From 7e6a1c129c201db4eff46f4dd68acdc7e935eaf2 Mon Sep 17 00:00:00 2001
From: Nathan Luehr <nluehr@nvidia.com>
Date: Mon, 19 Apr 2021 18:05:27 -0500
Subject: Device implementation of log for std::complex types.

---
 Eigen/src/Core/MathFunctions.h     | 30 +++++++++++++++++++++++++++---
 Eigen/src/Core/MathFunctionsImpl.h |  9 +++++++++
 2 files changed, 36 insertions(+), 3 deletions(-)

diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index 7f82090a9..d7ac4d64d 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -2,6 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (c) 2021, NVIDIA CORPORATION. All rights reserved.
 //
 // 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
@@ -687,6 +688,30 @@ struct expm1_retval
   typedef Scalar type;
 };
 
+/****************************************************************************
+* Implementation of log                                                     *
+****************************************************************************/
+
+// Complex log defined in MathFunctionsImpl.h.
+template<typename T> EIGEN_DEVICE_FUNC std::complex<T> complex_log(const std::complex<T>& z);
+
+template<typename Scalar>
+struct log_impl {
+  EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x)
+  {
+    EIGEN_USING_STD(log);
+    return static_cast<Scalar>(log(x));
+  }
+};
+
+template<typename Scalar>
+struct log_impl<std::complex<Scalar> > {
+  EIGEN_DEVICE_FUNC static inline std::complex<Scalar> run(const std::complex<Scalar>& z)
+  {
+    return complex_log(z);
+  }
+};
+
 /****************************************************************************
 * Implementation of log1p                                                   *
 ****************************************************************************/
@@ -700,7 +725,7 @@ namespace std_fallback {
     typedef typename NumTraits<Scalar>::Real RealScalar;
     EIGEN_USING_STD(log);
     Scalar x1p = RealScalar(1) + x;
-    Scalar log_1p = log(x1p);
+    Scalar log_1p = log_impl<Scalar>::run(x1p);
     const bool is_small = numext::equal_strict(x1p, Scalar(1));
     const bool is_inf = numext::equal_strict(x1p, log_1p);
     return (is_small || is_inf) ? x : x * (log_1p / (x1p - RealScalar(1)));
@@ -1460,8 +1485,7 @@ T rsqrt(const T& x)
 template<typename T>
 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
 T log(const T &x) {
-  EIGEN_USING_STD(log);
-  return static_cast<T>(log(x));
+  return internal::log_impl<T>::run(x);
 }
 
 #if defined(SYCL_DEVICE_ONLY)
diff --git a/Eigen/src/Core/MathFunctionsImpl.h b/Eigen/src/Core/MathFunctionsImpl.h
index 0d3f317bb..4eaaaa784 100644
--- a/Eigen/src/Core/MathFunctionsImpl.h
+++ b/Eigen/src/Core/MathFunctionsImpl.h
@@ -184,6 +184,15 @@ EIGEN_DEVICE_FUNC std::complex<T> complex_rsqrt(const std::complex<T>& z) {
       : std::complex<T>(numext::abs(y) / (2 * w * abs_z), y < zero ? woz : -woz );
 }
 
+template<typename T>
+EIGEN_DEVICE_FUNC std::complex<T> complex_log(const std::complex<T>& z) {
+  // Computes complex log.
+  T a = numext::abs(z);
+  EIGEN_USING_STD(atan2);
+  T b = atan2(z.imag(), z.real());
+  return std::complex<T>(numext::log(a), b);
+}
+
 } // end namespace internal
 
 } // end namespace Eigen
-- 
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