autodiff/cppad.hpp

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//
// Copyright (c) 2018-2023 CNRS INRIA
//
 
#ifndef __pinocchio_autodiff_cppad_hpp__
#define __pinocchio_autodiff_cppad_hpp__
 
#include "pinocchio/math/fwd.hpp"
#define PINOCCHIO_WITH_CPPAD_SUPPORT
 
// Do not include this file directly.
// Copy and use directly the intructions from <cppad/example/cppad_eigen.hpp>
// to avoid redifinition of EIGEN_MATRIXBASE_PLUGIN for Eigen 3.3.0 and later
// #include <cppad/example/cppad_eigen.hpp>
 
#define EIGEN_MATRIXBASE_PLUGIN <pinocchio/autodiff/cppad/math/eigen_plugin.hpp>
 
#include <boost/mpl/int.hpp>
#include <cppad/cppad.hpp>
#include <Eigen/Dense>
 
namespace boost
{
  namespace math
  {
    namespace constants
    {
      namespace detail
      {
        template<typename Scalar>
        struct constant_pi<CppAD::AD<Scalar>> : constant_pi<Scalar>
        {
          typedef CppAD::AD<Scalar> ADScalar;
 
          template<int N>
          static inline ADScalar get(const mpl::int_<N> & n)
          {
            return ADScalar(constant_pi<Scalar>::get(n));
          }
 
#if BOOST_VERSION >= 107700
          template<class T, T value>
          static inline ADScalar get(const std::integral_constant<T, value> & n)
          {
            return ADScalar(constant_pi<Scalar>::get(n));
          }
#else
          template<class T, T value>
          static inline ADScalar get(const boost::integral_constant<T, value> & n)
          {
            return ADScalar(constant_pi<Scalar>::get(n));
          }
#endif
        };
      } // namespace detail
    } // namespace constants
  } // namespace math
} // namespace boost
 
namespace Eigen
{
  namespace internal
  {
    // Specialization of Eigen::internal::cast_impl for CppAD input types
    template<typename Scalar>
    struct cast_impl<CppAD::AD<Scalar>, Scalar>
    {
#if EIGEN_VERSION_AT_LEAST(3, 2, 90)
      EIGEN_DEVICE_FUNC
#endif
      static inline Scalar run(const CppAD::AD<Scalar> & x)
      {
        return CppAD::Value(x);
      }
    };
  } // namespace internal
} // namespace Eigen
 
// Source from #include <cppad/example/cppad_eigen.hpp>
namespace Eigen
{
  template<class Base>
  struct NumTraits<CppAD::AD<Base>>
  { // type that corresponds to the real part of an AD<Base> value
    typedef CppAD::AD<Base> Real;
    // type for AD<Base> operations that result in non-integer values
    typedef CppAD::AD<Base> NonInteger;
    //  type to use for numeric literals such as "2" or "0.5".
    typedef CppAD::AD<Base> Literal;
    // type for nested value inside an AD<Base> expression tree
    typedef CppAD::AD<Base> Nested;
 
    enum
    {
      // does not support complex Base types
      IsComplex = 0,
      // does not support integer Base types
      IsInteger = 0,
      // only support signed Base types
      IsSigned = 1,
      // must initialize an AD<Base> object
      RequireInitialization = 1,
      // computational cost of the corresponding operations
      ReadCost = 1,
      AddCost = 2,
      MulCost = 2
    };
 
    // machine epsilon with type of real part of x
    // (use assumption that Base is not complex)
    static CppAD::AD<Base> epsilon(void)
    {
      return CppAD::numeric_limits<CppAD::AD<Base>>::epsilon();
    }
 
    // relaxed version of machine epsilon for comparison of different
    // operations that should result in the same value
    static CppAD::AD<Base> dummy_precision(void)
    {
      return 100. * CppAD::numeric_limits<CppAD::AD<Base>>::epsilon();
    }
 
    // minimum normalized positive value
    static CppAD::AD<Base> lowest(void)
    {
      return CppAD::numeric_limits<CppAD::AD<Base>>::min();
    }
 
    // maximum finite value
    static CppAD::AD<Base> highest(void)
    {
      return CppAD::numeric_limits<CppAD::AD<Base>>::max();
    }
 
    // number of decimal digits that can be represented without change.
    static int digits10(void)
    {
      return CppAD::numeric_limits<CppAD::AD<Base>>::digits10;
    }
  };
} // namespace Eigen
 
// Source from #include <cppad/example/cppad_eigen.hpp>
#include "pinocchio/utils/static-if.hpp"
 
namespace CppAD
{
  // functions that return references
  template<class Base>
  const AD<Base> & conj(const AD<Base> & x)
  {
    return x;
  }
  template<class Base>
  const AD<Base> & real(const AD<Base> & x)
  {
    return x;
  }
 
  // functions that return values (note abs is defined by cppad.hpp)
  template<class Base>
  AD<Base> imag(const AD<Base> & /*x*/)
  {
    return CppAD::AD<Base>(0.);
  }
  template<class Base>
  AD<Base> abs2(const AD<Base> & x)
  {
    return x * x;
  }
 
  template<typename Scalar>
  AD<Scalar> min(const AD<Scalar> & x, const AD<Scalar> & y)
  {
    using ::pinocchio::internal::if_then_else;
    using ::pinocchio::internal::LT;
    return if_then_else(LT, y, x, y, x);
  }
 
  template<typename Scalar>
  AD<Scalar> max(const AD<Scalar> & x, const AD<Scalar> & y)
  {
    using ::pinocchio::internal::if_then_else;
    using ::pinocchio::internal::LT;
    return if_then_else(LT, x, y, y, x);
  }
} // namespace CppAD
 
namespace CppAD
{
  template<class Scalar>
  bool isfinite(const AD<Scalar> & x)
  {
    return isfinite(Value(x));
  }
} // namespace CppAD
 
#include "pinocchio/utils/static-if.hpp"
 
namespace pinocchio
{
  template<typename Scalar>
  struct TaylorSeriesExpansion<CppAD::AD<Scalar>> : TaylorSeriesExpansion<Scalar>
  {
    typedef TaylorSeriesExpansion<Scalar> Base;
    typedef CppAD::AD<Scalar> ADScalar;
 
    template<int degree>
    static ADScalar precision()
    {
      return ADScalar(Base::template precision<degree>());
    }
  };
 
  template<typename Scalar, typename ADScalar>
  struct ScalarCast<Scalar, CppAD::AD<ADScalar>>
  {
    static Scalar cast(const CppAD::AD<ADScalar> & value)
    {
      return scalar_cast<Scalar>(CppAD::Value(value));
    }
  };
 
} // namespace pinocchio
 
#include "pinocchio/autodiff/cppad/spatial/se3-tpl.hpp"
#include "pinocchio/autodiff/cppad/spatial/log.hxx"
#include "pinocchio/autodiff/cppad/utils/static-if.hpp"
#include "pinocchio/autodiff/cppad/math/quaternion.hpp"
#include "pinocchio/autodiff/cppad/algorithm/aba.hpp"
 
#endif // #ifndef __pinocchio_autodiff_cppad_hpp__