Add Bessel functions to SpecialFunctions.

- Split SpecialFunctions files in to a separate BesselFunctions file.

In particular add:
    - Modified bessel functions of the second kind k0, k1, k0e, k1e
    - Bessel functions of the first kind j0, j1
    - Bessel functions of the second kind y0, y1

1 files changed, 130 insertions, 0 deletions

diff --git a/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h
new file mode 100644
index 000000000..70eaad5cd
--- /dev/null
+++ b/unsupported/Eigen/src/SpecialFunctions/BesselFunctionsPacketMath.h
@@ -0,0 +1,130 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_BESSELFUNCTIONS_PACKETMATH_H
+#define EIGEN_BESSELFUNCTIONS_PACKETMATH_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order zero i0(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pi0(const Packet& x) {
+  typedef typename unpacket_traits<Packet>::type ScalarType;
+  using internal::generic_i0; return generic_i0<Packet, ScalarType>::run(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order zero i0e(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pi0e(const Packet& x) {
+  typedef typename unpacket_traits<Packet>::type ScalarType;
+  using internal::generic_i0e; return generic_i0e<Packet, ScalarType>::run(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order one i1(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pi1(const Packet& x) {
+  typedef typename unpacket_traits<Packet>::type ScalarType;
+  using internal::generic_i1; return generic_i1<Packet, ScalarType>::run(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order one i1e(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pi1e(const Packet& x) {
+  typedef typename unpacket_traits<Packet>::type ScalarType;
+  using internal::generic_i1e; return generic_i1e<Packet, ScalarType>::run(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order zero j0(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pj0(const Packet& x) {
+  typedef typename unpacket_traits<Packet>::type ScalarType;
+  using internal::generic_j0; return generic_j0<Packet, ScalarType>::run(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order zero j1(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pj1(const Packet& x) {
+  typedef typename unpacket_traits<Packet>::type ScalarType;
+  using internal::generic_j1; return generic_j1<Packet, ScalarType>::run(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order one y0(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet py0(const Packet& x) {
+  typedef typename unpacket_traits<Packet>::type ScalarType;
+  using internal::generic_y0; return generic_y0<Packet, ScalarType>::run(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order one y1(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet py1(const Packet& x) {
+  typedef typename unpacket_traits<Packet>::type ScalarType;
+  using internal::generic_y1; return generic_y1<Packet, ScalarType>::run(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order zero k0(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pk0(const Packet& x) {
+  typedef typename unpacket_traits<Packet>::type ScalarType;
+  using internal::generic_k0; return generic_k0<Packet, ScalarType>::run(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order zero k0e(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pk0e(const Packet& x) {
+  typedef typename unpacket_traits<Packet>::type ScalarType;
+  using internal::generic_k0e; return generic_k0e<Packet, ScalarType>::run(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order one k1e(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pk1(const Packet& x) {
+  typedef typename unpacket_traits<Packet>::type ScalarType;
+  using internal::generic_k1; return generic_k1<Packet, ScalarType>::run(x);
+}
+
+/** \internal \returns the exponentially scaled modified Bessel function of
+ * order one k1e(\a a) (coeff-wise) */
+template <typename Packet>
+EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pk1e(const Packet& x) {
+  typedef typename unpacket_traits<Packet>::type ScalarType;
+  using internal::generic_k1e; return generic_k1e<Packet, ScalarType>::run(x);
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_BESSELFUNCTIONS_PACKETMATH_H
+