Introduce a variable_or_fixed<N> proxy returned by fix<N>(val) to pass both a compile-time and runtime fallback value in case N means "runtime".

This mechanism is used by the seq/seqN functions. The proxy object is immediately converted to pure compile-time (as fix<N>) or pure runtime (i.e., an Index) to avoid redundant template instantiations.

Eigen/src/Core/util/IntegralConstant.h

@@ -15,13 +15,35 @@ namespace Eigen {
 
 namespace internal {
 
+template<int N> struct fix_t;
+template<int N> class variable_or_fixed;
+
 template<int N> struct fix_t {
   static const int value = N;
   operator int() const { return value; }
-  fix_t (fix_t<N> (*)() ) {}
   fix_t() {}
+  fix_t(variable_or_fixed<N> other) {
+    EIGEN_ONLY_USED_FOR_DEBUG(other);
+    eigen_internal_assert(int(other)==N);
+  }
+
+#if EIGEN_HAS_CXX14
   // Needed in C++14 to allow fix<N>():
   fix_t operator() () const { return *this; }
+
+  variable_or_fixed<N> operator() (int val) const { return variable_or_fixed<N>(val); }
+#else
+  fix_t (fix_t<N> (*)() ) {}
+#endif
+};
+
+template<int N> class variable_or_fixed {
+public:
+  static const int value = N;
+  operator int() const { return m_value; }
+  variable_or_fixed(int val) { m_value = val; }
+protected:
+  int m_value;
 };
 
 template<typename T, int Default=Dynamic> struct get_compile_time {
@@ -32,6 +54,10 @@ template<int N,int Default> struct get_compile_time<fix_t<N>,Default> {
   enum { value = N };
 };
 
+template<int N,int Default> struct get_compile_time<variable_or_fixed<N>,Default> {
+  enum { value = N };
+};
+
 template<typename T, int N, int Default>
 struct get_compile_time<variable_if_dynamic<T,N>,Default> {
   enum { value = N };
@@ -45,12 +71,17 @@ template<int N> struct is_compile_time<fix_t<N> > { enum { value = true }; };
 
 #ifndef EIGEN_PARSED_BY_DOXYGEN
 
-#if __cplusplus > 201103L
+#if EIGEN_HAS_CXX14
 template<int N>
 static const internal::fix_t<N> fix{};
 #else
 template<int N>
 inline internal::fix_t<N> fix() { return internal::fix_t<N>(); }
+
+// The generic typename T is mandatory. Otherwise, a code like fix<N> could refer to either the function above or this next overload.
+// This way a code like fix<N> can only refer to the previous function.
+template<int N,typename T>
+inline internal::variable_or_fixed<N> fix(T val) { return internal::variable_or_fixed<N>(val); }
 #endif
 
 #else // EIGEN_PARSED_BY_DOXYGEN
@@ -67,6 +98,8 @@ inline internal::fix_t<N> fix() { return internal::fix_t<N>(); }
   * seqN(10,fix<4>,fix<-3>)   // <=> [10 7 4 1]
   * \endcode
   *
+  * See also the function fix(int) to pass both a compile-time and runtime value.
+  *
   * In c++14, it is implemented as:
   * \code
   * template<int N> static const internal::fix_t<N> fix{};
@@ -82,10 +115,42 @@ inline internal::fix_t<N> fix() { return internal::fix_t<N>(); }
   * Here internal::fix_t<N> is thus a pointer to function.
   *
   * If for some reason you want a true object in c++98 then you can write: \code fix<N>() \endcode which is also valid in c++14.
+  *
+  * \sa fix(int), seq, seqN
   */
 template<int N>
 static const auto fix;
 
+/** \fn fix(int)
+  * \ingroup Core_Module
+  *
+  * This function returns an object embedding both a compile-time integer \c N, and a runtime value \a val.
+  *
+  * \tparam N the compile-time integer value
+  * \param  val the runtime integer value
+  *
+  * This function is a more general version of the \ref fix identifier/function that can be used in template code
+  * where the compile-time value coudl turned out to actually mean "undefined at compile-time". For positive integers
+  * such as a size of a dimension, this case is identified by Eigen::Dynamic, whereas runtime signed integers (e.g., an increment/stride) are identified
+  * as Eigen::DynamicIndex.
+  *
+  * A typical use case would be:
+  * \code
+  * template<typename Derived> void foo(const MatrixBase<Derived> &mat) {
+  *   const int N = Derived::RowsAtCompileTime==Dynamic ? Dynamic : Derived::RowsAtCompileTime/2;
+  *   const int n = mat.rows()/2;
+  *   ... mat( seqN(0,fix<N>(n) ) ...;
+  * }
+  * \endcode
+  * In this example, the function Eigen::seqN knows that the second argument is expected to be a size.
+  * If the passed compile-time value N equals Eigen::Dynamic, then the proxy object returned by fix will be dissmissed, and converted to an Eigen::Index of value \c n.
+  * Otherwise, the runtime-value \c n will be dissmissed, and the returned ArithmeticSequence will be of the exact same type as <tt> seqN(0,fix<N>) </tt>.
+  *
+  * \sa fix, seqN, class ArithmeticSequence
+  */
+template<int N>
+static const auto fix(int val);
+
 #endif // EIGEN_PARSED_BY_DOXYGEN
 
 } // end namespace Eigen