Decimal

Arbitrary precision decimal arithmetic.

Usage

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

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

After you are done, 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<13>
iex> D.div(1, 3)
#Decimal<0.333333333>
iex> D.new("0.33")
#Decimal<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 currently set flags.

The context is stored in the process dictionary, this means that 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 also be temporarily set 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

The precision is used to limit the amount of decimal digits in the coefficient:

iex> D.Context.set(%D.Context{D.Context.get() | precision: 9})
:ok
iex> D.div(100, 3)
#Decimal<33.3333333>
iex> D.Context.set(%D.Context{D.Context.get() | precision: 2})
:ok
iex> D.div(100, 3)
#Decimal<33>

The rounding algorithm specifies how the result of an operation shall be rounded when it get be represented with the current precision:

iex> D.Context.set(%D.Context{D.Context.get() | rounding: :half_up})
:ok
iex> D.div(31, 2)
#Decimal<16>
iex> D.Context.set(%D.Context{D.Context.get() | rounding: :floor})
:ok
iex> D.div(31, 2)
#Decimal<15>

Comparisons

Using compare operators (<, =, >) directly with two decimals may not return the correct 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 context and if if the trap enabler is set Decimal.Error will be raised.

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<15>
iex> D.Context.get().flags
[:inexact, :rounded]

:inexact and :rounded were signaled 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. We can, however, set the trap enabler if we what this condition to raise.

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

Mitigating rounding errors

TODO

License

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.