Merge pull request #162 from BoostGSoC21/clarify_exact_arith_struct

Fix #161 via clarify and streamline exact_arithmetic struct

Author: ckormanyos

include/boost/multiprecision/cpp_df_qf/cpp_df_qf_detail.hpp

@@ -69,28 +69,30 @@ struct exact_arithmetic
 
    using float_type  = FloatingPointType;
    using float_pair  = std::pair<float_type, float_type>;
-   using float_tuple = std::tuple<float_type, float_type, float_type, float_type>;
 
-   static constexpr auto fast_sum(float_type a, float_type b) -> float_pair
+   static constexpr auto two_sum(const float_type a, const float_type b) -> float_pair
    {
-      // Exact addition of two floating point numbers, given |a| > |b|
-      const float_type a_plus_b = a + b;
+     const float_type hi { a + b };
+     const float_type a1 { hi - b };
+     const float_type b1 { hi - a1 };
 
-      const float_pair result(a_plus_b, b - (a_plus_b - a));
-
-      return result;
+     return { hi, float_type { (a - a1) + (b - b1) } };
    }
 
-   static constexpr void sum(float_pair& result, float_type a, float_type b)
+   static constexpr auto two_diff(const float_type a, const float_type b) -> float_pair
    {
-      // Exact addition of two floating point numbers
-      const float_type a_plus_b = a + b;
-      const float_type v        = a_plus_b - a;
+     const float_type hi { a - b };
+     const float_type a1 { hi + b };
+     const float_type b1 { hi - a1 };
+
+     return { hi, float_type { (a - a1) - (b + b1) } };
+   }
 
-      const float_pair tmp(a_plus_b, (a - (a_plus_b - v)) + (b - v));
+   static constexpr auto two_hilo_sum(const float_type a, const float_type b) -> float_pair
+   {
+      const float_type hi { a + b };
 
-      result.first  = tmp.first;
-      result.second = tmp.second;
+      return { hi, float_type { b - (hi - a) } };
    }
 
    static constexpr auto normalize(float_pair& result, float_type a, float_type b) -> void

include/boost/multiprecision/cpp_double_fp.hpp

@@ -478,13 +478,13 @@ class cpp_double_fp_backend
 
       const float_type xlo { data.second };
 
-      data = two_sum(data.first, v.data.first);
+      data = arithmetic::two_sum(data.first, v.data.first);
 
-      const rep_type thi_tlo { two_sum(xlo, v.data.second) };
+      const rep_type thi_tlo { arithmetic::two_sum(xlo, v.data.second) };
 
-      data = two_hilo_sum(data.first, data.second + thi_tlo.first);
+      data = arithmetic::two_hilo_sum(data.first, data.second + thi_tlo.first);
 
-      data = two_hilo_sum(data.first, thi_tlo.second + data.second);
+      data = arithmetic::two_hilo_sum(data.first, thi_tlo.second + data.second);
 
       return *this;
    }
@@ -539,13 +539,13 @@ class cpp_double_fp_backend
 
       const float_type xlo { data.second };
 
-      data = two_diff(data.first, v.data.first);
+      data = arithmetic::two_diff(data.first, v.data.first);
 
-      const rep_type thi_tlo { two_diff(xlo, v.data.second) };
+      const rep_type thi_tlo { arithmetic::two_diff(xlo, v.data.second) };
 
-      data = two_hilo_sum(data.first, data.second + thi_tlo.first);
+      data = arithmetic::two_hilo_sum(data.first, data.second + thi_tlo.first);
 
-      data = two_hilo_sum(data.first, thi_tlo.second + data.second);
+      data = arithmetic::two_hilo_sum(data.first, thi_tlo.second + data.second);
 
       return *this;
    }
@@ -975,7 +975,7 @@ class cpp_double_fp_backend
       return
          cpp_double_fp_backend
          (
-            arithmetic::fast_sum
+            arithmetic::two_hilo_sum
             (
                static_cast<float_type>
                (
@@ -1065,31 +1065,6 @@ class cpp_double_fp_backend
 
    bool rd_string(const char* pstr);
 
-   static constexpr rep_type two_sum(const float_type a, const float_type b)
-   {
-     const float_type hi { a + b };
-     const float_type a1 { hi - b };
-     const float_type b1 { hi - a1 };
-
-     return { hi, float_type { (a - a1) + (b - b1) } };
-   }
-
-   static constexpr rep_type two_diff(const float_type a, const float_type b)
-   {
-     const float_type hi { a - b };
-     const float_type a1 { hi + b };
-     const float_type b1 { hi - a1 };
-
-     return { hi, float_type { (a - a1) - (b + b1) } };
-   }
-
-   static constexpr rep_type two_hilo_sum(const float_type a, const float_type b)
-   {
-      const float_type hi { a + b };
-
-      return { hi, float_type { b - (hi - a) } };
-   }
-
    template <typename OtherFloatingPointType,
              typename ::std::enable_if<(cpp_df_qf_detail::is_floating_point_or_float128<OtherFloatingPointType>::value && ((cpp_df_qf_detail::ccmath::numeric_limits<OtherFloatingPointType>::digits10 * 2) < 16))>::type const*>
    friend constexpr void eval_exp(cpp_double_fp_backend<OtherFloatingPointType>& result, const cpp_double_fp_backend<OtherFloatingPointType>& x);