libs/math/example/bernoulli_example.cpp
// 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] */