Decimals.jl
Basic routines for decimal arithmetic in Julia. Supports addition, subtraction, negation, multiplication, division, and equality operations; exponentiation coming as soon as I find the time to write it. This is a pure Julia implementation, so if you are concerned about pure speed, calling libmpdec functions directly is likely to be faster. Tested in Julia 0.3.
Background
Why is this needed? Because floating point arithmetic does things like this:
julia> 0.1 + 0.2
0.30000000000000004
Clearly, this is not okay for fields like finance, where it's important to be able to trust that $0.30 is actually 30 cents, rather than 30.000000000000004 cents.
(For an in-depth explanation of the underlying problem - "ordinary" decimals like 0.1 and 0.2 are base-10 numbers, many of which do not have an exact representation in binary - check out the amusingly-named floating-point-gui.de.)
Installation and use
julia> Pkg.add("Decimals")
julia> using Decimals
The Decimal object
You can create Decimal objects from either strings or numbers, using decimal():
julia> decimal("0.2")
Decimal(0,2,-1)
julia> decimal(0.1)
Decimal(0,1,-1)
julia> decimal("-2.5e6")
Decimal(1,25,5)
To convert back to a string or a float:
julia> x = decimal("0.2");
julia> string(x)
"0.2"
julia> float(x)
0.2
It is also possible to call the Decimal constructor directly, by specifying the sign (s), coefficient (c), and exponent (q):
julia> Decimal(1,2,-2)
The numerical value of a Decimal is given by (-1)^s * c * 10^q. s must be 0 (positive) or 1 (negative). c must be non-negative; c and q must be integers.
Operations
julia> x, y = decimal("0.2"), decimal("0.1");
Addition:
julia> string(x + y)
"0.3"
Subtraction:
julia> string(x - y)
"0.1"
Negation:
julia> string(-x)
"-0.2"
Multiplication:
julia> string(x * y)
"0.02"
Division:
julia> string(x / y)
"2"
Inversion:
julia> string(inv(x))
"5"
Broadcasting:
julia> [x y] .* 2
2-element Array{Decimal,1}:
Decimal(0,1,-1)
Decimal(0,5,-2)
Equals (== and isequal):
julia> x == decimal("0.2")
true
julia> x != decimal("0.1")
true
== returns true for Decimal vs. Number comparisons:
julia> x == 0.2
true
is only returns true between two equivalent Decimal objects:
julia> is(x, decimal("0.2"))
true
julia> is(x, 0.2)
false
Rounding:
julia> round(decimal(3.1415), 2)
Decimal(0,314,-2)
julia> string(ans)
"3.14"
Tests
Unit tests are in test/. To run the tests:
$ julia test/runtests.jl