Fix BigInt to Float (#6365)

base/float.jl

@@ -416,3 +416,7 @@ Rounding.set_rounding_raw(Float64, Rounding.JL_FE_TONEAREST)
 ## byte order swaps for arbitrary-endianness serialization/deserialization ##
 bswap(x::Float32) = box(Float32,bswap_int(unbox(Float32,x)))
 bswap(x::Float64) = box(Float64,bswap_int(unbox(Float64,x)))
+
+# bit patterns
+reinterpret(::Type{Unsigned}, x::Float64) = reinterpret(UInt64,x)
+reinterpret(::Type{Unsigned}, x::Float32) = reinterpret(UInt32,x)

base/float16.jl

@@ -161,3 +161,5 @@ exponent(x::Float16) = exponent(Float32(x))
 ^(x::Float16, y::Integer) = Float16(Float32(x)^y)
 
 rationalize{T<:Integer}(::Type{T}, x::Float16; tol::Real=eps(x)) = rationalize(T, Float32(x); tol=tol)
+
+reinterpret(::Type{Unsigned}, x::Float16) = reinterpret(UInt16,x)

base/gmp.jl

@@ -193,12 +193,48 @@ 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)
 
@@ -208,6 +244,7 @@ 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

test/numbers.jl

@@ -926,6 +926,14 @@ 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))
+ end
+end
+
 @test prevfloat(big(pi)) < pi
 @test nextfloat(big(pi)) > pi
 @test !(prevfloat(big(pi)) > pi)