Dfp
org.apache.commons.math3.dfp

Class Dfp

  • All Implemented Interfaces:
    FieldElement<Dfp>, RealFieldElement<Dfp>
    Direct Known Subclasses:
    DfpDec


    public class Dfpextends Objectimplements RealFieldElement<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)

    Trade offs:

    1. Memory foot print. I'm using more memory than necessary to represent numbers to get better performance.
    2. Digits are bigger, so rounding is a greater loss. So, if you really need 12 decimal digits, better use 4 base 10000 digits there can be one partially filled.

    Numbers are represented in the following form:

      n  =  sign × mant × (radix)exp;

    where sign is ±1, mantissa represents a fractional number between zero and one. mant[0] is the least significant digit. exp is in the range of -32767 to 32768

    IEEE 854-1987 Notes and differences

    IEEE 854 requires the radix to be either 2 or 10. The radix here is 10000, so that requirement is not met, but it is possible that a subclassed can be made to make it behave as a radix 10 number. It is my opinion that if it looks and behaves as a radix 10 number then it is one and that requirement would be met.

    The radix of 10000 was chosen because it should be faster to operate on 4 decimal digits at once instead of one at a time. Radix 10 behavior can be realized by 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:
    DfpField
    • Field Detail

      • RADIX

        public static final int RADIX
        The radix, or base of this system. Set to 10000
        See Also:
        Constant Field Values
      • MIN_EXP

        public static final int MIN_EXP
        The minimum exponent before underflow is signaled. Flush to zero occurs at minExp-DIGITS
        See Also:
        Constant Field Values
      • MAX_EXP

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

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

        public static final byte FINITE
        Indicator value for normal finite numbers.
        See Also:
        Constant Field Values
    • Constructor Detail

      • Dfp

        public Dfp(Dfp d)
        Copy constructor.
        Parameters:
        d - instance to copy
    • Method Detail

      • newInstance

        public Dfp newInstance()
        Create an instance with a value of 0. Use this internally in preference to constructors to facilitate subclasses
        Returns:
        a new instance with a value of 0
      • newInstance

        public Dfp newInstance(byte x)
        Create an instance from a byte value.
        Parameters:
        x - value to convert to an instance
        Returns:
        a new instance with value x
      • newInstance

        public Dfp newInstance(int x)
        Create an instance from an int value.
        Parameters:
        x - value to convert to an instance
        Returns:
        a new instance with value x
      • newInstance

        public Dfp newInstance(long x)
        Create an instance from a long value.
        Parameters:
        x - value to convert to an instance
        Returns:
        a new instance with value x
      • newInstance

        public Dfp newInstance(double x)
        Create an instance from a double value.
        Parameters:
        x - value to convert to an instance
        Returns:
        a new instance with value x
      • newInstance

        public Dfp newInstance(Dfp d)
        Create an instance by copying an existing one. Use this internally in preference to constructors to facilitate subclasses.
        Parameters:
        d - instance to copy
        Returns:
        a new instance with the same value as d
      • newInstance

        public Dfp newInstance(String s)
        Create an instance from a String representation. Use this internally in preference to constructors to facilitate subclasses.
        Parameters:
        s - string representation of the instance
        Returns:
        a new instance parsed from specified string
      • newInstance

        public Dfp newInstance(byte sig,              byte code)
        Creates an instance with a non-finite value.
        Parameters:
        sig - sign of the Dfp to create
        code - code of the value, must be one of INFINITE, SNAN, QNAN
        Returns:
        a new instance with a non-finite value
      • getField

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

        The field is linked to the number of digits and acts as a factory for Dfp instances.

        Specified by:
        getField in interface FieldElement<Dfp>
        Returns:
        Field (really a DfpField) to which the instance belongs
      • getRadixDigits

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

        public Dfp getZero()
        Get the constant 0.
        Returns:
        a Dfp with value zero
      • getOne

        public Dfp getOne()
        Get the constant 1.
        Returns:
        a Dfp with value one
      • getTwo

        public Dfp getTwo()
        Get the constant 2.
        Returns:
        a Dfp with value two
      • 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()
        Get the absolute value of instance.
        Specified by:
        abs in interface RealFieldElement<Dfp>
        Returns:
        absolute value of instance
      • isInfinite

        public boolean isInfinite()
        Check if instance is infinite.
        Returns:
        true if instance is infinite
      • isNaN

        public boolean isNaN()
        Check if instance is not a number.
        Returns:
        true if instance is not a number
      • isZero

        public boolean isZero()
        Check if instance is equal to zero.
        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 RealFieldElement<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 RealFieldElement<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 RealFieldElement<Dfp>
        Returns:
        rounded value
      • remainder

        public Dfp remainder(Dfp d)
        Returns the IEEE remainder.
        Specified by:
        remainder in interface RealFieldElement<Dfp>
        Parameters:
        d - divisor
        Returns:
        this less n × d, where n is the integer closest to this/d
      • 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
      • 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 FieldElement<Dfp>
        Parameters:
        x - number to subtract
        Returns:
        difference of this and a
      • 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
      • sqrt

        public Dfp sqrt()
        Compute the square root.
        Specified by:
        sqrt in interface RealFieldElement<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
      • 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
      • 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 RealFieldElement<Dfp>
        Returns:
        real value
      • add

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

        public Dfp divide(double a)
        '÷s;' operator.
        Specified by:
        divide in interface RealFieldElement<Dfp>
        Parameters:
        a - right hand side parameter of the operator
        Returns:
        this÷s;a
      • remainder

        public Dfp remainder(double a)
        IEEE remainder operator.
        Specified by:
        remainder in interface RealFieldElement<Dfp>
        Parameters:
        a - right hand side parameter of the operator
        Returns:
        this - n × a where n is the closest integer to this/a (the even integer is chosen for n if this/a is halfway between two integers)
      • signum

        public Dfp signum()
        Compute the signum of the instance. The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise
        Specified by:
        signum in interface RealFieldElement<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 RealFieldElement<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 RealFieldElement<Dfp>
        Parameters:
        s - the sign for the returned value
        Returns:
        the instance with the same sign as the sign argument
      • scalb

        public Dfp scalb(int n)
        Multiply the instance by a power of 2.
        Specified by:
        scalb in interface RealFieldElement<Dfp>
        Parameters:
        n - power of 2
        Returns:
        this × 2n
      • 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 RealFieldElement<Dfp>
        Parameters:
        y - a value
        Returns:
        sqrt(this2 +y2)
      • rootN

        public Dfp rootN(int n)
        Nth root.
        Specified by:
        rootN in interface RealFieldElement<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 RealFieldElement<Dfp>
        Parameters:
        p - power to apply
        Returns:
        thisp
      • pow

        public Dfp pow(int n)
        Integer power operation.
        Specified by:
        pow in interface RealFieldElement<Dfp>
        Parameters:
        n - power to apply
        Returns:
        thisn
      • expm1

        public Dfp expm1()
        Exponential minus 1.
        Specified by:
        expm1 in interface RealFieldElement<Dfp>
        Returns:
        exponential minus one of the instance
      • log

        public Dfp log()
        Natural logarithm.
        Specified by:
        log in interface RealFieldElement<Dfp>
        Returns:
        logarithm of the instance
      • log1p

        public Dfp log1p()
        Shifted natural logarithm.
        Specified by:
        log1p in interface RealFieldElement<Dfp>
        Returns:
        logarithm of one plus the instance
      • log10

        @Deprecatedpublic int log10()
        Deprecated. as of 3.2, replaced by intLog10(), in 4.0 the return type will be changed to Dfp
        Get the exponent of the greatest power of 10 that is less than or equal to abs(this).
        Returns:
        integer base 10 logarithm
      • acosh

        public Dfp acosh()
        Inverse hyperbolic cosine operation.
        Specified by:
        acosh in interface RealFieldElement<Dfp>
        Returns:
        acosh(this)
      • atanh

        public Dfp atanh()
        Inverse hyperbolic tangent operation.
        Specified by:
        atanh in interface RealFieldElement<Dfp>
        Returns:
        atanh(this)

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