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diff --git a/internal/ceres/autodiff_local_parameterization_test.cc b/internal/ceres/autodiff_local_parameterization_test.cc
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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2013 Google Inc. All rights reserved.
+// http://code.google.com/p/ceres-solver/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+//   this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+//   used to endorse or promote products derived from this software without
+//   specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+
+#include <cmath>
+#include "ceres/autodiff_local_parameterization.h"
+#include "ceres/fpclassify.h"
+#include "ceres/local_parameterization.h"
+#include "ceres/rotation.h"
+#include "gtest/gtest.h"
+
+namespace ceres {
+namespace internal {
+
+struct IdentityPlus {
+  template <typename T>
+  bool operator()(const T* x, const T* delta, T* x_plus_delta) const {
+    for (int i = 0; i < 3; ++i) {
+      x_plus_delta[i] = x[i] + delta[i];
+    }
+    return true;
+  }
+};
+
+
+TEST(AutoDiffLocalParameterizationTest, IdentityParameterization) {
+  AutoDiffLocalParameterization<IdentityPlus, 3, 3>
+      parameterization;
+
+  double x[3] = {1.0, 2.0, 3.0};
+  double delta[3] = {0.0, 1.0, 2.0};
+  double x_plus_delta[3] = {0.0, 0.0, 0.0};
+  parameterization.Plus(x, delta, x_plus_delta);
+
+  EXPECT_EQ(x_plus_delta[0], 1.0);
+  EXPECT_EQ(x_plus_delta[1], 3.0);
+  EXPECT_EQ(x_plus_delta[2], 5.0);
+
+  double jacobian[9];
+  parameterization.ComputeJacobian(x, jacobian);
+  int k = 0;
+  for (int i = 0; i < 3; ++i) {
+    for (int j = 0; j < 3; ++j, ++k) {
+      EXPECT_EQ(jacobian[k], (i == j) ? 1.0 : 0.0);
+    }
+  }
+}
+
+struct QuaternionPlus {
+  template<typename T>
+  bool operator()(const T* x, const T* delta, T* x_plus_delta) const {
+    const T squared_norm_delta =
+        delta[0] * delta[0] + delta[1] * delta[1] + delta[2] * delta[2];
+
+    T q_delta[4];
+    if (squared_norm_delta > T(0.0)) {
+      T norm_delta = sqrt(squared_norm_delta);
+      const T sin_delta_by_delta = sin(norm_delta) / norm_delta;
+      q_delta[0] = cos(norm_delta);
+      q_delta[1] = sin_delta_by_delta * delta[0];
+      q_delta[2] = sin_delta_by_delta * delta[1];
+      q_delta[3] = sin_delta_by_delta * delta[2];
+    } else {
+      // We do not just use q_delta = [1,0,0,0] here because that is a
+      // constant and when used for automatic differentiation will
+      // lead to a zero derivative. Instead we take a first order
+      // approximation and evaluate it at zero.
+      q_delta[0] = T(1.0);
+      q_delta[1] = delta[0];
+      q_delta[2] = delta[1];
+      q_delta[3] = delta[2];
+    }
+
+    QuaternionProduct(q_delta, x, x_plus_delta);
+    return true;
+  }
+};
+
+void QuaternionParameterizationTestHelper(const double* x,
+                                          const double* delta) {
+  const double kTolerance = 1e-14;
+  double x_plus_delta_ref[4] = {0.0, 0.0, 0.0, 0.0};
+  double jacobian_ref[12];
+
+
+  QuaternionParameterization ref_parameterization;
+  ref_parameterization.Plus(x, delta, x_plus_delta_ref);
+  ref_parameterization.ComputeJacobian(x, jacobian_ref);
+
+  double x_plus_delta[4] = {0.0, 0.0, 0.0, 0.0};
+  double jacobian[12];
+  AutoDiffLocalParameterization<QuaternionPlus, 4, 3> parameterization;
+  parameterization.Plus(x, delta, x_plus_delta);
+  parameterization.ComputeJacobian(x, jacobian);
+
+  for (int i = 0; i < 4; ++i) {
+    EXPECT_NEAR(x_plus_delta[i], x_plus_delta_ref[i], kTolerance);
+  }
+
+  const double x_plus_delta_norm =
+      sqrt(x_plus_delta[0] * x_plus_delta[0] +
+           x_plus_delta[1] * x_plus_delta[1] +
+           x_plus_delta[2] * x_plus_delta[2] +
+           x_plus_delta[3] * x_plus_delta[3]);
+
+  EXPECT_NEAR(x_plus_delta_norm, 1.0, kTolerance);
+
+  for (int i = 0; i < 12; ++i) {
+    EXPECT_TRUE(IsFinite(jacobian[i]));
+    EXPECT_NEAR(jacobian[i], jacobian_ref[i], kTolerance)
+        << "Jacobian mismatch: i = " << i
+        << "\n Expected \n" << ConstMatrixRef(jacobian_ref, 4, 3)
+        << "\n Actual \n" << ConstMatrixRef(jacobian, 4, 3);
+  }
+}
+
+TEST(AutoDiffLocalParameterization, QuaternionParameterizationZeroTest) {
+  double x[4] = {0.5, 0.5, 0.5, 0.5};
+  double delta[3] = {0.0, 0.0, 0.0};
+  QuaternionParameterizationTestHelper(x, delta);
+}
+
+
+TEST(AutoDiffLocalParameterization, QuaternionParameterizationNearZeroTest) {
+  double x[4] = {0.52, 0.25, 0.15, 0.45};
+  double norm_x = sqrt(x[0] * x[0] +
+                       x[1] * x[1] +
+                       x[2] * x[2] +
+                       x[3] * x[3]);
+  for (int i = 0; i < 4; ++i) {
+    x[i] = x[i] / norm_x;
+  }
+
+  double delta[3] = {0.24, 0.15, 0.10};
+  for (int i = 0; i < 3; ++i) {
+    delta[i] = delta[i] * 1e-14;
+  }
+
+  QuaternionParameterizationTestHelper(x, delta);
+}
+
+TEST(AutoDiffLocalParameterization, QuaternionParameterizationNonZeroTest) {
+  double x[4] = {0.52, 0.25, 0.15, 0.45};
+  double norm_x = sqrt(x[0] * x[0] +
+                       x[1] * x[1] +
+                       x[2] * x[2] +
+                       x[3] * x[3]);
+
+  for (int i = 0; i < 4; ++i) {
+    x[i] = x[i] / norm_x;
+  }
+
+  double delta[3] = {0.24, 0.15, 0.10};
+  QuaternionParameterizationTestHelper(x, delta);
+}
+
+}  // namespace internal
+}  // namespace ceres