Julia: Rounding floating point numbers

If a floating point number don’t has exact representation, then by default that number is rounded to nearest representable value.

For example,

julia> x=2.1234567;

julia> x=x+0.1
2.2234567000000003

When I add 0.1 to 2.1234567, I am expection 2.2234567, but actual result is 2.2234567000000003. It is because, Julia rounded it to the nearest value.

Currently following rounding modes are supported by julia

a. RoundNearest

It is the default rounding mode, rounds the floating point to nearest number, with ties (fractional values of 0.5) being rounded to the nearest even integer.

You can get the current rounding mode using get_rounding method. You can set the rounding mode for given type using set_rounding method.

julia> get_rounding(Float64)
RoundingMode{:Nearest}()

julia> x=1.1;

julia> x=x+0.1
1.2000000000000002

b. RoundNearestTiesAway

Rounds to nearest integer, with ties rounded away from zero.

c. RoundNearestTiesUp

Rounds to nearest integer, with ties rounded toward positive infinity

d. RoundToZero

Returns the nearest integral value of the same type as x whose absolute value is less than or equal to x

julia> set_rounding(Float64,RoundingMode{:ToZero}())
0

julia> get_rounding(Float64)
RoundingMode{:ToZero}()

julia> x=1.1;

julia> x=x+0.1
1.2

e. RoundUp

Returns the nearest integral value of the same type as x that is greater than or equal to x.

julia> set_rounding(Float64,RoundingMode{:Up}())
0

julia> get_rounding(Float64)
RoundingMode{:Up}()

julia> x=1.1;

julia> x=x+0.1
1.2000000000000002

julia> x=x+0.1
1.3000000000000003

julia> x=x+0.1123
1.4123000000000003

julia> x=x+0.1
1.5123000000000004

f. RoundDown

Returns the nearest integral value of the same type as x that is less than or equal to x.

julia> get_rounding(Float64)
RoundingMode{:Down}()

julia> x=1.1;

julia> x=x+0.1
1.2

You can change the rounding mode for particular block of code using ‘with_rounding(f::Function, T, mode)’.

julia> with_rounding(BigFloat,RoundUp) do

           BigFloat(1) + parse(BigFloat, "0.001")

       end
1.001000000000000000000000000000000000000000000000000000000000000000000000000001

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