test_rational.hpp

Boost provides free peer-reviewed portable C++ source libraries. We emphasize libraries that work

   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n2a, static_cast<T>(1.0f - 1.0f/64.0f)),
      static_cast<T>(0.3984375e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n2a, static_cast<T>(6.5)),
      static_cast<T>(0.95e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n2a, static_cast<T>(10247.25)),
      static_cast<T>(0.1025025e5L),
      tolerance);

   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2c, static_cast<T>(0.125), 2),
      static_cast<T>(0.3015625e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2c, static_cast<T>(0.25), 2),
      static_cast<T>(0.30625e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2c, static_cast<T>(0.75), 2),
      static_cast<T>(0.35625e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2c, static_cast<T>(1.0f - 1.0f/64.0f), 2),
      static_cast<T>(0.3968994140625e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2c, static_cast<T>(6.5f), 2),
      static_cast<T>(0.4525e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2c, static_cast<T>(10247.25f), 2),
      static_cast<T>(0.1050061355625e9L),
      tolerance);

   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2c, static_cast<T>(0.125)),
      static_cast<T>(0.3015625e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2c, static_cast<T>(0.25)),
      static_cast<T>(0.30625e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2c, static_cast<T>(0.75)),
      static_cast<T>(0.35625e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2c, static_cast<T>(1.0f - 1.0f/64.0f)),
      static_cast<T>(0.3968994140625e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2c, static_cast<T>(6.5f)),
      static_cast<T>(0.4525e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2c, static_cast<T>(10247.25f)),
      static_cast<T>(0.1050061355625e9L),
      tolerance);

   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2a, static_cast<T>(0.125)),
      static_cast<T>(0.3015625e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2a, static_cast<T>(0.25)),
      static_cast<T>(0.30625e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2a, static_cast<T>(0.75)),
      static_cast<T>(0.35625e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2a, static_cast<T>(1.0f - 1.0f/64.0f)),
      static_cast<T>(0.3968994140625e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2a, static_cast<T>(6.5f)),
      static_cast<T>(0.4525e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_even_polynomial(n2a, static_cast<T>(10247.25f)),
      static_cast<T>(0.1050061355625e9L),
      tolerance);

   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2c, static_cast<T>(0.125), 2),
      static_cast<T>(0.3125e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2c, static_cast<T>(0.25), 2),
      static_cast<T>(0.325e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2c, static_cast<T>(0.75), 2),
      static_cast<T>(0.375e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2c, static_cast<T>(1.0f - 1.0f/64.0f), 2),
      static_cast<T>(0.3984375e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2c, static_cast<T>(6.5f), 2),
      static_cast<T>(0.95e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2c, static_cast<T>(10247.25f), 2),
      static_cast<T>(0.1025025e5L),
      tolerance);

   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2c, static_cast<T>(0.125)),
      static_cast<T>(0.3125e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2c, static_cast<T>(0.25)),
      static_cast<T>(0.325e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2c, static_cast<T>(0.75)),
      static_cast<T>(0.375e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2c, static_cast<T>(1.0f - 1.0f/64.0f)),
      static_cast<T>(0.3984375e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2c, static_cast<T>(6.5f)),
      static_cast<T>(0.95e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2c, static_cast<T>(10247.25f)),
      static_cast<T>(0.1025025e5L),
      tolerance);

   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2a, static_cast<T>(0.125)),
      static_cast<T>(0.3125e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2a, static_cast<T>(0.25)),
      static_cast<T>(0.325e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2a, static_cast<T>(0.75)),
      static_cast<T>(0.375e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2a, static_cast<T>(1.0f - 1.0f/64.0f)),
      static_cast<T>(0.3984375e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2a, static_cast<T>(6.5f)),
      static_cast<T>(0.95e1L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_odd_polynomial(n2a, static_cast<T>(10247.25f)),
      static_cast<T>(0.1025025e5L),
      tolerance);

   //
   // Rational functions of order 1
   //
   static const U d2c[2] = { 5, 9 };
   static const boost::array<U, 2> d2a = { 5, 9 };
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2c, d2c, static_cast<T>(0.125), 2),
      static_cast<T>(0.5102040816326530612244897959183673469388e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2c, d2c, static_cast<T>(0.25), 2),
      static_cast<T>(0.4482758620689655172413793103448275862069e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2c, d2c, static_cast<T>(0.75), 2),
      static_cast<T>(0.3191489361702127659574468085106382978723e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2c, d2c, static_cast<T>(1.0f - 1.0f/64.0f), 2),
      static_cast<T>(0.2874859075535512965050732807215332581736e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2c, d2c, static_cast<T>(6.5f), 2),
      static_cast<T>(0.1496062992125984251968503937007874015748e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2c, d2c, static_cast<T>(10247.25f), 2),
      static_cast<T>(0.1111376148281068304596377002122405609873e0L),
      tolerance);

   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2c, d2c, static_cast<T>(0.125)),
      static_cast<T>(0.5102040816326530612244897959183673469388e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2c, d2c, static_cast<T>(0.25)),
      static_cast<T>(0.4482758620689655172413793103448275862069e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2c, d2c, static_cast<T>(0.75)),
      static_cast<T>(0.3191489361702127659574468085106382978723e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2c, d2c, static_cast<T>(1.0f - 1.0f/64.0f)),
      static_cast<T>(0.2874859075535512965050732807215332581736e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2c, d2c, static_cast<T>(6.5f)),
      static_cast<T>(0.1496062992125984251968503937007874015748e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2c, d2c, static_cast<T>(10247.25f)),
      static_cast<T>(0.1111376148281068304596377002122405609873e0L),
      tolerance);

   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2a, d2a, static_cast<T>(0.125)),
      static_cast<T>(0.5102040816326530612244897959183673469388e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2a, d2a, static_cast<T>(0.25)),
      static_cast<T>(0.4482758620689655172413793103448275862069e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2a, d2a, static_cast<T>(0.75)),
      static_cast<T>(0.3191489361702127659574468085106382978723e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2a, d2a, static_cast<T>(1.0f - 1.0f/64.0f)),
      static_cast<T>(0.2874859075535512965050732807215332581736e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2a, d2a, static_cast<T>(6.5f)),
      static_cast<T>(0.1496062992125984251968503937007874015748e0L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_rational(n2a, d2a, static_cast<T>(10247.25f)),
      static_cast<T>(0.1111376148281068304596377002122405609873e0L),
      tolerance);
}

template <class T, class U>
void do_test_spots2(T, U)
{
   //
   // Tolerance is 4 eps expressed as a persentage:
   //
   T tolerance = boost::math::tools::epsilon<T>() * 4 * 100;

   //
   // Polynomials of order 2
   //
   static const U n3c[3] = { 10, 6, 11 };
   static const boost::array<U, 3> n3a = { 10, 6, 11 };
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3c, static_cast<T>(0.125), 3),
      static_cast<T>(0.10921875e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3c, static_cast<T>(0.25), 3),
      static_cast<T>(0.121875e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3c, static_cast<T>(0.75), 3),
      static_cast<T>(0.206875e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3c, static_cast<T>(1.0f - 1.0f/64.0f), 3),
      static_cast<T>(0.26565185546875e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3c, static_cast<T>(6.5), 3),
      static_cast<T>(0.51375e3L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3c, static_cast<T>(10247.25), 3),
      static_cast<T>(0.11551289516875e10L),
      tolerance);

   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3c, static_cast<T>(0.125)),
      static_cast<T>(0.10921875e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3c, static_cast<T>(0.25)),
      static_cast<T>(0.121875e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3c, static_cast<T>(0.75)),
      static_cast<T>(0.206875e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3c, static_cast<T>(1.0f - 1.0f/64.0f)),
      static_cast<T>(0.26565185546875e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3c, static_cast<T>(6.5)),
      static_cast<T>(0.51375e3L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3c, static_cast<T>(10247.25)),
      static_cast<T>(0.11551289516875e10L),
      tolerance);

   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3a, static_cast<T>(0.125)),
      static_cast<T>(0.10921875e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3a, static_cast<T>(0.25)),
      static_cast<T>(0.121875e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3a, static_cast<T>(0.75)),
      static_cast<T>(0.206875e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3a, static_cast<T>(1.0f - 1.0f/64.0f)),
      static_cast<T>(0.26565185546875e2L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3a, static_cast<T>(6.5)),
      static_cast<T>(0.51375e3L),
      tolerance);
   BOOST_CHECK_CLOSE(
      boost::math::tools::evaluate_polynomial(n3a, static_cast<T>(10247.25)),
      static_cast<T>(0.11551289516875e10L),