java.lang.Object
- org.apache.commons.math.dfp.Dfp

All Implemented Interfaces:

FieldElement<Dfp>

Direct Known Subclasses:

DfpDec
```
public class Dfp
extends java.lang.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:

DfpField

Field Summary

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

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
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 java.lang.String`	`dfp2sci()`	Convert an instance to a string using scientific notation.
`protected java.lang.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, java.lang.String what, Dfp oper, Dfp result)`	Raises a trap.
`boolean`	`equals(java.lang.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(java.lang.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.
`java.lang.String`	`toString()`	Get a string representation of the instance.
`protected Dfp`	`trap(int type, java.lang.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 Detail
  - RADIX
```
public static final int RADIX
```
    The radix, or base of this system. Set to 10000
    
    See Also:
    
    Constant Field Values
  - MIN_EXP
```
public static final int MIN_EXP
```
    The minimum exponent before underflow is signaled. Flush to zero occurs at minExp-DIGITS
    
    See Also:
    
    Constant Field Values
  - MAX_EXP
```
public static final int MAX_EXP
```
    The maximum exponent before overflow is signaled and results flushed to infinity
    
    See Also:
    
    Constant Field Values
  - ERR_SCALE
```
public static final int ERR_SCALE
```
    The amount under/overflows are scaled by before going to trap handler
    
    See Also:
    
    Constant Field Values
  - FINITE
```
public static final byte FINITE
```
    Indicator value for normal finite numbers.
    
    See Also:
    
    Constant Field Values
  - INFINITE
```
public static final byte INFINITE
```
    Indicator value for Infinity.
    
    See Also:
    
    Constant Field Values
  - SNAN
```
public static final byte SNAN
```
    Indicator value for signaling NaN.
    
    See Also:
    
    Constant Field Values
  - QNAN
```
public static final byte QNAN
```
    Indicator value for quiet NaN.
    
    See Also:
    
    Constant Field Values
  - mant
```
protected int[] mant
```
    Mantissa.
  - sign
```
protected byte sign
```
    Sign bit: & for positive, -1 for negative.
  - exp
```
protected int exp
```
    Exponent.
  - nans
```
protected byte nans
```
    Indicator for non-finite / non-number values.
- Constructor Detail
  - 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,
              java.lang.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 Detail
  - 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(java.lang.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(java.lang.Object other)
```
    Check if instance is equal to x.
    
    Overrides:
    
    equals in class java.lang.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 java.lang.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:
    
    10000^e
  - 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:
    
    10^e
  - 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 java.lang.String toString()
```
    Get a string representation of the instance.
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    string representation of the instance
  - dfp2sci
```
protected java.lang.String dfp2sci()
```
    Convert an instance to a string using scientific notation.
    
    Returns:
    
    string representation of the instance in scientific notation
  - dfp2string
```
protected java.lang.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,
                  java.lang.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,
                   java.lang.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()
  - toSplitDouble
```
public double[] toSplitDouble()
```
    Convert the instance into a split double.
    
    Returns:
    
    an array of two doubles which sum represent the instance
    
    See Also:
    
    toDouble()

Class Dfp

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

RADIX

MIN_EXP

MAX_EXP

ERR_SCALE

FINITE

INFINITE

SNAN

QNAN

mant

sign

exp

nans

Constructor Detail

Dfp

Dfp

Dfp

Dfp

Dfp

Dfp

Dfp

Dfp

Method Detail

newInstance

newInstance

newInstance

newInstance

newInstance

newInstance

newInstance

newInstance

getField

getRadixDigits

getZero

getOne

getTwo

shiftLeft

shiftRight

align

lessThan

greaterThan

isInfinite

isNaN

equals

hashCode

unequal

rint

floor

ceil

remainder

trunc

intValue

log10K

power10K

log10

power10

complement

add

negate

subtract

round

multiply

multiply

divide

divide

sqrt

toString

dfp2sci

dfp2string

dotrap

trap

classify

copysign

nextAfter

toDouble