Fix initialization of static members

In particular, some members were declared but not defined, which
sometimes causes a linker error. See #806 for more discussion.

stan/math/fwd/core/std_numeric_limits.hpp

@@ -8,15 +8,15 @@ namespace std {
 
 template <typename T>
 struct numeric_limits<stan::math::fvar<T> > {
-  static const bool is_specialized = true;
+  static const bool is_specialized;
   static stan::math::fvar<T> min() { return numeric_limits<double>::min(); }
   static stan::math::fvar<T> max() { return numeric_limits<double>::max(); }
-  static const int digits = numeric_limits<double>::digits;
-  static const int digits10 = numeric_limits<double>::digits10;
-  static const bool is_signed = numeric_limits<double>::is_signed;
-  static const bool is_integer = numeric_limits<double>::is_integer;
-  static const bool is_exact = numeric_limits<double>::is_exact;
-  static const int radix = numeric_limits<double>::radix;
+  static const int digits;
+  static const int digits10;
+  static const bool is_signed;
+  static const bool is_integer;
+  static const bool is_exact;
+  static const int radix;
   static stan::math::fvar<T> epsilon() {
     return numeric_limits<double>::epsilon();
   }
@@ -24,18 +24,17 @@ struct numeric_limits<stan::math::fvar<T> > {
     return numeric_limits<double>::round_error();
   }
 
-  static const int min_exponent = numeric_limits<double>::min_exponent;
-  static const int min_exponent10 = numeric_limits<double>::min_exponent10;
-  static const int max_exponent = numeric_limits<double>::max_exponent;
-  static const int max_exponent10 = numeric_limits<double>::max_exponent10;
-
-  static const bool has_infinity = numeric_limits<double>::has_infinity;
-  static const bool has_quiet_NaN = numeric_limits<double>::has_quiet_NaN;
-  static const bool has_signaling_NaN
-      = numeric_limits<double>::has_signaling_NaN;
-  static const float_denorm_style has_denorm
-      = numeric_limits<double>::has_denorm;
-  static const bool has_denorm_loss = numeric_limits<double>::has_denorm_loss;
+  static const int min_exponent;
+  static const int min_exponent10;
+  static const int max_exponent;
+  static const int max_exponent10;
+
+  static const bool has_infinity;
+  static const bool has_quiet_NaN;
+  static const bool has_signaling_NaN;
+
+  static const float_denorm_style has_denorm;
+  static const bool has_denorm_loss;
   static stan::math::fvar<T> infinity() {
     return numeric_limits<double>::infinity();
   }
@@ -49,14 +48,68 @@ struct numeric_limits<stan::math::fvar<T> > {
     return numeric_limits<double>::denorm_min();
   }
 
-  static const bool is_iec559 = numeric_limits<double>::is_iec559;
-  static const bool is_bounded = numeric_limits<double>::is_bounded;
-  static const bool is_modulo = numeric_limits<double>::is_modulo;
+  static const bool is_iec559;
+  static const bool is_bounded;
+  static const bool is_modulo;
 
-  static const bool traps = numeric_limits<double>::traps;
-  static const bool tinyness_before = numeric_limits<double>::tinyness_before;
-  static const float_round_style round_style
-      = numeric_limits<double>::round_style;
+  static const bool traps;
+  static const bool tinyness_before;
+  static const float_round_style round_style;
 };
+
+template <typename T>
+  const bool numeric_limits<stan::math::fvar<T> >::is_specialized = true;
+template <typename T>
+  const int numeric_limits<stan::math::fvar<T> >::digits = numeric_limits<double>::digits;
+template <typename T>
+  const int numeric_limits<stan::math::fvar<T> >::digits10 = numeric_limits<double>::digits10;
+template <typename T>
+  const bool numeric_limits<stan::math::fvar<T> >::is_signed = numeric_limits<double>::is_signed;
+template <typename T>
+  const bool numeric_limits<stan::math::fvar<T> >::is_integer = numeric_limits<double>::is_integer;
+template <typename T>
+  const bool numeric_limits<stan::math::fvar<T> >::is_exact = numeric_limits<double>::is_exact;
+template <typename T>
+  const int numeric_limits<stan::math::fvar<T> >::radix = numeric_limits<double>::radix;
+template <typename T>
+  const int numeric_limits<stan::math::fvar<T> >::min_exponent = numeric_limits<double>::min_exponent;
+template <typename T>
+  const int numeric_limits<stan::math::fvar<T> >::min_exponent10 = numeric_limits<double>::min_exponent10;
+template <typename T>
+  const int numeric_limits<stan::math::fvar<T> >::max_exponent = numeric_limits<double>::max_exponent;
+template <typename T>
+  const int numeric_limits<stan::math::fvar<T> >::max_exponent10 = numeric_limits<double>::max_exponent10;
+
+
+
+template <typename T>
+  const bool numeric_limits<stan::math::fvar<T> >::has_infinity = numeric_limits<double>::has_infinity;
+template <typename T>
+  const bool numeric_limits<stan::math::fvar<T> >::has_quiet_NaN = numeric_limits<double>::has_quiet_NaN;
+template <typename T>
+  const bool numeric_limits<stan::math::fvar<T> >::has_signaling_NaN = numeric_limits<double>::has_signaling_NaN;
+template <typename T>
+  const float_denorm_style numeric_limits<stan::math::fvar<T> >::has_denorm = numeric_limits<double>::has_denorm;
+template <typename T>
+  const bool numeric_limits<stan::math::fvar<T> >::has_denorm_loss = numeric_limits<double>::has_denorm_loss;
+
+template <typename T>
+  const bool numeric_limits<stan::math::fvar<T> >::is_iec559
+    = numeric_limits<double>::is_iec559;
+template <typename T>
+  const bool numeric_limits<stan::math::fvar<T> >::is_bounded
+    = numeric_limits<double>::is_bounded;
+template <typename T>
+  const bool numeric_limits<stan::math::fvar<T> >::is_modulo
+    = numeric_limits<double>::is_modulo;
+
+template <typename T>
+  const bool numeric_limits<stan::math::fvar<T> >::traps = numeric_limits<double>::traps;
+template <typename T>
+  const bool numeric_limits<stan::math::fvar<T> >::tinyness_before = numeric_limits<double>::tinyness_before;
+template <typename T>
+  const float_round_style numeric_limits<stan::math::fvar<T> >::round_style
+    = numeric_limits<double>::round_style;
+
 }  // namespace std
 #endif