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
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 set 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

License

Copyright 2013 Eric Meadows-Jönsson

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.