Fix conversion Irrational => Rational (JuliaLang#16527)

Fixes JuliaLang#16513. Changes generated macro to pure macro, so as to avoid breaking in future compiler changes.

base/irrationals.jl

@@ -13,11 +13,27 @@ promote_rule{s,T<:Number}(::Type{Irrational{s}}, ::Type{T}) = promote_type(Float
 convert(::Type{AbstractFloat}, x::Irrational) = Float64(x)
 convert(::Type{Float16}, x::Irrational) = Float16(Float32(x))
 convert{T<:Real}(::Type{Complex{T}}, x::Irrational) = convert(Complex{T}, convert(T,x))
-convert{T<:Integer}(::Type{Rational{T}}, x::Irrational) = convert(Rational{T}, Float64(x))
 
-@generated function (t::Type{T}){T<:Union{Float32,Float64},s}(c::Irrational{s},r::RoundingMode)
- f = T(big(c()),r())
- :($f)
+@pure function convert{T<:Integer}(::Type{Rational{T}}, x::Irrational)
+ o = precision(BigFloat)
+ p = 256
+ while true
+ setprecision(BigFloat, p)
+ bx = BigFloat(x)
+ r = rationalize(T, bx, tol=0)
+ if abs(BigFloat(r) - bx) > eps(bx)
+ setprecision(BigFloat, o)
+ return r
+ end
+ p += 32
+ end
+end
+convert(::Type{Rational{BigInt}}, x::Irrational) = throw(ArgumentError("Cannot convert an Irrational to a Rational{BigInt}: use rationalize(Rational{BigInt}, x) instead"))
+
+@pure function (t::Type{T}){T<:Union{Float32,Float64}}(x::Irrational, r::RoundingMode)
+ setprecision(BigFloat, 256) do
+ T(BigFloat(x), r)
+ end
 end
 
 =={s}(::Irrational{s}, ::Irrational{s}) = true

test/numbers.jl

@@ -2082,6 +2082,12 @@ for f in (trunc, round, floor, ceil)
 
 @test isa(convert(Float64, big(1)//2), Float64)
 
+# issue 16513
+@test convert(Rational{Int32}, pi) == 1068966896 // 340262731
+@test convert(Rational{Int64}, pi) == 2646693125139304345 // 842468587426513207
+@test convert(Rational{Int128}, pi) == 60728338969805745700507212595448411044 // 19330430665609526556707216376512714945
+@test_throws ArgumentError convert(Rational{BigInt}, pi)
+
 # issue 5935
 @test rationalize(Int8, nextfloat(0.1)) == 1//10
 @test rationalize(Int64, nextfloat(0.1)) == 300239975158034//3002399751580339