# `Feel.Analysis.IntegerSet`
[🔗](https://github.com/FeeJai/BDM/blob/feel-v0.1.0/apps/feel/lib/feel/analysis/integer_set.ex#L1)

Sets of whole numbers, as sets of numbers (D-109).

The properties of a date and of a duration that are whole numbers (a year, a month, the hours of a duration) are
worked out as Elixir integers, and this makes the `Feel.Type.NumberSet` of them: the ranges of whole numbers that
are one after the other are one interval. A set of numbers lies within decimal128, so a bound of more than 34
digits is widened to the nearest bound that is not, which holds the same numbers and more: a lower bound
down, an upper bound up, to the end of the range of the numbers where it has to be.

    iex> Feel.Analysis.IntegerSet.from_values([3, 1, 2, 7]) |> Feel.Type.NumberSet.format()
    "[1..3], 7"
    iex> Feel.Analysis.IntegerSet.from_ranges([{0, Integer.pow(10, 40)}]) |> Feel.Type.NumberSet.format()
    "[0..max]"

# `from_ranges`

```elixir
@spec from_ranges([{integer(), integer()}]) :: Feel.Type.NumberSet.t()
```

The set of the whole numbers in ranges, `{first, last}` each.

# `from_values`

```elixir
@spec from_values([integer()]) :: Feel.Type.NumberSet.t()
```

The set of the whole numbers in a list.

# `merge`

```elixir
@spec merge([{integer(), integer()}]) :: [{integer(), integer()}]
```

Ranges of whole numbers in order, with those that overlap or are one after the other made one.

    iex> Feel.Analysis.IntegerSet.merge([{6, 9}, {1, 5}, {20, 21}, {8, 12}])
    [{1, 12}, {20, 21}]

# `numbers`

```elixir
@spec numbers([Feel.Type.Union.member()]) :: {:ok, Feel.Type.NumberSet.t()} | :error
```

The numbers that the number alternatives of a type have, `null` aside, or `:error` if there is an alternative that is
not a number. It is what a fact leaves of a property that is always a number (D-194).

    iex> {:ok, set} = Feel.Analysis.IntegerSet.numbers([{:number, Feel.Type.NumberSet.point(Decimal.new(3))}, :null])
    iex> Feel.Type.NumberSet.format(set)
    "3"
    iex> Feel.Analysis.IntegerSet.numbers([:string])
    :error

# `ranges`

```elixir
@spec ranges([integer()]) :: [{integer(), integer()}]
```

The values of a list of whole numbers as the ranges of numbers that are one after the other.

---

*Consult [api-reference.md](api-reference.md) for complete listing*