diff --git a/Project.toml b/Project.toml
index 6ef345f..12db6cf 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "StochasticRounding"
 uuid = "3843c9a1-1f18-49ff-9d99-1b4c8a8e97ed"
 authors = ["Milan Kloewer and StochasticRounding.jl contributors"]
-version = "0.8.3"
+version = "0.9.0"
 
 [deps]
 BFloat16s = "ab4f0b2a-ad5b-11e8-123f-65d77653426b"
diff --git a/src/general.jl b/src/general.jl
index 6831e51..73d9510 100644
--- a/src/general.jl
+++ b/src/general.jl
@@ -12,10 +12,10 @@ for t in (Int8, Int16, Int32, Int64, Int128, UInt8, UInt16, UInt32, UInt64, UInt
 end
 
 # other floats, irrational and rationals
-(::Type{T})(x::Real) where {T<:AbstractStochasticFloat} = stochastic_float(float(T)(x))
-(::Type{T})(x::Rational) where {T<:AbstractStochasticFloat} = stochastic_float(float(T)(x))
+(::Type{T})(x::Real) where {T<:AbstractStochasticFloat} = stochastic_round(T,x)
+(::Type{T})(x::Rational) where {T<:AbstractStochasticFloat} = stochastic_round(stochastic_float(float(T)),x)
 (::Type{T})(x::AbstractStochasticFloat) where {T<:AbstractFloat} = convert(T,float(x))
-(::Type{T})(x::AbstractStochasticFloat) where {T<:AbstractStochasticFloat} = stochastic_float(convert(float(T),float(x)))
+(::Type{T})(x::AbstractStochasticFloat) where {T<:AbstractStochasticFloat} = stochastic_round(T,float(x))
 DoubleFloats.Double64(x::T) where T<:AbstractStochasticFloat = Double64(float(x))
 
 # masks same as for deterministic floats
@@ -104,8 +104,8 @@ Base.abs(x::AbstractStochasticFloat) = stochastic_float(abs(float(x)))
 
 # stochastic rounding
 export stochastic_round
-stochastic_round(T::Type{<:AbstractFloat},x::Real) = stochastic_round(T,widen(stochastic_float(T))(x))
-stochastic_round(T::Type{<:AbstractStochasticFloat},x::AbstractFloat) = stochastic_float(stochastic_round(float(T),x))
+stochastic_round(T::Type{<:AbstractFloat}, x::Real) = stochastic_round(T,widen(stochastic_float(T))(x))
+stochastic_round(T::Type{<:AbstractStochasticFloat}, x::Real) = stochastic_float(stochastic_round(float(T),x))
 
 # Comparison
 for op in (:(==), :<, :<=, :isless)
diff --git a/test/conversions.jl b/test/conversions.jl
index 2de8f63..ad50e25 100644
--- a/test/conversions.jl
+++ b/test/conversions.jl
@@ -1,9 +1,9 @@
-@testset "Converting Stochastic FP to BFloat16sr" begin
+@testset "Deterministic conversion of Stochastic FP to BFloat16sr" begin
     for k in 1:100000
         trueVal = randn(Float64)
-        # Convert to each deterministic type to ensure the result is 
+        # Convert to each deterministic type to ensure the result is
         # representable in all precisions
-        trueVal=Float16(Float32(BFloat16(trueVal)))
+        trueVal = Float16(Float32(BFloat16(trueVal)))
         bfloatVal = BFloat16sr(trueVal)
         float16Val = Float16sr(trueVal)
         float32Val = Float32sr(trueVal)
@@ -14,12 +14,12 @@
     end
 end
 
-@testset "Converting Stochastic FP to Float16sr" begin
+@testset "Deterministic conversion of  Stochastic FP to Float16sr" begin
     for k in 1:100000
         trueVal = randn(Float64)
-        # Convert to each deterministic type to ensure the result is 
+        # Convert to each deterministic type to ensure the result is
         # representable in all precisions
-        trueVal=Float16(Float32(BFloat16(trueVal)))
+        trueVal = Float16(Float32(BFloat16(trueVal)))
         bfloatVal = BFloat16sr(trueVal)
         float16Val = Float16sr(trueVal)
         float32Val = Float32sr(trueVal)
@@ -30,12 +30,12 @@ end
     end
 end
 
-@testset "Converting Stochastic FP to Float32sr" begin
+@testset "Deterministic conversion of  Stochastic FP to Float32sr" begin
     for k in 1:100000
         trueVal = randn(Float64)
-        # Convert to each deterministic type to ensure the result is 
+        # Convert to each deterministic type to ensure the result is
         # representable in all precisions
-        trueVal=Float16(Float32(BFloat16(trueVal)))
+        trueVal = Float16(Float32(BFloat16(trueVal)))
         bfloatVal = BFloat16sr(trueVal)
         float16Val = Float16sr(trueVal)
         float32Val = Float32sr(trueVal)
@@ -45,3 +45,33 @@ end
         @test float32Val == Float32sr(float16Val)
     end
 end
+
+
+@testset "Stochastic conversion of Float64 to $(SR)" for SR in [Float16sr, BFloat16sr, Float32sr]
+
+    # corresponding FP type
+    FP = float(SR)
+
+    for k in 1:100
+        trueVal = randn(Float64)
+
+        # make sure that this is not representable by FP
+        if trueVal == FP(trueVal)
+            trueVal = nextfloat(trueVal)
+        end
+
+        roundedVal = SR(trueVal)
+
+        # check that rounding is not deterministic
+        is_stochastic = false
+        for l in 1:10000
+            if roundedVal != SR(trueVal)
+                is_stochastic = true
+                break
+            end
+        end
+
+        # the redundant "== true" produces a better error message in the test log
+        @test is_stochastic == true
+    end
+end