org.hipparchus.dfp.Dfp

All Implemented Interfaces:: CalculusFieldElement<Dfp>, FieldElement<Dfp>

Direct Known Subclasses:: DfpDec

public class Dfp extends Object implements CalculusFieldElement<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:

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

Trade offs:

Memory foot print. I'm using more memory than necessary to represent numbers to get better performance.
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: \[ n = \mathrm{sign} \times \mathrm{mant} \times \mathrm{radix}^\mathrm{exp} \] 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 adding 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.

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: 1 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

abs()

absolute value.

Dfp

acos()

Arc cosine operation.

Dfp

acosh()

Inverse hyperbolic cosine operation.

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

asin()

Arc sine operation.

Dfp

asinh()

Inverse hyperbolic sine operation.

Dfp

atan()

Arc tangent operation.

Dfp

atan2(Dfp x)

Two arguments arc tangent operation.

Dfp

atanh()

Inverse hyperbolic tangent operation.

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.

Dfp

copySign(double s)

Returns the instance with the sign of the argument.

Dfp

copySign(Dfp s)

Returns the instance with the sign of the argument.

Dfp

cos()

Cosine operation.

Dfp

cosh()

Hyperbolic cosine operation.

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

exp()

Exponential.

Dfp

expm1()

Exponential minus 1.

Dfp

floor()

Round to an integer using the round floor mode.

Dfp

getAddendum()

Get the addendum to the real value of the number.

int

getExponent()

Return the exponent of the instance, removing the bias.

DfpField

getField()

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

Dfp

getOne()

Get the constant 1.

Dfp

getPi()

Get the Archimedes constant π.

int

getRadixDigits()

Get the number of radix digits of the instance.

double

getReal()

Get the real value of the number.

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.

Dfp

hypot(Dfp y)

Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +y²) avoiding intermediate overflow or underflow.

int

intLog10()

Get the exponent of the greatest power of 10 that is less than or equal to abs(this).

int

intValue()

Convert this to an integer.

boolean

isInfinite()

Check if the instance is infinite.

boolean

isNaN()

Check if the instance is Not a Number.

boolean

isZero()

Check if instance is equal to zero.

boolean

lessThan(Dfp x)

Check if instance is less than x.

Dfp

linearCombination(double[] a, Dfp[] b)

Compute a linear combination.

Dfp

linearCombination(double a1, Dfp b1, double a2, Dfp b2)

Compute a linear combination.

Dfp

linearCombination(double a1, Dfp b1, double a2, Dfp b2, double a3, Dfp b3)

Compute a linear combination.

Dfp

linearCombination(double a1, Dfp b1, double a2, Dfp b2, double a3, Dfp b3, double a4, Dfp b4)

Compute a linear combination.

Dfp

linearCombination(Dfp[] a, Dfp[] b)

Compute a linear combination.

Dfp

linearCombination(Dfp a1, Dfp b1, Dfp a2, Dfp b2)

Compute a linear combination.

Dfp

linearCombination(Dfp a1, Dfp b1, Dfp a2, Dfp b2, Dfp a3, Dfp b3)

Compute a linear combination.

Dfp

linearCombination(Dfp a1, Dfp b1, Dfp a2, Dfp b2, Dfp a3, Dfp b3, Dfp a4, Dfp b4)

Compute a linear combination.

Dfp

log()

Natural logarithm.

Dfp

log10()

Base 10 logarithm.

int

log10K()

Get the exponent of the greatest power of 10000 that is less than or equal to the absolute value of this.

Dfp

log1p()

Shifted natural logarithm.

Dfp

multiply(int x)

Multiply this by a single digit x.

Dfp

multiply(Dfp x)

Multiply this by x.

Dfp

negate()

Returns a number that is this number with the sign bit reversed.

boolean

negativeOrNull()

Check if instance is less than or equal to 0.

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 corresponding to a constant real 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

newInstance(DfpField targetField, DfpField.RoundingMode rmode)

Creates an instance by converting the instance to a different field (i.e. different accuracy).

Dfp

nextAfter(Dfp x)

Returns the next number greater than this one in the direction of x.

boolean

positiveOrNull()

Check if instance is greater than or equal to 0.

Dfp

pow(double p)

Power operation.

Dfp

pow(int n)

Integer power operation.

Dfp

pow(Dfp e)

Power operation.

Dfp

power10(int e)

Return the specified power of 10.

Dfp

power10K(int e)

Get the specified power of 10000.

Dfp

reciprocal()

Returns the multiplicative inverse of this element.

Dfp

remainder(double a)

IEEE remainder operator.

Dfp

remainder(Dfp d)

Returns the IEEE remainder.

Dfp

rint()

Round to nearest integer using the round-half-even method.

Dfp

rootN(int n)

N^th root.

protected int

round(int n)

Round this given the next digit n using the current rounding mode.

Dfp

scalb(int n)

Multiply the instance by a power of 2.

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

sign()

Compute the sign of the instance.

Dfp

sin()

Sine operation.

Dfp

sinh()

Hyperbolic sine operation.

FieldSinhCosh<Dfp>

sinhCosh()

Combined hyperbolic sine and cosine operation.

Dfp

sqrt()

Compute the square root.

Dfp

square()

Compute this × this.

boolean

strictlyNegative()

Check if instance is strictly less than 0.

boolean

strictlyPositive()

Check if instance is strictly greater than 0.

Dfp

subtract(Dfp x)

Subtract x from this.

Dfp

tan()

Tangent operation.

Dfp

tanh()

Hyperbolic tangent operation.

Dfp

toDegrees()

Convert radians to degrees, with error of less than 0.5 ULP

double

toDouble()

Convert the instance into a double.

Dfp

toRadians()

Convert degrees to radians, with error of less than 0.5 ULP

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.

Dfp

ulp()

Compute least significant bit (Unit in Last Position) for a number.

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

Methods inherited from interface org.hipparchus.CalculusFieldElement
add, cbrt, divide, isFinite, multiply, norm, round, sinCos, subtract

Field Details
- 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: 1 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 corresponding to a constant real value.
  
  Specified by:
  
  newInstance in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  x - constant real value
  
  Returns:
  
  instance corresponding to a constant real value
- 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
- newInstance
  
  public Dfp newInstance(DfpField targetField, DfpField.RoundingMode rmode)
  
  Creates an instance by converting the instance to a different field (i.e. different accuracy).
  If the target field as a greater number of digits, the extra least significant digits will be set to zero.
  Parameters:
  
  targetField - field to convert the instance to
  
  rmode - rounding mode to use if target field as less digits than the instance, can be null otherwise
  
  Returns:
  
  converted instance (or the instance itself if it already has the required number of digits)
  
  Since:
  
  1.7
  
  See Also:
  
  DfpField.getExtendedField(int, boolean)
- 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
- negativeOrNull
  
  public boolean negativeOrNull()
  
  Check if instance is less than or equal to 0.
  
  Returns:
  
  true if instance is not NaN and less than or equal to 0, false otherwise
- strictlyNegative
  
  public boolean strictlyNegative()
  
  Check if instance is strictly less than 0.
  
  Returns:
  
  true if instance is not NaN and less than or equal to 0, false otherwise
- positiveOrNull
  
  public boolean positiveOrNull()
  
  Check if instance is greater than or equal to 0.
  
  Returns:
  
  true if instance is not NaN and greater than or equal to 0, false otherwise
- strictlyPositive
  
  public boolean strictlyPositive()
  
  Check if instance is strictly greater than 0.
  
  Returns:
  
  true if instance is not NaN and greater than or equal to 0, false otherwise
- abs
  
  public Dfp abs()
  
  absolute value.
  
  Specified by:
  
  abs in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  abs(this)
- isInfinite
  
  public boolean isInfinite()
  
  Check if the instance is infinite.
  
  Specified by:
  
  isInfinite in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  true if the instance is infinite
- isNaN
  
  public boolean isNaN()
  
  Check if the instance is Not a Number.
  
  Specified by:
  
  isNaN in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  true if the instance is Not a Number
- isZero
  
  public boolean isZero()
  
  Check if instance is equal to zero.
  
  Specified by:
  
  isZero in interface FieldElement<Dfp>
  
  Returns:
  
  true if instance is equal to zero
- 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.
  
  Specified by:
  
  rint in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  rounded value
- floor
  
  public Dfp floor()
  
  Round to an integer using the round floor mode. That is, round toward -Infinity
  
  Specified by:
  
  floor in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  rounded value
- ceil
  
  public Dfp ceil()
  
  Round to an integer using the round ceil mode. That is, round toward +Infinity
  
  Specified by:
  
  ceil in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  rounded value
- remainder
  
  public Dfp remainder(Dfp d)
  
  Returns the IEEE remainder.
  
  Specified by:
  
  remainder in interface CalculusFieldElement<Dfp>
  
  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
- intLog10
  
  public int intLog10()
  
  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.
  
  Specified by:
  
  negate in interface FieldElement<Dfp>
  
  Returns:
  
  the opposite of this
- subtract
  
  public Dfp subtract(Dfp x)
  
  Subtract x from this.
  
  Specified by:
  
  subtract in interface CalculusFieldElement<Dfp>
  
  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 x.
  
  Specified by:
  
  multiply in interface CalculusFieldElement<Dfp>
  
  Specified by:
  
  multiply in interface FieldElement<Dfp>
  
  Parameters:
  
  x - multiplicand
  
  Returns:
  
  product of this and x
- square
  
  public Dfp square()
  
  Compute this × this.
  
  Specified by:
  
  square in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  a new element representing this × this
- divide
  
  public Dfp divide(Dfp divisor)
  
  Divide this by divisor.
  
  Specified by:
  
  divide in interface CalculusFieldElement<Dfp>
  
  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
- reciprocal
  
  public Dfp reciprocal()
  
  Returns the multiplicative inverse of this element.
  
  Specified by:
  
  reciprocal in interface FieldElement<Dfp>
  
  Returns:
  
  the inverse of this.
- sqrt
  
  public Dfp sqrt()
  
  Compute the square root.
  
  Specified by:
  
  sqrt in interface CalculusFieldElement<Dfp>
  
  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()
- 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()
- getReal
  
  public double getReal()
  
  Get the real value of the number.
  
  Specified by:
  
  getReal in interface FieldElement<Dfp>
  
  Returns:
  
  real value
- getAddendum
  
  public Dfp getAddendum()
  
  Get the addendum to the real value of the number.
  The addendum is considered to be the part that when added back to the real part recovers the instance. This means that when e.getReal() is finite (i.e. neither infinite nor NaN), then e.getAddendum().add(e.getReal()) is e and e.subtract(e.getReal()) is e.getAddendum(). Beware that for non-finite numbers, these two equalities may not hold. The first equality (with the addition), always holds even for infinity and NaNs if the real part is independent of the addendum (this is the case for all derivatives types, as well as for complex and Dfp, but it is not the case for Tuple and FieldTuple). The second equality (with the subtraction), generally doesn't hold for non-finite numbers, because the subtraction generates NaNs.
  
  Specified by:
  
  getAddendum in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  real value
- remainder
  
  public Dfp remainder(double a)
  
  IEEE remainder operator.
  
  Specified by:
  
  remainder in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  a - right hand side parameter of the operator
  
  Returns:
  
  this - n × a where n is the closest integer to this/a
- sign
  
  public Dfp sign()
  
  Compute the sign of the instance. The sign is -1 for negative numbers, +1 for positive numbers and 0 otherwise, for Complex number, it is extended on the unit circle (equivalent to z/|z|, with special handling for 0 and NaN)
  
  Specified by:
  
  sign in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
- copySign
  
  public Dfp copySign(Dfp s)
  
  Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
  
  Specified by:
  
  copySign in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  s - the sign for the returned value
  
  Returns:
  
  the instance with the same sign as the sign argument
- copySign
  
  public Dfp copySign(double s)
  
  Returns the instance with the sign of the argument. A NaN sign argument is treated as positive.
  
  Specified by:
  
  copySign in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  s - the sign for the returned value
  
  Returns:
  
  the instance with the same sign as the sign argument
- getExponent
  
  public int getExponent()
  
  Return the exponent of the instance, removing the bias.
  For double numbers of the form 2^x, the unbiased exponent is exactly x.
  
  Specified by:
  
  getExponent in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  exponent for the instance, without bias
- scalb
  
  public Dfp scalb(int n)
  
  Multiply the instance by a power of 2.
  
  Specified by:
  
  scalb in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  n - power of 2
  
  Returns:
  
  this × 2ⁿ
- ulp
  
  public Dfp ulp()
  
  Compute least significant bit (Unit in Last Position) for a number.
  
  Specified by:
  
  ulp in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  ulp(this)
- hypot
  
  public Dfp hypot(Dfp y)
  Returns the hypotenuse of a triangle with sides this and y - sqrt(this² +y²) avoiding intermediate overflow or underflow.
  
  If either argument is infinite, then the result is positive infinity.
  
  else, if either argument is NaN then the result is NaN.
  Specified by:
  
  hypot in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  y - a value
  
  Returns:
  
  sqrt(this² +y²)
- rootN
  
  public Dfp rootN(int n)
  
  N^th root.
  
  Specified by:
  
  rootN in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  n - order of the root
  
  Returns:
  
  n^th root of the instance
- pow
  
  public Dfp pow(double p)
  
  Power operation.
  
  Specified by:
  
  pow in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  p - power to apply
  
  Returns:
  
  this^p
- pow
  
  public Dfp pow(int n)
  
  Integer power operation.
  
  Specified by:
  
  pow in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  n - power to apply
  
  Returns:
  
  thisⁿ
- pow
  
  public Dfp pow(Dfp e)
  
  Power operation.
  
  Specified by:
  
  pow in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  e - exponent
  
  Returns:
  
  this^e
- exp
  
  public Dfp exp()
  
  Exponential.
  
  Specified by:
  
  exp in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  exponential of the instance
- expm1
  
  public Dfp expm1()
  
  Exponential minus 1.
  
  Specified by:
  
  expm1 in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  exponential minus one of the instance
- log
  
  public Dfp log()
  
  Natural logarithm.
  
  Specified by:
  
  log in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  logarithm of the instance
- log1p
  
  public Dfp log1p()
  
  Shifted natural logarithm.
  
  Specified by:
  
  log1p in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  logarithm of one plus the instance
- log10
  
  public Dfp log10()
  
  Base 10 logarithm.
  
  Specified by:
  
  log10 in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  base 10 logarithm of the instance
- cos
  
  public Dfp cos()
  
  Cosine operation.
  
  Specified by:
  
  cos in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  cos(this)
- sin
  
  public Dfp sin()
  
  Sine operation.
  
  Specified by:
  
  sin in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  sin(this)
- tan
  
  public Dfp tan()
  
  Tangent operation.
  
  Specified by:
  
  tan in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  tan(this)
- acos
  
  public Dfp acos()
  
  Arc cosine operation.
  
  Specified by:
  
  acos in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  acos(this)
- asin
  
  public Dfp asin()
  
  Arc sine operation.
  
  Specified by:
  
  asin in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  asin(this)
- atan
  
  public Dfp atan()
  
  Arc tangent operation.
  
  Specified by:
  
  atan in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  atan(this)
- atan2
  
  public Dfp atan2(Dfp x) throws MathIllegalArgumentException
  
  Two arguments arc tangent operation.
  Beware of the order or arguments! As this is based on a two-arguments functions, in order to be consistent with arguments order, the instance is the first argument and the single provided argument is the second argument. In order to be consistent with programming languages atan2, this method computes atan2(this, x), i.e. the instance represents the y argument and the x argument is the one passed as a single argument. This may seem confusing especially for users of Wolfram alpha, as this site is not consistent with programming languages atan2 two-arguments arc tangent and puts x as its first argument.
  
  Specified by:
  
  atan2 in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  x - second argument of the arc tangent
  
  Returns:
  
  atan2(this, x)
  
  Throws:
  
  MathIllegalArgumentException - if number of free parameters or orders are inconsistent
- cosh
  
  public Dfp cosh()
  
  Hyperbolic cosine operation.
  
  Specified by:
  
  cosh in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  cosh(this)
- sinh
  
  public Dfp sinh()
  
  Hyperbolic sine operation.
  
  Specified by:
  
  sinh in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  sinh(this)
- sinhCosh
  
  public FieldSinhCosh<Dfp> sinhCosh()
  
  Combined hyperbolic sine and cosine operation.
  
  Specified by:
  
  sinhCosh in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  [sinh(this), cosh(this)]
- tanh
  
  public Dfp tanh()
  
  Hyperbolic tangent operation.
  
  Specified by:
  
  tanh in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  tanh(this)
- acosh
  
  public Dfp acosh()
  
  Inverse hyperbolic cosine operation.
  
  Specified by:
  
  acosh in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  acosh(this)
- asinh
  
  public Dfp asinh()
  
  Inverse hyperbolic sine operation.
  
  Specified by:
  
  asinh in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  asin(this)
- atanh
  
  public Dfp atanh()
  
  Inverse hyperbolic tangent operation.
  
  Specified by:
  
  atanh in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  atanh(this)
- toDegrees
  
  public Dfp toDegrees()
  
  Convert radians to degrees, with error of less than 0.5 ULP
  
  Specified by:
  
  toDegrees in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  instance converted into degrees
- toRadians
  
  public Dfp toRadians()
  
  Convert degrees to radians, with error of less than 0.5 ULP
  
  Specified by:
  
  toRadians in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  instance converted into radians
- linearCombination
  
  public Dfp linearCombination(Dfp[] a, Dfp[] b) throws MathIllegalArgumentException
  
  Compute a linear combination.
  
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  a - Factors.
  
  b - Factors.
  
  Returns:
  
  Σ_i a_i b_i.
  
  Throws:
  
  MathIllegalArgumentException - if arrays dimensions don't match
- linearCombination
  
  public Dfp linearCombination(double[] a, Dfp[] b) throws MathIllegalArgumentException
  
  Compute a linear combination.
  
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  a - Factors.
  
  b - Factors.
  
  Returns:
  
  Σ_i a_i b_i.
  
  Throws:
  
  MathIllegalArgumentException - if arrays dimensions don't match
- linearCombination
  
  public Dfp linearCombination(Dfp a1, Dfp b1, Dfp a2, Dfp b2)
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  a1 - first factor of the first term
  
  b1 - second factor of the first term
  
  a2 - first factor of the second term
  
  b2 - second factor of the second term
  
  Returns:
  
  a₁×b₁ + a₂×b₂
  
  See Also:
  
  CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
  
  CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
- linearCombination
  
  public Dfp linearCombination(double a1, Dfp b1, double a2, Dfp b2)
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  a1 - first factor of the first term
  
  b1 - second factor of the first term
  
  a2 - first factor of the second term
  
  b2 - second factor of the second term
  
  Returns:
  
  a₁×b₁ + a₂×b₂
  
  See Also:
  
  CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
  
  CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
- linearCombination
  
  public Dfp linearCombination(Dfp a1, Dfp b1, Dfp a2, Dfp b2, Dfp a3, Dfp b3)
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  a1 - first factor of the first term
  
  b1 - second factor of the first term
  
  a2 - first factor of the second term
  
  b2 - second factor of the second term
  
  a3 - first factor of the third term
  
  b3 - second factor of the third term
  
  Returns:
  
  a₁×b₁ + a₂×b₂ + a₃×b₃
  
  See Also:
  
  CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
  
  CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
- linearCombination
  
  public Dfp linearCombination(double a1, Dfp b1, double a2, Dfp b2, double a3, Dfp b3)
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  a1 - first factor of the first term
  
  b1 - second factor of the first term
  
  a2 - first factor of the second term
  
  b2 - second factor of the second term
  
  a3 - first factor of the third term
  
  b3 - second factor of the third term
  
  Returns:
  
  a₁×b₁ + a₂×b₂ + a₃×b₃
  
  See Also:
  
  CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement)
  
  CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement, double, FieldElement)
- linearCombination
  
  public Dfp linearCombination(Dfp a1, Dfp b1, Dfp a2, Dfp b2, Dfp a3, Dfp b3, Dfp a4, Dfp b4)
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  a1 - first factor of the first term
  
  b1 - second factor of the first term
  
  a2 - first factor of the second term
  
  b2 - second factor of the second term
  
  a3 - first factor of the third term
  
  b3 - second factor of the third term
  
  a4 - first factor of the fourth term
  
  b4 - second factor of the fourth term
  
  Returns:
  
  a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
  
  See Also:
  
  CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement)
  
  CalculusFieldElement.linearCombination(FieldElement, FieldElement, FieldElement, FieldElement, FieldElement, FieldElement)
- linearCombination
  
  public Dfp linearCombination(double a1, Dfp b1, double a2, Dfp b2, double a3, Dfp b3, double a4, Dfp b4)
  
  Compute a linear combination.
  Specified by:
  
  linearCombination in interface CalculusFieldElement<Dfp>
  
  Parameters:
  
  a1 - first factor of the first term
  
  b1 - second factor of the first term
  
  a2 - first factor of the second term
  
  b2 - second factor of the second term
  
  a3 - first factor of the third term
  
  b3 - second factor of the third term
  
  a4 - first factor of the fourth term
  
  b4 - second factor of the fourth term
  
  Returns:
  
  a₁×b₁ + a₂×b₂ + a₃×b₃ + a₄×b₄
  
  See Also:
  
  CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement)
  
  CalculusFieldElement.linearCombination(double, FieldElement, double, FieldElement, double, FieldElement)
- getPi
  
  public Dfp getPi()
  
  Get the Archimedes constant π.
  Archimedes constant is the ratio of a circle's circumference to its diameter.
  
  Specified by:
  
  getPi in interface CalculusFieldElement<Dfp>
  
  Returns:
  
  Archimedes constant π

Class Dfp

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface org.hipparchus.CalculusFieldElement

Field Details

RADIX

MIN_EXP

MAX_EXP

ERR_SCALE

FINITE

INFINITE

SNAN

QNAN

mant

sign

exp

nans

Constructor Details

Dfp

Dfp

Dfp

Dfp

Dfp

Dfp

Dfp

Dfp

Method Details

newInstance

newInstance

newInstance

newInstance

newInstance

newInstance

newInstance

newInstance

newInstance

getField

getRadixDigits

getZero

getOne

getTwo

shiftLeft

shiftRight

align

lessThan

greaterThan

negativeOrNull

strictlyNegative

positiveOrNull

strictlyPositive

abs

isInfinite

isNaN

isZero

equals

hashCode

unequal

rint

floor

ceil

remainder

trunc

intValue

log10K

power10K

intLog10

power10

complement

add

negate

subtract

round

multiply

multiply

square

divide

divide

reciprocal