Inconsistent Integer results

[kimikage]

The return types of Integer(::Fixed) and Integer(::Normed) are based on different manners.

Fixed{T}: T

julia> typeof(Integer(1Q1f6))
Int8

julia> typeof(Integer(1Q1f14))
Int16

Normed: Int with (non-intuitive) promotions

julia> typeof(Integer(1N0f8))
Int64

julia> typeof(Integer(1N0f16))
Int64

julia> typeof(Integer(1N0f32))
Int64

julia> typeof(Integer(1N0f64)) # !?
BigInt

Float: Int w/o promotions

julia> typeof(Integer(Float16(1)))
Int64

julia> typeof(Integer(1.0f0))
Int64

julia> typeof(Integer(1.0))
Int64

julia> typeof(Integer(0x1p63))
ERROR: InexactError: Int64(9.223372036854776e18)

I think it is better to unify the manners, even though it will be a breaking change.
I consider it appropriate for FixedPoint to return numbers in the rawtype T as Integer(::Fixed) returns.

FYI, with fix for issue #153, we can use floor(Integer, x) etc.

[kimikage]

BTW, there is no longer a zero-argument InexactError().

> julia> Integer(1.5Q1f6)
ERROR: MethodError: no method matching InexactError()
Closest candidates are:
  InexactError(::Symbol, ::Any, ::Any) at boot.jl:280

FixedPointNumbers.jl/src/fixed.jl

Lines 67 to 74 in 7ad0f0c

	function Base.Integer(x::Fixed{T,f}) where {T,f}
	isinteger(x) || throw(InexactError())
	Integer(x.i>>f)
	end
	function (::Type{TI})(x::Fixed{T,f}) where {TI <: Integer,T,f}
	isinteger(x) || throw(InexactError())
	TI(x.i>>f)
	end

Also, I don't think this specialization makes much sense. (There is no ambiguity.)

[kimikage]

There is the problem of type inconsistency in Rational, too.

julia> typeof(Rational(0.5Q1f6))
Rational{Int64}

julia> typeof(Rational(0.5Q0f7))
Rational{Int64}

julia> typeof(Rational(0.5Q1f62))
Rational{Int128}

julia> typeof(Rational(0.5Q0f63))
Rational{Int128}

julia> typeof(Rational(0.5N0f8))
Rational{UInt8}

julia> typeof(Rational(0.5N0f64))
Rational{UInt64}

I also think it is better to use the rawtype T for Rational, but it should be noted that the rawone (i.e. the denominator) of Fixed{T,f} exceeds the range of T at f == 8sizeof(T)-1.