Merging eigen/eigen.

12 files changed, 507 insertions, 321 deletions

diff --git a/test/packetmath.cpp b/test/packetmath.cpp
index 0f9ce6d06..2c7fb5aeb 100644
--- a/test/packetmath.cpp
+++ b/test/packetmath.cpp
@@ -609,12 +609,12 @@ template<typename Scalar,typename Packet> void packetmath_real()
   CHECK_CWISE1_IF(PacketTraits::HasSqrt, std::sqrt, internal::psqrt);
   CHECK_CWISE1_IF(PacketTraits::HasSqrt, Scalar(1)/std::sqrt, internal::prsqrt);
   CHECK_CWISE1_IF(PacketTraits::HasLog, std::log, internal::plog);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::i0, internal::pi0);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::i0e, internal::pi0e);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::i1, internal::pi1);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::i1e, internal::pi1e);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::j0, internal::pj0);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::j1, internal::pj1);
+  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i0, internal::pbessel_i0);
+  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i0e, internal::pbessel_i0e);
+  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i1, internal::pbessel_i1);
+  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_i1e, internal::pbessel_i1e);
+  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_j0, internal::pbessel_j0);
+  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_j1, internal::pbessel_j1);
 
   // Use a smaller data range for the positive bessel operations as these
   // can have much more error at very small and very large values.
@@ -624,12 +624,12 @@ template<typename Scalar,typename Packet> void packetmath_real()
       data2[i] = internal::random<Scalar>(0.01,1) * std::pow(
           Scalar(10), internal::random<Scalar>(-1,2));
   }
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::y0, internal::py0);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::y1, internal::py1);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::k0, internal::pk0);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::k0e, internal::pk0e);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::k1, internal::pk1);
-  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::k1e, internal::pk1e);
+  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_y0, internal::pbessel_y0);
+  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_y1, internal::pbessel_y1);
+  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_k0, internal::pbessel_k0);
+  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_k0e, internal::pbessel_k0e);
+  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_k1, internal::pbessel_k1);
+  CHECK_CWISE1_IF(PacketTraits::HasBessel, numext::bessel_k1e, internal::pbessel_k1e);
 
 #if EIGEN_HAS_C99_MATH && (__cplusplus > 199711L)
   CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasLGamma, std::lgamma, internal::plgamma);
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h b/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
index 48e0217e5..a951bea6d 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorBase.h
@@ -137,73 +137,73 @@ class TensorBase<Derived, ReadOnlyAccessors>
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_i0_op<Scalar>, const Derived>
-    i0() const {
+    bessel_i0() const {
       return unaryExpr(internal::scalar_bessel_i0_op<Scalar>());
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_i0e_op<Scalar>, const Derived>
-    i0e() const {
+    bessel_i0e() const {
       return unaryExpr(internal::scalar_bessel_i0e_op<Scalar>());
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_i1_op<Scalar>, const Derived>
-    i1() const {
+    bessel_i1() const {
       return unaryExpr(internal::scalar_bessel_i1_op<Scalar>());
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_i1e_op<Scalar>, const Derived>
-    i1e() const {
+    bessel_i1e() const {
       return unaryExpr(internal::scalar_bessel_i1e_op<Scalar>());
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_j0_op<Scalar>, const Derived>
-    j0() const {
+    bessel_j0() const {
       return unaryExpr(internal::scalar_bessel_j0_op<Scalar>());
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_y0_op<Scalar>, const Derived>
-    y0() const {
+    bessel_y0() const {
       return unaryExpr(internal::scalar_bessel_y0_op<Scalar>());
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_j1_op<Scalar>, const Derived>
-    j1() const {
+    bessel_j1() const {
       return unaryExpr(internal::scalar_bessel_j1_op<Scalar>());
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_y1_op<Scalar>, const Derived>
-    y1() const {
+    bessel_y1() const {
       return unaryExpr(internal::scalar_bessel_y1_op<Scalar>());
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_k0_op<Scalar>, const Derived>
-    k0() const {
+    bessel_k0() const {
       return unaryExpr(internal::scalar_bessel_k0_op<Scalar>());
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_k0e_op<Scalar>, const Derived>
-    k0e() const {
+    bessel_k0e() const {
       return unaryExpr(internal::scalar_bessel_k0e_op<Scalar>());
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_k1_op<Scalar>, const Derived>
-    k1() const {
+    bessel_k1() const {
       return unaryExpr(internal::scalar_bessel_k1_op<Scalar>());
     }
 
     EIGEN_DEVICE_FUNC
     EIGEN_STRONG_INLINE const TensorCwiseUnaryOp<internal::scalar_bessel_k1e_op<Scalar>, const Derived>
-    k1e() const {
+    bessel_k1e() const {
       return unaryExpr(internal::scalar_bessel_k1e_op<Scalar>());
     }
 
diff --git a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h
index 4adfeb560..ba3a80f97 100644
--- a/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h
+++ b/unsupported/Eigen/CXX11/src/Tensor/TensorContractionThreadPool.h
@@ -379,7 +379,8 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
                         bool parallel_pack,
                         bool parallelize_by_sharding_dim_only,
                         DoneCallback done)
-        : done_(this, std::move(done)),
+        : created_by_thread_id_(std::this_thread::get_id()),
+          done_(this, std::move(done)),
           device_(self->m_device),
           lhs_(self->m_leftImpl, self->m_left_nocontract_strides,
                self->m_i_strides, self->m_left_contracting_strides,
@@ -408,7 +409,20 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
           gn_(gn),
           nm0_(nm0),
           nn0_(nn0),
-          kernel_(m_, k_, n_, bm_, bk_, bn_) {
+          kernel_(m_, k_, n_, bm_, bk_, bn_),
+          num_thread_local_allocations_(0),
+          // We reserve 2X more capacity for a thread local values, than the
+          // number of threads in the pool to efficiently handle task stealing
+          // by threads that are not managed by the pool.
+          thread_local_capacity(2 * (parallelize_by_sharding_dim_only_
+                                         ? device_.numThreadsInPool()
+                                         : 0)),
+          // We will use only one of the Lhs/Rhs thread local storage depending
+          // on the shard_by_col value and we parallelize by sharding dim ONLY.
+          lhs_thread_local_blocks_(shard_by_col_ ? 0 : thread_local_capacity,
+                                   {*this}, {*this}),
+          rhs_thread_local_blocks_(shard_by_col_ ? thread_local_capacity : 0,
+                                   {*this}, {*this}) {
       // These two options are mutually exclusive.
       eigen_assert(!(parallel_pack && parallelize_by_sharding_dim_only));
 
@@ -455,12 +469,12 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
                                                   std::memory_order_relaxed);
 
           Index num_blocks = num_worker_threads * gn_;
-          thread_local_packed_mem_ = kernel_.allocateSlices(  //
-              device_,                                        //
-              /*num_lhs=*/0,                                  //
-              /*num_rhs=*/num_blocks,                         //
-              /*num_slices=*/1,                               //
-              /*lhs_blocks=*/nullptr, &thread_local_packed_rhs_);
+          thread_local_pre_alocated_mem_ = kernel_.allocateSlices(  //
+              device_,                                              //
+              /*num_lhs=*/0,                                        //
+              /*num_rhs=*/num_blocks,                               //
+              /*num_slices=*/1,                                     //
+              /*lhs_blocks=*/nullptr, &rhs_thread_local_pre_allocated_);
 
         } else {
           can_use_thread_local_packed_ = new std::atomic<bool>[nm_];
@@ -469,11 +483,11 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
                                                   std::memory_order_relaxed);
 
           Index num_blocks = num_worker_threads * gm_;
-          thread_local_packed_mem_ = kernel_.allocateSlices(  //
-              device_,                                        //
-              /*num_lhs=*/num_blocks,                         //
-              /*num_rhs=*/0,                                  //
-              /*num_slices=*/1, &thread_local_packed_lhs_,    //
+          thread_local_pre_alocated_mem_ = kernel_.allocateSlices(  //
+              device_,                                              //
+              /*num_lhs=*/num_blocks,                               //
+              /*num_rhs=*/0,                                        //
+              /*num_slices=*/1, &lhs_thread_local_pre_allocated_,   //
               /*rhs_blocks=*/nullptr);
         }
       }
@@ -486,7 +500,7 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
       }
       kernel_.deallocate(device_, packed_mem_);
       if (parallelize_by_sharding_dim_only_) {
-        kernel_.deallocate(device_, thread_local_packed_mem_);
+        kernel_.deallocate(device_, thread_local_pre_alocated_mem_);
         delete[] can_use_thread_local_packed_;
       }
     }
@@ -512,6 +526,8 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
     }
 
    private:
+    std::thread::id created_by_thread_id_;
+
     // This notification is specialized on the type of DoneCallback and can be
     // blocking or non-blocking.
     EvalParallelNotification<DoneCallback, EvalParallelContext> done_;
@@ -606,11 +622,185 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
     // completion of the K-1 kernel, so we have to allocate "global" packed_lhs_
     // and packed_rhs_ to allow kernels to be executed later on a thread
     // different from the thread that was used for packing.
-    BlockMemHandle thread_local_packed_mem_;
 
-    // Only one of these will be initialized depending on shard_by_col value.
-    std::vector<LhsBlock> thread_local_packed_lhs_;
-    std::vector<RhsBlock> thread_local_packed_rhs_;
+    // Handle for pre-allocated thread local memory buffers.
+    BlockMemHandle thread_local_pre_alocated_mem_;
+
+    // Only one of these will be initialized depending on shard_by_col value
+    // (the size will be `num_worker_threads * num_grains_in_the_sharding_dim`).
+    std::vector<LhsBlock> lhs_thread_local_pre_allocated_;
+    std::vector<RhsBlock> rhs_thread_local_pre_allocated_;
+
+    // How many thread local blocks were already allocated.
+    std::atomic<int> num_thread_local_allocations_;
+    const int thread_local_capacity;
+
+    // We will use pre-allocated Lhs/Rhs blocks defined above, if the number of
+    // unique threads in a system is below or equal to the number of threads in
+    // a thread pool. We will fallback on dynamic memory allocation after that.
+
+    // ThreadLocalBlocks is a container for Lhs or Rhs thread local buffers. Its
+    // size is equal to the grain size in Lhs/Rhs sharding dimension.
+    template <typename BlockType>
+    class ThreadLocalBlocks {
+     public:
+      ThreadLocalBlocks() = default;
+
+      ThreadLocalBlocks(BlockType* base, size_t grain_size)
+          : is_pre_allocated_(true),
+            thread_local_pre_allocated_base_(base),
+            grain_size_(grain_size) {}
+
+      ThreadLocalBlocks(BlockMemHandle mem_handle,
+                        std::vector<BlockType> blocks)
+          : is_pre_allocated_(false),
+            mem_handle_(std::move(mem_handle)),
+            blocks_(std::move(blocks)) {}
+
+      BlockType& block(int grain_index) {
+        eigen_assert(grain_index >= 0);
+        eigen_assert(static_cast<size_t>(grain_index) < size());
+        return is_pre_allocated_ ? thread_local_pre_allocated_base_[grain_index]
+                                 : blocks_[grain_index];
+      }
+
+      void Release(EvalParallelContext& ctx) const {
+        if (!is_pre_allocated_) {
+          ctx.kernel_.deallocate(ctx.device_, mem_handle_);
+        }
+      }
+
+      size_t size() const {
+        return is_pre_allocated_ ? grain_size_ : blocks_.size();
+      }
+
+     private:
+      bool is_pre_allocated_;
+
+      // Reuse pre-allocated thread local buffers.
+      BlockType* thread_local_pre_allocated_base_ = nullptr;
+      size_t grain_size_ = 0;
+
+      // These will be initialized only if `is_pre_allocated == false`.
+      BlockMemHandle mem_handle_{};
+      std::vector<BlockType> blocks_;
+    };
+
+    // ThreadLocalBlocksInitialize callable does custom thread local blocks
+    // initialization, and will reuse pre-allocated buffers if possible, or will
+    // dynamically allocate new memory.
+    //
+    // Lhs/Rhs blocks might be of the same type, so we have to pass explicitly
+    // for what side do we plan to do block allocation.
+    template <typename BlockType, bool is_rhs>
+    class ThreadLocalBlocksInitialize {
+      static constexpr bool kIsLhs =
+          !is_rhs && std::is_same<BlockType, LhsBlock>::value;
+      static const bool kIsRhs =
+          is_rhs && std::is_same<BlockType, RhsBlock>::value;
+      static_assert(kIsLhs || kIsRhs, "Unkown block type");
+
+      using Blocks = ThreadLocalBlocks<BlockType>;
+
+     public:
+      ThreadLocalBlocksInitialize(EvalParallelContext& ctx)
+          : ctx_(ctx),
+            num_worker_threads_(ctx_.device_.numThreadsInPool()) {}
+
+      void operator()(Blocks& blocks) {
+        const int n = ctx_.num_thread_local_allocations_.fetch_add(
+            1, std::memory_order_relaxed);
+
+        if (n >= num_worker_threads_) {
+          ThreadLocalBlocksAllocator<is_rhs>::allocate(ctx_, blocks);
+        } else {
+          ThreadLocalBlocksAllocator<is_rhs>::reuse(ctx_, n, blocks);
+        }
+      }
+
+     private:
+      // NOTE(ezhulenev): Without 'if constexpr' we have to put calls to
+      // TensorContractionKernel::allocateSlices into template specializations.
+      // Also explicit specializations are not allowed at class scope in C++03,
+      // EvalCtx type parameter is just a workaround for that limitation.
+      template <bool pack_rhs, typename EvalCtx = EvalParallelContext>
+      struct ThreadLocalBlocksAllocator;
+
+      template <typename EvalCtx>
+      struct ThreadLocalBlocksAllocator</*pack_rhs=*/true, EvalCtx> {
+        static void allocate(EvalCtx& ctx, Blocks& blocks) {
+          std::vector<RhsBlock> rhs_blocks;
+          BlockMemHandle mem_handle = ctx.kernel_.allocateSlices(
+              ctx.device_,
+              /*num_lhs=*/0,
+              /*num_rhs=*/ctx.gn_,
+              /*num_slices=*/1,
+              /*lhs_blocks=*/nullptr, /*rhs_blocks=*/&rhs_blocks);
+
+          blocks = ThreadLocalBlocks<RhsBlock>(std::move(mem_handle),
+                                               std::move(rhs_blocks));
+        }
+
+        static void reuse(EvalCtx& ctx, int index, Blocks& blocks) {
+          RhsBlock* ptr = &ctx.rhs_thread_local_pre_allocated_[ctx.gn_ * index];
+          blocks = ThreadLocalBlocks<RhsBlock>(ptr, ctx.gn_);
+        }
+      };
+
+      template <typename EvalCtx>
+      struct ThreadLocalBlocksAllocator</*pack_rhs=*/false, EvalCtx> {
+        static void allocate(EvalCtx& ctx, Blocks& blocks) {
+          std::vector<RhsBlock> lhs_blocks;
+          BlockMemHandle mem_handle = ctx.kernel_.allocateSlices(
+              ctx.device_,
+              /*num_lhs=*/ctx.gm_,
+              /*num_rhs=*/0,
+              /*num_slices=*/1,
+              /*lhs_blocks=*/&lhs_blocks, /*rhs_blocks=*/nullptr);
+
+          blocks = ThreadLocalBlocks<RhsBlock>(std::move(mem_handle),
+                                               std::move(lhs_blocks));
+        }
+
+        static void reuse(EvalCtx& ctx, int index, Blocks& blocks) {
+          LhsBlock* ptr = &ctx.lhs_thread_local_pre_allocated_[ctx.gm_ * index];
+          blocks = ThreadLocalBlocks<LhsBlock>(ptr, ctx.gm_);
+        }
+      };
+
+      EvalParallelContext& ctx_;
+      const int num_worker_threads_;
+    };
+
+    template <typename BlockType>
+    class ThreadLocalBlocksRelease {
+     public:
+      using Blocks = ThreadLocalBlocks<BlockType>;
+      ThreadLocalBlocksRelease(EvalParallelContext& ctx) : ctx_(ctx) {}
+      void operator()(Blocks& blocks) { blocks.Release(ctx_); }
+
+     private:
+      EvalParallelContext& ctx_;
+    };
+
+    // ThreadLocalBlocks initialization callables.
+    using ThreadLocalLhsInit =
+        ThreadLocalBlocksInitialize<LhsBlock, /*is_rhs=*/false>;
+    using ThreadLocalRhsInit =
+        ThreadLocalBlocksInitialize<RhsBlock, /*is_rhs=*/true>;
+
+    // ThreadLocalBlocks release callables.
+    using ThreadLocalLhsRelease = ThreadLocalBlocksRelease<LhsBlock>;
+    using ThreadLocalRhsRelease = ThreadLocalBlocksRelease<RhsBlock>;
+
+    // Thread local containers for Lhs/Rhs block packs. In practice only one of
+    // them will be used, depending on the shard_by_col value.
+    Eigen::ThreadLocal<ThreadLocalBlocks<LhsBlock>, ThreadLocalLhsInit,
+                       ThreadLocalLhsRelease>
+        lhs_thread_local_blocks_;
+    Eigen::ThreadLocal<ThreadLocalBlocks<RhsBlock>, ThreadLocalRhsInit,
+                       ThreadLocalRhsRelease>
+        rhs_thread_local_blocks_;
 
     // After a particular shard for Kth slice missed thread local execution
     // opportunity (K-1 slice didn't complete kernels execution), we can no
@@ -630,12 +820,10 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
     LhsBlock& packed_lhs(Index m, Index k, Index m1, bool use_thread_local) {
       if (use_thread_local) {
         eigen_assert(!shard_by_col_);
+        ThreadLocalBlocks<LhsBlock>& blocks = lhs_thread_local_blocks_.local();
 
-        Index base_idx = gm_ * device_.currentThreadId();
-        Index grain_idx = m1 - m * gm_;
-        Index block_idx = base_idx + grain_idx;
-
-        return thread_local_packed_lhs_[block_idx];
+        Index grain_index = m1 - m * gm_;
+        return blocks.block(grain_index);
       } else {
         return packed_lhs_[k % (P - 1)][m1];
       }
@@ -644,12 +832,10 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
     RhsBlock& packed_rhs(Index n, Index k, Index n1, bool use_thread_local) {
       if (use_thread_local) {
         eigen_assert(shard_by_col_);
+        ThreadLocalBlocks<RhsBlock>& blocks = rhs_thread_local_blocks_.local();
 
-        Index base_idx = gn_ * device_.currentThreadId();
-        Index grain_idx = n1 - n * gn_;
-        Index block_idx = base_idx + grain_idx;
-
-        return thread_local_packed_rhs_[block_idx];
+        Index grain_index = n1 - n * gn_;
+        return blocks.block(grain_index);
       } else {
         return packed_rhs_[k % (P - 1)][n1];
       }
@@ -877,11 +1063,11 @@ struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgT
         //     to the execution of the first kernel of the k+1 slice, before
         //     completing a call to the last kernel of the k slice.
         // (2) all pack tasks for sharded dim must be executed in a thread
-        //     pool.
+        //     pool to get pre-allocated thead local buffers.
         bool pack_async =
           (start == 0) &&
           (parallelize_by_sharding_dim_only_&& shard_by_col_ == rhs) &&
-          (k > 0 || device_.currentThreadId() < 0);
+          (k > 0 || std::this_thread::get_id() == created_by_thread_id_);
 
         if (pack_async) {
           device_.enqueueNoNotification(
diff --git a/unsupported/Eigen/SpecialFunctions b/unsupported/Eigen/SpecialFunctions
index ffa348eb4..6e8132fb2 100644
--- a/unsupported/Eigen/SpecialFunctions
+++ b/unsupported/Eigen/SpecialFunctions
@@ -39,18 +39,18 @@ namespace Eigen {
   * - betainc
   *
   * Bessel Functions
-  * - i0
-  * - i0e
-  * - i1
-  * - i1e
-  * - j0
-  * - j1
-  * - y0
-  * - y1
-  * - k0
-  * - k0e
-  * - k1
-  * - k1e
+  * - bessel_i0
+  * - bessel_i0e
+  * - bessel_i1
+  * - bessel_i1e
+  * - bessel_j0
+  * - bessel_j1
+  * - bessel_k0
+  * - bessel_k0e
+  * - bessel_k1
+  * - bessel_k1e
+  * - bessel_y0
+  * - bessel_y1
   *
   * \code
   * #include <unsupported/Eigen/SpecialFunctions>
diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsArrayAPI.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsArrayAPI.h
index 8f96c2ae7..41d2bf61c 100644
--- a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsArrayAPI.h
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsArrayAPI.h
@@ -24,12 +24,12 @@ namespace Eigen {
   * other scalar types, the user has to provide implementations of i0(T) for
   * any scalar type T to be supported.
   *
-  * \sa ArrayBase::i0()
+  * \sa ArrayBase::bessel_i0()
   */
 template <typename Derived>
 EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
     Eigen::internal::scalar_bessel_i0_op<typename Derived::Scalar>, const Derived>
-i0(const Eigen::ArrayBase<Derived>& x) {
+bessel_i0(const Eigen::ArrayBase<Derived>& x) {
   return Eigen::CwiseUnaryOp<
       Eigen::internal::scalar_bessel_i0_op<typename Derived::Scalar>,
       const Derived>(x.derived());
@@ -47,12 +47,12 @@ i0(const Eigen::ArrayBase<Derived>& x) {
   * other scalar types, the user has to provide implementations of i0e(T) for
   * any scalar type T to be supported.
   *
-  * \sa ArrayBase::i0e()
+  * \sa ArrayBase::bessel_i0e()
   */
 template <typename Derived>
 EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
     Eigen::internal::scalar_bessel_i0e_op<typename Derived::Scalar>, const Derived>
-i0e(const Eigen::ArrayBase<Derived>& x) {
+bessel_i0e(const Eigen::ArrayBase<Derived>& x) {
   return Eigen::CwiseUnaryOp<
       Eigen::internal::scalar_bessel_i0e_op<typename Derived::Scalar>,
       const Derived>(x.derived());
@@ -69,12 +69,12 @@ i0e(const Eigen::ArrayBase<Derived>& x) {
   * other scalar types, the user has to provide implementations of i1(T) for
   * any scalar type T to be supported.
   *
-  * \sa ArrayBase::i1()
+  * \sa ArrayBase::bessel_i1()
   */
 template <typename Derived>
 EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
     Eigen::internal::scalar_bessel_i1_op<typename Derived::Scalar>, const Derived>
-i1(const Eigen::ArrayBase<Derived>& x) {
+bessel_i1(const Eigen::ArrayBase<Derived>& x) {
   return Eigen::CwiseUnaryOp<
       Eigen::internal::scalar_bessel_i1_op<typename Derived::Scalar>,
       const Derived>(x.derived());
@@ -92,12 +92,12 @@ i1(const Eigen::ArrayBase<Derived>& x) {
   * other scalar types, the user has to provide implementations of i1e(T) for
   * any scalar type T to be supported.
   *
-  * \sa ArrayBase::i1e()
+  * \sa ArrayBase::bessel_i1e()
   */
 template <typename Derived>
 EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
     Eigen::internal::scalar_bessel_i1e_op<typename Derived::Scalar>, const Derived>
-i1e(const Eigen::ArrayBase<Derived>& x) {
+bessel_i1e(const Eigen::ArrayBase<Derived>& x) {
   return Eigen::CwiseUnaryOp<
       Eigen::internal::scalar_bessel_i1e_op<typename Derived::Scalar>,
       const Derived>(x.derived());
@@ -114,12 +114,12 @@ i1e(const Eigen::ArrayBase<Derived>& x) {
   * other scalar types, the user has to provide implementations of k0(T) for
   * any scalar type T to be supported.
   *
-  * \sa ArrayBase::k0()
+  * \sa ArrayBase::bessel_k0()
   */
 template <typename Derived>
 EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
     Eigen::internal::scalar_bessel_k0_op<typename Derived::Scalar>, const Derived>
-k0(const Eigen::ArrayBase<Derived>& x) {
+bessel_k0(const Eigen::ArrayBase<Derived>& x) {
   return Eigen::CwiseUnaryOp<
       Eigen::internal::scalar_bessel_k0_op<typename Derived::Scalar>,
       const Derived>(x.derived());
@@ -137,12 +137,12 @@ k0(const Eigen::ArrayBase<Derived>& x) {
   * other scalar types, the user has to provide implementations of k0e(T) for
   * any scalar type T to be supported.
   *
-  * \sa ArrayBase::k0e()
+  * \sa ArrayBase::bessel_k0e()
   */
 template <typename Derived>
 EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
     Eigen::internal::scalar_bessel_k0e_op<typename Derived::Scalar>, const Derived>
-k0e(const Eigen::ArrayBase<Derived>& x) {
+bessel_k0e(const Eigen::ArrayBase<Derived>& x) {
   return Eigen::CwiseUnaryOp<
       Eigen::internal::scalar_bessel_k0e_op<typename Derived::Scalar>,
       const Derived>(x.derived());
@@ -159,12 +159,12 @@ k0e(const Eigen::ArrayBase<Derived>& x) {
   * other scalar types, the user has to provide implementations of k1(T) for
   * any scalar type T to be supported.
   *
-  * \sa ArrayBase::k1()
+  * \sa ArrayBase::bessel_k1()
   */
 template <typename Derived>
 EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
     Eigen::internal::scalar_bessel_k1_op<typename Derived::Scalar>, const Derived>
-k1(const Eigen::ArrayBase<Derived>& x) {
+bessel_k1(const Eigen::ArrayBase<Derived>& x) {
   return Eigen::CwiseUnaryOp<
       Eigen::internal::scalar_bessel_k1_op<typename Derived::Scalar>,
       const Derived>(x.derived());
@@ -182,12 +182,12 @@ k1(const Eigen::ArrayBase<Derived>& x) {
   * other scalar types, the user has to provide implementations of k1e(T) for
   * any scalar type T to be supported.
   *
-  * \sa ArrayBase::k1e()
+  * \sa ArrayBase::bessel_k1e()
   */
 template <typename Derived>
 EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
     Eigen::internal::scalar_bessel_k1e_op<typename Derived::Scalar>, const Derived>
-k1e(const Eigen::ArrayBase<Derived>& x) {
+bessel_k1e(const Eigen::ArrayBase<Derived>& x) {
   return Eigen::CwiseUnaryOp<
       Eigen::internal::scalar_bessel_k1e_op<typename Derived::Scalar>,
       const Derived>(x.derived());
@@ -204,12 +204,12 @@ k1e(const Eigen::ArrayBase<Derived>& x) {
   * other scalar types, the user has to provide implementations of j0(T) for
   * any scalar type T to be supported.
   *
-  * \sa ArrayBase::j0()
+  * \sa ArrayBase::bessel_j0()
   */
 template <typename Derived>
 EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
     Eigen::internal::scalar_bessel_j0_op<typename Derived::Scalar>, const Derived>
-j0(const Eigen::ArrayBase<Derived>& x) {
+bessel_j0(const Eigen::ArrayBase<Derived>& x) {
   return Eigen::CwiseUnaryOp<
       Eigen::internal::scalar_bessel_j0_op<typename Derived::Scalar>,
       const Derived>(x.derived());
@@ -226,12 +226,12 @@ j0(const Eigen::ArrayBase<Derived>& x) {
   * other scalar types, the user has to provide implementations of y0(T) for
   * any scalar type T to be supported.
   *
-  * \sa ArrayBase::y0()
+  * \sa ArrayBase::bessel_y0()
   */
 template <typename Derived>
 EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
     Eigen::internal::scalar_bessel_y0_op<typename Derived::Scalar>, const Derived>
-y0(const Eigen::ArrayBase<Derived>& x) {
+bessel_y0(const Eigen::ArrayBase<Derived>& x) {
   return Eigen::CwiseUnaryOp<
       Eigen::internal::scalar_bessel_y0_op<typename Derived::Scalar>,
       const Derived>(x.derived());
@@ -248,12 +248,12 @@ y0(const Eigen::ArrayBase<Derived>& x) {
   * other scalar types, the user has to provide implementations of j1(T) for
   * any scalar type T to be supported.
   *
-  * \sa ArrayBase::j1()
+  * \sa ArrayBase::bessel_j1()
   */
 template <typename Derived>
 EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
     Eigen::internal::scalar_bessel_j1_op<typename Derived::Scalar>, const Derived>
-j1(const Eigen::ArrayBase<Derived>& x) {
+bessel_j1(const Eigen::ArrayBase<Derived>& x) {
   return Eigen::CwiseUnaryOp<
       Eigen::internal::scalar_bessel_j1_op<typename Derived::Scalar>,
       const Derived>(x.derived());
@@ -270,12 +270,12 @@ j1(const Eigen::ArrayBase<Derived>& x) {
   * other scalar types, the user has to provide implementations of y1(T) for
   * any scalar type T to be supported.
   *
-  * \sa ArrayBase::y1()
+  * \sa ArrayBase::bessel_y1()
   */
 template <typename Derived>
 EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
     Eigen::internal::scalar_bessel_y1_op<typename Derived::Scalar>, const Derived>
-y1(const Eigen::ArrayBase<Derived>& x) {
+bessel_y1(const Eigen::ArrayBase<Derived>& x) {
   return Eigen::CwiseUnaryOp<
       Eigen::internal::scalar_bessel_y1_op<typename Derived::Scalar>,
       const Derived>(x.derived());
diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsFunctors.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsFunctors.h
index e57d5042b..8606a9f8e 100644
--- a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsFunctors.h
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsFunctors.h
@@ -18,18 +18,18 @@ namespace internal {
 /** \internal
  * \brief Template functor to compute the modified Bessel function of the first
  * kind of order zero.
- * \sa class CwiseUnaryOp, Cwise::i0()
+ * \sa class CwiseUnaryOp, Cwise::bessel_i0()
  */
 template <typename Scalar>
 struct scalar_bessel_i0_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_i0_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
-    using numext::i0;
-    return i0(x);
+    using numext::bessel_i0;
+    return bessel_i0(x);
   }
   typedef typename packet_traits<Scalar>::type Packet;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
-    return internal::pi0(x);
+    return internal::pbessel_i0(x);
   }
 };
 template <typename Scalar>
@@ -46,18 +46,18 @@ struct functor_traits<scalar_bessel_i0_op<Scalar> > {
 /** \internal
  * \brief Template functor to compute the exponentially scaled modified Bessel
  * function of the first kind of order zero
- * \sa class CwiseUnaryOp, Cwise::i0e()
+ * \sa class CwiseUnaryOp, Cwise::bessel_i0e()
  */
 template <typename Scalar>
 struct scalar_bessel_i0e_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_i0e_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
-    using numext::i0e;
-    return i0e(x);
+    using numext::bessel_i0e;
+    return bessel_i0e(x);
   }
   typedef typename packet_traits<Scalar>::type Packet;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
-    return internal::pi0e(x);
+    return internal::pbessel_i0e(x);
   }
 };
 template <typename Scalar>
@@ -73,18 +73,18 @@ struct functor_traits<scalar_bessel_i0e_op<Scalar> > {
 /** \internal
  * \brief Template functor to compute the modified Bessel function of the first
  * kind of order one
- * \sa class CwiseUnaryOp, Cwise::i1()
+ * \sa class CwiseUnaryOp, Cwise::bessel_i1()
  */
 template <typename Scalar>
 struct scalar_bessel_i1_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_i1_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
-    using numext::i1;
-    return i1(x);
+    using numext::bessel_i1;
+    return bessel_i1(x);
   }
   typedef typename packet_traits<Scalar>::type Packet;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
-    return internal::pi1(x);
+    return internal::pbessel_i1(x);
   }
 };
 template <typename Scalar>
@@ -101,18 +101,18 @@ struct functor_traits<scalar_bessel_i1_op<Scalar> > {
 /** \internal
  * \brief Template functor to compute the exponentially scaled modified Bessel
  * function of the first kind of order zero
- * \sa class CwiseUnaryOp, Cwise::i1e()
+ * \sa class CwiseUnaryOp, Cwise::bessel_i1e()
  */
 template <typename Scalar>
 struct scalar_bessel_i1e_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_i1e_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
-    using numext::i1e;
-    return i1e(x);
+    using numext::bessel_i1e;
+    return bessel_i1e(x);
   }
   typedef typename packet_traits<Scalar>::type Packet;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
-    return internal::pi1e(x);
+    return internal::pbessel_i1e(x);
   }
 };
 template <typename Scalar>
@@ -128,18 +128,18 @@ struct functor_traits<scalar_bessel_i1e_op<Scalar> > {
 /** \internal
  * \brief Template functor to compute the Bessel function of the second kind of
  * order zero
- * \sa class CwiseUnaryOp, Cwise::j0()
+ * \sa class CwiseUnaryOp, Cwise::bessel_j0()
  */
 template <typename Scalar>
 struct scalar_bessel_j0_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_j0_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
-    using numext::j0;
-    return j0(x);
+    using numext::bessel_j0;
+    return bessel_j0(x);
   }
   typedef typename packet_traits<Scalar>::type Packet;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
-    return internal::pj0(x);
+    return internal::pbessel_j0(x);
   }
 };
 template <typename Scalar>
@@ -156,18 +156,18 @@ struct functor_traits<scalar_bessel_j0_op<Scalar> > {
 /** \internal
  * \brief Template functor to compute the Bessel function of the second kind of
  * order zero
- * \sa class CwiseUnaryOp, Cwise::y0()
+ * \sa class CwiseUnaryOp, Cwise::bessel_y0()
  */
 template <typename Scalar>
 struct scalar_bessel_y0_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_y0_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
-    using numext::y0;
-    return y0(x);
+    using numext::bessel_y0;
+    return bessel_y0(x);
   }
   typedef typename packet_traits<Scalar>::type Packet;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
-    return internal::py0(x);
+    return internal::pbessel_y0(x);
   }
 };
 template <typename Scalar>
@@ -184,18 +184,18 @@ struct functor_traits<scalar_bessel_y0_op<Scalar> > {
 /** \internal
  * \brief Template functor to compute the Bessel function of the first kind of
  * order one
- * \sa class CwiseUnaryOp, Cwise::j1()
+ * \sa class CwiseUnaryOp, Cwise::bessel_j1()
  */
 template <typename Scalar>
 struct scalar_bessel_j1_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_j1_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
-    using numext::j1;
-    return j1(x);
+    using numext::bessel_j1;
+    return bessel_j1(x);
   }
   typedef typename packet_traits<Scalar>::type Packet;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
-    return internal::pj1(x);
+    return internal::pbessel_j1(x);
   }
 };
 template <typename Scalar>
@@ -212,18 +212,18 @@ struct functor_traits<scalar_bessel_j1_op<Scalar> > {
 /** \internal
  * \brief Template functor to compute the Bessel function of the second kind of
  * order one
- * \sa class CwiseUnaryOp, Cwise::j1e()
+ * \sa class CwiseUnaryOp, Cwise::bessel_j1e()
  */
 template <typename Scalar>
 struct scalar_bessel_y1_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_y1_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
-    using numext::y1;
-    return y1(x);
+    using numext::bessel_y1;
+    return bessel_y1(x);
   }
   typedef typename packet_traits<Scalar>::type Packet;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
-    return internal::py1(x);
+    return internal::pbessel_y1(x);
   }
 };
 template <typename Scalar>
@@ -240,18 +240,18 @@ struct functor_traits<scalar_bessel_y1_op<Scalar> > {
 /** \internal
  * \brief Template functor to compute the modified Bessel function of the second
  * kind of order zero
- * \sa class CwiseUnaryOp, Cwise::k0()
+ * \sa class CwiseUnaryOp, Cwise::bessel_k0()
  */
 template <typename Scalar>
 struct scalar_bessel_k0_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_k0_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
-    using numext::k0;
-    return k0(x);
+    using numext::bessel_k0;
+    return bessel_k0(x);
   }
   typedef typename packet_traits<Scalar>::type Packet;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
-    return internal::pk0(x);
+    return internal::pbessel_k0(x);
   }
 };
 template <typename Scalar>
@@ -268,18 +268,18 @@ struct functor_traits<scalar_bessel_k0_op<Scalar> > {
 /** \internal
  * \brief Template functor to compute the exponentially scaled modified Bessel
  * function of the second kind of order zero
- * \sa class CwiseUnaryOp, Cwise::k0e()
+ * \sa class CwiseUnaryOp, Cwise::bessel_k0e()
  */
 template <typename Scalar>
 struct scalar_bessel_k0e_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_k0e_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
-    using numext::k0e;
-    return k0e(x);
+    using numext::bessel_k0e;
+    return bessel_k0e(x);
   }
   typedef typename packet_traits<Scalar>::type Packet;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
-    return internal::pk0e(x);
+    return internal::pbessel_k0e(x);
   }
 };
 template <typename Scalar>
@@ -296,18 +296,18 @@ struct functor_traits<scalar_bessel_k0e_op<Scalar> > {
 /** \internal
  * \brief Template functor to compute the modified Bessel function of the
  * second kind of order one
- * \sa class CwiseUnaryOp, Cwise::k1()
+ * \sa class CwiseUnaryOp, Cwise::bessel_k1()
  */
 template <typename Scalar>
 struct scalar_bessel_k1_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_k1_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
-    using numext::k1;
-    return k1(x);
+    using numext::bessel_k1;
+    return bessel_k1(x);
   }
   typedef typename packet_traits<Scalar>::type Packet;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
-    return internal::pk1(x);
+    return internal::pbessel_k1(x);
   }
 };
 template <typename Scalar>
@@ -324,18 +324,18 @@ struct functor_traits<scalar_bessel_k1_op<Scalar> > {
 /** \internal
  * \brief Template functor to compute the exponentially scaled modified Bessel
  * function of the second kind of order one
- * \sa class CwiseUnaryOp, Cwise::k1e()
+ * \sa class CwiseUnaryOp, Cwise::bessel_k1e()
  */
 template <typename Scalar>
 struct scalar_bessel_k1e_op {
   EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_k1e_op)
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
-    using numext::k1e;
-    return k1e(x);
+    using numext::bessel_k1e;
+    return bessel_k1e(x);
   }
   typedef typename packet_traits<Scalar>::type Packet;
   EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
-    return internal::pk1e(x);
+    return internal::pbessel_k1e(x);
   }
 };
 template <typename Scalar>
diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsHalf.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsHalf.h
index 9aad7ac96..8930d1a3c 100644
--- a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsHalf.h
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsHalf.h
@@ -13,50 +13,50 @@ namespace numext {
 
 #if EIGEN_HAS_C99_MATH
 template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half i0(const Eigen::half& x) {
-  return Eigen::half(Eigen::numext::i0(static_cast<float>(x)));
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_i0(const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::bessel_i0(static_cast<float>(x)));
 }
 template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half i0e(const Eigen::half& x) {
-  return Eigen::half(Eigen::numext::i0e(static_cast<float>(x)));
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_i0e(const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::bessel_i0e(static_cast<float>(x)));
 }
 template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half i1(const Eigen::half& x) {
-  return Eigen::half(Eigen::numext::i1(static_cast<float>(x)));
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_i1(const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::bessel_i1(static_cast<float>(x)));
 }
 template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half i1e(const Eigen::half& x) {
-  return Eigen::half(Eigen::numext::i1e(static_cast<float>(x)));
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_i1e(const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::bessel_i1e(static_cast<float>(x)));
 }
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half j0(const Eigen::half& x) {
-  return Eigen::half(Eigen::numext::j0(static_cast<float>(x)));
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_j0(const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::bessel_j0(static_cast<float>(x)));
 }
 template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half j1(const Eigen::half& x) {
-  return Eigen::half(Eigen::numext::j1(static_cast<float>(x)));
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_j1(const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::bessel_j1(static_cast<float>(x)));
 }
 template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half y0(const Eigen::half& x) {
-  return Eigen::half(Eigen::numext::y0(static_cast<float>(x)));
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_y0(const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::bessel_y0(static_cast<float>(x)));
 }
 template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half y1(const Eigen::half& x) {
-  return Eigen::half(Eigen::numext::y1(static_cast<float>(x)));
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_y1(const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::bessel_y1(static_cast<float>(x)));
 }
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half k0(const Eigen::half& x) {
-  return Eigen::half(Eigen::numext::k0(static_cast<float>(x)));
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_k0(const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::bessel_k0(static_cast<float>(x)));
 }
 template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half k0e(const Eigen::half& x) {
-  return Eigen::half(Eigen::numext::k0e(static_cast<float>(x)));
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_k0e(const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::bessel_k0e(static_cast<float>(x)));
 }
 template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half k1(const Eigen::half& x) {
-  return Eigen::half(Eigen::numext::k1(static_cast<float>(x)));
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_k1(const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::bessel_k1(static_cast<float>(x)));
 }
 template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half k1e(const Eigen::half& x) {
-  return Eigen::half(Eigen::numext::k1e(static_cast<float>(x)));
+EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_k1e(const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::bessel_k1e(static_cast<float>(x)));
 }
 #endif
 
diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsImpl.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsImpl.h
index b279687c2..c7c4f2649 100644
--- a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsImpl.h
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsImpl.h
@@ -42,7 +42,7 @@ namespace internal {
  ****************************************************************************/
 
 template <typename Scalar>
-struct i0e_retval {
+struct bessel_i0e_retval {
   typedef Scalar type;
 };
 
@@ -202,7 +202,7 @@ struct generic_i0e<T, double> {
 };
 
 template <typename Scalar>
-struct i0e_impl {
+struct bessel_i0e_impl {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
     return generic_i0e<Scalar, Scalar>::run(x);
@@ -210,7 +210,7 @@ struct i0e_impl {
 };
 
 template <typename Scalar>
-struct i0_retval {
+struct bessel_i0_retval {
   typedef Scalar type;
 };
 
@@ -225,7 +225,7 @@ struct generic_i0 {
 };
 
 template <typename Scalar>
-struct i0_impl {
+struct bessel_i0_impl {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
     return generic_i0<Scalar, Scalar>::run(x);
@@ -233,7 +233,7 @@ struct i0_impl {
 };
 
 template <typename Scalar>
-struct i1e_retval {
+struct bessel_i1e_retval {
   typedef Scalar type;
 };
 
@@ -397,7 +397,7 @@ struct generic_i1e<T, double> {
 };
 
 template <typename Scalar>
-struct i1e_impl {
+struct bessel_i1e_impl {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
     return generic_i1e<Scalar, Scalar>::run(x);
@@ -405,7 +405,7 @@ struct i1e_impl {
 };
 
 template <typename Scalar>
-struct i1_retval {
+struct bessel_i1_retval {
   typedef Scalar type;
 };
 
@@ -420,7 +420,7 @@ struct generic_i1 {
 };
 
 template <typename Scalar>
-struct i1_impl {
+struct bessel_i1_impl {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
     return generic_i1<Scalar, Scalar>::run(x);
@@ -428,7 +428,7 @@ struct i1_impl {
 };
 
 template <typename Scalar>
-struct k0e_retval {
+struct bessel_k0e_retval {
   typedef Scalar type;
 };
 
@@ -583,7 +583,7 @@ struct generic_k0e<T, double> {
 };
 
 template <typename Scalar>
-struct k0e_impl {
+struct bessel_k0e_impl {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
     return generic_k0e<Scalar, Scalar>::run(x);
@@ -591,7 +591,7 @@ struct k0e_impl {
 };
 
 template <typename Scalar>
-struct k0_retval {
+struct bessel_k0_retval {
   typedef Scalar type;
 };
 
@@ -755,7 +755,7 @@ struct generic_k0<T, double> {
 };
 
 template <typename Scalar>
-struct k0_impl {
+struct bessel_k0_impl {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
     return generic_k0<Scalar, Scalar>::run(x);
@@ -763,7 +763,7 @@ struct k0_impl {
 };
 
 template <typename Scalar>
-struct k1e_retval {
+struct bessel_k1e_retval {
   typedef Scalar type;
 };
 
@@ -911,7 +911,7 @@ struct generic_k1e<T, double> {
 };
 
 template <typename Scalar>
-struct k1e_impl {
+struct bessel_k1e_impl {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
     return generic_k1e<Scalar, Scalar>::run(x);
@@ -919,7 +919,7 @@ struct k1e_impl {
 };
 
 template <typename Scalar>
-struct k1_retval {
+struct bessel_k1_retval {
   typedef Scalar type;
 };
 
@@ -1077,7 +1077,7 @@ struct generic_k1<T, double> {
 };
 
 template <typename Scalar>
-struct k1_impl {
+struct bessel_k1_impl {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
     return generic_k1<Scalar, Scalar>::run(x);
@@ -1085,7 +1085,7 @@ struct k1_impl {
 };
 
 template <typename Scalar>
-struct j0_retval {
+struct bessel_j0_retval {
   typedef Scalar type;
 };
 
@@ -1277,7 +1277,7 @@ struct generic_j0<T, double> {
 };
 
 template <typename Scalar>
-struct j0_impl {
+struct bessel_j0_impl {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
     return generic_j0<Scalar, Scalar>::run(x);
@@ -1285,7 +1285,7 @@ struct j0_impl {
 };
 
 template <typename Scalar>
-struct y0_retval {
+struct bessel_y0_retval {
   typedef Scalar type;
 };
 
@@ -1475,7 +1475,7 @@ struct generic_y0<T, double> {
 };
 
 template <typename Scalar>
-struct y0_impl {
+struct bessel_y0_impl {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
     return generic_y0<Scalar, Scalar>::run(x);
@@ -1483,7 +1483,7 @@ struct y0_impl {
 };
 
 template <typename Scalar>
-struct j1_retval {
+struct bessel_j1_retval {
   typedef Scalar type;
 };
 
@@ -1666,7 +1666,7 @@ struct generic_j1<T, double> {
 };
 
 template <typename Scalar>
-struct j1_impl {
+struct bessel_j1_impl {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
     return generic_j1<Scalar, Scalar>::run(x);
@@ -1674,7 +1674,7 @@ struct j1_impl {
 };
 
 template <typename Scalar>
-struct y1_retval {
+struct bessel_y1_retval {
   typedef Scalar type;
 };
 
@@ -1869,7 +1869,7 @@ struct generic_y1<T, double> {
 };
 
 template <typename Scalar>
-struct y1_impl {
+struct bessel_y1_impl {
   EIGEN_DEVICE_FUNC
   static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
     return generic_y1<Scalar, Scalar>::run(x);
@@ -1881,75 +1881,75 @@ struct y1_impl {
 namespace numext {
 
 template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(i0, Scalar)
-    i0(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(i0, Scalar)::run(x);
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_i0, Scalar)
+    bessel_i0(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(bessel_i0, Scalar)::run(x);
 }
 
 template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(i0e, Scalar)
-    i0e(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(i0e, Scalar)::run(x);
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_i0e, Scalar)
+    bessel_i0e(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(bessel_i0e, Scalar)::run(x);
 }
 
 template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(i1, Scalar)
-    i1(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(i1, Scalar)::run(x);
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_i1, Scalar)
+    bessel_i1(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(bessel_i1, Scalar)::run(x);
 }
 
 template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(i1e, Scalar)
-    i1e(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(i1e, Scalar)::run(x);
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_i1e, Scalar)
+    bessel_i1e(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(bessel_i1e, Scalar)::run(x);
 }
 
 template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(k0, Scalar)
-    k0(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(k0, Scalar)::run(x);
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_k0, Scalar)
+    bessel_k0(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(bessel_k0, Scalar)::run(x);
 }
 
 template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(k0e, Scalar)
-    k0e(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(k0e, Scalar)::run(x);
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_k0e, Scalar)
+    bessel_k0e(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(bessel_k0e, Scalar)::run(x);
 }
 
 template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(k1, Scalar)
-    k1(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(k1, Scalar)::run(x);
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_k1, Scalar)
+    bessel_k1(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(bessel_k1, Scalar)::run(x);
 }
 
 template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(k1e, Scalar)
-    k1e(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(k1e, Scalar)::run(x);
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_k1e, Scalar)
+    bessel_k1e(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(bessel_k1e, Scalar)::run(x);
 }
 
 template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(j0, Scalar)
-    j0(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(j0, Scalar)::run(x);
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_j0, Scalar)
+    bessel_j0(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(bessel_j0, Scalar)::run(x);
 }
 
 template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(y0, Scalar)
-    y0(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(y0, Scalar)::run(x);
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_y0, Scalar)
+    bessel_y0(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(bessel_y0, Scalar)::run(x);
 }
 
 template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(j1, Scalar)
-    j1(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(j1, Scalar)::run(x);
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_j1, Scalar)
+    bessel_j1(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(bessel_j1, Scalar)::run(x);
 }
 
 template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(y1, Scalar)
-    y1(const Scalar& x) {
-  return EIGEN_MATHFUNC_IMPL(y1, Scalar)::run(x);
+EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_y1, Scalar)
+    bessel_y1(const Scalar& x) {
+  return EIGEN_MATHFUNC_IMPL(bessel_y1, Scalar)::run(x);
 }
 
 }  // end namespace numext
diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h
index 70eaad5cd..efc6d9c8f 100644
--- a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h
@@ -18,7 +18,7 @@ namespace internal {
  * order zero i0(\a a) (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pi0(const Packet& x) {
+Packet pbessel_i0(const Packet& x) {
   typedef typename unpacket_traits<Packet>::type ScalarType;
   using internal::generic_i0; return generic_i0<Packet, ScalarType>::run(x);
 }
@@ -27,7 +27,7 @@ Packet pi0(const Packet& x) {
  * order zero i0e(\a a) (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pi0e(const Packet& x) {
+Packet pbessel_i0e(const Packet& x) {
   typedef typename unpacket_traits<Packet>::type ScalarType;
   using internal::generic_i0e; return generic_i0e<Packet, ScalarType>::run(x);
 }
@@ -36,7 +36,7 @@ Packet pi0e(const Packet& x) {
  * order one i1(\a a) (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pi1(const Packet& x) {
+Packet pbessel_i1(const Packet& x) {
   typedef typename unpacket_traits<Packet>::type ScalarType;
   using internal::generic_i1; return generic_i1<Packet, ScalarType>::run(x);
 }
@@ -45,7 +45,7 @@ Packet pi1(const Packet& x) {
  * order one i1e(\a a) (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pi1e(const Packet& x) {
+Packet pbessel_i1e(const Packet& x) {
   typedef typename unpacket_traits<Packet>::type ScalarType;
   using internal::generic_i1e; return generic_i1e<Packet, ScalarType>::run(x);
 }
@@ -54,7 +54,7 @@ Packet pi1e(const Packet& x) {
  * order zero j0(\a a) (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pj0(const Packet& x) {
+Packet pbessel_j0(const Packet& x) {
   typedef typename unpacket_traits<Packet>::type ScalarType;
   using internal::generic_j0; return generic_j0<Packet, ScalarType>::run(x);
 }
@@ -63,7 +63,7 @@ Packet pj0(const Packet& x) {
  * order zero j1(\a a) (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pj1(const Packet& x) {
+Packet pbessel_j1(const Packet& x) {
   typedef typename unpacket_traits<Packet>::type ScalarType;
   using internal::generic_j1; return generic_j1<Packet, ScalarType>::run(x);
 }
@@ -72,7 +72,7 @@ Packet pj1(const Packet& x) {
  * order one y0(\a a) (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet py0(const Packet& x) {
+Packet pbessel_y0(const Packet& x) {
   typedef typename unpacket_traits<Packet>::type ScalarType;
   using internal::generic_y0; return generic_y0<Packet, ScalarType>::run(x);
 }
@@ -81,7 +81,7 @@ Packet py0(const Packet& x) {
  * order one y1(\a a) (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet py1(const Packet& x) {
+Packet pbessel_y1(const Packet& x) {
   typedef typename unpacket_traits<Packet>::type ScalarType;
   using internal::generic_y1; return generic_y1<Packet, ScalarType>::run(x);
 }
@@ -90,7 +90,7 @@ Packet py1(const Packet& x) {
  * order zero k0(\a a) (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pk0(const Packet& x) {
+Packet pbessel_k0(const Packet& x) {
   typedef typename unpacket_traits<Packet>::type ScalarType;
   using internal::generic_k0; return generic_k0<Packet, ScalarType>::run(x);
 }
@@ -99,7 +99,7 @@ Packet pk0(const Packet& x) {
  * order zero k0e(\a a) (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pk0e(const Packet& x) {
+Packet pbessel_k0e(const Packet& x) {
   typedef typename unpacket_traits<Packet>::type ScalarType;
   using internal::generic_k0e; return generic_k0e<Packet, ScalarType>::run(x);
 }
@@ -108,7 +108,7 @@ Packet pk0e(const Packet& x) {
  * order one k1e(\a a) (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pk1(const Packet& x) {
+Packet pbessel_k1(const Packet& x) {
   typedef typename unpacket_traits<Packet>::type ScalarType;
   using internal::generic_k1; return generic_k1<Packet, ScalarType>::run(x);
 }
@@ -117,7 +117,7 @@ Packet pk1(const Packet& x) {
  * order one k1e(\a a) (coeff-wise) */
 template <typename Packet>
 EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pk1e(const Packet& x) {
+Packet pbessel_k1e(const Packet& x) {
   typedef typename unpacket_traits<Packet>::type ScalarType;
   using internal::generic_k1e; return generic_k1e<Packet, ScalarType>::run(x);
 }
diff --git a/unsupported/Eigen/src/SpecialFunctions/arch/GPU/GpuSpecialFunctions.h b/unsupported/Eigen/src/SpecialFunctions/arch/GPU/GpuSpecialFunctions.h
index b886e278c..dd3bf4dd1 100644
--- a/unsupported/Eigen/src/SpecialFunctions/arch/GPU/GpuSpecialFunctions.h
+++ b/unsupported/Eigen/src/SpecialFunctions/arch/GPU/GpuSpecialFunctions.h
@@ -205,159 +205,159 @@ double2 pbetainc<double2>(const double2& a, const double2& b, const double2& x)
 }
 
 template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pi0e<float4>(const float4& x) {
-  using numext::i0e;
-  return make_float4(i0e(x.x), i0e(x.y), i0e(x.z), i0e(x.w));
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_i0e<float4>(const float4& x) {
+  using numext::bessel_i0e;
+  return make_float4(bessel_i0e(x.x), bessel_i0e(x.y), bessel_i0e(x.z), bessel_i0e(x.w));
 }
 
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pi0e<double2>(const double2& x) {
-  using numext::i0e;
-  return make_double2(i0e(x.x), i0e(x.y));
+pbessel_i0e<double2>(const double2& x) {
+  using numext::bessel_i0e;
+  return make_double2(bessel_i0e(x.x), bessel_i0e(x.y));
 }
 
 template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pi0<float4>(const float4& x) {
-  using numext::i0;
-  return make_float4(i0(x.x), i0(x.y), i0(x.z), i0(x.w));
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_i0<float4>(const float4& x) {
+  using numext::bessel_i0;
+  return make_float4(bessel_i0(x.x), bessel_i0(x.y), bessel_i0(x.z), bessel_i0(x.w));
 }
 
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pi0<double2>(const double2& x) {
-  using numext::i0;
-  return make_double2(i0(x.x), i0(x.y));
+pbessel_i0<double2>(const double2& x) {
+  using numext::bessel_i0;
+  return make_double2(bessel_i0(x.x), bessel_i0(x.y));
 }
 
 template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pi1e<float4>(const float4& x) {
-  using numext::i1e;
-  return make_float4(i1e(x.x), i1e(x.y), i1e(x.z), i1e(x.w));
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_i1e<float4>(const float4& x) {
+  using numext::bessel_i1e;
+  return make_float4(bessel_i1e(x.x), bessel_i1e(x.y), bessel_i1e(x.z), bessel_i1e(x.w));
 }
 
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pi1e<double2>(const double2& x) {
-  using numext::i1e;
-  return make_double2(i1e(x.x), i1e(x.y));
+pbessel_i1e<double2>(const double2& x) {
+  using numext::bessel_i1e;
+  return make_double2(bessel_i1e(x.x), bessel_i1e(x.y));
 }
 
 template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pi1<float4>(const float4& x) {
-  using numext::i1;
-  return make_float4(i1(x.x), i1(x.y), i1(x.z), i1(x.w));
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_i1<float4>(const float4& x) {
+  using numext::bessel_i1;
+  return make_float4(bessel_i1(x.x), bessel_i1(x.y), bessel_i1(x.z), bessel_i1(x.w));
 }
 
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pi1<double2>(const double2& x) {
-  using numext::i1;
-  return make_double2(i1(x.x), i1(x.y));
+pbessel_i1<double2>(const double2& x) {
+  using numext::bessel_i1;
+  return make_double2(bessel_i1(x.x), bessel_i1(x.y));
 }
 
 template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pk0e<float4>(const float4& x) {
-  using numext::k0e;
-  return make_float4(k0e(x.x), k0e(x.y), k0e(x.z), k0e(x.w));
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_k0e<float4>(const float4& x) {
+  using numext::bessel_k0e;
+  return make_float4(bessel_k0e(x.x), bessel_k0e(x.y), bessel_k0e(x.z), bessel_k0e(x.w));
 }
 
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pk0e<double2>(const double2& x) {
-  using numext::k0e;
-  return make_double2(k0e(x.x), k0e(x.y));
+pbessel_k0e<double2>(const double2& x) {
+  using numext::bessel_k0e;
+  return make_double2(bessel_k0e(x.x), bessel_k0e(x.y));
 }
 
 template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pk0<float4>(const float4& x) {
-  using numext::k0;
-  return make_float4(k0(x.x), k0(x.y), k0(x.z), k0(x.w));
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_k0<float4>(const float4& x) {
+  using numext::bessel_k0;
+  return make_float4(bessel_k0(x.x), bessel_k0(x.y), bessel_k0(x.z), bessel_k0(x.w));
 }
 
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pk0<double2>(const double2& x) {
-  using numext::k0;
-  return make_double2(k0(x.x), k0(x.y));
+pbessel_k0<double2>(const double2& x) {
+  using numext::bessel_k0;
+  return make_double2(bessel_k0(x.x), bessel_k0(x.y));
 }
 
 template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pk1e<float4>(const float4& x) {
-  using numext::k1e;
-  return make_float4(k1e(x.x), k1e(x.y), k1e(x.z), k1e(x.w));
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_k1e<float4>(const float4& x) {
+  using numext::bessel_k1e;
+  return make_float4(bessel_k1e(x.x), bessel_k1e(x.y), bessel_k1e(x.z), bessel_k1e(x.w));
 }
 
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pk1e<double2>(const double2& x) {
-  using numext::k1e;
-  return make_double2(k1e(x.x), k1e(x.y));
+pbessel_k1e<double2>(const double2& x) {
+  using numext::bessel_k1e;
+  return make_double2(bessel_k1e(x.x), bessel_k1e(x.y));
 }
 
 template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pk1<float4>(const float4& x) {
-  using numext::k1;
-  return make_float4(k1(x.x), k1(x.y), k1(x.z), k1(x.w));
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_k1<float4>(const float4& x) {
+  using numext::bessel_k1;
+  return make_float4(bessel_k1(x.x), bessel_k1(x.y), bessel_k1(x.z), bessel_k1(x.w));
 }
 
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pk1<double2>(const double2& x) {
-  using numext::k1;
-  return make_double2(k1(x.x), k1(x.y));
+pbessel_k1<double2>(const double2& x) {
+  using numext::bessel_k1;
+  return make_double2(bessel_k1(x.x), bessel_k1(x.y));
 }
 
 template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pj0<float4>(const float4& x) {
-  using numext::j0;
-  return make_float4(j0(x.x), j0(x.y), j0(x.z), j0(x.w));
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_j0<float4>(const float4& x) {
+  using numext::bessel_j0;
+  return make_float4(bessel_j0(x.x), bessel_j0(x.y), bessel_j0(x.z), bessel_j0(x.w));
 }
 
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pj0<double2>(const double2& x) {
-  using numext::j0;
-  return make_double2(j0(x.x), j0(x.y));
+pbessel_j0<double2>(const double2& x) {
+  using numext::bessel_j0;
+  return make_double2(bessel_j0(x.x), bessel_j0(x.y));
 }
 
 template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pj1<float4>(const float4& x) {
-  using numext::j1;
-  return make_float4(j1(x.x), j1(x.y), j1(x.z), j1(x.w));
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_j1<float4>(const float4& x) {
+  using numext::bessel_j1;
+  return make_float4(bessel_j1(x.x), bessel_j1(x.y), bessel_j1(x.z), bessel_j1(x.w));
 }
 
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pj1<double2>(const double2& x) {
-  using numext::j1;
-  return make_double2(j1(x.x), j1(x.y));
+pbessel_j1<double2>(const double2& x) {
+  using numext::bessel_j1;
+  return make_double2(bessel_j1(x.x), bessel_j1(x.y));
 }
 
 template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 py0<float4>(const float4& x) {
-  using numext::y0;
-  return make_float4(y0(x.x), y0(x.y), y0(x.z), y0(x.w));
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_y0<float4>(const float4& x) {
+  using numext::bessel_y0;
+  return make_float4(bessel_y0(x.x), bessel_y0(x.y), bessel_y0(x.z), bessel_y0(x.w));
 }
 
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-py0<double2>(const double2& x) {
-  using numext::y0;
-  return make_double2(y0(x.x), y0(x.y));
+pbessel_y0<double2>(const double2& x) {
+  using numext::bessel_y0;
+  return make_double2(bessel_y0(x.x), bessel_y0(x.y));
 }
 
 template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 py1<float4>(const float4& x) {
-  using numext::y1;
-  return make_float4(y1(x.x), y1(x.y), y1(x.z), y1(x.w));
+EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_y1<float4>(const float4& x) {
+  using numext::bessel_y1;
+  return make_float4(bessel_y1(x.x), bessel_y1(x.y), bessel_y1(x.z), bessel_y1(x.w));
 }
 
 template <>
 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-py1<double2>(const double2& x) {
-  using numext::y1;
-  return make_double2(y1(x.x), y1(x.y));
+pbessel_y1<double2>(const double2& x) {
+  using numext::bessel_y1;
+  return make_double2(bessel_y1(x.x), bessel_y1(x.y));
 }
 
 #endif
diff --git a/unsupported/test/bessel_functions.cpp b/unsupported/test/bessel_functions.cpp
index 2b6bb6b2c..06765bfab 100644
--- a/unsupported/test/bessel_functions.cpp
+++ b/unsupported/test/bessel_functions.cpp
@@ -43,7 +43,7 @@ template<typename ArrayType> void array_bessel_functions()
        1.89489253e+04, 1.29418563e+05, 8.93446228e+05, 6.21841242e+06,
        4.35582826e+07;
 
-    CALL_SUBTEST(res = i0(x);
+    CALL_SUBTEST(res = bessel_i0(x);
                  verify_component_wise(res, expected););
   }
 
@@ -63,7 +63,7 @@ template<typename ArrayType> void array_bessel_functions()
         0.116426221213, 0.107615251671, 0.100544127361, 0.0947062952128,
         0.0897803118848;
 
-    CALL_SUBTEST(res = i0e(x);
+    CALL_SUBTEST(res = bessel_i0e(x);
                  verify_component_wise(res, expected););
   }
 
@@ -83,7 +83,7 @@ template<typename ArrayType> void array_bessel_functions()
         1.81413488e+04,  1.24707259e+05,  8.65059436e+05,  6.04313324e+06,
         4.24549734e+07;
 
-    CALL_SUBTEST(res = i1(x);
+    CALL_SUBTEST(res = bessel_i1(x);
                  verify_component_wise(res, expected););
   }
 
@@ -103,7 +103,7 @@ template<typename ArrayType> void array_bessel_functions()
         0.11146429929, 0.103697667463, 0.0973496147565, 0.092036796872,
         0.0875062221833;
 
-    CALL_SUBTEST(res = i1e(x);
+    CALL_SUBTEST(res = bessel_i1e(x);
                  verify_component_wise(res, expected););
   }
 
@@ -139,7 +139,7 @@ template<typename ArrayType> void array_bessel_functions()
              -0.08636798,  0.05120815,  0.13807901,  0.09727067, -0.03042119,
              -0.12684568, -0.10556738,  0.01086237,  0.11433274;
 
-    CALL_SUBTEST(res = j0(x);
+    CALL_SUBTEST(res = bessel_j0(x);
                  verify_component_wise(res, expected););
   }
 
@@ -176,7 +176,7 @@ template<typename ArrayType> void array_bessel_functions()
               0.04399094, -0.08232981, -0.13058004, -0.05916189,  0.0640561 ,
               0.12603832;
 
-    CALL_SUBTEST(res = j1(x);
+    CALL_SUBTEST(res = bessel_j1(x);
                  verify_component_wise(res, expected););
   }
   // Test Bessel function k0e. Reference results obtained with SciPy.
@@ -200,7 +200,7 @@ template<typename ArrayType> void array_bessel_functions()
              0.21736123, 0.21416406, 0.21110397, 0.20817141, 0.20535778,
              0.20265524, 0.20005668, 0.19755558;
 
-    CALL_SUBTEST(res = k0e(x);
+    CALL_SUBTEST(res = bessel_k0e(x);
                  verify_component_wise(res, expected););
   }
 
@@ -227,7 +227,7 @@ template<typename ArrayType> void array_bessel_functions()
              1.33103515e-16, 4.82858338e-17, 1.75232770e-17, 6.36161716e-18,
              2.31029936e-18, 8.39286110e-19;
 
-    CALL_SUBTEST(res = k0(x);
+    CALL_SUBTEST(res = bessel_k0(x);
                  verify_component_wise(res, expected););
   }
 
@@ -254,7 +254,7 @@ template<typename ArrayType> void array_bessel_functions()
              0.21110397, 0.20817141, 0.20535778, 0.20265524,
              0.20005668, 0.19755558;
 
-    CALL_SUBTEST(res = k0e(x);
+    CALL_SUBTEST(res = bessel_k0e(x);
                  verify_component_wise(res, expected););
   }
 
@@ -281,7 +281,7 @@ template<typename ArrayType> void array_bessel_functions()
              1.34991783e-16, 4.89519373e-17, 1.77585196e-17, 6.44478588e-18,
              2.33973340e-18, 8.49713195e-19;
 
-    CALL_SUBTEST(res = k1(x);
+    CALL_SUBTEST(res = bessel_k1(x);
                  verify_component_wise(res, expected););
   }
 
@@ -308,7 +308,7 @@ template<typename ArrayType> void array_bessel_functions()
              0.21409878, 0.21104314, 0.20811462, 0.20530466,
              0.20260547, 0.20000997;
 
-    CALL_SUBTEST(res = k1e(x);
+    CALL_SUBTEST(res = bessel_k1e(x);
                  verify_component_wise(res, expected););
   }
 
@@ -333,7 +333,7 @@ template<typename ArrayType> void array_bessel_functions()
              0.13340405,  0.04579799, -0.08085609, -0.13071488, -0.06066076,
              0.06262353,  0.12593642;
 
-    CALL_SUBTEST(res = y0(x);
+    CALL_SUBTEST(res = bessel_y0(x);
                  verify_component_wise(res, expected););
   }
 
@@ -358,7 +358,7 @@ template<typename ArrayType> void array_bessel_functions()
              -0.09578012,  0.03238588,  0.12751273, 0.10445477, -0.01262946,
              -0.11514066, -0.11056411, -0.00579351;
 
-    CALL_SUBTEST(res = y1(x);
+    CALL_SUBTEST(res = bessel_y1(x);
                  verify_component_wise(res, expected););
   }
 }
diff --git a/unsupported/test/cxx11_tensor_gpu.cu b/unsupported/test/cxx11_tensor_gpu.cu
index aa8470123..137d0d596 100644
--- a/unsupported/test/cxx11_tensor_gpu.cu
+++ b/unsupported/test/cxx11_tensor_gpu.cu
@@ -1317,7 +1317,7 @@ void test_gpu_i0e()
   Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in(d_in, 21);
   Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 21);
 
-  gpu_out.device(gpu_device) = gpu_in.i0e();
+  gpu_out.device(gpu_device) = gpu_in.bessel_i0e();
 
   assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost,
                          gpu_device.stream()) == gpuSuccess);
@@ -1372,7 +1372,7 @@ void test_gpu_i1e()
   Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_in(d_in, 21);
   Eigen::TensorMap<Eigen::Tensor<Scalar, 1> > gpu_out(d_out, 21);
 
-  gpu_out.device(gpu_device) = gpu_in.i1e();
+  gpu_out.device(gpu_device) = gpu_in.bessel_i1e();
 
   assert(gpuMemcpyAsync(out.data(), d_out, bytes, gpuMemcpyDeviceToHost,
                          gpu_device.stream()) == gpuSuccess);