Add conversion CalciumField, QQBar -> Float64 (#1893)

Also avoid ccalls in conversion to ComplexF64

src/calcium/ca.jl

@@ -1363,15 +1363,19 @@ end
 
 function (::Type{ComplexF64})(x::CalciumFieldElem)
   z = AcbField(53, cached = false)(x)
-  x = ArbFieldElem()
-  ccall((:acb_get_real, libflint), Nothing, (Ref{ArbFieldElem}, Ref{AcbFieldElem}), x, z)
+  x = real(z)
   xx = Float64(x)
-  y = ArbFieldElem()
-  ccall((:acb_get_imag, libflint), Nothing, (Ref{ArbFieldElem}, Ref{AcbFieldElem}), y, z)
+  y = imag(z)
   yy = Float64(y)
   return ComplexF64(xx, yy)
 end
 
+function (::Type{Float64})(a::CalciumFieldElem)
+  isreal(a) || throw(InexactError(:Float64, Float64, a))
+  x = ArbField(53, cached = false)(a)
+  return Float64(x)
+end
+
 ###############################################################################
 #
 #   Unsafe functions

src/calcium/qqbar.jl

@@ -1476,17 +1476,21 @@ function ZZRingElem(a::QQBarFieldElem)
   return z
 end
 
-function (::Type{ComplexF64})(x::QQBarFieldElem)
-  z = AcbField(53, cached = false)(x)
-  x = ArbFieldElem()
-  ccall((:acb_get_real, libflint), Nothing, (Ref{ArbFieldElem}, Ref{AcbFieldElem}), x, z)
+function (::Type{ComplexF64})(a::QQBarFieldElem)
+  z = AcbField(53, cached = false)(a)
+  x = real(z)
   xx = Float64(x)
-  y = ArbFieldElem()
-  ccall((:acb_get_imag, libflint), Nothing, (Ref{ArbFieldElem}, Ref{AcbFieldElem}), y, z)
+  y = imag(z)
   yy = Float64(y)
   return ComplexF64(xx, yy)
 end
 
+function (::Type{Float64})(a::QQBarFieldElem)
+  isreal(a) || throw(InexactError(:Float64, Float64, a))
+  x = ArbField(53, cached = false)(a)
+  return Float64(x)
+end
+
 ###############################################################################
 #
 #   Unsafe functions

test/calcium/ca-test.jl

@@ -278,6 +278,14 @@ end
   s = 1 * one(C) + 2 * onei(C)
   @test ComplexF64(s) == 1 + 2 * im
 
+  x = sqrt(C(2))
+  @test isapprox(Float64(x), sqrt(2))
+  @test isapprox(ComplexF64(x), sqrt(2))
+
+  x = sqrt(C(-2))
+  @test_throws InexactError Float64(x)
+  @test isapprox(ComplexF64(x), sqrt(complex(-2)))
+
   # verify precision bug https://github.com/Nemocas/Nemo.jl/issues/1580 is fixed
   x = C(pi)
   F = ArbField(333)

test/calcium/qqbar-test.jl

@@ -400,6 +400,14 @@ end
       @test contains(ComplexField()(a), ComplexField()(b))
     end
   end
+
+  x = sqrt(R(2))
+  @test isapprox(Float64(x), sqrt(2))
+  @test isapprox(ComplexF64(x), sqrt(2))
+
+  x = sqrt(R(-2))
+  @test_throws InexactError Float64(x)
+  @test isapprox(ComplexF64(x),sqrt(complex(-2)))
 end
 
 function test_elem(R::QQBarField)