From 87ca15c4e8810777fd884d7f661f2c178fccd441 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Wed, 13 Apr 2016 14:12:38 -0700
Subject: [PATCH 1/2] Added support for sin, cos, tan, and tanh on fp16

---
 Eigen/src/Core/arch/CUDA/Half.h | 19 ++++++++++++++++++-
 1 file changed, 18 insertions(+), 1 deletion(-)

diff --git a/Eigen/src/Core/arch/CUDA/Half.h b/Eigen/src/Core/arch/CUDA/Half.h
index dd4cb10d9..4fbf8f412 100644
--- a/Eigen/src/Core/arch/CUDA/Half.h
+++ b/Eigen/src/Core/arch/CUDA/Half.h
@@ -424,13 +424,30 @@ template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half sqrt(const Eigen::h
 template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half pow(const Eigen::half& a, const Eigen::half& b) {
   return Eigen::half(::powf(float(a), float(b)));
 }
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half sin(const Eigen::half& a) {
+  return Eigen::half(::sinf(float(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half cos(const Eigen::half& a) {
+  return Eigen::half(::cosf(float(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half tan(const Eigen::half& a) {
+  return Eigen::half(::tanf(float(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half tanh(const Eigen::half& a) {
+  return Eigen::half(::tanhf(float(a)));
+}
 template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half floor(const Eigen::half& a) {
   return Eigen::half(::floorf(float(a)));
 }
 template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half ceil(const Eigen::half& a) {
   return Eigen::half(::ceilf(float(a)));
 }
-
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erf(const Eigen::half& a) {
+  return Eigen::half(erff(float(a)));
+}
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erfc(const Eigen::half& a) {
+  return Eigen::half(erfcf(float(a)));
+}
 } // end namespace numext
 
 } // end namespace Eigen

From 29862532599ca4d0e02ab759813604fa1f2e2067 Mon Sep 17 00:00:00 2001
From: Benoit Steiner <benoit.steiner.goog@gmail.com>
Date: Wed, 13 Apr 2016 14:24:06 -0700
Subject: [PATCH 2/2] Cleaned up the implementation of digamma

---
 Eigen/src/Core/SpecialFunctions.h | 20 +++++++++-----------
 1 file changed, 9 insertions(+), 11 deletions(-)

diff --git a/Eigen/src/Core/SpecialFunctions.h b/Eigen/src/Core/SpecialFunctions.h
index adb055b15..a3857ae1f 100644
--- a/Eigen/src/Core/SpecialFunctions.h
+++ b/Eigen/src/Core/SpecialFunctions.h
@@ -281,20 +281,18 @@ struct digamma_impl {
      */
 
     Scalar p, q, nz, s, w, y;
-    bool negative;
+    bool negative = false;
 
     const Scalar maxnum = NumTraits<Scalar>::infinity();
-    const Scalar m_pi = EIGEN_PI;
+    const Scalar m_pi(EIGEN_PI);
 
-    negative = 0;
-    nz = 0.0;
-
-    const Scalar zero = 0.0;
-    const Scalar one = 1.0;
-    const Scalar half = 0.5;
+    const Scalar zero = Scalar(0);
+    const Scalar one = Scalar(1);
+    const Scalar half = Scalar(0.5);
+    nz = zero;
 
     if (x <= zero) {
-      negative = one;
+      negative = true;
       q = x;
       p = numext::floor(q);
       if (p == q) {
@@ -463,7 +461,7 @@ template <typename Scalar>
 struct igammac_impl {
   EIGEN_DEVICE_FUNC
   static Scalar run(Scalar a, Scalar x) {
-    /*							igamc()
+    /*  igamc()
      *
      *	Incomplete gamma integral (modified for Eigen)
      *
@@ -618,7 +616,7 @@ template <typename Scalar>
 struct igamma_impl {
   EIGEN_DEVICE_FUNC
   static Scalar run(Scalar a, Scalar x) {
-    /*							igam()
+    /*	igam()
      *	Incomplete gamma integral
      *
      *