against
      Returns:
      true if instance is not equal to x and neither are NaN, false otherwise

    • rint

      public Dfp rint()
      Round to nearest integer using the round-half-even method. That is round to nearest integer unless both are equidistant. In which case round to the even one.
      Returns:
      rounded value

    • floor

      public Dfp floor()
      Round to an integer using the round floor mode. That is, round toward -Infinity
      Returns:
      rounded value

    • ceil

      public Dfp ceil()
      Round to an integer using the round ceil mode. That is, round toward +Infinity
      Returns:
      rounded value

    • remainder

      public Dfp remainder(Dfp d)
      Returns the IEEE remainder.
      Parameters:
      d - divisor
      Returns:
      this less n × d, where n is the integer closest to this/d

    • trunc

      protected Dfp trunc(DfpField.RoundingMode rmode)
      Does the integer conversions with the specified rounding.
      Parameters:
      rmode - rounding mode to use
      Returns:
      truncated value

    • intValue

      public int intValue()
      Convert this to an integer. If greater than 2147483647, it returns 2147483647. If less than -2147483648 it returns -2147483648.
      Returns:
      converted number

    • log10K

      public int log10K()
      Get the exponent of the greatest power of 10000 that is less than or equal to the absolute value of this. I.E. if this is 106 then log10K would return 1.
      Returns:
      integer base 10000 logarithm

    • power10K

      public Dfp power10K(int e)
      Get the specified power of 10000.
      Parameters:
      e - desired power
      Returns:
      10000e

    • log10

      public int log10()
      Get the exponent of the greatest power of 10 that is less than or equal to abs(this).
      Returns:
      integer base 10 logarithm

    • power10

      public Dfp power10(int e)
      Return the specified power of 10.
      Parameters:
      e - desired power
      Returns:
      10e

    • complement

      protected int complement(int extra)
      Negate the mantissa of this by computing the complement. Leaves the sign bit unchanged, used internally by add. Denormalized numbers are handled properly here.
      Parameters:
      extra - ???
      Returns:
      ???

    • add

      public Dfp add(Dfp x)
      Add x to this.
      Specified by:
      add in interface FieldElement<Dfp>
      Parameters:
      x - number to add
      Returns:
      sum of this and x

    • negate

      public Dfp negate()
      Returns a number that is this number with the sign bit reversed.
      Returns:
      the opposite of this

    • subtract

      public Dfp subtract(Dfp x)
      Subtract x from this.
      Specified by:
      subtract in interface FieldElement<Dfp>
      Parameters:
      x - number to subtract
      Returns:
      difference of this and a

    • round

      protected int round(int n)
      Round this given the next digit n using the current rounding mode.
      Parameters:
      n - ???
      Returns:
      the IEEE flag if an exception occurred

    • multiply

      public Dfp multiply(Dfp x)
      Multiply this by x.
      Specified by:
      multiply in interface FieldElement<Dfp>
      Parameters:
      x - multiplicand
      Returns:
      product of this and x

    • multiply

      public Dfp multiply(int x)
      Multiply this by a single digit 0<=x<radix. There are speed advantages in this special case
      Parameters:
      x - multiplicand
      Returns:
      product of this and x

    • divide

      public Dfp divide(Dfp divisor)
      Divide this by divisor.
      Specified by:
      divide in interface FieldElement<Dfp>
      Parameters:
      divisor - divisor
      Returns:
      quotient of this by divisor

    • divide

      public Dfp divide(int divisor)
      Divide by a single digit less than radix. Special case, so there are speed advantages. 0 <= divisor < radix
      Parameters:
      divisor - divisor
      Returns:
      quotient of this by divisor

    • sqrt

      public Dfp sqrt()
      Compute the square root.
      Returns:
      square root of the instance

    • toString

      public String toString()
      Get a string representation of the instance.
      Overrides:
      toString in class Object
      Returns:
      string representation of the instance

    • dfp2sci

      protected String dfp2sci()
      Convert an instance to a string using scientific notation.
      Returns:
      string representation of the instance in scientific notation

    • dfp2string

      protected String dfp2string()
      Convert an instance to a string using normal notation.
      Returns:
      string representation of the instance in normal notation

    • dotrap

      public Dfp dotrap(int type, String what, Dfp oper, Dfp result)
      Raises a trap. This does not set the corresponding flag however.
      Parameters:
      type - the trap type
      what - - name of routine trap occurred in
      oper - - input operator to function
      result - - the result computed prior to the trap
      Returns:
      The suggested return value from the trap handler

    • trap

      protected Dfp trap(int type, String what, Dfp oper, Dfp def, Dfp result)
      Trap handler. Subclasses may override this to provide trap functionality per IEEE 854-1987.
      Parameters:
      type - The exception type - e.g. FLAG_OVERFLOW
      what - The name of the routine we were in e.g. divide()
      oper - An operand to this function if any
      def - The default return value if trap not enabled
      result - The result that is specified to be delivered per IEEE 854, if any
      Returns:
      the value that should be return by the operation triggering the trap

    • classify

      public int classify()
      Returns the type - one of FINITE, INFINITE, SNAN, QNAN.
      Returns:
      type of the number

    • copysign

      public static Dfp copysign(Dfp x, Dfp y)
      Creates an instance that is the same as x except that it has the sign of y. abs(x) = dfp.copysign(x, dfp.one)
      Parameters:
      x - number to get the value from
      y - number to get the sign from
      Returns:
      a number with the value of x and the sign of y

    • nextAfter

      public Dfp nextAfter(Dfp x)
      Returns the next number greater than this one in the direction of x. If this==x then simply returns this.
      Parameters:
      x - direction where to look at
      Returns:
      closest number next to instance in the direction of x

    • toDouble

      public double toDouble()
      Convert the instance into a double.
      Returns:
      a double approximating the instance
      See Also:

    • toSplitDouble

      public double[] toSplitDouble()
      Convert the instance into a split double.
      Returns:
      an array of two doubles which sum represent the instance
      See Also: