decimal

# Decimal

Arbitrary precision decimal arithmetic.

## Concept

Decimal represents values internally using three integers: a sign, a coefficient, and an exponent.
In this way, numbers of any size and with any number of decimal places can be represented exactly.

```elixir
Decimal.new(_sign = 1, _coefficient = 42, _exponent = 0) #=> Decimal.new("42")
Decimal.new(-1, 42, 0) #=> Decimal.new("-42")
Decimal.new(1, 42, -1) #=> Decimal.new("4.2")
Decimal.new(1, 42, -20) #=> Decimal.new("4.2E-19")
Decimal.new(1, 42, 20) #=> Decimal.new("4.2E+21")
Decimal.new(1, 123456789987654321, -9) #=> Decimal.new("123456789.987654321")
```

For calculations, the amount of desired precision - that is, the number of
decimal digits in the coefficient - can be specified.

## Handling untrusted input

Decimal can represent compact values with very large exponents, such as
`1e1000000`. These values are valid decimals, but some operations can require
memory or CPU proportional to the expanded size of the number. This matters when
decimals are parsed from user input, JSON payloads, form fields, database
fields, or other external data.

Use bounded parsing for untrusted input:

```elixir
Decimal.parse(input, max_digits: 100, max_exponent: 1000)
Decimal.cast(input, max_digits: 100, max_exponent: 1000)
```

`Decimal.new/1` with an integer and `Decimal.new/3` take their arguments as
given, without limits. Use `Decimal.cast/2`, which applies the limits to
integers and decimals as well as strings, when those come from untrusted input.

Use bounded output when rendering decimals in formats that may expand the
exponent:

```elixir
Decimal.to_string(decimal, :normal, max_digits: 1000)
Decimal.to_string(decimal, :xsd, max_digits: 1000)
```

The default scientific string format is compact for large positive exponents,
but `:normal` and `:xsd` output can materialize many zeroes. APIs that convert
to an integer or otherwise need the expanded value may also be expensive for
large exponents. `Decimal.Context` supports finite `emax` and `emin` values to
limit operation results, but context limits do not validate already-created
decimals and should not replace parse/cast limits for untrusted input.

## Usage

Add Decimal as a dependency in your `mix.exs` file:

```elixir
def deps do
  [{:decimal, "~> 2.0"}]
end
```

Next, run `mix deps.get` in your shell to fetch and compile `Decimal`. Start an
interactive Elixir shell with `iex -S mix`:

```elixir
iex> alias Decimal, as: D
iex> D.add(6, 7)
Decimal.new("13")
iex> D.div(1, 3)
Decimal.new("0.3333333333333333333333333333")
iex> D.new("0.33")
Decimal.new("0.33")
```

## Examples

### Using the context

The context specifies the maximum precision of the result of calculations and
the rounding algorithm if the result has a higher precision than the specified
maximum. It also holds the list of trap enablers and the current set
flags.

The context is stored in the process dictionary. You don't have to pass the
context around explicitly and the flags