const type: bitset

Sets of integer numbers.

const type: set of (attr integer)

Alternate name for bitset.

set of integer

is an alternate name for bitset.

const bitset: (attr bitset) . value

Default value of bitset ({}).

const func bitset: (in bitset: set1) | (in bitset: set2)

Union of two sets.

{1, 2} | {1, 3}  returns  {1, 2, 3}

Returns:

the union of the two sets.

Raises:

MEMORY_ERROR - Not enough memory for the result.

const func bitset: (in bitset: set1) & (in bitset: set2)

Intersection of two sets.

{1, 2} & {1, 3}  returns  {1}

Returns:

the intersection of the two sets.

Raises:

MEMORY_ERROR - Not enough memory for the result.

const func bitset: (in bitset: set1) >< (in bitset: set2)

Symmetric difference of two sets.

{1, 2} >< {1, 3}  returns  {2, 3}

Returns:

the symmetric difference of the two sets.

Raises:

MEMORY_ERROR - Not enough memory for the result.

const func bitset: (in bitset: set1) - (in bitset: set2)

Difference of two sets.

{1, 2} - {1, 3}  returns  {2}

Returns:

the difference of the two sets.

Raises:

MEMORY_ERROR - Not enough memory for the result.

const proc: (inout bitset: dest) |:= (in bitset: set2)

Assign the union of dest and set2 to dest.

Raises:

MEMORY_ERROR - Not enough memory to create dest.

const proc: (inout bitset: dest) &:= (in bitset: set2)

Assign the intersection of dest and set2 to dest.

Raises:

MEMORY_ERROR - Not enough memory to create dest.

const proc: (inout bitset: dest) -:= (in bitset: set2)

Assign the difference of dest and set2 to dest.

Raises:

MEMORY_ERROR - Not enough memory to create dest.

const func boolean: (in bitset: set1) = (in bitset: set2)

Check if two sets are equal.

Returns:

TRUE if the two sets are equal, FALSE otherwise.

const func boolean: (in bitset: set1) <> (in bitset: set2)

Check if two sets are not equal.

Returns:

FALSE if the two sets are equal, TRUE otherwise.

const func boolean: (in bitset: set1) < (in bitset: set2)

Determine if set1 is a proper subset of set2. set1 is a proper subset of set2 if

set1 <= set2 and set1 <> set2

holds.

Returns:

TRUE if set1 is a proper subset of set2, FALSE otherwise.

const func boolean: (in bitset: set1) > (in bitset: set2)

Determine if set1 is a proper superset of set2. set1 is a proper superset of set2 if

set1 >= set2 and set1 <> set2

holds.

Returns:

TRUE if set1 is a proper superset of set2, FALSE otherwise.

const func boolean: (in bitset: set1) <= (in bitset: set2)

Determine if set1 is a subset of set2. set1 is a subset of set2 if no element X exists for which

X in set1 and X not in set2

holds.

Returns:

TRUE if set1 is a subset of set2, FALSE otherwise.

const func boolean: (in bitset: set1) >= (in bitset: set2)

Determine if set1 is a superset of set2. set1 is a superset of set2 if no element X exists for which

X in set2 and X not in set1

holds.

Returns:

TRUE if set1 is a superset of set2, FALSE otherwise.

const func boolean: (in integer: number) in (in bitset: aSet)

Set membership test. Determine if number is a member of the set aSet.

2 in {2, 3, 5, 7}  returns  TRUE
4 in {2, 3, 5, 7}  returns  FALSE

Returns:

TRUE if number is a member of aSet, FALSE otherwise.

const func boolean: (in integer: number) not in (in bitset: aSet)

Negated set membership test. Determine if number is not a member of the set aSet.

2 not in {2, 3, 5, 7}  returns  FALSE
4 not in {2, 3, 5, 7}  returns  TRUE

Returns:

FALSE if number is a member of aSet, TRUE otherwise.

const proc: (inout bitset: aSet) @:= [ (in integer: number) ] (in boolean: isElement)

Add or remove aValue to respectively from sSet. Adding an existing value or remove a non-existing value leaves aSet unchanged.

Raises:

MEMORY_ERROR - If there is not enough memory.

const func bitset: { (in integer: aNumber) }

Create bitset with the element aNumber.

{42}    returns a bitset with the element 42.

const func bitset: { (in tuple integer: numberTuple) }

Create bitset with elements from a comma separated list.

{2, 3, 5, 7, 11}    returns a bitset with the elements 2, 3, 5, 7 and 11.

const func bitset: { (in integer: lowValue) .. (in integer: highValue) }

Create bitset with all elements from lowValue to highValue inclusive.

{1 .. 5}    returns a bitset with the elements 1, 2, 3, 4 and 5.

const func integer: (attr integer) conv (in bitset: aSet)

Convert a bitset to integer.

integer conv {2, 3, 5, 7, 11}    returns 2220

Returns:

an integer which corresponds to the given bitset.

Raises:

RANGE_ERROR - If aSet contains negative values or if it does not fit into a non-negative integer.

const func bitset: (attr bitset) conv (in integer: number)

Convert an integer number to a bitset.

bitset conv 2220    returns {2, 3, 5, 7, 11}

Returns:

a bitset which corresponds to the given integer.

Raises:

RANGE_ERROR - Number is negative.

MEMORY_ERROR - Not enough memory to represent the result.

const func bitset: (attr bitset) parse (in string: stri)

Convert a string to a bitset.

Returns:

the integer result of the conversion.

Raises:

RANGE_ERROR - If the string is empty or cannot be converted to a bitset.

const func integer: compare (in bitset: set1, in bitset: set2)

Compares two sets to make them useable as key in a hash table. The sets are compared by determining the biggest element that is not present or absent in both sets. The set in which this element is not present is the smaller one. Note that the set comparison is not related to the concepts of subset or superset. With the comparison function compare it is possible to sort an array of sets or to use sets as key in a hash table.

Returns:

-1, 0 or 1 if the first argument is considered to be respectively less than, equal to, or greater than the second.

const func integer: hashCode (in bitset: aSet)

Compute the hash value of a bitset.

Returns:

the hash value.

const proc: incl (inout bitset: aSet, in integer: number)

Add number to the set aSet. If number is already in aSet then aSet stays unchanged.

Raises:

MEMORY_ERROR - If there is not enough memory.

const proc: excl (inout bitset: aSet, in integer: number)

Remove number from the set aSet. If number is not element of aSet then aSet stays unchanged.

const func integer: card (in bitset: aSet)

Compute the cardinality of a set.

card({2, 3, 5, 7, 11})  returns  5
card(EMPTY_SET)         returns  0

Returns:

the number of elements in aSet.

Raises:

RANGE_ERROR - Result does not fit into an integer.

const func integer: rand (in bitset: aSet)

Compute pseudo-random element from aSet. The random values are uniform distributed.

rand(EMPTY_SET)  raises  RANGE_ERROR

Returns:

a random number such that rand(aSet) in aSet holds.

Raises:

RANGE_ERROR - If aSet is empty.

const func integer: min (in bitset: aSet)

Minimum element of a set. Delivers the element from aSet for which the following condition holds:

element <= X

for all X which are in the set.

min({2, 3, 5, 7, 11})  returns  2
min(EMPTY_SET)         raises   RANGE_ERROR

Returns:

the minimum element of aSet.

Raises:

RANGE_ERROR - If aSet is the empty set.

const func integer: max (in bitset: aSet)

Maximum element of a set. Delivers the element from aSet for which the following condition holds:

element >= X

for all X which are in the set.

max({2, 3, 5, 7, 11})  returns  11
max(EMPTY_SET)         raises   RANGE_ERROR

Returns:

the maximum element of aSet.

Raises:

RANGE_ERROR - If aSet is the empty set.

const func integer: next (in bitset: aSet, in integer: number)

Minimum element of aSet that is larger than number.

next({2, 3, 5, 7, 11},  2)  returns  3
next({2, 3, 5, 7, 11},  3)  returns  5
next({2, 3, 5, 7, 11},  7)  returns  11
next({2, 3, 5, 7, 11}, 11)  raises   RANGE_ERROR
next({}, 1)                 raises   RANGE_ERROR

Returns:

the minimum element of aSet that is larger than number.

Raises:

RANGE_ERROR - If aSet has no element larger than number.

const func integer: integer (in bitset: aSet)

Convert a bitset to integer.

integer({2, 3, 5, 7, 11})    returns 2220

Returns:

an integer which corresponds to the given bitset.

Raises:

RANGE_ERROR - If aSet contains negative values or if it does not fit into a non-negative integer.

const func bitset: bitset (in integer: number)

Convert an integer number to a bitset.

bitset(2220)    returns {2, 3, 5, 7, 11}

Returns:

a bitset which corresponds to the given integer.

Raises:

RANGE_ERROR - Number is negative.

MEMORY_ERROR - Not enough memory to represent the result.

const proc: for (inout integer: forVar) range (in bitset: aSet) do (in proc: statements) end for

For-loop where forVar loops over the elements of the set aSet.

const func array integer: toArray (in bitset: aSet)

Obtain an array containing all the values in aSet.

toArray({2, 3, 5})  returns  [](2, 3, 5)

Returns:

all the values from aSet.

const func string: str (in bitset: aSet)

Convert a bitset to a string.

str({})      returns  "{}"
str({1, 2})  returns  "{1, 2}"

Returns:

the string result of the conversion.

Raises:

MEMORY_ERROR - Not enough memory to represent the result.

const func bitset: bitset (in var string: stri)

Convert a string to a bitset.

bitset("{}")            returns  {},
bitset("{2, 3, 5, 7}")  returns  {2, 3, 5, 7} )

Returns:

a bitset which corresponds to the given literal.

Raises:

RANGE_ERROR - If the string is empty or cannot be converted to a bitset.