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Diffstat (limited to 'src/boost/libs/math/example/bernoulli_example.cpp')
| -rw-r--r-- | src/boost/libs/math/example/bernoulli_example.cpp | 207 |
1 files changed, 207 insertions, 0 deletions
diff --git a/src/boost/libs/math/example/bernoulli_example.cpp b/src/boost/libs/math/example/bernoulli_example.cpp new file mode 100644 index 000000000..5a2c58969 --- /dev/null +++ b/src/boost/libs/math/example/bernoulli_example.cpp @@ -0,0 +1,207 @@ +// 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] + + + +*/ + + |