I’m curious about the possibility to convert Float64 numbers to Rational numbers for exact computations. I’m a little puzzled by the following: julia> x = 2.64 2.64 julia> y = Rational(x) 5944751508129055//2251799813685248 julia> z = 264//100 66//25 julia> Float64(y) 2.64 julia> Float64(z) 2.64…

… I already noticed that Floats such as 2 + 2^{-1} + 2^{-3}, etc. (which can be represented accurately in binary numbers) work as I had hoped…

The rational constructor isn’t doing anything incorrect. There isn’t an exact floating point representation of 2.64. So when you create that float it isn’t exactly 2.64, because it can’t be. When you convert it to a rational it creates a rational of the actual value you have, which again isn’t exact…

So the following function handles my problem: julia> function rationalize(x;sigdigits=16) return Int(round(x*10^(sigdigits-1),digits=0))//10^(sigdigits-1) end rationalize (generic function with 1 method) julia> x = 2.64 2.64 julia> round(x;sigdigits=3) 2.64 julia> round(x;sigdigits…

There’s already a built-in rationalize function: julia> rationalize(2.64) 66//25 The Rational constructor and convert do exact conversion, however. If you want to do inexact conversion, you need to explicitly call rationalize.

Ah, so I have reinvented the wheel :-o .

I’m not sure that using such a function is a good idea, as it suffers from several issues: issue #1: your implementation works only for number of magnitude approximately equal to 1: julia> rationalize(1e-20) 0//1 This would be relatively easy to fix, taking into account the magnitude of x in the …

The built-in function doesn’t have this issue: julia> rationalize(0.1) 1//10 julia> rationalize(nextfloat(0.1)) 300239975158034//3002399751580339

…but the built-in function makes 10^{-20} equal to 0//1.

Float -> Rational numbers?

General Usage

Skoffer April 19, 2020, 4:23pm 2

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Float -> Rational numbers?

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