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Changes to reflect new signatures of bessel zeros

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[SVN r82732]
This commit is contained in:
Paul A. Bristow
2013-02-04 18:02:37 +00:00
parent 8730f6099a
commit b6e135c144
2 changed files with 264 additions and 37 deletions
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38
example/numerical_derivative_example.cpp
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@@ -14,6 +14,7 @@
#include <boost/static_assert.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/math/special_functions/next.hpp> // for float_distance
//[numeric_derivative_example
/*`The following example shows how multiprecision calculations can be used to
@@ -101,16 +102,15 @@ typedef number<mp_backend> mp_type;
int main()
{
{
const double d =
derivative
( 1.5, // x = 3.2
std::ldexp (1., -9), // step size 2^-9 = see below for choice.
[](const double & x)->double // Function f(x).
{
return std::sqrt((x * x) - 1.) - std::acos(1. / x);
}
);
const double d =
derivative
( 1.5, // x = 3.2
std::ldexp (1., -9), // step size 2^-9 = see below for choice.
[](const double & x)->double // Function f(x).
{
return std::sqrt((x * x) - 1.) - std::acos(1. / x);
}
);
// The 'exactly right' result is [sqrt]5 / 3 = 0.74535599249992989880.
const double rel_error = (d - 0.74535599249992989880) / 0.74535599249992989880;
@@ -123,6 +123,10 @@ int main()
// Can compute an 'exact' value using multiprecision type.
std::cout << " expected : " << sqrt(static_cast<mp_type>(5))/3U << std::endl;
std::cout << " bit_error : " << static_cast<unsigned long>(bit_error) << std::endl;
std::cout.precision(6);
std::cout << "float_distance = " << boost::math::float_distance(0.74535599249992989880, d) << std::endl;
}
{ // Compute using multiprecision type with an extra 5 decimal digits of precision.
@@ -141,9 +145,16 @@ int main()
std::cout.precision (std::numeric_limits <double>::digits10); // All guaranteed decimal digits.
std::cout << std::showpoint ; // Ensure that any trailing zeros are shown too.
std::cout << " derivative : " << d << std::endl;
// Can compute an 'exact' value using multiprecision type.
std::cout << " expected : " << sqrt(static_cast<mp_type>(5))/3U << std::endl;
std::cout << " expected : " << 0.74535599249992989880
<< std::endl;
std::cout << " bit_error : " << static_cast<unsigned long>(bit_error) << std::endl;
std::cout.precision(6);
std::cout << "float_distance = " << boost::math::float_distance(0.74535599249992989880, d) << std::endl;
}
@@ -178,8 +189,6 @@ to an ill-conditioned calculation that suffers from precision loss. When the res
of the multiprecision calculation is converted to a built-in type such as double,
the entire precision of the result in double is preserved.
*/
/*
@@ -189,8 +198,11 @@ the entire precision of the result in double is preserved.
expected : 0.745355992499930
expected : 0.745355992499930
bit_error : 78
float_distance = 117.000
derivative : 0.745355992499930
expected : 0.745355992499930
expected : 0.745355992499930
bit_error : 0
float_distance = 0.000000
*/
*/