What would be the recommended way of getting the base 10 mantissa and exponent of a floating point number? Is there a package that does this? Or should I just reparse from printed representation, as in using Printf function get_mantissa_exponent(x) str = @sprintf "%.15e" x # specialize 15 based on type _mantissa, exponent = split(str, 'e') (; mantissa = filter(!isequal('.'), _mantissa), exponent = parse(Int, exponent)) end julia> get_mantissa_exponent(3.17) (mantissa = "3170000000000000", exponent = 0)

[image] Tamas_Papp: What would be the recommended way of getting the base 10 mantissa and exponent of a floating point number? It depends on what you mean by “the” base-10 mantissa and exponent. I assume you are mainly interested in binary floating-point types like Float64 and Float32. The one that is shown in the default printed representation of a Float64 is only an approximation — it is the shortest decimal representation that rounds to the same Float64 value. If this is what you want, I’m not aware of a documented API other than parsing the printed representation. If you are willing to use an undocumented API, there is mantissa, exponent = Base.Ryu.reduce_shortest(x). Of course, there is an exact decimal representation too, but it typically requires a large number of digits.

Thanks! Sorry for not being clear, yes, I am after the printed approximation.

[image] Tamas_Papp: julia> get_mantissa_exponent(3.17) (mantissa = "3170000000000000", exponent = 0) Is this the result you expected? Based on the title, I would have expected mantissa 317 and exponent -2 (or an equivalent alternative like 3170 and -3) because 317 * 10^-2 = 3.17. Coincidentally, I work on JuliaMath/Decimals.jl these days. You could use that package to parse a number and get the mantissa and exponent from the resulting Decimal: using Decimals x = parse(Decimal, "3.17") mantissa = x.c # 317 exponent = x.q # -2 The package has some bugs (parsing has been fixed recently in a pending PR), but I am trying to improve it and it might already be sufficient for your case now.

[image] barucden: Is this the result you expected? Technically you are right, but I am after a string which I can just cut off at some point and insert a decimal dot, so I am flexible. The point of the exercise is for printing, into LaTeX. That is, I want to generate output like raw"$4.92 \cdot 10^{-3}$" and raw"$22.71 \cdot 10^{6}$" (engineering notation).

How about a simplistic regex? julia> replace(string((10rand())^10), r"(\d+.\d+)[ef]\+?(-?\d+)"=>s"$\1 \\cdot 10^{\2}$") |> println $6.71626435914464 \cdot 10^{6}$

This works for positive floating point number. Just check if number is negative and manually insert a negative sign yourself. julia> a = log(10, Float64(π) ) 0.4971498726941338 julia> println("$(10.0^(a-trunc(a))) * 10^$(Int64(trunc(a)))") 3.1415926535897927 * 10^0 julia> a = log(10, 123.456*Float64(π) ) 2.5886620743219053 julia> println("$(10.0^(a-trunc(a))) * 10^$(Int64(trunc(a)))") 3.8784846264158133 * 10^2 julia> 123.456*Float64(π) 387.84846264158153

Doing something with a numeric log is highly likely to have catastrophic rounding problems around powers of 10. In my view, the best answer in this case is to use standard tooling (like @sprintf) and fix it up as strings — either as a split like Tamas first suggested or with a regex. Both are really fine.

I don’t think the original poster cares about rounding errors. He said “Thanks! Sorry for not being clear, yes, I am after the printed approximation.” I take that to mean approximation in base 10 (not approximation in base 2)

The problem I was worried about isn’t small errors. I suspect that it’s possible the exponent and mantissa might round different ways. Around powers of 10 that could easily lead to a factor of 10 error — something that I suspect everyone would care about. I might be wrong — and I think you might be doing it in a way that’s safe — but regardless it’s worrisome.

Get base10 mantissa and exponent of real (eg Float64)

General Usage

rafael.guerra October 21, 2024, 2:12pm 7

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Get base10 mantissa and exponent of real (eg Float64)

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