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- // Copyright Paul A. Bristow 2013.
- // Copyright Nakhar Agrawal 2013.
- // Copyright John Maddock 2013.
- // Copyright Christopher Kormanyos 2013.
- // Use, modification and distribution are subject to the
- // Boost Software License, Version 1.0. (See accompanying file
- // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
- #pragma warning (disable : 4100) // unreferenced formal parameter.
- #pragma warning (disable : 4127) // conditional expression is constant.
- //#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
- #include <boost/multiprecision/cpp_dec_float.hpp>
- #include <boost/math/special_functions/bernoulli.hpp>
- #include <iostream>
- /* First 50 from 2 to 100 inclusive: */
- /* TABLE[N[BernoulliB[n], 200], {n,2,100,2}] */
- //SC_(0.1666666666666666666666666666666666666666),
- //SC_(-0.0333333333333333333333333333333333333333),
- //SC_(0.0238095238095238095238095238095238095238),
- //SC_(-0.0333333333333333333333333333333333333333),
- //SC_(0.0757575757575757575757575757575757575757),
- //SC_(-0.2531135531135531135531135531135531135531),
- //SC_(1.1666666666666666666666666666666666666666),
- //SC_(-7.0921568627450980392156862745098039215686),
- //SC_(54.9711779448621553884711779448621553884711),
- int main()
- {
- //[bernoulli_example_1
- /*`A simple example computes the value of B[sub 4] where the return type is `double`,
- note that the argument to bernoulli_b2n is ['2] not ['4] since it computes B[sub 2N].
- */
- try
- { // It is always wise to use try'n'catch blocks around Boost.Math functions
- // so that any informative error messages can be displayed in the catch block.
- std::cout
- << std::setprecision(std::numeric_limits<double>::digits10)
- << boost::math::bernoulli_b2n<double>(2) << std::endl;
- /*`So B[sub 4] == -1/30 == -0.0333333333333333
- If we use Boost.Multiprecision and its 50 decimal digit floating-point type `cpp_dec_float_50`,
- we can calculate the value of much larger numbers like B[sub 200]
- and also obtain much higher precision.
- */
- std::cout
- << std::setprecision(std::numeric_limits<boost::multiprecision::cpp_dec_float_50>::digits10)
- << boost::math::bernoulli_b2n<boost::multiprecision::cpp_dec_float_50>(100) << std::endl;
-
- //] //[/bernoulli_example_1]
- //[bernoulli_example_2
- /*`We can compute and save all the float-precision Bernoulli numbers from one call.
- */
- std::vector<float> bn; // Space for 32-bit `float` precision Bernoulli numbers.
- // Start with Bernoulli number 0.
- boost::math::bernoulli_b2n<float>(0, 32, std::back_inserter(bn)); // Fill vector with even Bernoulli numbers.
- for(size_t i = 0; i < bn.size(); i++)
- { // Show vector of even Bernoulli numbers, showing all significant decimal digits.
- std::cout << std::setprecision(std::numeric_limits<float>::digits10)
- << i*2 << ' '
- << bn[i]
- << std::endl;
- }
- //] //[/bernoulli_example_2]
- }
- catch(const std::exception& ex)
- {
- std::cout << "Thrown Exception caught: " << ex.what() << std::endl;
- }
- //[bernoulli_example_3
- /*`Of course, for any floating-point type, there is a maximum Bernoulli number that can be computed
- before it overflows the exponent.
- By default policy, if we try to compute too high a Bernoulli number, an exception will be thrown.
- */
- try
- {
- std::cout
- << std::setprecision(std::numeric_limits<float>::digits10)
- << "Bernoulli number " << 33 * 2 <<std::endl;
- std::cout << boost::math::bernoulli_b2n<float>(33) << std::endl;
- }
- catch (std::exception ex)
- {
- std::cout << "Thrown Exception caught: " << ex.what() << std::endl;
- }
- /*`
- and we will get a helpful error message (provided try'n'catch blocks are used).
- */
- //] //[/bernoulli_example_3]
- //[bernoulli_example_4
- /*For example:
- */
- std::cout << "boost::math::max_bernoulli_b2n<float>::value = " << boost::math::max_bernoulli_b2n<float>::value << std::endl;
- std::cout << "Maximum Bernoulli number using float is " << boost::math::bernoulli_b2n<float>( boost::math::max_bernoulli_b2n<float>::value) << std::endl;
- std::cout << "boost::math::max_bernoulli_b2n<double>::value = " << boost::math::max_bernoulli_b2n<double>::value << std::endl;
- std::cout << "Maximum Bernoulli number using double is " << boost::math::bernoulli_b2n<double>( boost::math::max_bernoulli_b2n<double>::value) << std::endl;
- //] //[/bernoulli_example_4]
- //[tangent_example_1
- /*`We can compute and save a few Tangent numbers.
- */
- std::vector<float> tn; // Space for some `float` precision Tangent numbers.
- // Start with Bernoulli number 0.
- boost::math::tangent_t2n<float>(1, 6, std::back_inserter(tn)); // Fill vector with even Tangent numbers.
- for(size_t i = 0; i < tn.size(); i++)
- { // Show vector of even Tangent numbers, showing all significant decimal digits.
- std::cout << std::setprecision(std::numeric_limits<float>::digits10)
- << " "
- << tn[i];
- }
- std::cout << std::endl;
- //] [/tangent_example_1]
- // 1, 2, 16, 272, 7936, 353792, 22368256, 1903757312
- } // int main()
- /*
- //[bernoulli_output_1
- -3.6470772645191354362138308865549944904868234686191e+215
- //] //[/bernoulli_output_1]
- //[bernoulli_output_2
- 0 1
- 2 0.166667
- 4 -0.0333333
- 6 0.0238095
- 8 -0.0333333
- 10 0.0757576
- 12 -0.253114
- 14 1.16667
- 16 -7.09216
- 18 54.9712
- 20 -529.124
- 22 6192.12
- 24 -86580.3
- 26 1.42552e+006
- 28 -2.72982e+007
- 30 6.01581e+008
- 32 -1.51163e+010
- 34 4.29615e+011
- 36 -1.37117e+013
- 38 4.88332e+014
- 40 -1.92966e+016
- 42 8.41693e+017
- 44 -4.03381e+019
- 46 2.11507e+021
- 48 -1.20866e+023
- 50 7.50087e+024
- 52 -5.03878e+026
- 54 3.65288e+028
- 56 -2.84988e+030
- 58 2.38654e+032
- 60 -2.14e+034
- 62 2.0501e+036
- //] //[/bernoulli_output_2]
- //[bernoulli_output_3
- Bernoulli number 66
- Thrown Exception caught: Error in function boost::math::bernoulli_b2n<float>(n):
- Overflow evaluating function at 33
- //] //[/bernoulli_output_3]
- //[bernoulli_output_4
- boost::math::max_bernoulli_b2n<float>::value = 32
- Maximum Bernoulli number using float is -2.0938e+038
- boost::math::max_bernoulli_b2n<double>::value = 129
- Maximum Bernoulli number using double is 1.33528e+306
- //] //[/bernoulli_output_4]
-
- //[tangent_output_1
- 1 2 16 272 7936 353792
- //] [/tangent_output_1]
- */
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