Exact decimal arithmetic in Julia

Question

Due to the nature of floating-point math, .4 * .4 = 0.16000000000000003 in Julia. I want to get the mathematically correct answer of 0.16, in a CPU-efficient way. I know round() works, but that requires prior knowledge of the number of decimal places the answer occupies, so it isn't a general solution.

Answer 1

Some options:

1. Use the inbuilt Rational type. The most accurate and fastest way would be

   16//100 * 16//100

If you're using very big numbers these might overflow, in which case you can use BigInts instead,

big(16)//big(100) * big(16)//big(100)

(you don't actually need to wrap them all in bigs, as the rationals will promote automatically).

You can also use rationalize(0.16), but this may not be quite as accurate or efficient, as the literal 0.16 has already been converted to a Float64 by the time Julia sees it, so you're converting to a binary floating point and then to a Rational.

2. DecFP.jl wraps the Intel implementation of IEEE-754 Decimal floating point. This should be reasonably fast (though not as efficient as binary), but has fixed precision, so you will have to round at some point.

3. Decimals.jl is a "big decimal" floating point library: as it uses arbitrary precision arithmetic, it is going to be slower than DecFP.

To say which is the best would require more information about your intended use.

Answer 2

You can use Python's decimal.Decimal with PyCall, but efficiency is going to be Python bound

Import the package:

julia> using PyCall

julia> @pyimport decimal

julia> const Dec = decimal.Decimal
PyObject <class 'decimal.Decimal'>

Meta-define operations (I think all of these kind of definitions should be part of PyCall!):

julia> py_methods = Dict(
           :+ => :__add__,
           :* => :__mul__,
           :- => :__sub__,
           (:/) => :__truediv__
       )
Dict{Symbol,Symbol} with 4 entries:
  :/ => :__truediv__
  :+ => :__add__
  :* => :__mul__
  :- => :__sub__

julia> for (op, meth) in py_methods
           op = Expr(:quote, op)
           meth = Expr(:quote, meth)
           @eval Base.($op){T<:PyObject}(x::T, y::T) = x[$meth](y)
       end

Do some math with them:

julia> x = Dec("0.4")
PyObject Decimal('0.4')

julia> x * x
PyObject Decimal('0.16')

julia> x + x
PyObject Decimal('0.8')

julia> x - x
PyObject Decimal('0.0')

julia> x / x
PyObject Decimal('1')

julia> y = x + x * x / x - x
PyObject Decimal('0.4')

Get result:

julia> y[:to_eng_string]() |> float
0.4