org.hipparchus.dfp

## Class 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:

1. Decimal math, or close to it
2. Settable precision (but no mix between numbers using different settings)
3. Portability. Code should be kept 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)

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 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.

DfpField
• ### Field Summary

Fields
Modifier and Type Field and 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: 1 for positive, -1 for negative.
static byte SNAN
Indicator value for signaling NaN.
• ### Constructor Summary

Constructors
Modifier Constructor and 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

All Methods
Modifier and Type Method and Description
Dfp abs()
absolute value.
Dfp acos()
Arc cosine operation.
Dfp acosh()
Inverse hyperbolic cosine operation.
Dfp add(Dfp x)
Dfp add(double a)
'+' operator.
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 cbrt()
Cubic root.
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.
Dfp copySign(Dfp s)
Returns the instance with the sign of the argument.
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 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(Dfp divisor)
Divide this by divisor.
Dfp divide(double a)
'÷' operator.
Dfp divide(int divisor)
Divide by a single digit less than radix.
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.
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(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 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 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(Dfp x)
Multiply this by x.
Dfp multiply(double a)
'×' operator.
Dfp multiply(int x)
Multiply this by a single digit 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(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.
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 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(Dfp e)
Power operation.
Dfp pow(double p)
Power operation.
Dfp pow(int n)
Integer 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(Dfp d)
Returns the IEEE remainder.
Dfp remainder(double a)
IEEE remainder operator.
Dfp rint()
Round to nearest integer using the round-half-even method.
Dfp rootN(int n)
Nth 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.
FieldSinCos<Dfp> sinCos()
Combined Sine and Cosine operation.
Dfp sinh()
Hyperbolic sine operation.
FieldSinhCosh<Dfp> sinhCosh()
Combined hyperbolic sine and sosine operation.
Dfp sqrt()
Compute the square root.
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 subtract(double a)
'-' operator.
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

isFinite, norm, round
• ### Field Detail

public static final int RADIX
The radix, or base of this system. Set to 10000
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
Constant Field Values
• #### MAX_EXP

public static final int MAX_EXP
The maximum exponent before overflow is signaled and results flushed to infinity
Constant Field Values
• #### ERR_SCALE

public static final int ERR_SCALE
The amount under/overflows are scaled by before going to trap handler
Constant Field Values
• #### FINITE

public static final byte FINITE
Indicator value for normal finite numbers.
Constant Field Values
• #### INFINITE

public static final byte INFINITE
Indicator value for Infinity.
Constant Field Values
• #### SNAN

public static final byte SNAN
Indicator value for signaling NaN.
Constant Field Values
• #### QNAN

public static final byte QNAN
Indicator value for quiet NaN.
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 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,
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 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
DfpField.getExtendedField(int, boolean)

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

Just another name for CalculusFieldElement.norm()

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:
10000e
• #### 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:
10e
• #### complement

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

public Dfp add(Dfp x)
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 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 FieldElement<Dfp>
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
• #### reciprocal

public Dfp reciprocal()
Returns the multiplicative inverse of this element.
Specified by:
reciprocal in interface CalculusFieldElement<Dfp>
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
toSplitDouble()
• #### toSplitDouble

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

public double getReal()
Get the real value of the number.
Specified by:
getReal in interface FieldElement<Dfp>
Returns:
real value

public Dfp add(double a)
'+' operator.
Specified by:
add in interface CalculusFieldElement<Dfp>
Parameters:
a - right hand side parameter of the operator
Returns:
this+a
• #### subtract

public Dfp subtract(double a)
'-' operator.
Specified by:
subtract in interface CalculusFieldElement<Dfp>
Parameters:
a - right hand side parameter of the operator
Returns:
this-a
• #### multiply

public Dfp multiply(double a)
'×' operator.
Specified by:
multiply in interface CalculusFieldElement<Dfp>
Parameters:
a - right hand side parameter of the operator
Returns:
this×a
• #### divide

public Dfp divide(double a)
'÷' operator.
Specified by:
divide in interface CalculusFieldElement<Dfp>
Parameters:
a - right hand side parameter of the operator
Returns:
this÷a
• #### 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 2x, 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)
• #### cbrt

public Dfp cbrt()
Cubic root.
Specified by:
cbrt in interface CalculusFieldElement<Dfp>
Returns:
cubic root of the instance
• #### rootN

public Dfp rootN(int n)
Nth root.
Specified by:
rootN in interface CalculusFieldElement<Dfp>
Parameters:
n - order of the root
Returns:
nth 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:
thisp
• #### 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:
thise
• #### 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)
• #### sinCos

public FieldSinCos<Dfp> sinCos()
Combined Sine and Cosine operation.
Specified by:
sinCos in interface CalculusFieldElement<Dfp>
Returns:
[sin(this), cos(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 sosine 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

public Dfp toRadians()
Convert degrees to radians, with error of less than 0.5 ULP
Specified by:
toRadians in interface CalculusFieldElement<Dfp>
Returns:
• #### 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:
Σi ai bi.
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:
Σi ai bi.
Throws:
MathIllegalArgumentException - if arrays dimensions don't match
• #### 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