include/ceres/internal/compensated_math.h

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2026 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// 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: sergiu.deitsch@gmail.com (Sergiu Deitsch)

#ifndef CERES_PUBLIC_INTERNAL_COMPENSATED_MATH_H_
#define CERES_PUBLIC_INTERNAL_COMPENSATED_MATH_H_

#include <type_traits>
#include <utility>

namespace ceres::internal {

// Similar to Fast2Sum, but without requiring ordering or a specific radix.
template <typename T>
constexpr auto TwoSum(T a, T b)
    -> std::enable_if_t<std::is_floating_point_v<T>, std::pair<T, T>> {
  const T s = a + b;
  const T a_prime = s - b;
  const T b_prime = s - a_prime;
  const T delta_a = a - a_prime;
  const T delta_b = b - b_prime;
  const T t = delta_a + delta_b;
  return std::make_pair(s, t);
}

}  // namespace ceres::internal

#endif  // CERES_PUBLIC_INTERNAL_COMPENSATED_MATH_H_