org.apache.commons.math3.dfp
Class DfpField

java.lang.Object
  extended by org.apache.commons.math3.dfp.DfpField
All Implemented Interfaces:
Field<Dfp>

public class DfpField
extends Object
implements Field<Dfp>

Field for Decimal floating point instances.

Since:
2.2
Version:
$Id: DfpField.java 1416643 2012-12-03 19:37:14Z tn $

Nested Class Summary
static class DfpField.RoundingMode
          Enumerate for rounding modes.
 
Field Summary
static int FLAG_DIV_ZERO
          IEEE 854-1987 flag for division by zero.
static int FLAG_INEXACT
          IEEE 854-1987 flag for inexact result.
static int FLAG_INVALID
          IEEE 854-1987 flag for invalid operation.
static int FLAG_OVERFLOW
          IEEE 854-1987 flag for overflow.
static int FLAG_UNDERFLOW
          IEEE 854-1987 flag for underflow.
 
Constructor Summary
DfpField(int decimalDigits)
          Create a factory for the specified number of radix digits.
 
Method Summary
 void clearIEEEFlags()
          Clears the IEEE 854 status flags.
static Dfp computeExp(Dfp a, Dfp one)
          Compute exp(a).
static Dfp computeLn(Dfp a, Dfp one, Dfp two)
          Compute ln(a).
 Dfp getE()
          Get the constant e.
 Dfp[] getESplit()
          Get the constant e split in two pieces.
 int getIEEEFlags()
          Get the IEEE 854 status flags.
 Dfp getLn10()
          Get the constant ln(10).
 Dfp getLn2()
          Get the constant ln(2).
 Dfp[] getLn2Split()
          Get the constant ln(2) split in two pieces.
 Dfp getLn5()
          Get the constant ln(5).
 Dfp[] getLn5Split()
          Get the constant ln(5) split in two pieces.
 Dfp getOne()
          Get the constant 1.
 Dfp getPi()
          Get the constant π.
 Dfp[] getPiSplit()
          Get the constant π split in two pieces.
 int getRadixDigits()
          Get the number of radix digits of the Dfp instances built by this factory.
 DfpField.RoundingMode getRoundingMode()
          Get the current rounding mode.
 Class<? extends FieldElement<Dfp>> getRuntimeClass()
          Returns the runtime class of the FieldElement.
 Dfp getSqr2()
          Get the constant √2.
 Dfp getSqr2Reciprocal()
          Get the constant √2 / 2.
 Dfp[] getSqr2Split()
          Get the constant √2 split in two pieces.
 Dfp getSqr3()
          Get the constant √3.
 Dfp getSqr3Reciprocal()
          Get the constant √3 / 3.
 Dfp getTwo()
          Get the constant 2.
 Dfp getZero()
          Get the constant 0.
 Dfp newDfp()
          Makes a Dfp with a value of 0.
 Dfp newDfp(byte x)
          Create an instance from a byte value.
 Dfp newDfp(byte sign, byte nans)
          Creates a Dfp with a non-finite value.
 Dfp newDfp(Dfp d)
          Copy constructor.
 Dfp newDfp(double x)
          Create an instance from a double value.
 Dfp newDfp(int x)
          Create an instance from an int value.
 Dfp newDfp(long x)
          Create an instance from a long value.
 Dfp newDfp(String s)
          Create a Dfp given a String representation.
 void setIEEEFlags(int flags)
          Sets the IEEE 854 status flags.
 void setIEEEFlagsBits(int bits)
          Sets some bits in the IEEE 854 status flags, without changing the already set bits.
 void setRoundingMode(DfpField.RoundingMode mode)
          Set the rounding mode.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

FLAG_INVALID

public static final int FLAG_INVALID
IEEE 854-1987 flag for invalid operation.

See Also:
Constant Field Values

FLAG_DIV_ZERO

public static final int FLAG_DIV_ZERO
IEEE 854-1987 flag for division by zero.

See Also:
Constant Field Values

FLAG_OVERFLOW

public static final int FLAG_OVERFLOW
IEEE 854-1987 flag for overflow.

See Also:
Constant Field Values

FLAG_UNDERFLOW

public static final int FLAG_UNDERFLOW
IEEE 854-1987 flag for underflow.

See Also:
Constant Field Values

FLAG_INEXACT

public static final int FLAG_INEXACT
IEEE 854-1987 flag for inexact result.

See Also:
Constant Field Values
Constructor Detail

DfpField

public DfpField(int decimalDigits)
Create a factory for the specified number of radix digits.

Note that since the Dfp class uses 10000 as its radix, each radix digit is equivalent to 4 decimal digits. This implies that asking for 13, 14, 15 or 16 decimal digits will really lead to a 4 radix 10000 digits in all cases.

Parameters:
decimalDigits - minimal number of decimal digits.
Method Detail

getRadixDigits

public int getRadixDigits()
Get the number of radix digits of the Dfp instances built by this factory.

Returns:
number of radix digits

setRoundingMode

public void setRoundingMode(DfpField.RoundingMode mode)
Set the rounding mode. If not set, the default value is DfpField.RoundingMode.ROUND_HALF_EVEN.

Parameters:
mode - desired rounding mode Note that the rounding mode is common to all Dfp instances belonging to the current DfpField in the system and will affect all future calculations.

getRoundingMode

public DfpField.RoundingMode getRoundingMode()
Get the current rounding mode.

Returns:
current rounding mode

getIEEEFlags

public int getIEEEFlags()
Get the IEEE 854 status flags.

Returns:
IEEE 854 status flags
See Also:
clearIEEEFlags(), setIEEEFlags(int), setIEEEFlagsBits(int), FLAG_INVALID, FLAG_DIV_ZERO, FLAG_OVERFLOW, FLAG_UNDERFLOW, FLAG_INEXACT

clearIEEEFlags

public void clearIEEEFlags()
Clears the IEEE 854 status flags.

See Also:
getIEEEFlags(), setIEEEFlags(int), setIEEEFlagsBits(int), FLAG_INVALID, FLAG_DIV_ZERO, FLAG_OVERFLOW, FLAG_UNDERFLOW, FLAG_INEXACT

setIEEEFlags

public void setIEEEFlags(int flags)
Sets the IEEE 854 status flags.

Parameters:
flags - desired value for the flags
See Also:
getIEEEFlags(), clearIEEEFlags(), setIEEEFlagsBits(int), FLAG_INVALID, FLAG_DIV_ZERO, FLAG_OVERFLOW, FLAG_UNDERFLOW, FLAG_INEXACT

setIEEEFlagsBits

public void setIEEEFlagsBits(int bits)
Sets some bits in the IEEE 854 status flags, without changing the already set bits.

Calling this method is equivalent to call setIEEEFlags(getIEEEFlags() | bits)

Parameters:
bits - bits to set
See Also:
getIEEEFlags(), clearIEEEFlags(), setIEEEFlags(int), FLAG_INVALID, FLAG_DIV_ZERO, FLAG_OVERFLOW, FLAG_UNDERFLOW, FLAG_INEXACT

newDfp

public Dfp newDfp()
Makes a Dfp with a value of 0.

Returns:
a new Dfp with a value of 0

newDfp

public Dfp newDfp(byte x)
Create an instance from a byte value.

Parameters:
x - value to convert to an instance
Returns:
a new Dfp with the same value as x

newDfp

public Dfp newDfp(int x)
Create an instance from an int value.

Parameters:
x - value to convert to an instance
Returns:
a new Dfp with the same value as x

newDfp

public Dfp newDfp(long x)
Create an instance from a long value.

Parameters:
x - value to convert to an instance
Returns:
a new Dfp with the same value as x

newDfp

public Dfp newDfp(double x)
Create an instance from a double value.

Parameters:
x - value to convert to an instance
Returns:
a new Dfp with the same value as x

newDfp

public Dfp newDfp(Dfp d)
Copy constructor.

Parameters:
d - instance to copy
Returns:
a new Dfp with the same value as d

newDfp

public Dfp newDfp(String s)
Create a Dfp given a String representation.

Parameters:
s - string representation of the instance
Returns:
a new Dfp parsed from specified string

newDfp

public Dfp newDfp(byte sign,
                  byte nans)
Creates a Dfp with a non-finite value.

Parameters:
sign - sign of the Dfp to create
nans - code of the value, must be one of Dfp.INFINITE, Dfp.SNAN, Dfp.QNAN
Returns:
a new Dfp with a non-finite value

getZero

public Dfp getZero()
Get the constant 0.

Specified by:
getZero in interface Field<Dfp>
Returns:
a Dfp with value 0

getOne

public Dfp getOne()
Get the constant 1.

Specified by:
getOne in interface Field<Dfp>
Returns:
a Dfp with value 1

getRuntimeClass

public Class<? extends FieldElement<Dfp>> getRuntimeClass()
Returns the runtime class of the FieldElement.

Specified by:
getRuntimeClass in interface Field<Dfp>
Returns:
The Class object that represents the runtime class of this object.

getTwo

public Dfp getTwo()
Get the constant 2.

Returns:
a Dfp with value 2

getSqr2

public Dfp getSqr2()
Get the constant √2.

Returns:
a Dfp with value √2

getSqr2Split

public Dfp[] getSqr2Split()
Get the constant √2 split in two pieces.

Returns:
a Dfp with value √2 split in two pieces

getSqr2Reciprocal

public Dfp getSqr2Reciprocal()
Get the constant √2 / 2.

Returns:
a Dfp with value √2 / 2

getSqr3

public Dfp getSqr3()
Get the constant √3.

Returns:
a Dfp with value √3

getSqr3Reciprocal

public Dfp getSqr3Reciprocal()
Get the constant √3 / 3.

Returns:
a Dfp with value √3 / 3

getPi

public Dfp getPi()
Get the constant π.

Returns:
a Dfp with value π

getPiSplit

public Dfp[] getPiSplit()
Get the constant π split in two pieces.

Returns:
a Dfp with value π split in two pieces

getE

public Dfp getE()
Get the constant e.

Returns:
a Dfp with value e

getESplit

public Dfp[] getESplit()
Get the constant e split in two pieces.

Returns:
a Dfp with value e split in two pieces

getLn2

public Dfp getLn2()
Get the constant ln(2).

Returns:
a Dfp with value ln(2)

getLn2Split

public Dfp[] getLn2Split()
Get the constant ln(2) split in two pieces.

Returns:
a Dfp with value ln(2) split in two pieces

getLn5

public Dfp getLn5()
Get the constant ln(5).

Returns:
a Dfp with value ln(5)

getLn5Split

public Dfp[] getLn5Split()
Get the constant ln(5) split in two pieces.

Returns:
a Dfp with value ln(5) split in two pieces

getLn10

public Dfp getLn10()
Get the constant ln(10).

Returns:
a Dfp with value ln(10)

computeExp

public static Dfp computeExp(Dfp a,
                             Dfp one)
Compute exp(a).

Parameters:
a - number for which we want the exponential
one - constant with value 1 at desired precision
Returns:
exp(a)

computeLn

public static Dfp computeLn(Dfp a,
                            Dfp one,
                            Dfp two)
Compute ln(a). Let f(x) = ln(x), We know that f'(x) = 1/x, thus from Taylor's theorem we have: ----- n+1 n f(x) = \ (-1) (x - 1) / ---------------- for 1 <= n <= infinity ----- n or 2 3 4 (x-1) (x-1) (x-1) ln(x) = (x-1) - ----- + ------ - ------ + ... 2 3 4 alternatively, 2 3 4 x x x ln(x+1) = x - - + - - - + ... 2 3 4 This series can be used to compute ln(x), but it converges too slowly. If we substitute -x for x above, we get 2 3 4 x x x ln(1-x) = -x - - - - - - + ... 2 3 4 Note that all terms are now negative. Because the even powered ones absorbed the sign. Now, subtract the series above from the previous one to get ln(x+1) - ln(1-x). Note the even terms cancel out leaving only the odd ones 3 5 7 2x 2x 2x ln(x+1) - ln(x-1) = 2x + --- + --- + ---- + ... 3 5 7 By the property of logarithms that ln(a) - ln(b) = ln (a/b) we have: 3 5 7 x+1 / x x x \ ln ----- = 2 * | x + ---- + ---- + ---- + ... | x-1 \ 3 5 7 / But now we want to find ln(a), so we need to find the value of x such that a = (x+1)/(x-1). This is easily solved to find that x = (a-1)/(a+1).

Parameters:
a - number for which we want the exponential
one - constant with value 1 at desired precision
two - constant with value 2 at desired precision
Returns:
ln(a)


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