Provided by: libbit-vector-perl_7.4-1build5_amd64 bug

NAME

       Bit::Vector::Overload - Overloaded operators add-on for Bit::Vector

USAGE

       Note that you do not need to ""use Bit::Vector;"" in addition to this module.

       Simply ""use Bit::Vector::Overload;"" INSTEAD of ""use Bit::Vector;"". You can still use
       all the methods from the "Bit::Vector" module in addition to the overloaded operators and
       methods provided here after that.

SYNOPSIS

         Configuration
             $config = Bit::Vector->Configuration();
             Bit::Vector->Configuration($config);
             $oldconfig = Bit::Vector->Configuration($newconfig);

         String Conversion
             $string = "$vector";             #  depending on configuration
             print "\$vector = '$vector'\n";

         Emptyness
             if ($vector)  #  if not empty (non-zero)
             if (! $vector)  #  if empty (zero)
             unless ($vector)  #  if empty (zero)

         Complement (one's complement)
             $vector2 = ~$vector1;
             $vector = ~$vector;

         Negation (two's complement)
             $vector2 = -$vector1;
             $vector = -$vector;

         Norm
             $norm = abs($vector);  #  depending on configuration

         Absolute
             $vector2 = abs($vector1);  #  depending on configuration

         Concatenation
             $vector3 = $vector1 . $vector2;
             $vector1 .= $vector2;
             $vector1 = $vector2 . $vector1;
             $vector2 = $vector1 . $scalar;  #  depending on configuration
             $vector2 = $scalar . $vector1;
             $vector .= $scalar;

         Duplication
             $vector2 = $vector1 x $factor;
             $vector x= $factor;

         Shift Left
             $vector2 = $vector1 << $bits;
             $vector <<= $bits;

         Shift Right
             $vector2 = $vector1 >> $bits;
             $vector >>= $bits;

         Union
             $vector3 = $vector1 | $vector2;
             $vector1 |= $vector2;
             $vector2 = $vector1 | $scalar;
             $vector |= $scalar;

             $vector3 = $vector1 + $vector2;  #  depending on configuration
             $vector1 += $vector2;
             $vector2 = $vector1 + $scalar;
             $vector += $scalar;

         Intersection
             $vector3 = $vector1 & $vector2;
             $vector1 &= $vector2;
             $vector2 = $vector1 & $scalar;
             $vector &= $scalar;

             $vector3 = $vector1 * $vector2;  #  depending on configuration
             $vector1 *= $vector2;
             $vector2 = $vector1 * $scalar;
             $vector *= $scalar;

         ExclusiveOr
             $vector3 = $vector1 ^ $vector2;
             $vector1 ^= $vector2;
             $vector2 = $vector1 ^ $scalar;
             $vector ^= $scalar;

         Set Difference
             $vector3 = $vector1 - $vector2;  #  depending on configuration
             $vector1 -= $vector2;
             $vector1 = $vector2 - $vector1;
             $vector2 = $vector1 - $scalar;
             $vector2 = $scalar - $vector1;
             $vector -= $scalar;

         Addition
             $vector3 = $vector1 + $vector2;  #  depending on configuration
             $vector1 += $vector2;
             $vector2 = $vector1 + $scalar;
             $vector += $scalar;

         Subtraction
             $vector3 = $vector1 - $vector2;  #  depending on configuration
             $vector1 -= $vector2;
             $vector1 = $vector2 - $vector1;
             $vector2 = $vector1 - $scalar;
             $vector2 = $scalar - $vector1;
             $vector -= $scalar;

         Multiplication
             $vector3 = $vector1 * $vector2;  #  depending on configuration
             $vector1 *= $vector2;
             $vector2 = $vector1 * $scalar;
             $vector *= $scalar;

         Division
             $vector3 = $vector1 / $vector2;
             $vector1 /= $vector2;
             $vector1 = $vector2 / $vector1;
             $vector2 = $vector1 / $scalar;
             $vector2 = $scalar / $vector1;
             $vector /= $scalar;

         Modulo
             $vector3 = $vector1 % $vector2;
             $vector1 %= $vector2;
             $vector1 = $vector2 % $vector1;
             $vector2 = $vector1 % $scalar;
             $vector2 = $scalar % $vector1;
             $vector %= $scalar;

         Exponentiation
             $vector3 = $vector1 ** $vector2;
             $vector1 **= $vector2;
             $vector2 = $vector1 ** $scalar;
             $vector2 = $scalar ** $vector1;
             $vector **= $scalar;

         Increment
             ++$vector;
             $vector++;

         Decrement
             --$vector;
             $vector--;

         Lexical Comparison (unsigned)
             $cmp = $vector1 cmp $vector2;
             if ($vector1 lt $vector2)
             if ($vector1 le $vector2)
             if ($vector1 gt $vector2)
             if ($vector1 ge $vector2)

             $cmp = $vector cmp $scalar;
             if ($vector lt $scalar)
             if ($vector le $scalar)
             if ($vector gt $scalar)
             if ($vector ge $scalar)

         Comparison (signed)
             $cmp = $vector1 <=> $vector2;
             if ($vector1 < $vector2)  #  depending on configuration
             if ($vector1 <= $vector2)
             if ($vector1 > $vector2)
             if ($vector1 >= $vector2)

             $cmp = $vector <=> $scalar;
             if ($vector < $scalar)  #  depending on configuration
             if ($vector <= $scalar)
             if ($vector > $scalar)
             if ($vector >= $scalar)

         Equality
             if ($vector1 eq $vector2)
             if ($vector1 ne $vector2)
             if ($vector eq $scalar)
             if ($vector ne $scalar)

             if ($vector1 == $vector2)
             if ($vector1 != $vector2)
             if ($vector == $scalar)
             if ($vector != $scalar)

         Subset Relationship
             if ($vector1 <= $vector2)  #  depending on configuration

         True Subset Relationship
             if ($vector1 < $vector2)  #  depending on configuration

         Superset Relationship
             if ($vector1 >= $vector2)  #  depending on configuration

         True Superset Relationship
             if ($vector1 > $vector2)  #  depending on configuration

IMPORTANT NOTES

       · Boolean values

         Boolean values in this module are always a numeric zero ("0") for "false" and a numeric
         one ("1") for "true".

       · Negative numbers

         Numeric factors (as needed for the ""<<"", "">>"" and ""x"" operators) and bit numbers
         are always regarded as being UNSIGNED.

         As a consequence, whenever you pass a negative number for such a factor or bit number,
         it will be treated as a (usually very large) positive number due to its internal two's
         complement binary representation, usually resulting in malfunctions or an "index out of
         range" error message and program abortion.

         Note that this does not apply to "big integer" decimal numbers, which are (usually)
         passed as strings, and which may of course be negative (see also the section "Big
         integers" a little further below).

       · Overloaded operators configuration

         Note that the behaviour of certain overloaded operators can be changed in various ways
         by means of the ""Configuration()"" method (for more details, see the description of
         this method further below).

         For instance, scalars (i.e., numbers and strings) provided as operands to overloaded
         operators are automatically converted to bit vectors, internally.

         These scalars are thereby automatically assumed to be indices or to be in hexadecimal,
         binary, decimal or enumeration format, depending on the configuration.

         Similarly, when converting bit vectors to strings using double quotes (""), the output
         format will also depend on the previously chosen configuration.

         Finally, some overloaded operators may have different semantics depending on the proper
         configuration; for instance, the operator "+" can be the "union" operator from set
         theory or the arithmetic "add" operator.

         In all cases (input, output and operator semantics), the defaults have been chosen in
         such a way so that the behaviour of the module is backward compatible with previous
         versions.

       · "Big integers"

         As long as "big integers" (for "big integer" arithmetic) are small enough so that Perl
         doesn't need scientific notation (exponents) to be able to represent them internally,
         you can provide these "big integer" constants to the overloaded operators of this module
         (or to the method ""from_Dec()"") in numeric form (i.e., either as a numeric constant or
         expression or as a Perl variable containing a numeric value).

         Note that you will get an error message (resulting in program abortion) if your "big
         integer" numbers exceed that limit.

         Because this limit is machine-dependent and not obvious to find out, it is strongly
         recommended that you enclose ALL your "big integer" constants in your programs in
         (double or single) quotes.

         Examples:

             $vector /= 10;  #  ok because number is small

             $vector /= -10;  #  ok for same reason

             $vector /= "10";  #  always correct

             $vector += "1152921504606846976";  #  quotes probably required here

         All examples assume

             Bit::Vector->Configuration("input=decimal");

         having been set beforehand.

         Note also that this module does not support scientific notation (exponents) for "big
         integer" decimal numbers because you can always make the bit vector large enough for the
         whole number to fit without loss of precision (as it would occur if scientific notation
         were used).

         Finally, note that the only characters allowed in "big integer" constant strings are the
         digits 0..9 and an optional leading sign (""+"" or ""-"").

         All other characters produce a syntax error.

       · Valid operands for overloaded operators

         All overloaded operators expect at least one bit vector operand, in order for the
         operator to "know" that not the usual operation is to be carried out, but rather the
         overloaded variant.

         This is especially true for all unary operators:

                             "$vector"
                             if ($vector)
                             if (!$vector)
                             ~$vector
                             -$vector
                             abs($vector)
                             ++$vector
                             $vector++
                             --$vector

                             $vector--
         For obvious reasons the left operand (the "lvalue") of all assignment operators is also
         required to be a bit vector:

                                 .=
                                 x=
                                 <<=
                                 >>=
                                 |=
                                 &=
                                 ^=
                                 +=
                                 -=
                                 *=
                                 /=
                                 %=
                                **=

         In the case of three special operators, namely ""<<"", "">>"" and ""x"", as well as
         their related assignment variants, ""<<="", "">>="" and ""x="", the left operand is
         ALWAYS a bit vector and the right operand is ALWAYS a number (which is the factor
         indicating how many times the operator is to be applied).

         In all truly binary operators, i.e.,

                                 .
                                 |
                                 &
                                 ^
                                 +
                                 -
                                 *
                                 /
                                 %
                                **
                             <=>   cmp
                              ==    eq
                              !=    ne
                              <     lt
                              <=    le
                              >     gt
                              >=    ge

         one of either operands may be replaced by a Perl scalar, i.e., a number or a string,
         either as a Perl constant, a Perl expression or a Perl variable yielding a number or a
         string.

         The same applies to the right side operand (the "rvalue") of the remaining assignment
         operators, i.e.,

                                 .=
                                 |=
                                 &=
                                 ^=
                                 +=
                                 -=
                                 *=
                                 /=
                                 %=
                                **=

         Note that this Perl scalar should be of the correct type, i.e., numeric or string, for
         the chosen configuration, because otherwise a warning message will occur if your program
         runs under the ""-w"" switch of Perl.

         The acceptable scalar types for each possible configuration are the following:

             input = bit indices    (default)  :    numeric
             input = hexadecimal               :    string
             input = binary                    :    string
             input = decimal                   :    string     (in general)
             input = decimal                   :    numeric    (if small enough)
             input = enumeration               :    string

         NOTE ALSO THAT THESE SCALAR OPERANDS ARE CONVERTED TO BIT VECTORS OF THE SAME SIZE AS
         THE BIT VECTOR WHICH IS THE OTHER OPERAND.

         The only exception from this rule is the concatenation operator (""."") and its
         assignment variant ("".=""):

         If one of the two operands of the concatenation operator (""."") is not a bit vector
         object but a Perl scalar, the contents of the remaining bit vector operand are converted
         into a string (the format of which depends on the configuration set with the
         ""Configuration()"" method), which is then concatenated in the proper order (i.e., as
         indicated by the order of the two operands) with the Perl scalar (in other words, a
         string is returned in such a case instead of a bit vector object!).

         If the right side operand (the "rvalue") of the assignment variant ("".="") of the
         concatenation operator is a Perl scalar, it is converted internally to a bit vector of
         the same size as the left side operand provided that the configuration states that
         scalars are to be regarded as indices, decimal strings or enumerations.

         If the configuration states that scalars are to be regarded as hexadecimal or boolean
         strings, however, these strings are converted to bit vectors of a size matching the
         length of the input string, i.e., four times the length for hexadecimal strings (because
         each hexadecimal digit is worth 4 bits) and once the length for binary strings.

         If a decimal number ("big integer") is too large to be stored in a bit vector of the
         given size, a "numeric overflow error" occurs.

         If a bit index is out of range for the given bit vector, an "index out of range" error
         occurs.

         If a scalar operand cannot be converted successfully due to invalid syntax, a fatal
         "input string syntax error" is issued.

         If the two operands of the operator ""<<"", "">>"" or ""x"" are reversed, a fatal
         "reversed operands error" occurs.

         If an operand is neither a bit vector nor a scalar, then a fatal "illegal operand type
         error" occurs.

       · Bit order

         Note that bit vectors are stored least order bit and least order word first internally.

         I.e., bit #0 of any given bit vector corresponds to bit #0 of word #0 in the array of
         machine words representing the bit vector.

         (Where word #0 comes first in memory, i.e., it is stored at the least memory address in
         the allocated block of memory holding the given bit vector.)

         Note however that machine words can be stored least order byte first or last, depending
         on your system's implementation.

         Note further that whenever bit vectors are converted to and from (binary or hexadecimal)
         strings, the RIGHTMOST bit is always the LEAST SIGNIFICANT one, and the LEFTMOST bit is
         always the MOST SIGNIFICANT bit.

         This is because in our western culture, numbers are always represented in this way
         (least significant to most significant digits go from right to left).

         Of course this requires an internal reversion of order, which the corresponding
         conversion methods perform automatically (without any additional overhead, it's just a
         matter of starting the internal loop at the bottom or the top end).

       · Matching sizes

         In general, for methods involving several bit vectors at the same time, all bit vector
         arguments must have identical sizes (number of bits), or a fatal "size mismatch" error
         will occur.

         Exceptions from this rule are the methods ""Concat()"", ""Concat_List()"", ""Copy()"",
         ""Interval_Copy()"" and ""Interval_Substitute()"", where no conditions at all are
         imposed on the size of their bit vector arguments.

         In method ""Multiply()"", all three bit vector arguments must in principle obey the rule
         of matching sizes, but the bit vector in which the result of the multiplication is to be
         stored may be larger than the two bit vector arguments containing the factors for the
         multiplication.

         In method ""Power()"", the bit vector for the result must be the same size or greater
         than the base of the exponentiation term. The exponent can be any size.

         The same applies to the corresponding overloaded operators.

       · Index ranges

         All indices for any given bits must lie between "0" and ""$vector->Size()-1"", or a
         fatal "index out of range" error will occur.

DESCRIPTION

       · "$config = Bit::Vector->Configuration();"

       · "Bit::Vector->Configuration($config);"

       · "$oldconfig = Bit::Vector->Configuration($newconfig);"

         This method serves to alter the semantics (i.e., behaviour) of certain overloaded
         operators (which are all implemented in Perl, by the way).

         It does not have any effect whatsoever on anything else. In particular, it does not
         affect the methods implemented in C.

         The method accepts an (optional) string as input in which certain keywords are expected,
         which influence some or almost all of the overloaded operators in several possible ways.

         The method always returns a string (which you do not need to take care of, i.e., to
         store, in case you aren't interested in keeping it) which is a complete representation
         of the current configuration (i.e., BEFORE any modifications are applied) and which can
         be fed back to this method later in order to restore the previous configuration.

         There are three aspects of the way certain overloaded operators behave which can be
         controlled with this method:

           +  the way scalar operands (replacing one of the two
              bit vector object operands) are automatically
              converted internally into a bit vector object of
              their own,

           +  the operation certain overloaded operators perform,
              i.e., an operation with sets or an arithmetic
              operation,

           +  the format to which bit vectors are converted
              automatically when they are enclosed in double
              quotes.

         The input string may contain any number of assignments, each of which controls one of
         these three aspects.

         Each assignment has the form ""<which>=<value>"".

         ""<which>"" and ""<value>"" thereby consist of letters ("[a-zA-Z]") and white space.

         Multiple assignments have to be separated by one or more comma (","), semi-colon (";"),
         colon (":"), vertical bar ("|"), slash ("/"), newline ("\n"), ampersand ("&"), plus
         ("+") or dash ("-").

         Empty lines or statements (only white space) are allowed but will be ignored.

         ""<which>"" has to contain one or more keywords from one of three groups, each group
         representing one of the three aspects that the ""Configuration()"" method controls:

           +  "^scalar", "^input", "^in$"

           +  "^operator", "^semantic", "^ops$"

           +  "^string", "^output", "^out$"

         The character "^" thereby denotes the beginning of a word, and "$" denotes the end. Case
         is ignored (!).

         Using these keywords, you can build any phrase you like to select one of the three
         aspects (see also examples given below).

         The only condition is that no other keyword from any of the other two groups may match -
         otherwise a syntax error will occur (i.e., ambiguities are forbidden). A syntax error
         also occurs if none of the keywords matches.

         This same principle applies to ""<value>"":

         Depending on which aspect you specified for ""<which>"", there are different groups of
         keywords that determine the value the selected aspect will be set to:

           +  "<which>" = "^scalar", "^input", "^in$":

                "<value>" =

                *  "^bit$", "^index", "^indice"
                *  "^hex"
                *  "^bin"
                *  "^dec"
                *  "^enum"

           +  "<which>" = "^operator", "^semantic", "^ops$":

                "<value>" =

                *  "^set$"
                *  "^arithmetic"

           +  "<which>" = "^string", "^output", "^out$":

                "<value>" =

                *  "^hex"
                *  "^bin"
                *  "^dec"
                *  "^enum"

         Examples:

           "Any scalar input I provide should be considered to be = a bit index"

           "I want to have operator semantics suitable for = arithmetics"

           "Any bit vector in double quotes is to be output as = an enumeration"

         SCALAR INPUT:

         In the case of scalar input, ""^bit$"", ""^index"", or ""^indice"" all cause scalar
         input to be considered to represent a bit index, i.e., ""$vector ^= 5;"" will flip bit
         #5 in the given bit vector (this is essentially the same as ""$vector->bit_flip(5);"").

         Note that "bit indices" is the default setting for "scalar input".

         The keyword ""^hex"" will cause scalar input to be considered as being in hexadecimal,
         i.e., ""$vector ^= 5;"" will flip bit #0 and bit #2 (because hexadecimal "5" is binary
         "0101").

         (Note though that hexadecimal input should always be enclosed in quotes, otherwise it
         will be interpreted as a decimal number by Perl! The example relies on the fact that
         hexadecimal "0-9" and decimal "0-9" are the same.)

         The keyword ""^bin"" will cause scalar input to be considered as being in binary format.
         All characters except "0" and "1" are forbidden in this case (i.e., produce a syntax
         error).

         ""$vector ^= '0101';"", for instance, will flip bit #0 and bit #2.

         The keyword ""^dec"" causes scalar input to be considered as integers in decimal format,
         i.e., ""$vector ^= 5;"" will flip bit #0 and bit #2 (because decimal "5" is binary
         "0101").

         (Note though that all decimal input should be enclosed in quotes, because for large
         numbers, Perl will use scientific notation internally for representing them, which
         produces a syntax error because scientific notation is neither supported by this module
         nor needed.)

         Finally, the keyword ""^enum"" causes scalar input to be considered as being a list
         ("enumeration") of indices and ranges of (contiguous) indices, i.e., ""$vector |=
         '2,3,5,7-13,17-23';"" will cause bits #2, #3, #5, #7 through #13 and #17 through #23 to
         be set.

         OPERATOR SEMANTICS:

         Several overloaded operators can have two distinct functions depending on this setting.

         The affected operators are: ""+"", ""-"", ""*"", ""<"", ""<="", "">"" and "">="".

         With the default setting, "set operations", these operators perform:

           +       set union                           ( set1  u   set2 )
           -       set difference                      ( set1  \   set2 )
           *       set intersection                    ( set1  n   set2 )
           <       true subset relationship            ( set1  <   set2 )
           <=      subset relationship                 ( set1  <=  set2 )
           >       true superset relationship          ( set1  >   set2 )
           >=      superset relationship               ( set1  >=  set2 )

         With the alternative setting, "arithmetic operations", these operators perform:

           +       addition                            ( num1  +   num2 )
           -       subtraction                         ( num1  -   num2 )
           *       multiplication                      ( num1  *   num2 )
           <       "less than" comparison              ( num1  <   num2 )
           <=      "less than or equal" comparison     ( num1  <=  num2 )
           >       "greater than" comparison           ( num1  >   num2 )
           >=      "greater than or equal" comparison  ( num1  >=  num2 )

         Note that these latter comparison operators (""<"", ""<="", "">"" and "">="") regard
         their operands as being SIGNED.

         To perform comparisons with UNSIGNED operands, use the operators ""lt"", ""le"", ""gt""
         and ""ge"" instead (in contrast to the operators above, these operators are NOT affected
         by the "operator semantics" setting).

         STRING OUTPUT:

         There are four methods which convert the contents of a given bit vector into a string:
         ""to_Hex()"", ""to_Bin()"", ""to_Dec()"" and ""to_Enum()"" (not counting
         ""Block_Read()"", since this method does not return a human-readable string).

         (For conversion to octal, see the description of the method ""Chunk_List_Read()"".)

         Therefore, there are four possible formats into which a bit vector can be converted when
         it is enclosed in double quotes, for example:

           print "\$vector = '$vector'\n";
           $string = "$vector";

         Hence you can set "string output" to four different values: To "hex" for hexadecimal
         format (which is the default), to "bin" for binary format, to "dec" for conversion to
         decimal numbers and to "enum" for conversion to enumerations (".newsrc" style sets).

         BEWARE that the conversion to decimal numbers is inherently slow; it can easily take up
         several seconds for a single large bit vector!

         Therefore you should store the decimal strings returned to you rather than converting a
         given bit vector again.

         EXAMPLES:

         The default setting as returned by the method ""Configuration()"" is:

                 Scalar Input       = Bit Index
                 Operator Semantics = Set Operators
                 String Output      = Hexadecimal

         Performing a statement such as:

           Bit::Vector->Configuration("in=bin,ops=arithmetic,out=bin");
           print Bit::Vector->Configuration(), "\n";

         yields the following output:

                 Scalar Input       = Binary
                 Operator Semantics = Arithmetic Operators
                 String Output      = Binary

         Note that you can always feed this output back into the ""Configuration()"" method to
         restore that setting later.

         This also means that you can enter the same given setting with almost any degree of
         verbosity you like (as long as the required keywords appear and no ambiguities arise).

         Note further that any aspect you do not specify is not changed, i.e., the statement

           Bit::Vector->Configuration("operators = arithmetic");

         leaves all other aspects unchanged.

       · "$vector"

         Remember that variables enclosed in double quotes are always interpolated in Perl.

         Whenever a Perl variable containing the reference of a "Bit::Vector" object is enclosed
         in double quotes (either alone or together with other text and/or variables), the
         contents of the corresponding bit vector are converted into a printable string.

         Since there are several conversion methods available in this module (see the description
         of the methods ""to_Hex()"", ""to_Bin()"", ""to_Dec()"" and ""to_Enum()""), it is of
         course desirable to be able to choose which of these methods should be applied in this
         case.

         This can actually be done by changing the configuration of this module using the method
         ""Configure()"" (see the previous chapter, immediately above).

         The default is conversion to hexadecimal.

       · "if ($vector)"

         It is possible to use a Perl variable containing the reference of a "Bit::Vector" object
         as a boolean expression.

         The condition above is true if the corresponding bit vector contains at least one set
         bit, and it is false if ALL bits of the corresponding bit vector are cleared.

       · "if (!$vector)"

         Since it is possible to use a Perl variable containing the reference of a "Bit::Vector"
         object as a boolean expression, you can of course also negate this boolean expression.

         The condition above is true if ALL bits of the corresponding bit vector are cleared, and
         it is false if the corresponding bit vector contains at least one set bit.

         Note that this is NOT the same as using the method ""is_full()"", which returns true if
         ALL bits of the corresponding bit vector are SET.

       · "~$vector"

         This term returns a new bit vector object which is the one's complement of the given bit
         vector.

         This is equivalent to inverting all bits.

       · "-$vector" (unary minus)

         This term returns a new bit vector object which is the two's complement of the given bit
         vector.

         This is equivalent to inverting all bits and incrementing the result by one.

         (This is the same as changing the sign of a number in two's complement binary
         representation.)

       · "abs($vector)"

         Depending on the configuration (see the description of the method ""Configuration()""
         for more details), this term either returns the number of set bits in the given bit
         vector (this is the same as calculating the number of elements which are contained in
         the given set) - which is the default behaviour, or it returns a new bit vector object
         which contains the absolute value of the number stored in the given bit vector.

       · "$vector1 . $vector2"

         This term usually returns a new bit vector object which is the result of the
         concatenation of the two bit vector operands.

         The left operand becomes the most significant, and the right operand becomes the least
         significant part of the new bit vector object.

         If one of the two operands is not a bit vector object but a Perl scalar, however, the
         contents of the remaining bit vector operand are converted into a string (the format of
         which depends on the configuration set with the ""Configuration()"" method), which is
         then concatenated in the proper order (i.e., as indicated by the order of the two
         operands) with the Perl scalar.

         In other words, a string is returned in such a case instead of a bit vector object!

       · "$vector x $factor"

         This term returns a new bit vector object which is the concatenation of as many copies
         of the given bit vector operand (the left operand) as the factor (the right operand)
         specifies.

         If the factor is zero, a bit vector object with a length of zero bits is returned.

         If the factor is one, just a new copy of the given bit vector is returned.

         Note that a fatal "reversed operands error" occurs if the two operands are swapped.

       · "$vector << $bits"

         This term returns a new bit vector object which is a copy of the given bit vector (the
         left operand), which is then shifted left (towards the most significant bit) by as many
         places as the right operand, "$bits", specifies.

         This means that the "$bits" most significant bits are lost, all other bits move up by
         "$bits" positions, and the "$bits" least significant bits that have been left unoccupied
         by this shift are all set to zero.

         If "$bits" is greater than the number of bits of the given bit vector, this term returns
         an empty bit vector (i.e., with all bits cleared) of the same size as the given bit
         vector.

         Note that a fatal "reversed operands error" occurs if the two operands are swapped.

       · "$vector >> $bits"

         This term returns a new bit vector object which is a copy of the given bit vector (the
         left operand), which is then shifted right (towards the least significant bit) by as
         many places as the right operand, "$bits", specifies.

         This means that the "$bits" least significant bits are lost, all other bits move down by
         "$bits" positions, and the "$bits" most significant bits that have been left unoccupied
         by this shift are all set to zero.

         If "$bits" is greater than the number of bits of the given bit vector, this term returns
         an empty bit vector (i.e., with all bits cleared) of the same size as the given bit
         vector.

         Note that a fatal "reversed operands error" occurs if the two operands are swapped.

       · "$vector1 | $vector2"

         This term returns a new bit vector object which is the result of a bitwise OR operation
         between the two bit vector operands.

         This is the same as calculating the union of two sets.

       · "$vector1 & $vector2"

         This term returns a new bit vector object which is the result of a bitwise AND operation
         between the two bit vector operands.

         This is the same as calculating the intersection of two sets.

       · "$vector1 ^ $vector2"

         This term returns a new bit vector object which is the result of a bitwise XOR
         (exclusive-or) operation between the two bit vector operands.

         This is the same as calculating the symmetric difference of two sets.

       · "$vector1 + $vector2"

         Depending on the configuration (see the description of the method ""Configuration()""
         for more details), this term either returns a new bit vector object which is the result
         of a bitwise OR operation between the two bit vector operands (this is the same as
         calculating the union of two sets) - which is the default behaviour, or it returns a new
         bit vector object which contains the sum of the two numbers stored in the two bit vector
         operands.

       · "$vector1 - $vector2"

         Depending on the configuration (see the description of the method ""Configuration()""
         for more details), this term either returns a new bit vector object which is the set
         difference of the two sets represented in the two bit vector operands - which is the
         default behaviour, or it returns a new bit vector object which contains the difference
         of the two numbers stored in the two bit vector operands.

       · "$vector1 * $vector2"

         Depending on the configuration (see the description of the method ""Configuration()""
         for more details), this term either returns a new bit vector object which is the result
         of a bitwise AND operation between the two bit vector operands (this is the same as
         calculating the intersection of two sets) - which is the default behaviour, or it
         returns a new bit vector object which contains the product of the two numbers stored in
         the two bit vector operands.

       · "$vector1 / $vector2"

         This term returns a new bit vector object containing the result of the division of the
         two numbers stored in the two bit vector operands.

       · "$vector1 % $vector2"

         This term returns a new bit vector object containing the remainder of the division of
         the two numbers stored in the two bit vector operands.

       · "$vector1 ** $vector2"

         This term returns a new bit vector object containing the result of the exponentiation of
         the left bit vector elevated to the right bit vector's power.

       · "$vector1 .= $vector2;"

         This statement "appends" the right bit vector operand (the "rvalue") to the left one
         (the "lvalue").

         The former contents of the left operand become the most significant part of the
         resulting bit vector, and the right operand becomes the least significant part.

         Since bit vectors are stored in "least order bit first" order, this actually requires
         the left operand to be shifted "up" by the length of the right operand, which is then
         copied to the now freed least significant part of the left operand.

         If the right operand is a Perl scalar, it is first converted to a bit vector of the same
         size as the left operand, provided that the configuration states that scalars are to be
         regarded as indices, decimal strings or enumerations.

         If the configuration states that scalars are to be regarded as hexadecimal or boolean
         strings, however, these strings are converted to bit vectors of a size matching the
         length of the input string, i.e., four times the length for hexadecimal strings (because
         each hexadecimal digit is worth 4 bits) and once the length for binary strings.

       · "$vector x= $factor;"

         This statement replaces the given bit vector by a concatenation of as many copies of the
         original contents of the given bit vector as the factor (the right operand) specifies.

         If the factor is zero, the given bit vector is resized to a length of zero bits.

         If the factor is one, the given bit vector is not changed at all.

       · "$vector <<= $bits;"

         This statement moves the contents of the given bit vector left by "$bits" positions
         (towards the most significant bit).

         This means that the "$bits" most significant bits are lost, all other bits move up by
         "$bits" positions, and the "$bits" least significant bits that have been left unoccupied
         by this shift are all set to zero.

         If "$bits" is greater than the number of bits of the given bit vector, the given bit
         vector is erased completely (i.e., all bits are cleared).

       · "$vector >>= $bits;"

         This statement moves the contents of the given bit vector right by "$bits" positions
         (towards the least significant bit).

         This means that the "$bits" least significant bits are lost, all other bits move down by
         "$bits" positions, and the "$bits" most significant bits that have been left unoccupied
         by this shift are all set to zero.

         If "$bits" is greater than the number of bits of the given bit vector, the given bit
         vector is erased completely (i.e., all bits are cleared).

       · "$vector1 |= $vector2;"

         This statement performs a bitwise OR operation between the two bit vector operands and
         stores the result in the left operand.

         This is the same as calculating the union of two sets.

       · "$vector1 &= $vector2;"

         This statement performs a bitwise AND operation between the two bit vector operands and
         stores the result in the left operand.

         This is the same as calculating the intersection of two sets.

       · "$vector1 ^= $vector2;"

         This statement performs a bitwise XOR (exclusive-or) operation between the two bit
         vector operands and stores the result in the left operand.

         This is the same as calculating the symmetric difference of two sets.

       · "$vector1 += $vector2;"

         Depending on the configuration (see the description of the method ""Configuration()""
         for more details), this statement either performs a bitwise OR operation between the two
         bit vector operands (this is the same as calculating the union of two sets) - which is
         the default behaviour, or it calculates the sum of the two numbers stored in the two bit
         vector operands.

         The result of this operation is stored in the left operand.

       · "$vector1 -= $vector2;"

         Depending on the configuration (see the description of the method ""Configuration()""
         for more details), this statement either calculates the set difference of the two sets
         represented in the two bit vector operands - which is the default behaviour, or it
         calculates the difference of the two numbers stored in the two bit vector operands.

         The result of this operation is stored in the left operand.

       · "$vector1 *= $vector2;"

         Depending on the configuration (see the description of the method ""Configuration()""
         for more details), this statement either performs a bitwise AND operation between the
         two bit vector operands (this is the same as calculating the intersection of two sets) -
         which is the default behaviour, or it calculates the product of the two numbers stored
         in the two bit vector operands.

         The result of this operation is stored in the left operand.

       · "$vector1 /= $vector2;"

         This statement puts the result of the division of the two numbers stored in the two bit
         vector operands into the left operand.

       · "$vector1 %= $vector2;"

         This statement puts the remainder of the division of the two numbers stored in the two
         bit vector operands into the left operand.

       · "$vector1 **= $vector2;"

         This statement puts the result of the exponentiation of the left operand elevated to the
         right operand's power into the left operand.

       · "++$vector", "$vector++"

         This operator performs pre- and post-incrementation of the given bit vector.

         The value returned by this term is a reference of the given bit vector object (after or
         before the incrementation, respectively).

       · "--$vector", "$vector--"

         This operator performs pre- and post-decrementation of the given bit vector.

         The value returned by this term is a reference of the given bit vector object (after or
         before the decrementation, respectively).

       · "($vector1 cmp $vector2)"

         This term returns ""-1"" if "$vector1" is less than "$vector2", "0" if "$vector1" and
         "$vector2" are the same, and "1" if "$vector1" is greater than "$vector2".

         This comparison assumes UNSIGNED bit vectors.

       · "($vector1 eq $vector2)"

         This term returns true ("1") if the contents of the two bit vector operands are the same
         and false ("0") otherwise.

       · "($vector1 ne $vector2)"

         This term returns true ("1") if the two bit vector operands differ and false ("0")
         otherwise.

       · "($vector1 lt $vector2)"

         This term returns true ("1") if "$vector1" is less than "$vector2", and false ("0")
         otherwise.

         This comparison assumes UNSIGNED bit vectors.

       · "($vector1 le $vector2)"

         This term returns true ("1") if "$vector1" is less than or equal to "$vector2", and
         false ("0") otherwise.

         This comparison assumes UNSIGNED bit vectors.

       · "($vector1 gt $vector2)"

         This term returns true ("1") if "$vector1" is greater than "$vector2", and false ("0")
         otherwise.

         This comparison assumes UNSIGNED bit vectors.

       · "($vector1 ge $vector2)"

         This term returns true ("1") if "$vector1" is greater than or equal to "$vector2", and
         false ("0") otherwise.

         This comparison assumes UNSIGNED bit vectors.

       · "($vector1 <=> $vector2)"

         This term returns ""-1"" if "$vector1" is less than "$vector2", "0" if "$vector1" and
         "$vector2" are the same, and "1" if "$vector1" is greater than "$vector2".

         This comparison assumes SIGNED bit vectors.

       · "($vector1 == $vector2)"

         This term returns true ("1") if the contents of the two bit vector operands are the same
         and false ("0") otherwise.

       · "($vector1 != $vector2)"

         This term returns true ("1") if the two bit vector operands differ and false ("0")
         otherwise.

       · "($vector1 < $vector2)"

         Depending on the configuration (see the description of the method ""Configuration()""
         for more details), this term either returns true ("1") if "$vector1" is a true subset of
         "$vector2" (and false ("0") otherwise) - which is the default behaviour, or it returns
         true ("1") if "$vector1" is less than "$vector2" (and false ("0") otherwise).

         The latter comparison assumes SIGNED bit vectors.

       · "($vector1 <= $vector2)"

         Depending on the configuration (see the description of the method ""Configuration()""
         for more details), this term either returns true ("1") if "$vector1" is a subset of
         "$vector2" (and false ("0") otherwise) - which is the default behaviour, or it returns
         true ("1") if "$vector1" is less than or equal to "$vector2" (and false ("0")
         otherwise).

         The latter comparison assumes SIGNED bit vectors.

       · "($vector1 > $vector2)"

         Depending on the configuration (see the description of the method ""Configuration()""
         for more details), this term either returns true ("1") if "$vector1" is a true superset
         of "$vector2" (and false ("0") otherwise) - which is the default behaviour, or it
         returns true ("1") if "$vector1" is greater than "$vector2" (and false ("0") otherwise).

         The latter comparison assumes SIGNED bit vectors.

       · "($vector1 >= $vector2)"

         Depending on the configuration (see the description of the method ""Configuration()""
         for more details), this term either returns true ("1") if "$vector1" is a superset of
         "$vector2" (and false ("0") otherwise) - which is the default behaviour, or it returns
         true ("1") if "$vector1" is greater than or equal to "$vector2" (and false ("0")
         otherwise).

         The latter comparison assumes SIGNED bit vectors.

SEE ALSO

       Bit::Vector(3), Bit::Vector::String(3).

VERSION

       This man page documents "Bit::Vector::Overload" version 7.4.

AUTHOR

         Steffen Beyer
         mailto:STBEY@cpan.org
         http://www.engelschall.com/u/sb/download/

COPYRIGHT

       Copyright (c) 2000 - 2013 by Steffen Beyer. All rights reserved.

LICENSE

       This package is free software; you can redistribute it and/or modify it under the same
       terms as Perl itself, i.e., under the terms of the "Artistic License" or the "GNU General
       Public License".

       The C library at the core of this Perl module can additionally be redistributed and/or
       modified under the terms of the "GNU Library General Public License".

       Please refer to the files "Artistic.txt", "GNU_GPL.txt" and "GNU_LGPL.txt" in this
       distribution for details!

DISCLAIMER

       This package is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
       without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

       See the "GNU General Public License" for more details.