mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2025-10-30 20:40:28 -04:00
208 lines
6.1 KiB
C++
208 lines
6.1 KiB
C++
// 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]
|
|
|
|
|
|
|
|
*/
|
|
|
|
|