[R] BUG: atan(1i) / 5 = NaN+Infi ?

[Jeff Newmiller]

atan(1i) -> 0 + Inf i
complex(1/5) -> 0.2 + 0i
atan(1i) -> (0 + Inf i) * (0.2 + 0i)
-> 0*0.2 + 0*0i + Inf i * 0.2 + Inf i * 0i
infinity times zero is undefined
-> 0 + 0i + Inf i + NaN * i^2
-> 0 + 0i + Inf i - NaN
-> NaN + Inf i

I am not sure how complex arithmetic could arrive at another answer.

I advise against messing with infinities... use atan2() if you don't actually need complex arithmetic.

On September 5, 2024 3:38:33 PM PDT, Bert Gunter <bgunter.4567 using gmail.com> wrote:
>> complex(real = 0, imaginary = Inf)
>[1] 0+Infi
>
>> Inf*1i
>[1] NaN+Infi
>
>>> complex(real = 0, imaginary = Inf)/5
>[1] NaN+Infi
>
>See the Note in ?complex for the explanation, I think.  Duncan can correct
>if I'm wrong.
>
>-- Bert
>
>On Thu, Sep 5, 2024 at 3:20 PM Leo Mada <leo.mada using syonic.eu> wrote:
>
>> Dear Bert,
>>
>> These behave like real divisions/multiplications:
>> complex(re=Inf, im = Inf) * 5
>> # Inf+Infi
>> complex(re=-Inf, im = Inf) * 5
>> # -Inf+Infi
>>
>> The real division / multiplication should be faster and also is well
>> behaved. I was expecting R to do the real division/multiplication on a
>> complex number. Which R actually does for these very particular cases; but
>> not when only Im(x) is Inf.
>>
>> Sincerely,
>>
>> Leonard
>>
>> ------------------------------
>> *From:* Bert Gunter <bgunter.4567 using gmail.com>
>> *Sent:* Friday, September 6, 2024 1:12 AM
>> *To:* Duncan Murdoch <murdoch.duncan using gmail.com>
>> *Cc:* Leo Mada <leo.mada using syonic.eu>; r-help using r-project.org <
>> r-help using r-project.org>
>> *Subject:* Re: [R] BUG: atan(1i) / 5 = NaN+Infi ?
>>
>> Perhaps
>>
>> > Inf*1i
>> [1] NaN+Infi
>>
>> clarifies why it is *not* a bug.
>> (Boy, did that jog some long dusty math memories :-)  )
>>
>> -- Bert
>>
>> On Thu, Sep 5, 2024 at 2:48 PM Duncan Murdoch <murdoch.duncan using gmail.com>
>> wrote:
>>
>> On 2024-09-05 4:23 p.m., Leo Mada via R-help wrote:
>> > Dear R Users,
>> >
>> > Is this desired behaviour?
>> > I presume it's a bug.
>> >
>> > atan(1i)
>> > # 0+Infi
>> >
>> > tan(atan(1i))
>> > # 0+1i
>> >
>> > atan(1i) / 5
>> > # NaN+Infi
>>
>> There's no need to involve atan() and tan() in this:
>>
>>  > (0+Inf*1i)/5
>> [1] NaN+Infi
>>
>> Why do you think this is a bug?
>>
>> Duncan Murdoch
>>
>> ______________________________________________
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>> and provide commented, minimal, self-contained, reproducible code.
>>
>>
>
>	[[alternative HTML version deleted]]
>
>______________________________________________
>R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
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>PLEASE do read the posting guide https://www.R-project.org/posting-guide.html
>and provide commented, minimal, self-contained, reproducible code.

-- 
Sent from my phone. Please excuse my brevity.