Decimal
Arbitrary precision decimal arithmetic.
Documentation: https://hexdocs.pm/decimal/
Usage
Add Decimal as a dependency in your mix.exs
file.
def deps do
[{:decimal, "~> 1.0"}]
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.get_context/0
and set with
Decimal.set_context/1
. It can also be temporarily set with
Decimal.with_context/2
.
iex> D.get_context
%Decimal.Context{flags: [:rounded, :inexact], precision: 9, rounding: :half_up,
traps: [:invalid_operation, :division_by_zero]}
iex> D.with_context %D.Context{precision: 2}, fn -> IO.inspect D.get_context 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.set_context(%D.Context{D.get_context | traps: []})
:ok
iex> Decimal.get_context
%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.set_context(%D.Context{D.get_context | precision: 9})
:ok
iex> D.div(100, 3)
#Decimal<33.3333333>
iex> D.set_context(%D.Context{D.get_context | 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.set_context(%D.Context{D.get_context | rounding: :half_up})
:ok
iex> D.div(31, 2)
#Decimal<16>
iex> D.set_context(%D.Context{D.get_context | 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.cmp(-1, 0)
:lt
iex> D.cmp(0, -1)
:gt
iex> D.cmp(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.set_context(%D.Context{D.get_context | rounding: :floor, precision: 2})
:ok
iex> D.get_context.traps
[:invalid_operation, :division_by_zero]
iex> D.get_context.flags
[]
iex> D.div(31, 2)
#Decimal<15>
iex> D.get_context.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.set_context(%D.Context{D.get_context | traps: D.get_context.traps ++ [:inexact]})
:ok
iex> D.div(31, 2)
** (Decimal.Error)
The default trap enablers, such as :division_by_zero
can be unset:
iex> D.get_context.traps
[:invalid_operation, :division_by_zero]
iex> D.div(42, 0)
** (Decimal.Error)
iex> D.set_context(%D.Context{D.get_context | traps: [], flags: []})
:ok
iex> D.div(42, 0)
#Decimal<Infinity>
iex> D.get_context.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.