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The set type models the mathematical notion of a set. The set's basetype can
only be an ordinal type of a certain size, namely:
* `int8`-`int16`
* `uint8`/`byte`-`uint16`
* `char`
* `enum`
* Ordinal subrange types, i.e. `range[-10..10]`
or equivalent. When constructing a set with signed integer literals, the set's
base type is defined to be in the range `0 .. DefaultSetElements-1` where
`DefaultSetElements` is currently always 2^8. The maximum range length for the
base type of a set is `MaxSetElements` which is currently always 2^16. Types
with a bigger range length are coerced into the range `0 .. MaxSetElements-1`.
The reason is that sets are implemented as high performance bit vectors.
Attempting to declare a set with a larger type will result in an error:
```nim
var s: set[int64] # Error: set is too large; use `std/sets` for ordinal types
# with more than 2^16 elements
```
**Note:** Nim also offers [hash sets](sets.html) (which you need to import
with `import std/sets`), which have no such restrictions.
Sets can be constructed via the set constructor: `{}` is the empty set. The
empty set is type compatible with any concrete set type. The constructor
can also be used to include elements (and ranges of elements):
```nim
type
CharSet = set[char]
var
x: CharSet
x = {'a'..'z', '0'..'9'} # This constructs a set that contains the
# letters from 'a' to 'z' and the digits
# from '0' to '9'
```
The module [`std/setutils`](setutils.html) provides a way to initialize a set from an iterable:
```nim
import std/setutils
let uniqueChars = myString.toSet
```
These operations are supported by sets:
================== ========================================================
operation meaning
================== ========================================================
`A + B` union of two sets
`A * B` intersection of two sets
`A - B` difference of two sets (A without B's elements)
`A == B` set equality
`A <= B` subset relation (A is subset of B or equal to B)
`A < B` strict subset relation (A is a proper subset of B)
`e in A` set membership (A contains element e)
`e notin A` A does not contain element e
`contains(A, e)` A contains element e
`card(A)` the cardinality of A (number of elements in A)
`incl(A, elem)` same as `A = A + {elem}`
`excl(A, elem)` same as `A = A - {elem}`
================== ========================================================
### Bit fields
Sets are often used to define a type for the *flags* of a procedure.
This is a cleaner (and type safe) solution than defining integer
constants that have to be `or`'ed together.
Enum, sets and casting can be used together as in:
```nim
type
MyFlag* {.size: sizeof(cint).} = enum
A
B
C
D
MyFlags = set[MyFlag]
proc toNum(f: MyFlags): int = cast[cint](f)
proc toFlags(v: int): MyFlags = cast[MyFlags](v)
assert toNum({}) == 0
assert toNum({A}) == 1
assert toNum({D}) == 8
assert toNum({A, C}) == 5
assert toFlags(0) == {}
assert toFlags(7) == {A, B, C}
```
Note how the set turns enum values into powers of 2.
If using enums and sets with C, use distinct cint.
For interoperability with C see also the
[bitsize pragma](manual.html#implementation-specific-pragmas-bitsize-pragma).
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