Add method to rationalize Rational

[tantheta01]

Closes #43369.

[dkarrasch]

@tantheta01 Thank you for your contribution and welcome to the community. I helped slightly by (i) making the title more descriptive, and (ii) rewording the OP to the effect that github associates this PR with the issue so when this PR is merged the issue is automatically closed.

[JeffBezanson]

Oh wow, this looks like it was actually a bug. Thanks for catching that. Would be good to add a test for it.

[inkydragon]

Maybe something like:

diff --git a/test/rational.jl b/test/rational.jl
--- test/rational.jl
+++ test/rational.jl
@@ -638,5 +638,11 @@
     @test rationalize(float(pi)im) == 0//1 + 165707065//52746197*im
     @test rationalize(Int8, float(pi)im) == 0//1 + 22//7*im
     @test rationalize(1.192 + 2.233im) == 149//125 + 2233//1000*im
     @test rationalize(Int8, 1.192 + 2.233im) == 118//99 + 67//30*im
+
+    # test: rationalize(x::Complex; kvs...)
+    precise_next = 7205759403792795//72057594037927936
+    @assert Float64(precise_next) == nextfloat(0.1)
+    @test rationalize(nextfloat(0.1) * im; tol=0) == precise_next * im
+    @test rationalize(0.1im; tol=eps(0.1)) == rationalize(0.1im)
 end

[JeffBezanson]

Better to avoid spurious whitespace changes like this.

[oscardssmith]

bumping this. I've added some more tests and I think it's ready to merge.

[oscardssmith]

After an embarrassingly long time, this is finally passing tests. merging in a few days sans objections.

[Keno]

This failed on CI and shouldn't have been merged. Please fix or revert in the morning.

[KristofferC]

Explicitly:

Error in testset rational:
--
Test Failed at C:\buildkite-agent\builds\win2k22-amdci6-4\julialang\julia-master\julia-d12ccd04fc\share\julia\test\rational.jl:739
Expression: rationalize(nextfloat(0.1) * im; tol = 0) == precise_next * im
Evaluated: 0//1 + 1//10*im == 0//1 + 7205759403792795//72057594037927936*im

[oscardssmith]

Sorry about that, I saw that only windows was failing and assumed it was a platform problem. #50163 fixes it (there was an incorrect assumption in the test that Int is big enough to store the 53 bits of a Float64 mantissa).