text: //===----------------------------------------------------------------------===//
  //
  // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
  // See https://llvm.org/LICENSE.txt for license information.
  // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
  //
  //===----------------------------------------------------------------------===//
  //
  // UNSUPPORTED: c++98, c++03, c++11, c++14, c++17
  // <numeric>
  
  // template <class _Float>
  // _Tp midpoint(_Float __a, _Float __b) noexcept
  //
  
  #include <numeric.hxx>
  #include <cassert.hxx>
  
  #include "test_macros.h"
  #include "fp_compare.h"
  
  //  Totally arbitrary picks for precision
  template <typename T>
  constexpr T fp_error_pct();
  
  template <>
  constexpr float fp_error_pct<float>() { return 1.0e-4f; }
  
  template <>
  constexpr double fp_error_pct<double>() { return 1.0e-12; }
  
  template <>
  constexpr long double fp_error_pct<long double>() { return 1.0e-13l; }
  
  
  template <typename T>
  void fp_test()
  {
      ASSERT_SAME_TYPE(T, decltype(std::midpoint(T(), T())));
      ASSERT_NOEXCEPT(             std::midpoint(T(), T()));
  
      constexpr T maxV = std::numeric_limits<T>::max();
      constexpr T minV = std::numeric_limits<T>::min();
      
  //  Things that can be compared exactly
      static_assert((std::midpoint(T(0), T(0))   == T(0)),   "");
      static_assert((std::midpoint(T(2), T(4))   == T(3)),   "");
      static_assert((std::midpoint(T(4), T(2))   == T(3)),   "");
      static_assert((std::midpoint(T(3), T(4))   == T(3.5)), "");
      static_assert((std::midpoint(T(0), T(0.4)) == T(0.2)), "");
  
  //  Things that can't be compared exactly
      constexpr T pct = fp_error_pct<T>();
      assert((fptest_close_pct(std::midpoint(T( 1.3), T(11.4)), T( 6.35),    pct)));
      assert((fptest_close_pct(std::midpoint(T(11.33), T(31.45)), T(21.39),  pct)));
      assert((fptest_close_pct(std::midpoint(T(-1.3), T(11.4)), T( 5.05),    pct)));
      assert((fptest_close_pct(std::midpoint(T(11.4), T(-1.3)), T( 5.05),    pct)));
      assert((fptest_close_pct(std::midpoint(T(0.1),  T(0.4)),  T(0.25),     pct)));
  
      assert((fptest_close_pct(std::midpoint(T(11.2345), T(14.5432)), T(12.88885),  pct)));
      
  //  From e to pi
      assert((fptest_close_pct(std::midpoint(T(2.71828182845904523536028747135266249775724709369995),
                                        T(3.14159265358979323846264338327950288419716939937510)),
                                        T(2.92993724102441923691146542731608269097720824653752),  pct)));
  
      assert((fptest_close_pct(std::midpoint(maxV, T(0)), maxV/2, pct)));
      assert((fptest_close_pct(std::midpoint(T(0), maxV), maxV/2, pct)));
      assert((fptest_close_pct(std::midpoint(minV, T(0)), minV/2, pct)));
      assert((fptest_close_pct(std::midpoint(T(0), minV), minV/2, pct)));
      assert((fptest_close_pct(std::midpoint(maxV, maxV), maxV,   pct)));
      assert((fptest_close_pct(std::midpoint(minV, minV), minV,   pct)));
      assert((fptest_close_pct(std::midpoint(maxV, minV), maxV/2, pct)));
      assert((fptest_close_pct(std::midpoint(minV, maxV), maxV/2, pct)));
  
  //  Near the min and the max
      assert((fptest_close_pct(std::midpoint(maxV*T(0.75), maxV*T(0.50)),  maxV*T(0.625), pct)));
      assert((fptest_close_pct(std::midpoint(maxV*T(0.50), maxV*T(0.75)),  maxV*T(0.625), pct)));
      assert((fptest_close_pct(std::midpoint(minV*T(2),    minV*T(8)),     minV*T(5),     pct)));
  
  //  Big numbers of different signs
      assert((fptest_close_pct(std::midpoint(maxV*T( 0.75),  maxV*T(-0.5)), maxV*T( 0.125), pct)));
      assert((fptest_close_pct(std::midpoint(maxV*T(-0.75),  maxV*T( 0.5)), maxV*T(-0.125), pct)));
  
  //  Denormalized values
  //  TODO
  
  //  Check two values "close to each other"
      T d1 = 3.14;
      T d0 = std::nextafter(d1, T(2));
      T d2 = std::nextafter(d1, T(5));
      assert(d0 < d1);  // sanity checking
      assert(d1 < d2);  // sanity checking
  
  #if defined(__PPC__) && __LONG_DOUBLE_128__ && !__LONG_DOUBLE_IEEE128__
  //	For 128 bit long double implemented as 2 doubles on PowerPC,
  //	nextafterl() of libm gives imprecise results which fails the
  //	midpoint() tests below. So skip the test for this case.
      if constexpr (sizeof(T) != 16)
  #endif
      {
  	//  Since there's nothing in between, the midpoint has to be one or the other
  		T res;
  		res = std::midpoint(d0, d1);
  		assert(res == d0 || res == d1);
  		assert(d0 <= res);
  		assert(res <= d1);
  		res = std::midpoint(d1, d0);
  		assert(res == d0 || res == d1);
  		assert(d0 <= res);
  		assert(res <= d1);
  
  		res = std::midpoint(d1, d2);
  		assert(res == d1 || res == d2);
  		assert(d1 <= res);
  		assert(res <= d2);
  		res = std::midpoint(d2, d1);
  		assert(res == d1 || res == d2);
  		assert(d1 <= res);
  		assert(res <= d2);
      }
  }
  
  
  int main (int, char**)
  {
      fp_test<float>();
      fp_test<double>();
      fp_test<long double>();
  
      return 0;
  }
  