RE: [Caml-list] Float precision in OCaml

["Soegtrop, Michael" <michael.soegtrop@intel.com>]

Dear Daniel,

> 1. The latest RFC recommends [1] to support the range of IEEE 754 double
> precision numbers (those are OCaml's float) in JSON numbers. However since
> you are converting your floating point representation from binary to a decimal
> one you can't guarantee to round trip your floats with a JSON number.

I don't agree with this. It is possible to have a decimal representation of double precision numbers, which guarantees identity (maybe up to NaN and Inf variants) when serialized and desrialized. The point is that the example

4.94065645841e-324

Is probably a correctly rounded decimal representation of a precise double precision floating point number. There has been a lengthy discussion on the Maxima list on what floating point numbers mean and the final consensus there was that each floating point number is precisely an integer times a power of 2, even a denormalized one. Just that you can't convert decimal presentations exactly to floating point numbers doesn't mean that there is something like an imprecise floating point number, there are just imprecise representations of decimals numbers in floating point numbers.

Said that, one can define a mapping from floating point numbers to usual decimal string representations and back such that each floating point number results in a unique string. It is just quite tricky to get it right without extended precision arithmetic, though.

As far as I know the Lisp standard requires that certain floating point formats have this property (I need to check). One might be able to learn from them how to do this properly.

Best regards,

Michael
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