transcendental functions return Float32 on small integer inputs

[simonster]

On line 124 of math.jl, we set up transcendental functions of arbitrary reals so that they call f(float(x)). Because float(::Int8) and float(::Int16) return a Float32, this means e.g. log(uint8(2)) returns a Float32. This is consistent, but I'm not sure it's desirable. The input is exact, so precision of the result seems just as important as if the input were an Int.

[JeffBezanson]

That's true; we might as well let 'Float64' be the "default" float type, and only use others when requested or when necessary.

[stevengj]

Sounds reasonable to me. One of Kahan's standard "misconceptions of floating-point" is that "Arithmetic much more precise than the data it operates upon is needless, and wasteful," and it looks like we fell into that trap here by promoting integers by default to the narrowest fp type that can represent them exactly.

[StefanKarpinski]

My fault. Yes, we should just promote to Float64.

[ViralBShah]

Yes Float64 should really be the default float type.