exact comparisons with binary values/directed conversions

[simonbyrne]

Currently

julia> using DecFP

julia> d64"1e100" == 1e100
true

which might seem reasonable, except that

julia> big(1e100)
1.000000000000000015902891109759918046836080856394528138978132755774783877217038e+100

Since the library doesn't appear to offer comparisons, the one option would be to do it via directed conversions, e.g.

<(x::Float64, y::Dec64) = x < Float64(y, RoundUp)
<=(x::Float64, y::Dec64) = x <= Float64(y, RoundDown)
==(x::Float64, y::Dec64) = x == Float64(y, RoundUp) == Float64(y, RoundDown)

Is it possible to do this without touching the global rounding mode?

[ScottPJones]

Those comparisons won't be exact though. Although it might be slower, if you want accurate results you might do better making a grisu like conversion of the binary floating point value, and then do the comparison using those values. That technique would work for any binary floating point numbers, including BigFloat and the ones from DoubleFloat.jl, Quadmath.jl. Since they would be exact comparisions, no rounding would be needed.

[simonbyrne]

why wouldn't they be exact?

[simonbyrne]

e.g.

x = d64"1e100"
using DecFP
setrounding(Dec64, RoundDown)
x < 1e100

correctly returns false

[ScottPJones]

If you have to do rounding, how can they be exact?

[simonbyrne]

Because we can control the direction of rounding. It is similar to the way that we compare floats to Irrationals (https://simonbyrne.github.io/talks/juliacon2018#/11), though requires a few extra checks since they can be equal.

[jmkuhn]

For the comparison

d64"1e100" == 1e100

the Float64 1e100 is getting promoted to a Dec64. The comparison is really

d64"1e100" == convert(Dec64, 1e100)

Note

julia> convert(Dec64, 1e100)
1.0e100

That is exactly 1e100, not just approximately 1e100 rounded for printing.

Edit:

My original explanation of how the conversion is done was incorrect, but what remains above is true.

[jmkuhn]

julia> convert(Dec64, 1e100)
1.0e100

julia> convert(Dec128, 1e100)
1.000000000000000015902891109759918e100

julia> d64"1e100" == 1e100
true

julia> d128"1e100" == 1e100
false