diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index e9da359951..db27670be1 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -1374,6 +1374,11 @@ T sqrt(const T &x)
   return sqrt(x);
 }
 
+// Boolean specialization, avoids implicit float to bool conversion (-Wimplicit-conversion-floating-point-to-bool).
+template<>
+EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC
+bool sqrt<bool>(const bool &x) { return x; }
+
 #if defined(SYCL_DEVICE_ONLY)
 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sqrt, sqrt)
 #endif
diff --git a/Eigen/src/Core/arch/SSE/MathFunctions.h b/Eigen/src/Core/arch/SSE/MathFunctions.h
index 71ec6f858a..d5b62e86a4 100644
--- a/Eigen/src/Core/arch/SSE/MathFunctions.h
+++ b/Eigen/src/Core/arch/SSE/MathFunctions.h
@@ -99,6 +99,9 @@ Packet4f psqrt<Packet4f>(const Packet4f& x) { return _mm_sqrt_ps(x); }
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
 Packet2d psqrt<Packet2d>(const Packet2d& x) { return _mm_sqrt_pd(x); }
 
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet16b psqrt<Packet16b>(const Packet16b& x) { return x; }
+
 #if EIGEN_FAST_MATH
 
 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
diff --git a/Eigen/src/Core/arch/SSE/PacketMath.h b/Eigen/src/Core/arch/SSE/PacketMath.h
index 4db7014910..ef77ab6fa1 100755
--- a/Eigen/src/Core/arch/SSE/PacketMath.h
+++ b/Eigen/src/Core/arch/SSE/PacketMath.h
@@ -218,7 +218,8 @@ template<> struct packet_traits<bool> : default_packet_traits
     HasAbs2      = 0,
     HasMin       = 0,
     HasMax       = 0,
-    HasConj      = 0
+    HasConj      = 0,
+    HasSqrt      = 1
   };
 };
 
diff --git a/Eigen/src/Core/functors/UnaryFunctors.h b/Eigen/src/Core/functors/UnaryFunctors.h
index c7ed18c697..8c0ed84813 100644
--- a/Eigen/src/Core/functors/UnaryFunctors.h
+++ b/Eigen/src/Core/functors/UnaryFunctors.h
@@ -422,6 +422,18 @@ struct functor_traits<scalar_sqrt_op<Scalar> > {
   };
 };
 
+// Boolean specialization to eliminate -Wimplicit-conversion-floating-point-to-bool warnings.
+template<> struct scalar_sqrt_op<bool> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_sqrt_op)
+  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline bool operator() (const bool& a) const { return a; }
+  template <typename Packet>
+  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return a; }
+};
+template <>
+struct functor_traits<scalar_sqrt_op<bool> > {
+  enum { Cost = 1, PacketAccess = packet_traits<bool>::Vectorizable };
+};
+
 /** \internal
   * \brief Template functor to compute the reciprocal square root of a scalar
   * \sa class CwiseUnaryOp, Cwise::rsqrt()
@@ -719,6 +731,19 @@ template<typename Scalar>
 struct functor_traits<scalar_square_op<Scalar> >
 { enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
 
+// Boolean specialization to avoid -Wint-in-bool-context warnings on GCC.
+template<>
+struct scalar_square_op<bool> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_square_op)
+  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline bool operator() (const bool& a) const { return a; }
+  template<typename Packet>
+  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
+  { return a; }
+};
+template<>
+struct functor_traits<scalar_square_op<bool> >
+{ enum { Cost = 0, PacketAccess = packet_traits<bool>::Vectorizable }; };
+
 /** \internal
   * \brief Template functor to compute the cube of a scalar
   * \sa class CwiseUnaryOp, Cwise::cube()
@@ -735,6 +760,19 @@ template<typename Scalar>
 struct functor_traits<scalar_cube_op<Scalar> >
 { enum { Cost = 2*NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
 
+// Boolean specialization to avoid -Wint-in-bool-context warnings on GCC.
+template<>
+struct scalar_cube_op<bool> {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_cube_op)
+  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline bool operator() (const bool& a) const { return a; }
+  template<typename Packet>
+  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
+  { return a; }
+};
+template<>
+struct functor_traits<scalar_cube_op<bool> >
+{ enum { Cost = 0, PacketAccess = packet_traits<bool>::Vectorizable }; };
+
 /** \internal
   * \brief Template functor to compute the rounded value of a scalar
   * \sa class CwiseUnaryOp, ArrayBase::round()
diff --git a/unsupported/test/cxx11_tensor_block_eval.cpp b/unsupported/test/cxx11_tensor_block_eval.cpp
index a7a49fa1f5..b2e26ebb73 100644
--- a/unsupported/test/cxx11_tensor_block_eval.cpp
+++ b/unsupported/test/cxx11_tensor_block_eval.cpp
@@ -222,7 +222,7 @@ static void test_eval_tensor_unary_expr_block() {
   input.setRandom();
 
   VerifyBlockEvaluator<T, NumDims, Layout>(
-      input.square(), [&dims]() { return RandomBlock<Layout>(dims, 1, 10); });
+      input.abs(), [&dims]() { return RandomBlock<Layout>(dims, 1, 10); });
 }
 
 template <typename T, int NumDims, int Layout>
@@ -274,7 +274,7 @@ static void test_eval_tensor_broadcast() {
   // Check that desc.destination() memory is not shared between two broadcast
   // materializations.
   VerifyBlockEvaluator<T, NumDims, Layout>(
-      input.broadcast(bcast) * input.square().broadcast(bcast),
+      input.broadcast(bcast) * input.abs().broadcast(bcast),
       [&bcasted_dims]() { return SkewedInnerBlock<Layout>(bcasted_dims); });
 }
 
@@ -391,27 +391,46 @@ static void test_eval_tensor_chipping() {
 
   // Block expression assignment.
   VerifyBlockEvaluator<T, NumDims - 1, Layout>(
-      input.square().chip(chip_offset, chip_dim),
+      input.abs().chip(chip_offset, chip_dim),
       [&chipped_dims]() { return FixedSizeBlock(chipped_dims); });
 
   VerifyBlockEvaluator<T, NumDims - 1, Layout>(
-      input.square().chip(chip_offset, chip_dim),
+      input.abs().chip(chip_offset, chip_dim),
       [&chipped_dims]() { return RandomBlock<Layout>(chipped_dims, 1, 10); });
 }
 
+
+template<typename T, int NumDims>
+struct SimpleTensorGenerator {
+  T operator()(const array<Index, NumDims>& coords) const {
+    T result = static_cast<T>(0);
+    for (int i = 0; i < NumDims; ++i) {
+      result += static_cast<T>((i + 1) * coords[i]);
+    }
+    return result;
+  }
+};
+
+// Boolean specialization to avoid -Wint-in-bool-context warnings on GCC.
+template<int NumDims>
+struct SimpleTensorGenerator<bool, NumDims> {
+  bool operator()(const array<Index, NumDims>& coords) const {
+    bool result = false;
+    for (int i = 0; i < NumDims; ++i) {
+      result ^= coords[i];
+    }
+    return result;
+  }
+};
+
+
 template <typename T, int NumDims, int Layout>
 static void test_eval_tensor_generator() {
   DSizes<Index, NumDims> dims = RandomDims<NumDims>(10, 20);
   Tensor<T, NumDims, Layout> input(dims);
   input.setRandom();
 
-  auto generator = [](const array<Index, NumDims>& coords) -> T {
-    T result = static_cast<T>(0);
-    for (int i = 0; i < NumDims; ++i) {
-      result += static_cast<T>((i + 1) * coords[i]);
-    }
-    return result;
-  };
+  auto generator = SimpleTensorGenerator<T, NumDims>();
 
   VerifyBlockEvaluator<T, NumDims, Layout>(
       input.generate(generator), [&dims]() { return FixedSizeBlock(dims); });