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In the same way that Base exports the constants NaN16, NaN32, and NaN64, corresponding to the types Float16, Float32, and Float64, Quadmath.jl should export a NaN128 constant of type Float128.
To match the definitions in base/float.jl, we should define NaN128 as reinterpret(Float128, 0x7fff_8000_0000_0000_0000_0000_0000_0000), i.e., positive quiet NaN with all-zero payload. Note that we already do this for Inf128 but not NaN128 for some reason.
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