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Arbitrary precision decimal arithmetic

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# ericmj/decimal

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# 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.

```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.

## Usage

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

```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`:

```iex> alias Decimal, as: D
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 will be updated automatically.

The context is accessed with `Decimal.Context.get/0` and set with `Decimal.Context.set/1`. It can be set temporarily with `Decimal.Context.with/2`.

```iex> D.Context.get()
%Decimal.Context{flags: [:rounded, :inexact], precision: 9, rounding: :half_up,
traps: [:invalid_operation, :division_by_zero]}

iex> D.Context.with(%D.Context{precision: 2}, fn -> IO.inspect D.Context.get() end)
%Decimal.Context{flags: [], precision: 2, rounding: :half_up,
traps: [:invalid_operation, :division_by_zero]}
%Decimal.Context{flags: [], precision: 2, rounding: :half_up,
traps: [:invalid_operation, :division_by_zero]}

iex> D.Context.set(%D.Context{D.Context.get() | traps: []})
:ok

iex> D.Context.get()
%Decimal.Context{flags: [:rounded, :inexact], precision: 9, rounding: :half_up,
traps: []}```

### Precision and rounding

Use `:precision` option to limit the amount of decimal digits in the coefficient of any calculation result:

```iex> D.Context.set(%D.Context{D.Context.get() | precision: 9})
:ok

iex> D.div(100, 3)
Decimal.new("33.3333333")

iex> D.Context.set(%D.Context{D.Context.get() | precision: 2})
:ok

iex> D.div(100, 3)
Decimal.new("33")```

The `:rounding` option specifies the algorithm and precision of the rounding operation:

```iex> D.Context.set(%D.Context{D.Context.get() | rounding: :half_up})
:ok

iex> D.div(31, 2)
Decimal.new("16")

iex> D.Context.set(%D.Context{D.Context.get() | rounding: :floor})
:ok

iex> D.div(31, 2)
Decimal.new("15")```

### Comparisons

Using comparison operators (`<`, `=`, `>`) with two or more decimal digits may not produce accurate result. Instead, use comparison functions.

```iex> D.compare(-1, 0)
:lt
iex> D.compare(0, -1)
:gt
iex> D.compare(0, 0)
:eq

iex> D.equal?(-1, 0)
false
iex> D.equal?(0, "0.0")
true```

### Flags and trap enablers

When an exceptional condition is signalled, its flag is set in the current context. `Decimal.Error` will be raised if the trap enabler is set.

```iex> D.Context.set(%D.Context{D.Context.get() | rounding: :floor, precision: 2})
:ok

iex> D.Context.get().traps
[:invalid_operation, :division_by_zero]

iex> D.Context.get().flags
[]

iex> D.div(31, 2)
Decimal.new("15")

iex> D.Context.get().flags
[:inexact, :rounded]```

`:inexact` and `:rounded` flag were signalled above because the result of the operation was inexact given the context's precision and had to be rounded to fit the precision. `Decimal.Error` was not raised because the signals' trap enablers weren't set.

```iex> D.Context.set(%D.Context{D.Context.get() | traps: D.Context.get().traps ++ [:inexact]})
:ok

iex> D.div(31, 2)
** (Decimal.Error)```

The default trap enablers, such as `:division_by_zero`, can be unset:

```iex> D.Context.get().traps
[:invalid_operation, :division_by_zero]

iex> D.div(42, 0)
** (Decimal.Error)

iex> D.Context.set(%D.Context{D.Context.get() | traps: [], flags: []})
:ok

iex> D.div(42, 0)
Decimal.new("Infinity")

iex> D.Context.get().flags
[:division_by_zero]```

### Mitigating rounding errors

TODO

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

``````   http://www.apache.org/licenses/LICENSE-2.0
``````

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

Arbitrary precision decimal arithmetic

v2.0.0 Latest
Sep 8, 2020

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