Package org.apfloat

Class Apfloat

  • All Implemented Interfaces:
    Serializable, Comparable<Apfloat>, Formattable
    Direct Known Subclasses:
    Aprational

    public class Apfloat
    extends Apcomplex
    implements Comparable<Apfloat>
    Arbitrary precision floating-point number class.

    Apfloat numbers are immutable.

    A pitfall exists with the constructors Apfloat(float,long) and Apfloat(double,long). Since floats and doubles are always represented internally in radix 2, the conversion to any other radix usually causes round-off errors, and the resulting apfloat won't be accurate to the desired number of digits.

    For example, 0.3 can't be presented exactly in base 2. When you construct an apfloat like new Apfloat(0.3f, 1000), the resulting number won't be accurate to 1000 digits, but only to roughly 7 digits (in radix 10). In fact, the resulting number will be something like 0.30000001192092896...

    If you want an exact representation of a floating-point primitive (which is a rational number), you can use Aprational(double).

    Version:
    1.9.0
    Author:
    Mikko Tommila
    See Also:
    ApfloatMath, Serialized Form
    • Constructor Summary

      Constructors 
      Modifier Constructor Description
      protected Apfloat()
      Default constructor.
        Apfloat​(double value)
      Constructs an apfloat from the specified double.
        Apfloat​(double value, long precision)
      Constructs an apfloat from the specified double and precision.
        Apfloat​(double value, long precision, int radix)
      Constructs an apfloat from the specified double, precision and radix.
        Apfloat​(float value)
      Constructs an apfloat from the specified float.
        Apfloat​(float value, long precision)
      Constructs an apfloat from the specified float and precision.
        Apfloat​(float value, long precision, int radix)
      Constructs an apfloat from the specified float, precision and radix.
        Apfloat​(long value)
      Constructs an apfloat from the specified long.
        Apfloat​(long value, long precision)
      Constructs an apfloat from the specified long and precision.
        Apfloat​(long value, long precision, int radix)
      Constructs an apfloat from the specified long, precision and radix.
        Apfloat​(PushbackReader in)
      Reads an apfloat from a stream using default precision and radix.
        Apfloat​(PushbackReader in, long precision)
      Reads an apfloat from a stream using the specified precision.
        Apfloat​(PushbackReader in, long precision, int radix)
      Reads an apfloat from a stream using the specified precision and radix.
        Apfloat​(String value)
      Constructs an apfloat from the specified string.
        Apfloat​(String value, long precision)
      Constructs an apfloat from the specified string and precision.
        Apfloat​(String value, long precision, int radix)
      Constructs an apfloat from the specified string, precision and radix.
        Apfloat​(BigDecimal value)
      Creates an apfloat from a BigDecimal.
        Apfloat​(BigDecimal value, long precision)
      Creates an apfloat from a BigDecimal.
        Apfloat​(BigInteger value)
      Constructs an apfloat from a BigInteger.
        Apfloat​(BigInteger value, long precision)
      Constructs an apfloat from a BigInteger with the specified precision.
        Apfloat​(BigInteger value, long precision, int radix)
      Constructs an apfloat from a BigInteger with the specified precision and radix.
      protected Apfloat​(ApfloatImpl impl)
      Constructs an apfloat that is backed by the specified ApfloatImpl object.
    • Method Detail

      • radix

        public int radix()
        Radix of this apfloat.
        Overrides:
        radix in class Apcomplex
        Returns:
        Radix of this apfloat.
      • real

        public Apfloat real()
        Real part of this apfloat.
        Overrides:
        real in class Apcomplex
        Returns:
        this
      • precision

        public Apfloat precision​(long precision)
                          throws IllegalArgumentException,
                                 ApfloatRuntimeException
        Returns an apfloat with the same value as this apfloat accurate to the specified precision.

        If the requested precision less than this number's current precision, the functionality is quite obvious: the precision is simply truncated, and e.g. comparison and equality checking will work as expected. Some rounding errors in e.g. addition and subtraction may still occur, as "invisible" trailing digits can remain in the number.

        If the requested precision more than this number's current precision, the functionality is quite undefined: the digits up to this number's current precision are guaranteed to be the same, but the "new" digits are undefined: they may be zero, or they may be digits that have been previously discarded with a call to precision() with a smaller number of digits, or they may be something else, or any combination of these.

        These limitations allow various performance optimizations to be made.

        Overrides:
        precision in class Apcomplex
        Parameters:
        precision - Precision of the new apfloat.
        Returns:
        An apfloat with the specified precision and same value as this apfloat.
        Throws:
        IllegalArgumentException - If precision is <= 0.
        ApfloatRuntimeException
      • scale

        public long scale()
                   throws ApfloatRuntimeException
        Returns the scale of this apfloat. The scale is defined here as

        apfloat = signum * mantissa * radixscale

        where 1/radix <= mantissa < 1. In other words, scale = floor(logradix(apfloat)) + 1.

        For example, 1 has a scale of 1, and 100 has a scale of 3 (in radix 10). For integers, scale is equal to the number of digits in the apfloat.

        Zero has a scale of -INFINITE.

        Note that this definition of scale is different than in java.math.BigDecimal.

        Overrides:
        scale in class Apcomplex
        Returns:
        The exponent of this apfloat in number of digits of the radix in which it's presented.
        Throws:
        ApfloatRuntimeException
        See Also:
        scale()
      • size

        public long size()
                  throws ApfloatRuntimeException
        Returns the size of this apfloat. The size is defined here as

        apfloat = signum * mantissa * radixscale and

        mantissa = n / radixsize

        where 1/radix <= mantissa < 1 and n is the smallest possible integer. In other words, the size is the number of significant digits in the mantissa (excluding leading and trailing zeros but including all zeros between the first and last nonzero digit). For example, 1 has a size of 1, and 100 has also a size of 1 (in radix 10). 11 has a size of 2, and 10001000 has a size of 5.

        Zero has a size of 0.

        Overrides:
        size in class Apcomplex
        Returns:
        The number of digits in this number, from the most significant digit to the least significant nonzero digit, in the radix in which it's presented.
        Throws:
        ApfloatRuntimeException
        Since:
        1.6
        See Also:
        size()
      • signum

        public int signum()
        Returns the signum function of this apfloat.
        Returns:
        -1, 0 or 1 as the value of this apfloat is negative, zero or positive, correspondingly.
      • isInteger

        public boolean isInteger()
                          throws ApfloatRuntimeException
        Returns if this number has an integer value. Note that this does not necessarily mean that this object is an instance of Apint. Neither does it mean that the precision is infinite.
        Overrides:
        isInteger in class Apcomplex
        Returns:
        If this number's value is an integer.
        Throws:
        ApfloatRuntimeException
        Since:
        1.9.0
      • isShort

        public boolean isShort()
                        throws ApfloatRuntimeException
        Returns if this apfloat is "short". In practice an apfloat is "short" if its mantissa fits in one machine word. If the apfloat is "short", some algorithms can be performed faster.

        For example, division by a "short" apfloat requires only a single pass through the data, but that algorithm can't be used for divisors that aren't "short", where calculating an inverse root is required instead.

        The return value of this method is implementation dependent.

        Returns:
        true if the apfloat is "short", false if not.
        Throws:
        ApfloatRuntimeException
      • floor

        public Apint floor()
                    throws ApfloatRuntimeException
        Floor function. Returns the largest (closest to positive infinity) value that is not greater than this apfloat and is equal to a mathematical integer.
        Returns:
        This apfloat rounded towards negative infinity.
        Throws:
        ApfloatRuntimeException
      • ceil

        public Apint ceil()
                   throws ApfloatRuntimeException
        Ceiling function. Returns the smallest (closest to negative infinity) value that is not less than this apfloat and is equal to a mathematical integer.
        Returns:
        This apfloat rounded towards positive infinity.
        Throws:
        ApfloatRuntimeException
      • frac

        public Apfloat frac()
                     throws ApfloatRuntimeException
        Returns the fractional part. The fractional part is always 0 <= abs(frac()) < 1. The fractional part has the same sign as the number. For the fractional and integer parts, this always holds:

        x = x.truncate() + x.frac()

        Returns:
        The fractional part of this apfloat.
        Throws:
        ApfloatRuntimeException
        Since:
        1.7.0
      • doubleValue

        public double doubleValue()
        Returns the value of the this number as a double. If the number is too big to fit in a double, Double.POSITIVE_INFINITY or Double.NEGATIVE_INFINITY is returned.
        Overrides:
        doubleValue in class Apcomplex
        Returns:
        The numeric value represented by this object after conversion to type double.
        See Also:
        doubleValue()
      • floatValue

        public float floatValue()
        Returns the value of the this number as a float. If the number is too big to fit in a float, Float.POSITIVE_INFINITY or Float.NEGATIVE_INFINITY is returned.
        Overrides:
        floatValue in class Apcomplex
        Returns:
        The numeric value represented by this object after conversion to type float.
        See Also:
        floatValue()
      • byteValue

        public byte byteValue()
        Returns the value of the this number as a byte. If the number is too big to fit in a byte, Byte.MIN_VALUE or Byte.MAX_VALUE is returned.
        Overrides:
        byteValue in class Apcomplex
        Returns:
        The numeric value represented by this object after conversion to type byte.
        See Also:
        byteValue()
      • shortValue

        public short shortValue()
        Returns the value of the this number as a short. If the number is too big to fit in a short, Short.MIN_VALUE or Short.MAX_VALUE is returned.
        Overrides:
        shortValue in class Apcomplex
        Returns:
        The numeric value represented by this object after conversion to type short.
        See Also:
        shortValue()
      • intValue

        public int intValue()
        Returns the value of the this number as an int. If the number is too big to fit in an int, Integer.MIN_VALUE or Integer.MAX_VALUE is returned.
        Overrides:
        intValue in class Apcomplex
        Returns:
        The numeric value represented by this object after conversion to type int.
        See Also:
        intValue()
      • longValue

        public long longValue()
        Returns the value of the this number as a long. If the number is too big to fit in a long, Long.MIN_VALUE or Long.MAX_VALUE is returned.
        Overrides:
        longValue in class Apcomplex
        Returns:
        The numeric value represented by this object after conversion to type long.
        See Also:
        longValue()
      • longValueExact

        public long longValueExact()
                            throws ArithmeticException
        Description copied from class: Apcomplex
        Returns the value of the this number as a long, checking for lost information. If the value of this number is out of the range of the long type, then an ArithmeticException is thrown.
        Overrides:
        longValueExact in class Apcomplex
        Returns:
        The numeric value represented by this object after conversion to type long.
        Throws:
        ArithmeticException - If the value of this will not exactly fit in a long.
      • equalDigits

        public long equalDigits​(Apfloat x)
                         throws ApfloatRuntimeException
        Computes number of equal digits.

        Compares the digits of the numbers starting from the most significant digits. The exponent and sign are taken into consideration, so if either one doesn't match, the numbers are considered to have zero equal digits.

        For example, the numbers 12345 and 123456 have zero matching digits, and the numbers 12345 and 12355 have three matching digits.

        The result of this method is roughly equal to Math.min(scale(), x.scale()) - subtract(x).scale() but it typically is a lot more efficient to execute.

        Parameters:
        x - Number to compare with.
        Returns:
        Number of matching digits in the radix in which the numbers are presented.
        Throws:
        ApfloatRuntimeException
      • compareTo

        public int compareTo​(Apfloat x)
        Compare this apfloat to the specified apfloat.

        Note: if two apfloats are compared where one number doesn't have enough precise digits, the mantissa is assumed to contain zeros. For example:

         Apfloat x = new Apfloat("0.12", 2);
         Apfloat y = new Apfloat("0.12345", 5);
         
        Now x.compareTo(y) < 0 because x is assumed to be 0.12000.

        However, new Apfloat("0.12", 2) and new Apfloat("0.12", 5) would be considered equal.

        Specified by:
        compareTo in interface Comparable<Apfloat>
        Parameters:
        x - Apfloat to which this apfloat is to be compared.
        Returns:
        -1, 0 or 1 as this apfloat is numerically less than, equal to, or greater than x.
      • preferCompare

        public boolean preferCompare​(Apfloat x)
        Tests if the comparison with equals and compareTo should be done in the opposite order.

        Implementations should avoid infinite recursion.

        Parameters:
        x - The number to compare to.
        Returns:
        true if this object should invoke x.equals(this) and -x.compareTo(this) instead of comparing normally.
        Since:
        1.7.0
      • equals

        public boolean equals​(Object obj)
        Compares this object to the specified object.

        Note: if two apfloats are compared where one number doesn't have enough precise digits, the mantissa is assumed to contain zeros. See compareTo(Apfloat).

        Overrides:
        equals in class Apcomplex
        Parameters:
        obj - The object to compare with.
        Returns:
        true if the objects are equal; false otherwise.
      • hashCode

        public int hashCode()
        Returns a hash code for this apfloat.
        Overrides:
        hashCode in class Apcomplex
        Returns:
        The hash code value for this object.
      • toString

        public String toString​(boolean pretty)
                        throws ApfloatRuntimeException
        Returns a string representation of this apfloat.
        Overrides:
        toString in class Apcomplex
        Parameters:
        pretty - true to use a fixed-point notation, false to use an exponential notation.
        Returns:
        A string representing this object.
        Throws:
        ApfloatRuntimeException
      • formatTo

        public void formatTo​(Formatter formatter,
                             int flags,
                             int width,
                             int precision)
        Formats the object using the provided formatter.

        The format specifiers affect the output as follows:

        • By default, the exponential notation is used.
        • If the alternate format is specified ('#'), then the fixed-point notation is used.
        • Width is the minimum number of characters output. Any padding is done using spaces. Padding is on the left by default.
        • If the '-' flag is specified, then the padding will be on the right.
        • The precision is the number of significant digts output. If the precision of the number exceeds the number of characters output, the rounding mode for output is undefined.

        The decimal separator will be localized if the formatter specifies a locale. The digits will be localized also, but only if the radix is less than or equal to 10.

        Specified by:
        formatTo in interface Formattable
        Overrides:
        formatTo in class Apcomplex
        Parameters:
        formatter - The formatter.
        flags - The flags to modify the output format.
        width - The minimum number of characters to be written to the output, or -1 for no minimum.
        precision - The maximum number of characters to be written to the output, or -1 for no maximum.
        Since:
        1.3
        See Also:
        formatTo(Formatter,int,int,int)
      • getImpl

        protected ApfloatImpl getImpl​(long precision)
                               throws ApfloatRuntimeException
        Returns an ApfloatImpl representing the actual instance of this apfloat up to the requested precision.

        For apfloats this is simply the underlying ApfloatImpl, but e.g. the Aprational class implements this so that it only returns an approximation of the rational number.

        Parameters:
        precision - Precision of the ApfloatImpl that is needed.
        Returns:
        An ApfloatImpl representing this object to the requested precision.
        Throws:
        ApfloatRuntimeException