`rem(::Float128, ::Float128)` uses round-to-nearest instead of truncated

[langestefan]

Base.rem for Float128 uses libquadmath's remainderq:

Quadmath.jl/src/Quadmath.jl

Lines 330 to 331 in 9f739ce

	@assume_effects :foldable Base.rem(x::Float128, y::Float128) =
	Float128(@quad_ccall(libquadmath.remainderq(x::Cfloat128, y::Cfloat128)::Cfloat128))

Which implements round-to-nearest quotient. Julia's rem uses truncated division, round-to-zero.

This leads to inconsistencies in computations that use Base.rem, such as sind, cosd, tand.

MWE

julia> using Quadmath

julia> rem(Float128(7.5), Float128(2))
-0.5   # expected 1.5

julia> rem(7.5, 2.0)   # Float64 reference
1.5

julia> rem(Float128(200), Float128(360))
-160   # expected 200.0

Fix

Call fmodq instead of remainderq.

If we want to also support the current behaviour, remainderq corresponds toBase.rem(x, y, RoundNearest), which could be added as a separate method.