Augment NumTraits with min/max_exponent() again.

Replace usage of `std::numeric_limits<...>::min/max_exponent` in
codebase where possible.  Also replaced some other `numeric_limits`
usages in affected tests with the `NumTraits` equivalent.

The previous MR !443 failed for c++03 due to lack of `constexpr`.
Because of this, we need to keep around the `std::numeric_limits`
version in enum expressions until the switch to c++11.

Fixes #2148

3 files changed, 27 insertions, 7 deletions

diff --git a/Eigen/src/Core/NumTraits.h b/Eigen/src/Core/NumTraits.h
index 609e11402..fdd4d4f51 100644
--- a/Eigen/src/Core/NumTraits.h
+++ b/Eigen/src/Core/NumTraits.h
@@ -135,9 +135,18 @@ EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Tgt bit_cast(const Src& src) {
   * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default
   *     value by the fuzzy comparison operators.
   * \li highest() and lowest() functions returning the highest and lowest possible values respectively.
+  * \li digits() function returning the number of radix digits (non-sign digits for integers, mantissa for floating-point). This is
+  *     the analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits">std::numeric_limits<T>::digits</a>
+  *     which is used as the default implementation if specialized.
   * \li digits10() function returning the number of decimal digits that can be represented without change. This is
   *     the analogue of <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits10">std::numeric_limits<T>::digits10</a>
   *     which is used as the default implementation if specialized.
+  * \li min_exponent() and max_exponent() functions returning the highest and lowest possible values, respectively,
+  *     such that the radix raised to the power exponent-1 is a normalized floating-point number.  These are equivalent to
+  *     <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/min_exponent">std::numeric_limits<T>::min_exponent</a>/
+  *     <a href="http://en.cppreference.com/w/cpp/types/numeric_limits/max_exponent">std::numeric_limits<T>::max_exponent</a>.
+  * \li infinity() function returning a representation of positive infinity, if available.
+  * \li quiet_NaN function returning a non-signaling "not-a-number", if available.
   */
 
 template<typename T> struct GenericNumTraits
@@ -180,13 +189,24 @@ template<typename T> struct GenericNumTraits
   }
 
   EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+  static inline int min_exponent()
+  {
+    return numext::numeric_limits<T>::min_exponent;
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
+  static inline int max_exponent()
+  {
+    return numext::numeric_limits<T>::max_exponent;
+  }
+
+  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
   static inline Real dummy_precision()
   {
     // make sure to override this for floating-point types
     return Real(0);
   }
 
-
   EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
   static inline T highest() {
     return (numext::numeric_limits<T>::max)();
diff --git a/Eigen/src/Core/StableNorm.h b/Eigen/src/Core/StableNorm.h
index 04fe0b371..4a3f0cca8 100644
--- a/Eigen/src/Core/StableNorm.h
+++ b/Eigen/src/Core/StableNorm.h
@@ -134,9 +134,9 @@ blueNorm_impl(const EigenBase<Derived>& _vec)
   // statements can be replaced
   static const int ibeta = std::numeric_limits<RealScalar>::radix;  // base for floating-point numbers
   static const int it    = NumTraits<RealScalar>::digits();  // number of base-beta digits in mantissa
-  static const int iemin = std::numeric_limits<RealScalar>::min_exponent;  // minimum exponent
-  static const int iemax = std::numeric_limits<RealScalar>::max_exponent; // maximum exponent
-  static const RealScalar rbig   = (std::numeric_limits<RealScalar>::max)();  // largest floating-point number
+  static const int iemin = NumTraits<RealScalar>::min_exponent();  // minimum exponent
+  static const int iemax = NumTraits<RealScalar>::max_exponent();  // maximum exponent
+  static const RealScalar rbig   = NumTraits<RealScalar>::highest();  // largest floating-point number
   static const RealScalar b1     = RealScalar(pow(RealScalar(ibeta),RealScalar(-((1-iemin)/2))));  // lower boundary of midrange
   static const RealScalar b2     = RealScalar(pow(RealScalar(ibeta),RealScalar((iemax + 1 - it)/2)));  // upper boundary of midrange
   static const RealScalar s1m    = RealScalar(pow(RealScalar(ibeta),RealScalar((2-iemin)/2)));  // scaling factor for lower range
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 411640ee8..87e8c2703 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -135,7 +135,7 @@ Packet pldexp_generic(const Packet& a, const Packet& exponent) {
 // Explicitly multiplies 
 //    a * (2^e)
 // clamping e to the range
-// [numeric_limits<Scalar>::min_exponent-2, numeric_limits<Scalar>::max_exponent]
+// [NumTraits<Scalar>::min_exponent()-2, NumTraits<Scalar>::max_exponent()]
 //
 // This is approx 7x faster than pldexp_impl, but will prematurely over/underflow
 // if 2^e doesn't fit into a normal floating-point Scalar.
@@ -1480,8 +1480,8 @@ Packet generic_pow(const Packet& x, const Packet& y) {
   const Packet y_is_nan = pandnot(ptrue(y), pcmp_eq(y, y));
   const Packet abs_y_is_inf = pcmp_eq(pabs(y), cst_pos_inf);
   EIGEN_CONSTEXPR Scalar huge_exponent =
-      (std::numeric_limits<Scalar>::max_exponent * Scalar(EIGEN_LN2)) /
-      std::numeric_limits<Scalar>::epsilon();
+      (NumTraits<Scalar>::max_exponent() * Scalar(EIGEN_LN2)) /
+       NumTraits<Scalar>::epsilon();
   const Packet abs_y_is_huge = pcmp_le(pset1<Packet>(huge_exponent), pabs(y));
 
   // Predicates for whether y is integer and/or even.