von Mises distribution improvement

[Ulrich Drepper]

I'd like to check in this patch which would improve the performance of
the distribution quite a bit by pulling constant computations into the
constructor.  This patch will change the memory layout which can be
done easily only now.  It also fixes one small bug in operator== and
in a comment.

OK?


Index: libstdc++-v3/include/ext/random
===================================================================
--- libstdc++-v3/include/ext/random (revision 196416)
+++ libstdc++-v3/include/ext/random (working copy)
@@ -2621,6 +2621,12 @@
   const _RealType __pi = __gnu_cxx::__math_constants<_RealType>::__pi;
   _GLIBCXX_DEBUG_ASSERT(_M_mu >= -__pi && _M_mu <= __pi);
   _GLIBCXX_DEBUG_ASSERT(_M_kappa >= _RealType(0));
+
+  auto __tau = std::sqrt(_RealType(4) * _M_kappa * _M_kappa
+ + _RealType(1)) + _RealType(1);
+  auto __rho = ((__tau - std::sqrt(_RealType(2) * __tau))
+ / (_RealType(2) * _M_kappa));
+  _M_r = (_RealType(1) + __rho * __rho) / (_RealType(2) * __rho);
  }

  _RealType
@@ -2633,16 +2639,17 @@

  friend bool
  operator==(const param_type& __p1, const param_type& __p2)
- { return __p1._M_kappa == __p2._M_kappa; }
+ { return (__p1._M_mu == __p2._M_mu
+  && __p1._M_kappa == __p2._M_kappa); }

       private:
-
  _RealType _M_mu;
  _RealType _M_kappa;
+ _RealType _M_r;
       };

       /**
-       * @brief Constructs a beta distribution with parameters
+       * @brief Constructs a von Mises distribution with parameters
        * @f$\mu@f$ and @f$\kappa@f$.
        */
       explicit
@@ -2727,20 +2734,13 @@
     = __gnu_cxx::__math_constants<result_type>::__pi;
   std::__detail::_Adaptor<_UniformRandomNumberGenerator, result_type>
     __aurng(__urng);
-  result_type __tau = (std::sqrt(result_type(4) * this->kappa()
- * this->kappa() + result_type(1))
-       + result_type(1));
-  result_type __rho = ((__tau - std::sqrt(result_type(2) * __tau))
-       / (result_type(2) * this->kappa()));
-  result_type __r = ((result_type(1) + __rho * __rho)
-     / (result_type(2) * __rho));

   result_type __f;
   while (1)
     {
       result_type __rnd = std::cos(__pi * __aurng());
-      __f = (result_type(1) + __r * __rnd) / (__r + __rnd);
-      result_type __c = this->kappa() * (__r - __f);
+      __f = (result_type(1) + __p._M_r * __rnd) / (__p._M_r + __rnd);
+      result_type __c = __p._M_kappa * (__p._M_r - __f);

       result_type __rnd2 = __aurng();
       if (__c * (result_type(2) - __c) > __rnd2)
@@ -2756,7 +2756,7 @@
   if (__aurng() < result_type(0.5))
     __res = -__res;
 #endif
-  __res += this->mu();
+  __res += __p._M_mu;
   if (__res > __pi)
     __res -= result_type(2) * __pi;
   else if (__res < -__pi)