Package org.apache.commons.math3.dfp

Class DfpField

java.lang.Object
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

  • Field Details

    • FLAG_INVALID

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

    • FLAG_DIV_ZERO

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

    • FLAG_OVERFLOW

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

    • FLAG_UNDERFLOW

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

    • FLAG_INEXACT

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

    • sqr2String

      private static String sqr2String
      High precision string representation of √2.

    • sqr2ReciprocalString

      private static String sqr2ReciprocalString
      High precision string representation of √2 / 2.

    • sqr3String

      private static String sqr3String
      High precision string representation of √3.

    • sqr3ReciprocalString

      private static String sqr3ReciprocalString
      High precision string representation of √3 / 3.

    • piString

      private static String piString
      High precision string representation of π.

    • eString

      private static String eString
      High precision string representation of e.

    • ln2String

      private static String ln2String
      High precision string representation of ln(2).

    • ln5String

      private static String ln5String
      High precision string representation of ln(5).

    • ln10String

      private static String ln10String
      High precision string representation of ln(10).

    • radixDigits

      private final int radixDigits
      The number of radix digits. Note these depend on the radix which is 10000 digits, so each one is equivalent to 4 decimal digits.

    • zero

      private final Dfp zero
      A Dfp with value 0.

    • one

      private final Dfp one
      A Dfp with value 1.

    • two

      private final Dfp two
      A Dfp with value 2.

    • sqr2

      private final Dfp sqr2
      A Dfp with value √2.

    • sqr2Split

      private final Dfp[] sqr2Split
      A two elements Dfp array with value √2 split in two pieces.

    • sqr2Reciprocal

      private final Dfp sqr2Reciprocal
      A Dfp with value √2 / 2.

    • sqr3

      private final Dfp sqr3
      A Dfp with value √3.

    • sqr3Reciprocal

      private final Dfp sqr3Reciprocal
      A Dfp with value √3 / 3.

    • pi

      private final Dfp pi
      A Dfp with value π.

    • piSplit

      private final Dfp[] piSplit
      A two elements Dfp array with value π split in two pieces.

    • e

      private final Dfp e
      A Dfp with value e.

    • eSplit

      private final Dfp[] eSplit
      A two elements Dfp array with value e split in two pieces.

    • ln2

      private final Dfp ln2
      A Dfp with value ln(2).

    • ln2Split

      private final Dfp[] ln2Split
      A two elements Dfp array with value ln(2) split in two pieces.

    • ln5

      private final Dfp ln5
      A Dfp with value ln(5).

    • ln5Split

      private final Dfp[] ln5Split
      A two elements Dfp array with value ln(5) split in two pieces.

    • ln10

      private final Dfp ln10
      A Dfp with value ln(10).

    • rMode

      private DfpField.RoundingMode rMode
      Current rounding mode.

    • ieeeFlags

      private int ieeeFlags
      IEEE 854-1987 signals.

  • Constructor Details

    • 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.

    • DfpField

      private DfpField(int decimalDigits, boolean computeConstants)
      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
      computeConstants - if true, the transcendental constants for the given precision must be computed (setting this flag to false is RESERVED for the internal recursive call)

  • Method Details

    • 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

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

    • setIEEEFlags

      public void setIEEEFlags(int flags)
      Sets the IEEE 854 status flags.
      Parameters:
      flags - desired value for the flags
      See Also:

    • 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:

    • 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)

    • split

      private Dfp[] split(String a)
      Breaks a string representation up into two Dfp's. The split is such that the sum of them is equivalent to the input string, but has higher precision than using a single Dfp.
      Parameters:
      a - string representation of the number to split
      Returns:
      an array of two Dfp instances which sum equals a

    • computeStringConstants

      private static void computeStringConstants(int highPrecisionDecimalDigits)
      Recompute the high precision string constants.
      Parameters:
      highPrecisionDecimalDigits - precision at which the string constants mus be computed

    • computePi

      private static Dfp computePi(Dfp one, Dfp two, Dfp three)
      Compute π using Jonathan and Peter Borwein quartic formula.
      Parameters:
      one - constant with value 1 at desired precision
      two - constant with value 2 at desired precision
      three - constant with value 3 at desired precision
      Returns:
      π

    • 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 invalid input: '<'= n invalid input: '<'= 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)