diff --git a/base/gmp.jl b/base/gmp.jl
index 90a7161c64594..605ab5dd1539b 100644
--- a/base/gmp.jl
+++ b/base/gmp.jl
@@ -201,12 +201,48 @@ if sizeof(Int64) == sizeof(Clong)
 end
 convert(::Type{Int128}, x::BigInt) = copysign(UInt128(abs(x))%Int128,x)
 
-function convert(::Type{Float64}, n::BigInt)
-    # TODO: this should round to nearest but instead rounds to zero
+
+function call(::Type{Float64}, n::BigInt, ::RoundingMode{:ToZero})
     ccall((:__gmpz_get_d, :libgmp), Float64, (Ptr{BigInt},), &n)
 end
-convert(::Type{Float32}, n::BigInt) = Float32(Float64(n))
-convert(::Type{Float16}, n::BigInt) = Float16(Float64(n))
+
+function call{T<:Union(Float16,Float32)}(::Type{T}, n::BigInt, ::RoundingMode{:ToZero})
+    T(Float64(n,RoundToZero),RoundToZero)
+end
+
+function call{T<:CdoubleMax}(::Type{T}, n::BigInt, ::RoundingMode{:Down})
+    x = T(n,RoundToZero)
+    x > n ? prevfloat(x) : x
+end
+function call{T<:CdoubleMax}(::Type{T}, n::BigInt, ::RoundingMode{:Up})
+    x = T(n,RoundToZero)
+    x < n ? nextfloat(x) : x
+end
+function call{T<:CdoubleMax}(::Type{T}, n::BigInt, ::RoundingMode{:Nearest})
+    x = T(n,RoundToZero)
+    if maxintfloat(T) <= abs(x) < T(Inf)
+        r = n-BigInt(x)
+        h = eps(x)/2
+        if iseven(reinterpret(Unsigned,x)) # check if last bit is odd/even
+            if r < -h
+                return prevfloat(x)
+            elseif r > h
+                return nextfloat(x)
+            end
+        else
+            if r <= -h
+                return prevfloat(x)
+            elseif r >= h
+                return nextfloat(x)
+            end
+        end
+    end
+    x
+end
+
+convert(::Type{Float64}, n::BigInt) = Float64(n,RoundNearest)
+convert(::Type{Float32}, n::BigInt) = Float32(n,RoundNearest)
+convert(::Type{Float16}, n::BigInt) = Float16(n,RoundNearest)
 
 rem(x::BigInt, ::Type{Bool}) = ((x&1)!=0)
 
@@ -216,6 +252,7 @@ function rem{T<:Integer}(n::BigInt, ::Type{T})
     convert(T, (n-lo) & (widen(hi)-widen(lo)) + lo)
 end
 
+
 promote_rule{T<:Integer}(::Type{BigInt}, ::Type{T}) = BigInt
 
 # serialization
diff --git a/test/numbers.jl b/test/numbers.jl
index a55230465834f..3169ae585cdc9 100644
--- a/test/numbers.jl
+++ b/test/numbers.jl
@@ -926,6 +926,18 @@ end
 @test !(Float32(pi,RoundDown) > pi)
 @test !(Float32(pi,RoundUp) < pi)
 
+# issue #6365
+for T in (Float32, Float64)
+    for i = 9007199254740992:9007199254740996
+        @test T(i) == T(BigFloat(i))
+        @test T(-i) == T(BigFloat(-i))
+        for r in (RoundNearest,RoundUp,RoundDown,RoundToZero)
+            @test T(i,r) == T(BigFloat(i),r)
+            @test T(-i,r) == T(BigFloat(-i),r)
+        end
+    end
+end
+
 @test prevfloat(big(pi)) < pi
 @test nextfloat(big(pi)) > pi
 @test !(prevfloat(big(pi)) > pi)