Base.cis operating on angles in degrees first converts to radians

[jecs]

Base.cis, when called with an argument that is in degrees, first converts the argument to radians, and then calls sincos, resulting in output that is less precise. Possibly related to Issue 450.

This can be seen in the following snippet.

julia> cis(90u"°")
6.123233995736766e-17 + 1.0im

julia> @code_typed cis(90u"°")
CodeInfo(
1 ─ %1 = Base.getfield(x, :val)::Int64
│   %2 = Base.sitofp(Float64, %1)::Float64
│   %3 = Base.mul_float(%2, 0.017453292519943295)::Float64
│   %4 = invoke Base.sincos(%3::Float64)::Tuple{Float64, Float64}
│   %5 = Base.getfield(%4, 1)::Float64
│   %6 = Base.getfield(%4, 2)::Float64
│   %7 = %new(ComplexF64, %6, %5)::ComplexF64
└──      return %7
) => ComplexF64

However, when calling sincos directly, the correct method is chosen:

julia> sincos(90u"°")
(1.0, 0.0)

julia> @code_typed sincos(90u"°")
CodeInfo(
1 ─ %1 = Base.getfield(x, :val)::Int64
│   %2 = Base.sitofp(Float64, %1)::Float64
│   %3 = invoke Unitful.sind(%2::Float64)::Float64
│   %4 = invoke Unitful.cosd(%2::Float64)::Float64
│   %5 = Core.tuple(%3, %4)::Tuple{Float64, Float64}
└──      return %5
) => Tuple{Float64, Float64}

[sostock]

Using the more accurate method would unfortunately hurt performance (apparently, sincosd is quite a bit slower than sincos):

julia> d = 20.0u"°";

julia> @btime cis($d);
  14.307 ns (0 allocations: 0 bytes) # current method: convert to unitless, call sincos
  33.159 ns (0 allocations: 0 bytes) # better accuracy: call sincosd

I still think we should use the more accurate sincosd. What do you think?

[jecs]

Personally, I like dispatching to the degree versions. The user can always uconvert to rad before calling these functions if better performance is required.