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First revision to docs.

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This commit is contained in:
Paul Bristow
2014-01-10 18:12:06 +00:00
parent 6299b68fe6
commit 56b4ae4425
3 changed files with 193 additions and 63 deletions
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92
example/bernoulli_example.cpp
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@@ -30,26 +30,22 @@
//SC_(-7.0921568627450980392156862745098039215686),
//SC_(54.9711779448621553884711779448621553884711),
int main()
{
//[bernoulli_example_1
/*`A simple example computes the value of `Bernoulli(2)` where the return type is `double`.
*/
try
{ // It is always wise to use try'n'catch blocks around Boost.Math function
// so that informative error messages will be displayed.
//[bernoulli_example_1
/*`A simple example computes the value of `Bernoulli(2)` where the return type
is `double`.
[hint All odd Bernoulli numbers (> 1) are zero, so the parameter value 2 computes B[sub 4]. ]
*/
{ // 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
/*`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 `Bernoulli(100)`
@@ -65,7 +61,7 @@ and also obtain much higher precision.
//[bernoulli_example_2
/*`We can compute and save all the float-precision Bernoulli numbers from one call.
*/
std::vector<float> bn; // Space for all the 32-bit `float` precision Bernoulli numbers.
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.
@@ -80,22 +76,24 @@ and also obtain much higher precision.
//] //[/bernoulli_example_2]
}
catch(const std::exception&)
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 than can be computed
/*`Of course, for any floating-point type, there is a maximum Bernoulli number that can be computed
before it overflows the exponent.
If we try to compute too high a Bernoulli number, an exception will be thrown,
*/
try{
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;
std::cout << boost::math::bernoulli_b2n<float>(33) << std::endl;
}
catch (std::exception ex)
{
@@ -103,11 +101,46 @@ and also obtain much higher precision.
}
/*`
and (provided 'try'n'catch' blocks are used) we will get a helpful error message.
and we will get a helpful error message (provided try'n'catch blocks are used).
*/
//] //[/bernoulli_example_3]
//[bernoulli_example_4
/*`Users can determine from `max_bernoulli_b2n<>::value`
the largest Bernoulli number you can evaluate for any type
(or safely pass to `unchecked_bernoulli_b2n<>`).
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()
@@ -117,7 +150,6 @@ and (provided 'try'n'catch' blocks are used) we will get a helpful error message
-3.6470772645191354362138308865549944904868234686191e+215
//] //[/bernoulli_output_1]
//[bernoulli_output_2
0 1
@@ -156,8 +188,22 @@ and (provided 'try'n'catch' blocks are used) we will get a helpful error message
//[bernoulli_output_3
Bernoulli number 66
Thrown Exception caught: Error in function boost::math::bernoulli_b2n<float>(n): Overflow evaluating function at 33
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]
*/