diff --git a/internal/ceres/polynomial_test.cc b/internal/ceres/polynomial_test.cc
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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2012 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: moll.markus@arcor.de (Markus Moll)
+//         sameeragarwal@google.com (Sameer Agarwal)
+
+#include "ceres/polynomial.h"
+
+#include <limits>
+#include <cmath>
+#include <cstddef>
+#include <algorithm>
+#include "gtest/gtest.h"
+#include "ceres/test_util.h"
+
+namespace ceres {
+namespace internal {
+namespace {
+
+// For IEEE-754 doubles, machine precision is about 2e-16.
+const double kEpsilon = 1e-13;
+const double kEpsilonLoose = 1e-9;
+
+// Return the constant polynomial p(x) = 1.23.
+Vector ConstantPolynomial(double value) {
+  Vector poly(1);
+  poly(0) = value;
+  return poly;
+}
+
+// Return the polynomial p(x) = poly(x) * (x - root).
+Vector AddRealRoot(const Vector& poly, double root) {
+  Vector poly2(poly.size() + 1);
+  poly2.setZero();
+  poly2.head(poly.size()) += poly;
+  poly2.tail(poly.size()) -= root * poly;
+  return poly2;
+}
+
+// Return the polynomial
+// p(x) = poly(x) * (x - real - imag*i) * (x - real + imag*i).
+Vector AddComplexRootPair(const Vector& poly, double real, double imag) {
+  Vector poly2(poly.size() + 2);
+  poly2.setZero();
+  // Multiply poly by x^2 - 2real + abs(real,imag)^2
+  poly2.head(poly.size()) += poly;
+  poly2.segment(1, poly.size()) -= 2 * real * poly;
+  poly2.tail(poly.size()) += (real*real + imag*imag) * poly;
+  return poly2;
+}
+
+// Sort the entries in a vector.
+// Needed because the roots are not returned in sorted order.
+Vector SortVector(const Vector& in) {
+  Vector out(in);
+  std::sort(out.data(), out.data() + out.size());
+  return out;
+}
+
+// Run a test with the polynomial defined by the N real roots in roots_real.
+// If use_real is false, NULL is passed as the real argument to
+// FindPolynomialRoots. If use_imaginary is false, NULL is passed as the
+// imaginary argument to FindPolynomialRoots.
+template<int N>
+void RunPolynomialTestRealRoots(const double (&real_roots)[N],
+                                bool use_real,
+                                bool use_imaginary,
+                                double epsilon) {
+  Vector real;
+  Vector imaginary;
+  Vector poly = ConstantPolynomial(1.23);
+  for (int i = 0; i < N; ++i) {
+    poly = AddRealRoot(poly, real_roots[i]);
+  }
+  Vector* const real_ptr = use_real ? &real : NULL;
+  Vector* const imaginary_ptr = use_imaginary ? &imaginary : NULL;
+  bool success = FindPolynomialRoots(poly, real_ptr, imaginary_ptr);
+
+  EXPECT_EQ(success, true);
+  if (use_real) {
+    EXPECT_EQ(real.size(), N);
+    real = SortVector(real);
+    ExpectArraysClose(N, real.data(), real_roots, epsilon);
+  }
+  if (use_imaginary) {
+    EXPECT_EQ(imaginary.size(), N);
+    const Vector zeros = Vector::Zero(N);
+    ExpectArraysClose(N, imaginary.data(), zeros.data(), epsilon);
+  }
+}
+}  // namespace
+
+TEST(Polynomial, InvalidPolynomialOfZeroLengthIsRejected) {
+  // Vector poly(0) is an ambiguous constructor call, so
+  // use the constructor with explicit column count.
+  Vector poly(0, 1);
+  Vector real;
+  Vector imag;
+  bool success = FindPolynomialRoots(poly, &real, &imag);
+
+  EXPECT_EQ(success, false);
+}
+
+TEST(Polynomial, ConstantPolynomialReturnsNoRoots) {
+  Vector poly = ConstantPolynomial(1.23);
+  Vector real;
+  Vector imag;
+  bool success = FindPolynomialRoots(poly, &real, &imag);
+
+  EXPECT_EQ(success, true);
+  EXPECT_EQ(real.size(), 0);
+  EXPECT_EQ(imag.size(), 0);
+}
+
+TEST(Polynomial, LinearPolynomialWithPositiveRootWorks) {
+  const double roots[1] = { 42.42 };
+  RunPolynomialTestRealRoots(roots, true, true, kEpsilon);
+}
+
+TEST(Polynomial, LinearPolynomialWithNegativeRootWorks) {
+  const double roots[1] = { -42.42 };
+  RunPolynomialTestRealRoots(roots, true, true, kEpsilon);
+}
+
+TEST(Polynomial, QuadraticPolynomialWithPositiveRootsWorks) {
+  const double roots[2] = { 1.0, 42.42 };
+  RunPolynomialTestRealRoots(roots, true, true, kEpsilon);
+}
+
+TEST(Polynomial, QuadraticPolynomialWithOneNegativeRootWorks) {
+  const double roots[2] = { -42.42, 1.0 };
+  RunPolynomialTestRealRoots(roots, true, true, kEpsilon);
+}
+
+TEST(Polynomial, QuadraticPolynomialWithTwoNegativeRootsWorks) {
+  const double roots[2] = { -42.42, -1.0 };
+  RunPolynomialTestRealRoots(roots, true, true, kEpsilon);
+}
+
+TEST(Polynomial, QuadraticPolynomialWithCloseRootsWorks) {
+  const double roots[2] = { 42.42, 42.43 };
+  RunPolynomialTestRealRoots(roots, true, false, kEpsilonLoose);
+}
+
+TEST(Polynomial, QuadraticPolynomialWithComplexRootsWorks) {
+  Vector real;
+  Vector imag;
+
+  Vector poly = ConstantPolynomial(1.23);
+  poly = AddComplexRootPair(poly, 42.42, 4.2);
+  bool success = FindPolynomialRoots(poly, &real, &imag);
+
+  EXPECT_EQ(success, true);
+  EXPECT_EQ(real.size(), 2);
+  EXPECT_EQ(imag.size(), 2);
+  ExpectClose(real(0), 42.42, kEpsilon);
+  ExpectClose(real(1), 42.42, kEpsilon);
+  ExpectClose(std::abs(imag(0)), 4.2, kEpsilon);
+  ExpectClose(std::abs(imag(1)), 4.2, kEpsilon);
+  ExpectClose(std::abs(imag(0) + imag(1)), 0.0, kEpsilon);
+}
+
+TEST(Polynomial, QuarticPolynomialWorks) {
+  const double roots[4] = { 1.23e-4, 1.23e-1, 1.23e+2, 1.23e+5 };
+  RunPolynomialTestRealRoots(roots, true, true, kEpsilon);
+}
+
+TEST(Polynomial, QuarticPolynomialWithTwoClustersOfCloseRootsWorks) {
+  const double roots[4] = { 1.23e-1, 2.46e-1, 1.23e+5, 2.46e+5 };
+  RunPolynomialTestRealRoots(roots, true, true, kEpsilonLoose);
+}
+
+TEST(Polynomial, QuarticPolynomialWithTwoZeroRootsWorks) {
+  const double roots[4] = { -42.42, 0.0, 0.0, 42.42 };
+  RunPolynomialTestRealRoots(roots, true, true, kEpsilonLoose);
+}
+
+TEST(Polynomial, QuarticMonomialWorks) {
+  const double roots[4] = { 0.0, 0.0, 0.0, 0.0 };
+  RunPolynomialTestRealRoots(roots, true, true, kEpsilon);
+}
+
+TEST(Polynomial, NullPointerAsImaginaryPartWorks) {
+  const double roots[4] = { 1.23e-4, 1.23e-1, 1.23e+2, 1.23e+5 };
+  RunPolynomialTestRealRoots(roots, true, false, kEpsilon);
+}
+
+TEST(Polynomial, NullPointerAsRealPartWorks) {
+  const double roots[4] = { 1.23e-4, 1.23e-1, 1.23e+2, 1.23e+5 };
+  RunPolynomialTestRealRoots(roots, false, true, kEpsilon);
+}
+
+TEST(Polynomial, BothOutputArgumentsNullWorks) {
+  const double roots[4] = { 1.23e-4, 1.23e-1, 1.23e+2, 1.23e+5 };
+  RunPolynomialTestRealRoots(roots, false, false, kEpsilon);
+}
+
+TEST(Polynomial, DifferentiateConstantPolynomial) {
+  // p(x) = 1;
+  Vector polynomial(1);
+  polynomial(0) = 1.0;
+  const Vector derivative = DifferentiatePolynomial(polynomial);
+  EXPECT_EQ(derivative.rows(), 0);
+}
+
+TEST(Polynomial, DifferentiateQuadraticPolynomial) {
+  // p(x) = x^2 + 2x + 3;
+  Vector polynomial(3);
+  polynomial(0) = 1.0;
+  polynomial(1) = 2.0;
+  polynomial(2) = 3.0;
+
+  const Vector derivative = DifferentiatePolynomial(polynomial);
+  EXPECT_EQ(derivative.rows(), 2);
+  EXPECT_EQ(derivative(0), 2.0);
+  EXPECT_EQ(derivative(1), 2.0);
+}
+
+TEST(Polynomial, MinimizeConstantPolynomial) {
+  // p(x) = 1;
+  Vector polynomial(1);
+  polynomial(0) = 1.0;
+
+  double optimal_x = 0.0;
+  double optimal_value = 0.0;
+  double min_x = 0.0;
+  double max_x = 1.0;
+  MinimizePolynomial(polynomial, min_x, max_x, &optimal_x, &optimal_value);
+
+  EXPECT_EQ(optimal_value, 1.0);
+  EXPECT_LE(optimal_x, max_x);
+  EXPECT_GE(optimal_x, min_x);
+}
+
+TEST(Polynomial, MinimizeLinearPolynomial) {
+  // p(x) = x - 2
+  Vector polynomial(2);
+
+  polynomial(0) = 1.0;
+  polynomial(1) = 2.0;
+
+  double optimal_x = 0.0;
+  double optimal_value = 0.0;
+  double min_x = 0.0;
+  double max_x = 1.0;
+  MinimizePolynomial(polynomial, min_x, max_x, &optimal_x, &optimal_value);
+
+  EXPECT_EQ(optimal_x, 0.0);
+  EXPECT_EQ(optimal_value, 2.0);
+}
+
+
+TEST(Polynomial, MinimizeQuadraticPolynomial) {
+  // p(x) = x^2 - 3 x + 2
+  // min_x = 3/2
+  // min_value = -1/4;
+  Vector polynomial(3);
+  polynomial(0) = 1.0;
+  polynomial(1) = -3.0;
+  polynomial(2) = 2.0;
+
+  double optimal_x = 0.0;
+  double optimal_value = 0.0;
+  double min_x = -2.0;
+  double max_x = 2.0;
+  MinimizePolynomial(polynomial, min_x, max_x, &optimal_x, &optimal_value);
+  EXPECT_EQ(optimal_x, 3.0/2.0);
+  EXPECT_EQ(optimal_value, -1.0/4.0);
+
+  min_x = -2.0;
+  max_x = 1.0;
+  MinimizePolynomial(polynomial, min_x, max_x, &optimal_x, &optimal_value);
+  EXPECT_EQ(optimal_x, 1.0);
+  EXPECT_EQ(optimal_value, 0.0);
+
+  min_x = 2.0;
+  max_x = 3.0;
+  MinimizePolynomial(polynomial, min_x, max_x, &optimal_x, &optimal_value);
+  EXPECT_EQ(optimal_x, 2.0);
+  EXPECT_EQ(optimal_value, 0.0);
+}
+
+TEST(Polymomial, ConstantInterpolatingPolynomial) {
+  // p(x) = 1.0
+  Vector true_polynomial(1);
+  true_polynomial << 1.0;
+
+  vector<FunctionSample> samples;
+  FunctionSample sample;
+  sample.x = 1.0;
+  sample.value = 1.0;
+  sample.value_is_valid = true;
+  samples.push_back(sample);
+
+  const Vector polynomial = FindInterpolatingPolynomial(samples);
+  EXPECT_NEAR((true_polynomial - polynomial).norm(), 0.0, 1e-15);
+}
+
+TEST(Polynomial, LinearInterpolatingPolynomial) {
+  // p(x) = 2x - 1
+  Vector true_polynomial(2);
+  true_polynomial << 2.0, -1.0;
+
+  vector<FunctionSample> samples;
+  FunctionSample sample;
+  sample.x = 1.0;
+  sample.value = 1.0;
+  sample.value_is_valid = true;
+  sample.gradient = 2.0;
+  sample.gradient_is_valid = true;
+  samples.push_back(sample);
+
+  const Vector polynomial = FindInterpolatingPolynomial(samples);
+  EXPECT_NEAR((true_polynomial - polynomial).norm(), 0.0, 1e-15);
+}
+
+TEST(Polynomial, QuadraticInterpolatingPolynomial) {
+  // p(x) = 2x^2 + 3x + 2
+   Vector true_polynomial(3);
+   true_polynomial << 2.0, 3.0, 2.0;
+
+  vector<FunctionSample> samples;
+  {
+    FunctionSample sample;
+    sample.x = 1.0;
+    sample.value = 7.0;
+    sample.value_is_valid = true;
+    sample.gradient = 7.0;
+    sample.gradient_is_valid = true;
+    samples.push_back(sample);
+  }
+
+  {
+    FunctionSample sample;
+    sample.x = -3.0;
+    sample.value = 11.0;
+    sample.value_is_valid = true;
+    samples.push_back(sample);
+  }
+
+  Vector polynomial = FindInterpolatingPolynomial(samples);
+  EXPECT_NEAR((true_polynomial - polynomial).norm(), 0.0, 1e-15);
+}
+
+TEST(Polynomial, DeficientCubicInterpolatingPolynomial) {
+  // p(x) = 2x^2 + 3x + 2
+  Vector true_polynomial(4);
+  true_polynomial << 0.0, 2.0, 3.0, 2.0;
+
+  vector<FunctionSample> samples;
+  {
+    FunctionSample sample;
+    sample.x = 1.0;
+    sample.value = 7.0;
+    sample.value_is_valid = true;
+    sample.gradient = 7.0;
+    sample.gradient_is_valid = true;
+    samples.push_back(sample);
+  }
+
+  {
+    FunctionSample sample;
+    sample.x = -3.0;
+    sample.value = 11.0;
+    sample.value_is_valid = true;
+    sample.gradient = -9;
+    sample.gradient_is_valid = true;
+    samples.push_back(sample);
+  }
+
+  const Vector polynomial = FindInterpolatingPolynomial(samples);
+  EXPECT_NEAR((true_polynomial - polynomial).norm(), 0.0, 1e-14);
+}
+
+
+TEST(Polynomial, CubicInterpolatingPolynomialFromValues) {
+  // p(x) = x^3 + 2x^2 + 3x + 2
+ Vector true_polynomial(4);
+ true_polynomial << 1.0, 2.0, 3.0, 2.0;
+
+ vector<FunctionSample> samples;
+  {
+    FunctionSample sample;
+    sample.x = 1.0;
+    sample.value = EvaluatePolynomial(true_polynomial, sample.x);
+    sample.value_is_valid = true;
+    samples.push_back(sample);
+  }
+
+  {
+    FunctionSample sample;
+    sample.x = -3.0;
+    sample.value = EvaluatePolynomial(true_polynomial, sample.x);
+    sample.value_is_valid = true;
+    samples.push_back(sample);
+  }
+
+  {
+    FunctionSample sample;
+    sample.x = 2.0;
+    sample.value = EvaluatePolynomial(true_polynomial, sample.x);
+    sample.value_is_valid = true;
+    samples.push_back(sample);
+  }
+
+  {
+    FunctionSample sample;
+    sample.x = 0.0;
+    sample.value = EvaluatePolynomial(true_polynomial, sample.x);
+    sample.value_is_valid = true;
+    samples.push_back(sample);
+  }
+
+  const Vector polynomial = FindInterpolatingPolynomial(samples);
+  EXPECT_NEAR((true_polynomial - polynomial).norm(), 0.0, 1e-14);
+}
+
+TEST(Polynomial, CubicInterpolatingPolynomialFromValuesAndOneGradient) {
+  // p(x) = x^3 + 2x^2 + 3x + 2
+ Vector true_polynomial(4);
+ true_polynomial << 1.0, 2.0, 3.0, 2.0;
+ Vector true_gradient_polynomial = DifferentiatePolynomial(true_polynomial);
+
+ vector<FunctionSample> samples;
+  {
+    FunctionSample sample;
+    sample.x = 1.0;
+    sample.value = EvaluatePolynomial(true_polynomial, sample.x);
+    sample.value_is_valid = true;
+    samples.push_back(sample);
+  }
+
+  {
+    FunctionSample sample;
+    sample.x = -3.0;
+    sample.value = EvaluatePolynomial(true_polynomial, sample.x);
+    sample.value_is_valid = true;
+    samples.push_back(sample);
+  }
+
+  {
+    FunctionSample sample;
+    sample.x = 2.0;
+    sample.value = EvaluatePolynomial(true_polynomial, sample.x);
+    sample.value_is_valid = true;
+    sample.gradient = EvaluatePolynomial(true_gradient_polynomial, sample.x);
+    sample.gradient_is_valid = true;
+    samples.push_back(sample);
+  }
+
+  const Vector polynomial = FindInterpolatingPolynomial(samples);
+  EXPECT_NEAR((true_polynomial - polynomial).norm(), 0.0, 1e-14);
+}
+
+TEST(Polynomial, CubicInterpolatingPolynomialFromValuesAndGradients) {
+  // p(x) = x^3 + 2x^2 + 3x + 2
+ Vector true_polynomial(4);
+ true_polynomial << 1.0, 2.0, 3.0, 2.0;
+ Vector true_gradient_polynomial = DifferentiatePolynomial(true_polynomial);
+
+ vector<FunctionSample> samples;
+  {
+    FunctionSample sample;
+    sample.x = -3.0;
+    sample.value = EvaluatePolynomial(true_polynomial, sample.x);
+    sample.value_is_valid = true;
+    sample.gradient = EvaluatePolynomial(true_gradient_polynomial, sample.x);
+    sample.gradient_is_valid = true;
+    samples.push_back(sample);
+  }
+
+  {
+    FunctionSample sample;
+    sample.x = 2.0;
+    sample.value = EvaluatePolynomial(true_polynomial, sample.x);
+    sample.value_is_valid = true;
+    sample.gradient = EvaluatePolynomial(true_gradient_polynomial, sample.x);
+    sample.gradient_is_valid = true;
+    samples.push_back(sample);
+  }
+
+  const Vector polynomial = FindInterpolatingPolynomial(samples);
+  EXPECT_NEAR((true_polynomial - polynomial).norm(), 0.0, 1e-14);
+}
+
+}  // namespace internal
+}  // namespace ceres