Class OrderedTuple
- All Implemented Interfaces:
Comparable<OrderedTuple>
Ordering is done by encoding all components of the T-uple into a
single scalar value and using this value as the sorting
key. Encoding is performed using the method invented by Georg
Cantor in 1877 when he proved it was possible to establish a
bijection between a line and a plane. The binary representations of
the components of the T-uple are mixed together to form a single
scalar. This means that the 2k bit of component 0 is
followed by the 2k bit of component 1, then by the
2k bit of component 2 up to the 2k bit of
component t
, which is followed by the 2k-1
bit of component 0, followed by the 2k-1 bit of
component 1 ... The binary representations are extended as needed
to handle numbers with different scales and a suitable
2p offset is added to the components in order to avoid
negative numbers (this offset is adjusted as needed during the
comparison operations).
The more interesting property of the encoding method for our purpose is that it allows to select all the points that are in a given range. This is depicted in dimension 2 by the following picture:

This picture shows a set of 100000 random 2-D pairs having their first component between -50 and +150 and their second component between -350 and +50. We wanted to extract all pairs having their first component between +30 and +70 and their second component between -120 and -30. We built the lower left point at coordinates (30, -120) and the upper right point at coordinates (70, -30). All points smaller than the lower left point are drawn in red and all points larger than the upper right point are drawn in blue. The green points are between the two limits. This picture shows that all the desired points are selected, along with spurious points. In this case, we get 15790 points, 4420 of which really belonging to the desired rectangle. It is possible to extract very small subsets. As an example extracting from the same 100000 points set the points having their first component between +30 and +31 and their second component between -91 and -90, we get a subset of 11 points, 2 of which really belonging to the desired rectangle.
the previous selection technique can be applied in all dimensions, still using two points to define the interval. The first point will have all its components set to their lower bounds while the second point will have all its components set to their upper bounds.
T-uples with negative infinite or positive infinite components are sorted logically.
Since the specification of the Comparator
interface
allows only ClassCastException
errors, some arbitrary
choices have been made to handle specific cases. The rationale for
these choices is to keep regular and consistent T-uples
together.
- instances with different dimensions are sorted according to their dimension regardless of their components values
- instances with
Double.NaN
components are sorted after all other ones (even after instances with positive infinite components - instances with both positive and negative infinite components
are considered as if they had
Double.NaN
components
- Since:
- 3.0
-
Field Summary
FieldsModifier and TypeFieldDescriptionprivate double[]
Deprecated.Double components of the T-uple.private long[]
Deprecated.Ordering encoding of the double components.private static final long
Deprecated.Exponent bits mask.private static final long
Deprecated.Implicit MSB for normalized numbers.private int
Deprecated.Least Significant Bit scale.private static final long
Deprecated.Mantissa bits mask.private boolean
Deprecated.Not A Number marker.private boolean
Deprecated.Negative infinity marker.private int
Deprecated.Offset scale.private boolean
Deprecated.Positive infinity marker.private static final long
Deprecated.Sign bit mask. -
Constructor Summary
ConstructorsConstructorDescriptionOrderedTuple
(double... components) Deprecated.Build an ordered T-uple from its components. -
Method Summary
Modifier and TypeMethodDescriptionint
Deprecated.Compares this ordered T-uple with the specified object.private static int
computeLSB
(long l) Deprecated.Compute the least significant bit of a long.private static int
computeMSB
(long l) Deprecated.Compute the most significant bit of a long.private void
encode
(int minOffset) Deprecated.Encode the T-uple with a given offset.boolean
Deprecated.private static int
exponent
(long bits) Deprecated.Extract the exponent from the bits of a double.private int
getBit
(int i, int k) Deprecated.Get a bit from the mantissa of a double.double[]
Deprecated.Get the components array.int
hashCode()
Deprecated.private static long
mantissa
(long bits) Deprecated.Extract the mantissa from the bits of a double.private static long
sign
(long bits) Deprecated.Extract the sign from the bits of a double.
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Field Details
-
SIGN_MASK
private static final long SIGN_MASKDeprecated.Sign bit mask.- See Also:
-
EXPONENT_MASK
private static final long EXPONENT_MASKDeprecated.Exponent bits mask.- See Also:
-
MANTISSA_MASK
private static final long MANTISSA_MASKDeprecated.Mantissa bits mask.- See Also:
-
IMPLICIT_ONE
private static final long IMPLICIT_ONEDeprecated.Implicit MSB for normalized numbers.- See Also:
-
components
private double[] componentsDeprecated.Double components of the T-uple. -
offset
private int offsetDeprecated.Offset scale. -
lsb
private int lsbDeprecated.Least Significant Bit scale. -
encoding
private long[] encodingDeprecated.Ordering encoding of the double components. -
posInf
private boolean posInfDeprecated.Positive infinity marker. -
negInf
private boolean negInfDeprecated.Negative infinity marker. -
nan
private boolean nanDeprecated.Not A Number marker.
-
-
Constructor Details
-
OrderedTuple
public OrderedTuple(double... components) Deprecated.Build an ordered T-uple from its components.- Parameters:
components
- double components of the T-uple
-
-
Method Details
-
encode
private void encode(int minOffset) Deprecated.Encode the T-uple with a given offset.- Parameters:
minOffset
- minimal scale of the offset to add to all components (must be greater than the MSBs of all components)
-
compareTo
Deprecated.Compares this ordered T-uple with the specified object.The ordering method is detailed in the general description of the class. Its main property is to be consistent with distance: geometrically close T-uples stay close to each other when stored in a sorted collection using this comparison method.
T-uples with negative infinite, positive infinite are sorted logically.
Some arbitrary choices have been made to handle specific cases. The rationale for these choices is to keep normal and consistent T-uples together.
- instances with different dimensions are sorted according to their dimension regardless of their components values
- instances with
Double.NaN
components are sorted after all other ones (evan after instances with positive infinite components - instances with both positive and negative infinite components
are considered as if they had
Double.NaN
components
- Specified by:
compareTo
in interfaceComparable<OrderedTuple>
- Parameters:
ot
- T-uple to compare instance with- Returns:
- a negative integer if the instance is less than the object, zero if they are equal, or a positive integer if the instance is greater than the object
-
equals
Deprecated. -
hashCode
public int hashCode()Deprecated. -
getComponents
public double[] getComponents()Deprecated.Get the components array.- Returns:
- array containing the T-uple components
-
sign
private static long sign(long bits) Deprecated.Extract the sign from the bits of a double.- Parameters:
bits
- binary representation of the double- Returns:
- sign bit (zero if positive, non zero if negative)
-
exponent
private static int exponent(long bits) Deprecated.Extract the exponent from the bits of a double.- Parameters:
bits
- binary representation of the double- Returns:
- exponent
-
mantissa
private static long mantissa(long bits) Deprecated.Extract the mantissa from the bits of a double.- Parameters:
bits
- binary representation of the double- Returns:
- mantissa
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computeMSB
private static int computeMSB(long l) Deprecated.Compute the most significant bit of a long.- Parameters:
l
- long from which the most significant bit is requested- Returns:
- scale of the most significant bit of
l
, or 0 ifl
is zero - See Also:
-
computeLSB
private static int computeLSB(long l) Deprecated.Compute the least significant bit of a long.- Parameters:
l
- long from which the least significant bit is requested- Returns:
- scale of the least significant bit of
l
, or 63 ifl
is zero - See Also:
-
getBit
private int getBit(int i, int k) Deprecated.Get a bit from the mantissa of a double.- Parameters:
i
- index of the componentk
- scale of the requested bit- Returns:
- the specified bit (either 0 or 1), after the offset has been added to the double
-