update boost

linx64/include/boost/math/differentiation/autodiff_cpp11.hpp

@@ -0,0 +1,387 @@
+//           Copyright Matthew Pulver 2018 - 2019.
+// Distributed under the Boost Software License, Version 1.0.
+//      (See accompanying file LICENSE_1_0.txt or copy at
+//           https://www.boost.org/LICENSE_1_0.txt)
+
+// Contributors:
+//  * Kedar R. Bhat - C++11 compatibility.
+
+// Notes:
+//  * Any changes to this file should always be downstream from autodiff.cpp.
+//    C++17 is a higher-level language and is easier to maintain. For example, a number of functions which are
+//    lucidly read in autodiff.cpp are forced to be split into multiple structs/functions in this file for
+//    C++11.
+//  * Use of typename RootType and SizeType is a hack to prevent Visual Studio 2015 from compiling functions
+//    that are never called, that would otherwise produce compiler errors. Also forces functions to be inline.
+
+#ifndef BOOST_MATH_DIFFERENTIATION_AUTODIFF_HPP
+#error \
+    "Do not #include this file directly. This should only be #included by autodiff.hpp for C++11 compatibility."
+#endif
+
+#include <type_traits>
+#include <boost/math/tools/mp.hpp>
+
+namespace boost {
+namespace math {
+
+namespace mp = tools::meta_programming;
+
+namespace differentiation {
+inline namespace autodiff_v1 {
+namespace detail {
+
+template <typename RealType, size_t Order>
+fvar<RealType, Order>::fvar(root_type const& ca, bool const is_variable) {
+  fvar_cpp11(is_fvar<RealType>{}, ca, is_variable);
+}
+
+template <typename RealType, size_t Order>
+template <typename RootType>
+void fvar<RealType, Order>::fvar_cpp11(std::true_type, RootType const& ca, bool const is_variable) {
+  v.front() = RealType(ca, is_variable);
+  if (0 < Order)
+    std::fill(v.begin() + 1, v.end(), static_cast<RealType>(0));
+}
+
+template <typename RealType, size_t Order>
+template <typename RootType>
+void fvar<RealType, Order>::fvar_cpp11(std::false_type, RootType const& ca, bool const is_variable) {
+  v.front() = ca;
+  if (0 < Order) {
+    v[1] = static_cast<root_type>(static_cast<int>(is_variable));
+    if (1 < Order)
+      std::fill(v.begin() + 2, v.end(), static_cast<RealType>(0));
+  }
+}
+
+template <typename RealType, size_t Order>
+template <typename... Orders>
+get_type_at<RealType, sizeof...(Orders)> fvar<RealType, Order>::at_cpp11(std::true_type,
+                                                                         size_t order,
+                                                                         Orders...) const {
+  return v.at(order);
+}
+
+template <typename RealType, size_t Order>
+template <typename... Orders>
+get_type_at<RealType, sizeof...(Orders)> fvar<RealType, Order>::at_cpp11(std::false_type,
+                                                                         size_t order,
+                                                                         Orders... orders) const {
+  return v.at(order).at(orders...);
+}
+
+// Can throw "std::out_of_range: array::at: __n (which is 7) >= _Nm (which is 7)"
+template <typename RealType, size_t Order>
+template <typename... Orders>
+get_type_at<RealType, sizeof...(Orders)> fvar<RealType, Order>::at(size_t order, Orders... orders) const {
+  return at_cpp11(std::integral_constant<bool, sizeof...(orders) == 0>{}, order, orders...);
+}
+
+template <typename T, typename... Ts>
+constexpr T product(Ts...) {
+  return static_cast<T>(1);
+}
+
+template <typename T, typename... Ts>
+constexpr T product(T factor, Ts... factors) {
+  return factor * product<T>(factors...);
+}
+
+// Can throw "std::out_of_range: array::at: __n (which is 7) >= _Nm (which is 7)"
+template <typename RealType, size_t Order>
+template <typename... Orders>
+get_type_at<fvar<RealType, Order>, sizeof...(Orders)> fvar<RealType, Order>::derivative(
+    Orders... orders) const {
+  static_assert(sizeof...(Orders) <= depth,
+                "Number of parameters to derivative(...) cannot exceed fvar::depth.");
+  return at(static_cast<size_t>(orders)...) *
+         product(boost::math::factorial<root_type>(static_cast<unsigned>(orders))...);
+}
+
+template <typename RootType, typename Func>
+class Curry {
+  Func const& f_;
+  size_t const i_;
+
+ public:
+  template <typename SizeType>  // typename SizeType to force inline constructor.
+  Curry(Func const& f, SizeType i) : f_(f), i_(static_cast<std::size_t>(i)) {}
+  template <typename... Indices>
+  RootType operator()(Indices... indices) const {
+    using unsigned_t = typename std::make_unsigned<typename std::common_type<Indices>::type...>::type;
+    return f_(i_, static_cast<unsigned_t>(indices)...);
+  }
+};
+
+template <typename RealType, size_t Order>
+template <typename Func, typename Fvar, typename... Fvars>
+promote<fvar<RealType, Order>, Fvar, Fvars...> fvar<RealType, Order>::apply_coefficients(
+    size_t const order,
+    Func const& f,
+    Fvar const& cr,
+    Fvars&&... fvars) const {
+  fvar<RealType, Order> const epsilon = fvar<RealType, Order>(*this).set_root(0);
+  size_t i = order < order_sum ? order : order_sum;
+  using return_type = promote<fvar<RealType, Order>, Fvar, Fvars...>;
+  return_type accumulator = cr.apply_coefficients(
+      order - i, Curry<typename return_type::root_type, Func>(f, i), std::forward<Fvars>(fvars)...);
+  while (i--)
+    (accumulator *= epsilon) += cr.apply_coefficients(
+        order - i, Curry<typename return_type::root_type, Func>(f, i), std::forward<Fvars>(fvars)...);
+  return accumulator;
+}
+
+template <typename RealType, size_t Order>
+template <typename Func, typename Fvar, typename... Fvars>
+promote<fvar<RealType, Order>, Fvar, Fvars...> fvar<RealType, Order>::apply_coefficients_nonhorner(
+    size_t const order,
+    Func const& f,
+    Fvar const& cr,
+    Fvars&&... fvars) const {
+  fvar<RealType, Order> const epsilon = fvar<RealType, Order>(*this).set_root(0);
+  fvar<RealType, Order> epsilon_i = fvar<RealType, Order>(1);  // epsilon to the power of i
+  using return_type = promote<fvar<RealType, Order>, Fvar, Fvars...>;
+  return_type accumulator = cr.apply_coefficients_nonhorner(
+      order, Curry<typename return_type::root_type, Func>(f, 0), std::forward<Fvars>(fvars)...);
+  size_t const i_max = order < order_sum ? order : order_sum;
+  for (size_t i = 1; i <= i_max; ++i) {
+    epsilon_i = epsilon_i.epsilon_multiply(i - 1, 0, epsilon, 1, 0);
+    accumulator += epsilon_i.epsilon_multiply(
+        i,
+        0,
+        cr.apply_coefficients_nonhorner(
+            order - i, Curry<typename return_type::root_type, Func>(f, i), std::forward<Fvars>(fvars)...),
+        0,
+        0);
+  }
+  return accumulator;
+}
+
+template <typename RealType, size_t Order>
+template <typename Func, typename Fvar, typename... Fvars>
+promote<fvar<RealType, Order>, Fvar, Fvars...> fvar<RealType, Order>::apply_derivatives(
+    size_t const order,
+    Func const& f,
+    Fvar const& cr,
+    Fvars&&... fvars) const {
+  fvar<RealType, Order> const epsilon = fvar<RealType, Order>(*this).set_root(0);
+  size_t i = order < order_sum ? order : order_sum;
+  using return_type = promote<fvar<RealType, Order>, Fvar, Fvars...>;
+  return_type accumulator =
+      cr.apply_derivatives(
+          order - i, Curry<typename return_type::root_type, Func>(f, i), std::forward<Fvars>(fvars)...) /
+      factorial<root_type>(static_cast<unsigned>(i));
+  while (i--)
+    (accumulator *= epsilon) +=
+        cr.apply_derivatives(
+            order - i, Curry<typename return_type::root_type, Func>(f, i), std::forward<Fvars>(fvars)...) /
+        factorial<root_type>(static_cast<unsigned>(i));
+  return accumulator;
+}
+
+template <typename RealType, size_t Order>
+template <typename Func, typename Fvar, typename... Fvars>
+promote<fvar<RealType, Order>, Fvar, Fvars...> fvar<RealType, Order>::apply_derivatives_nonhorner(
+    size_t const order,
+    Func const& f,
+    Fvar const& cr,
+    Fvars&&... fvars) const {
+  fvar<RealType, Order> const epsilon = fvar<RealType, Order>(*this).set_root(0);
+  fvar<RealType, Order> epsilon_i = fvar<RealType, Order>(1);  // epsilon to the power of i
+  using return_type = promote<fvar<RealType, Order>, Fvar, Fvars...>;
+  return_type accumulator = cr.apply_derivatives_nonhorner(
+      order, Curry<typename return_type::root_type, Func>(f, 0), std::forward<Fvars>(fvars)...);
+  size_t const i_max = order < order_sum ? order : order_sum;
+  for (size_t i = 1; i <= i_max; ++i) {
+    epsilon_i = epsilon_i.epsilon_multiply(i - 1, 0, epsilon, 1, 0);
+    accumulator += epsilon_i.epsilon_multiply(
+        i,
+        0,
+        cr.apply_derivatives_nonhorner(
+            order - i, Curry<typename return_type::root_type, Func>(f, i), std::forward<Fvars>(fvars)...) /
+            factorial<root_type>(static_cast<unsigned>(i)),
+        0,
+        0);
+  }
+  return accumulator;
+}
+
+template <typename RealType, size_t Order>
+template <typename SizeType>
+fvar<RealType, Order> fvar<RealType, Order>::epsilon_multiply_cpp11(std::true_type,
+                                                                    SizeType z0,
+                                                                    size_t isum0,
+                                                                    fvar<RealType, Order> const& cr,
+                                                                    size_t z1,
+                                                                    size_t isum1) const {
+  size_t const m0 = order_sum + isum0 < Order + z0 ? Order + z0 - (order_sum + isum0) : 0;
+  size_t const m1 = order_sum + isum1 < Order + z1 ? Order + z1 - (order_sum + isum1) : 0;
+  size_t const i_max = m0 + m1 < Order ? Order - (m0 + m1) : 0;
+  fvar<RealType, Order> retval = fvar<RealType, Order>();
+  for (size_t i = 0, j = Order; i <= i_max; ++i, --j)
+    retval.v[j] = epsilon_inner_product(z0, isum0, m0, cr, z1, isum1, m1, j);
+  return retval;
+}
+
+template <typename RealType, size_t Order>
+template <typename SizeType>
+fvar<RealType, Order> fvar<RealType, Order>::epsilon_multiply_cpp11(std::false_type,
+                                                                    SizeType z0,
+                                                                    size_t isum0,
+                                                                    fvar<RealType, Order> const& cr,
+                                                                    size_t z1,
+                                                                    size_t isum1) const {
+  using ssize_t = typename std::make_signed<std::size_t>::type;
+  RealType const zero(0);
+  size_t const m0 = order_sum + isum0 < Order + z0 ? Order + z0 - (order_sum + isum0) : 0;
+  size_t const m1 = order_sum + isum1 < Order + z1 ? Order + z1 - (order_sum + isum1) : 0;
+  size_t const i_max = m0 + m1 < Order ? Order - (m0 + m1) : 0;
+  fvar<RealType, Order> retval = fvar<RealType, Order>();
+  for (size_t i = 0, j = Order; i <= i_max; ++i, --j)
+    retval.v[j] = std::inner_product(
+        v.cbegin() + ssize_t(m0), v.cend() - ssize_t(i + m1), cr.v.crbegin() + ssize_t(i + m0), zero);
+  return retval;
+}
+
+template <typename RealType, size_t Order>
+fvar<RealType, Order> fvar<RealType, Order>::epsilon_multiply(size_t z0,
+                                                              size_t isum0,
+                                                              fvar<RealType, Order> const& cr,
+                                                              size_t z1,
+                                                              size_t isum1) const {
+  return epsilon_multiply_cpp11(is_fvar<RealType>{}, z0, isum0, cr, z1, isum1);
+}
+
+template <typename RealType, size_t Order>
+template <typename SizeType>
+fvar<RealType, Order> fvar<RealType, Order>::epsilon_multiply_cpp11(std::true_type,
+                                                                    SizeType z0,
+                                                                    size_t isum0,
+                                                                    root_type const& ca) const {
+  fvar<RealType, Order> retval(*this);
+  size_t const m0 = order_sum + isum0 < Order + z0 ? Order + z0 - (order_sum + isum0) : 0;
+  for (size_t i = m0; i <= Order; ++i)
+    retval.v[i] = retval.v[i].epsilon_multiply(z0, isum0 + i, ca);
+  return retval;
+}
+
+template <typename RealType, size_t Order>
+template <typename SizeType>
+fvar<RealType, Order> fvar<RealType, Order>::epsilon_multiply_cpp11(std::false_type,
+                                                                    SizeType z0,
+                                                                    size_t isum0,
+                                                                    root_type const& ca) const {
+  fvar<RealType, Order> retval(*this);
+  size_t const m0 = order_sum + isum0 < Order + z0 ? Order + z0 - (order_sum + isum0) : 0;
+  for (size_t i = m0; i <= Order; ++i)
+    if (retval.v[i] != static_cast<RealType>(0))
+      retval.v[i] *= ca;
+  return retval;
+}
+
+template <typename RealType, size_t Order>
+fvar<RealType, Order> fvar<RealType, Order>::epsilon_multiply(size_t z0,
+                                                              size_t isum0,
+                                                              root_type const& ca) const {
+  return epsilon_multiply_cpp11(is_fvar<RealType>{}, z0, isum0, ca);
+}
+
+template <typename RealType, size_t Order>
+template <typename RootType>
+fvar<RealType, Order>& fvar<RealType, Order>::multiply_assign_by_root_type_cpp11(std::true_type,
+                                                                                 bool is_root,
+                                                                                 RootType const& ca) {
+  auto itr = v.begin();
+  itr->multiply_assign_by_root_type(is_root, ca);
+  for (++itr; itr != v.end(); ++itr)
+    itr->multiply_assign_by_root_type(false, ca);
+  return *this;
+}
+
+template <typename RealType, size_t Order>
+template <typename RootType>
+fvar<RealType, Order>& fvar<RealType, Order>::multiply_assign_by_root_type_cpp11(std::false_type,
+                                                                                 bool is_root,
+                                                                                 RootType const& ca) {
+  auto itr = v.begin();
+  if (is_root || *itr != 0)
+    *itr *= ca;  // Skip multiplication of 0 by ca=inf to avoid nan, except when is_root.
+  for (++itr; itr != v.end(); ++itr)
+    if (*itr != 0)
+      *itr *= ca;
+  return *this;
+}
+
+template <typename RealType, size_t Order>
+fvar<RealType, Order>& fvar<RealType, Order>::multiply_assign_by_root_type(bool is_root,
+                                                                           root_type const& ca) {
+  return multiply_assign_by_root_type_cpp11(is_fvar<RealType>{}, is_root, ca);
+}
+
+template <typename RealType, size_t Order>
+template <typename RootType>
+fvar<RealType, Order>& fvar<RealType, Order>::negate_cpp11(std::true_type, RootType const&) {
+  std::for_each(v.begin(), v.end(), [](RealType& r) { r.negate(); });
+  return *this;
+}
+
+template <typename RealType, size_t Order>
+template <typename RootType>
+fvar<RealType, Order>& fvar<RealType, Order>::negate_cpp11(std::false_type, RootType const&) {
+  std::for_each(v.begin(), v.end(), [](RealType& a) { a = -a; });
+  return *this;
+}
+
+template <typename RealType, size_t Order>
+fvar<RealType, Order>& fvar<RealType, Order>::negate() {
+  return negate_cpp11(is_fvar<RealType>{}, static_cast<root_type>(*this));
+}
+
+template <typename RealType, size_t Order>
+template <typename RootType>
+fvar<RealType, Order>& fvar<RealType, Order>::set_root_cpp11(std::true_type, RootType const& root) {
+  v.front().set_root(root);
+  return *this;
+}
+
+template <typename RealType, size_t Order>
+template <typename RootType>
+fvar<RealType, Order>& fvar<RealType, Order>::set_root_cpp11(std::false_type, RootType const& root) {
+  v.front() = root;
+  return *this;
+}
+
+template <typename RealType, size_t Order>
+fvar<RealType, Order>& fvar<RealType, Order>::set_root(root_type const& root) {
+  return set_root_cpp11(is_fvar<RealType>{}, root);
+}
+
+template <typename RealType, size_t Order, size_t... Is>
+auto make_fvar_for_tuple(mp::index_sequence<Is...>, RealType const& ca)
+    -> decltype(make_fvar<RealType, zero<Is>::value..., Order>(ca)) {
+  return make_fvar<RealType, zero<Is>::value..., Order>(ca);
+}
+
+template <typename RealType, size_t... Orders, size_t... Is, typename... RealTypes>
+auto make_ftuple_impl(mp::index_sequence<Is...>, RealTypes const&... ca)
+    -> decltype(std::make_tuple(make_fvar_for_tuple<RealType, Orders>(mp::make_index_sequence<Is>{},
+                                                                      ca)...)) {
+  return std::make_tuple(make_fvar_for_tuple<RealType, Orders>(mp::make_index_sequence<Is>{}, ca)...);
+}
+
+}  // namespace detail
+
+template <typename RealType, size_t... Orders, typename... RealTypes>
+auto make_ftuple(RealTypes const&... ca)
+    -> decltype(detail::make_ftuple_impl<RealType, Orders...>(mp::index_sequence_for<RealTypes...>{},
+                                                              ca...)) {
+  static_assert(sizeof...(Orders) == sizeof...(RealTypes),
+                "Number of Orders must match number of function parameters.");
+  return detail::make_ftuple_impl<RealType, Orders...>(mp::index_sequence_for<RealTypes...>{}, ca...);
+}
+
+}  // namespace autodiff_v1
+}  // namespace differentiation
+}  // namespace math
+}  // namespace boost