Add ishalfodd function

[hyrodium]

This PR adds a new function ishalfoddinteger.

julia> ishalfoddinteger(3.5)
true
julia> ishalfoddinteger(2)
false
julia> ishalfoddinteger(1//3)
false

Note that halving an integer does not always produce a half-integer; this is only true for odd integers. For this reason, half-integers are also sometimes called half-odd-integers.

https://en.wikipedia.org/wiki/Half-integer

[hyrodium]

Should I rename this function to ishalfodd, like isinteger and isodd?

[sostock]

I don’t think it needs to be renamed (although it is quite long). To me, ishalfoddinteger seems clearer than ishalfodd, but I’m fine with either name.

[hyrodium]

Thank you for the review! I named the function referring to the word "half-odd-integers" in the Wikipedia article.
But I now think consistency with Base.odd and Base.isinteger has priority, so I will update the name. (I think ishalfodd is still clear enough.)

[sostock]

I don’t understand this. To me, ishalfodd seems consistent with Base.isodd and ishalfoddinteger seems consistent with Base.isinteger. Why do you think that ishalfoddinteger is more consistent with both of them?

[hyrodium]

Sorry for confusing. I was just trying to clarify the pros and cons of these function names. The reason of ishalfoddinteger was just borrowing from the wikipedia article. I now changed the name to ishalfodd which is consistent with Base.

[hyrodium]

#59 (comment) was written before the commit b0bc2e5.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (d4dc006) 98.81% compared to head (b0bc2e5) 98.85%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #59      +/-   ##
==========================================
+ Coverage   98.81%   98.85%   +0.03%     
==========================================
  Files           1        1              
  Lines         253      261       +8     
==========================================
+ Hits          250      258       +8     
  Misses          3        3              

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[sostock]

I think this is not necessarily correct, because nothing prevents a user from defining an AbstractIrrational subtype that is equal to a rational number. The AbstractIrrational docstring even mentions this possibility:

If a subtype is used to represent values that may occasionally be rational (e.g. a square-root type that represents √n for integers n will give a rational result when n is a perfect square), then it should also implement isinteger, iszero, isone, and == with Real values (since all of these default to false for AbstractIrrational types), as well as defining hash to equal that of the corresponding Rational.

Since we cannot add ishalfoddinteger to that list, maybe we should let it fall back to the generic _isodd(twice(x))? Or should we just add a note to the ishalfoddinteger docstring?

[hyrodium]

Ah, I see. I added the method referring to the Base.isinteger method.

https://github.com/JuliaLang/julia/blob/9c6fec13ed3a106a4c1e30d07d55eaa3701b5a59/base/irrationals.jl#L143

I now think we can just drop the method definition, and ishalfinteger(x::Number) can handle it.

[hyrodium]

Gentle bump 😄

[sostock]

Sorry for the long wait! I will make a release with this soon.

[hyrodium]

Thank you for the merge!