Fix cpp_bin_float conversions,

fix inverse trig logic to get as many digits as possible from std::asin.
Add test case.
Fixes: https://svn.boost.org/trac/boost/ticket/11764

include/boost/multiprecision/cpp_bin_float.hpp

@@ -43,7 +43,7 @@ class cpp_bin_float
 
    typedef typename rep_type::signed_types                        signed_types;
    typedef typename rep_type::unsigned_types                      unsigned_types;
-   typedef boost::mpl::list<double, long double>                  float_types;
+   typedef boost::mpl::list<float, double, long double>           float_types;
    typedef Exponent                                               exponent_type;
 
    static const exponent_type max_exponent_limit = boost::integer_traits<exponent_type>::const_max - 2 * static_cast<exponent_type>(bit_count);
@@ -104,6 +104,18 @@ class cpp_bin_float
       this->assign_float(f);
    }
 
+   template <class Float>
+   explicit cpp_bin_float(const Float& f,
+      typename boost::enable_if_c<
+      (number_category<Float>::value == number_kind_floating_point)
+      && (std::numeric_limits<Float>::digits > (int)bit_count)
+      && (std::numeric_limits<Float>::radix == 2)
+      >::type const* = 0)
+      : m_data(), m_exponent(0), m_sign(false)
+   {
+      this->assign_float(f);
+   }
+
    cpp_bin_float& operator=(const cpp_bin_float &o) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<rep_type&>() = std::declval<const rep_type&>()))
    {
       m_data = o.m_data;
@@ -125,7 +137,7 @@ class cpp_bin_float
    template <class Float>
    typename boost::enable_if_c<
       (number_category<Float>::value == number_kind_floating_point)
-      && (std::numeric_limits<Float>::digits <= (int)bit_count)
+      //&& (std::numeric_limits<Float>::digits <= (int)bit_count)
       && (std::numeric_limits<Float>::radix == 2), cpp_bin_float&>::type operator=(const Float& f)
    {
       return assign_float(f);
@@ -1405,6 +1417,8 @@ namespace detail{
 
 template<unsigned D1, backends::digit_base_type B1, class A1, class E1, E1 M1, E1 M2, unsigned D2, backends::digit_base_type B2, class A2, class E2, E2 M3, E2 M4>
 struct is_explicitly_convertible<backends::cpp_bin_float<D1, B1, A1, E1, M1, M2>, backends::cpp_bin_float<D2, B2, A2, E2, M3, M4> > : public mpl::true_ {};
+template<class FloatT, unsigned D2, backends::digit_base_type B2, class A2, class E2, E2 M3, E2 M4>
+struct is_explicitly_convertible<FloatT, backends::cpp_bin_float<D2, B2, A2, E2, M3, M4> > : public boost::is_floating_point<FloatT> {};
 
 }
 #endif

include/boost/multiprecision/detail/functions/trig.hpp

@@ -488,12 +488,12 @@ void eval_asin(T& result, const T& x)
    }
 
    // Get initial estimate using standard math function asin.
-   double dd;
+   long double dd;
    eval_convert_to(&dd, xx);
 
-   result = fp_type(std::asin(dd));
+   result = (long double)(std::asin(dd));
 
-   unsigned current_digits = std::numeric_limits<double>::digits - 5;
+   unsigned current_digits = std::numeric_limits<long double>::digits - 5;
    unsigned target_precision = boost::multiprecision::detail::digits2<number<T, et_on> >::value;
 
    // Newton-Raphson iteration

test/Jamfile.v2

@@ -681,7 +681,10 @@ run test_mixed_cpp_bin_float.cpp ;
 run test_mixed_cpp_dec_float.cpp ;
 run test_mixed_mpf_float.cpp gmp : : : [ check-target-builds ../config//has_gmp : : <build>no ] ;
 run test_mixed_mpfr_float.cpp  mpfr gmp : : : [ check-target-builds ../config//has_mpfr : : <build>no ] ;
-
+#
+# Check for narrowing conversions:
+#
+run test_float_conversions.cpp ;
 
 if $(enable-specfun)
 {

test/test_float_conversions.cpp

@@ -0,0 +1,40 @@
+///////////////////////////////////////////////////////////////
+//  Copyright 2015 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_
+//
+
+#ifdef _MSC_VER
+#  define _SCL_SECURE_NO_WARNINGS
+#endif
+
+#include <boost/detail/lightweight_test.hpp>
+#include <boost/array.hpp>
+#include "test.hpp"
+
+#include <boost/multiprecision/cpp_bin_float.hpp>
+#include <boost/math/constants/constants.hpp>
+
+int main()
+{
+   using namespace boost::multiprecision;
+
+   BOOST_STATIC_ASSERT(boost::is_convertible<float, cpp_bin_float_single>::value);
+   BOOST_STATIC_ASSERT(!boost::is_convertible<double, cpp_bin_float_single>::value);
+   BOOST_STATIC_ASSERT(!boost::is_convertible<long double, cpp_bin_float_single>::value);
+
+   cpp_bin_float_single s = boost::math::constants::pi<cpp_bin_float_single>();
+
+   typedef number<backends::cpp_bin_float<11, backends::digit_base_2, void, boost::int8_t, -14, 15>, et_off> cpp_bin_float_half;
+
+   BOOST_STATIC_ASSERT(!boost::is_convertible<float, cpp_bin_float_half>::value);
+   BOOST_STATIC_ASSERT(!boost::is_convertible<double, cpp_bin_float_half>::value);
+   BOOST_STATIC_ASSERT(!boost::is_convertible<long double, cpp_bin_float_half>::value);
+
+   cpp_bin_float_half hs = boost::math::constants::pi<cpp_bin_float_half>();
+
+   return boost::report_errors();
+}
+
+
+