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Fixed distributions so new accessors actually compile!

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Added elliptic integrals plus tests (no docs yet).
Added some refs to Remez docs. Added comment about Erlang=gamma distribution.


[SVN r3559]
This commit is contained in:
John Maddock
2006-12-23 10:30:16 +00:00
parent 3cd72e6865
commit eec6aaf0a0
52 changed files with 6583 additions and 145 deletions
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11
doc/distributions/gamma.qbk
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@@ -1,4 +1,4 @@
[section:gamma_dist Gamma Distribution]
[section:gamma_dist Gamma (and Erlang) Distribution]
``#include <boost/math/distributions/gamma.hpp>``
@@ -53,6 +53,15 @@ varies as the parameters vary:
[$../graphs/gamma_dist2.png]
The [*Erland Distribution] is the same as the Gamma, but with the shape parameter
an integer. It is often expressed using a /rate/ rather than a /scale/ as the
second parameter (remember that the rate is the reciprocal of the scale).
Internally the functions used to implement the Gamma Distribution are
already optimised for small-integer arguments, so in general there should
be no great loss of performance from using a Gamma Distribution rather than
a dedicated Erland Distribution.
[h4 Member Functions]
gamma_distribution(RealType shape, RealType scale = 1);

46
doc/remez.qbk
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@@ -318,6 +318,52 @@ and then re-minimise.
* Keep absissa values small: use a change of variable to keep the abscissa
over, say \[0, b\], for some smallish value /b/.
[h4 References]
The original references for the Remez Method and it's extension
to rational functions are unfortunately in Russian:
Remez, E.Ya., ['Fundamentals of numerical methods for Chebyshev approximations],
"Naukova Dumka", Kiev, 1969.
Remez, E.Ya., Gavrilyuk, V.T., ['Computer development of certain approaches
to the approximate construction of solutions of Chebyshev problems
nonlinearly depending on parameters], Ukr. Mat. Zh. 12 (1960), 324-338.
Gavrilyuk, V.T., ['Generalization of the first polynomial algorithm of
E.Ya.Remez for the problem of constructing rational-fractional
Chebyshev approximations], Ukr. Mat. Zh. 16 (1961), 575-585.
Some English language sources include:
Fraser, W., Hart, J.F., ['On the computation of rational approximations
to continuous functions], Comm. of the ACM 5 (1962), 401-403, 414.
Ralston, A., ['Rational Chebyshev approximation by Remes' algorithms],
Numer.Math. 7 (1965), no. 4, 322-330.
A. Ralston, ['Rational Chebyshev approximation, Mathematical
Methods for Digital Computers v. 2] (Ralston A., Wilf H., eds.),
Wiley, New York, 1967, pp. 264-284.
Hart, J.F. e.a., ['Computer approximations], Wiley, New York a.o., 1968.
Cody, W.J., Fraser, W., Hart, J.F., ['Rational Chebyshev approximation
using linear equations], Numer.Math. 12 (1968), 242-251.
Cody, W.J., ['A survey of practical rational and polynomial
approximation of functions], SIAM Review 12 (1970), no. 3, 400-423.
Barrar, R.B., Loeb, H.J., ['On the Remez algorithm for non-linear
families], Numer.Math. 15 (1970), 382-391.
Dunham, Ch.B., ['Convergence of the Fraser-Hart algorithm for rational
Chebyshev approximation], Math. Comp. 29 (1975), no. 132, 1078-1082.
G. L. Litvinov, ['Approximate construction of rational
approximations and the effect of error autocorrection],
Russian Journal of Mathematical Physics, vol.1, No. 3, 1994.
[endsect][/section:remez The Remez Method]

4
include/boost/math/distributions/binomial.hpp
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@@ -298,14 +298,14 @@ namespace boost
const std::pair<RealType, RealType> range(const binomial_distribution<RealType>& dist)
{ // Range of permissible values for random variable k.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(static_cast<RealType>(0), dist.trials());
return std::pair<RealType, RealType>(static_cast<RealType>(0), dist.trials());
}
template <class RealType>
const std::pair<RealType, RealType> support(const binomial_distribution<RealType>& dist)
{ // Range of supported values for random variable k.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
return const std::pair<RealType, RealType>(0, dist.trials());
return std::pair<RealType, RealType>(0, dist.trials());
}
template <class RealType>

4
include/boost/math/distributions/cauchy.hpp
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@@ -159,14 +159,14 @@ template <class RealType>
const std::pair<RealType, RealType> range(const cauchy_distribution<RealType>& dist)
{ // Range of permissible values for random variable x.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(-max_value(), +max_value()); // - to + infinity.
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + infinity.
}
template <class RealType>
const std::pair<RealType, RealType> support(const cauchy_distribution<RealType>& dist)
{ // Range of supported values for random variable x.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
return const std::pair<RealType, RealType>(-max_value(), +max_value()); // - to + infinity.
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + infinity.
}
template <class RealType>

4
include/boost/math/distributions/chi_squared.hpp
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@@ -56,14 +56,14 @@ template <class RealType>
const std::pair<RealType, RealType> range(const chi_squared_distribution<RealType>& dist)
{ // Range of permissible values for random variable x.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value()); // 0 to + infinity.
return std::pair<RealType, RealType>(0, max_value<RealType>()); // 0 to + infinity.
}
template <class RealType>
const std::pair<RealType, RealType> support(const chi_squared_distribution<RealType>& dist)
{ // Range of supported values for random variable x.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
return const std::pair<RealType, RealType>(0, +max_value()); // 0 to + infinity.
return std::pair<RealType, RealType>(0, max_value<RealType>()); // 0 to + infinity.
}
template <class RealType>

4
include/boost/math/distributions/exponential.hpp
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@@ -79,7 +79,7 @@ template <class RealType>
const std::pair<RealType, RealType> range(const exponential_distribution<RealType>& dist)
{ // Range of permissible values for random variable x.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(static_cast<RealType>(0), +max_value());
return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>());
}
template <class RealType>
@@ -87,7 +87,7 @@ const std::pair<RealType, RealType> support(const exponential_distribution<RealT
{ // Range of supported values for random variable x.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value());
return std::pair<RealType, RealType>(0, max_value<RealType>());
}
template <class RealType>

4
include/boost/math/distributions/extreme_value.hpp
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@@ -74,7 +74,7 @@ template <class RealType>
const std::pair<RealType, RealType> range(const extreme_value_distribution<RealType>& dist)
{ // Range of permissible values for random variable x.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(-max_value(), +max_value());
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
}
template <class RealType>
@@ -82,7 +82,7 @@ const std::pair<RealType, RealType> support(const extreme_value_distribution<Rea
{ // Range of supported values for random variable x.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(-max_value(), +max_value());
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
}

4
include/boost/math/distributions/fisher_f.hpp
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@@ -55,7 +55,7 @@ template <class RealType>
const std::pair<RealType, RealType> range(const fisher_f_distribution<RealType>& dist)
{ // Range of permissible values for random variable x.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value());
return std::pair<RealType, RealType>(0, max_value<RealType>());
}
template <class RealType>
@@ -63,7 +63,7 @@ const std::pair<RealType, RealType> support(const fisher_f_distribution<RealType
{ // Range of supported values for random variable x.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value());
return std::pair<RealType, RealType>(0, max_value<RealType>());
}
template <class RealType>

4
include/boost/math/distributions/gamma.hpp
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@@ -101,7 +101,7 @@ template <class RealType>
const std::pair<RealType, RealType> range(const gamma_distribution<RealType>& dist)
{ // Range of permissible values for random variable x.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value());
return std::pair<RealType, RealType>(0, max_value<RealType>());
}
template <class RealType>
@@ -109,7 +109,7 @@ const std::pair<RealType, RealType> support(const gamma_distribution<RealType>&
{ // Range of supported values for random variable x.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value());
return std::pair<RealType, RealType>(0, max_value<RealType>());
}
template <class RealType>

4
include/boost/math/distributions/lognormal.hpp
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@@ -76,7 +76,7 @@ template <class RealType>
const std::pair<RealType, RealType> range(const lognormal_distribution<RealType>& dist)
{ // Range of permissible values for random variable x.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value());
return std::pair<RealType, RealType>(0, max_value<RealType>());
}
template <class RealType>
@@ -84,7 +84,7 @@ const std::pair<RealType, RealType> support(const lognormal_distribution<RealTyp
{ // Range of supported values for random variable x.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value());
return std::pair<RealType, RealType>(0, max_value<RealType>());
}

4
include/boost/math/distributions/negative_binomial.hpp
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@@ -247,7 +247,7 @@ namespace boost
const std::pair<RealType, RealType> range(const negative_binomial_distribution<RealType>& dist)
{ // Range of permissible values for random variable k.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value()); // max_integer?
return std::pair<RealType, RealType>(0, max_value<RealType>()); // max_integer?
}
template <class RealType>
@@ -255,7 +255,7 @@ namespace boost
{ // Range of supported values for random variable k.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value()); // max_integer?
return std::pair<RealType, RealType>(0, max_value<RealType>()); // max_integer?
}
template <class RealType>

4
include/boost/math/distributions/normal.hpp
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@@ -52,7 +52,7 @@ template <class RealType>
const std::pair<RealType, RealType> range(const normal_distribution<RealType>& dist)
{ // Range of permissible values for random variable x.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(-max_value(), +max_value()); // - to + infinity.
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + infinity.
}
template <class RealType>
@@ -60,7 +60,7 @@ const std::pair<RealType, RealType> support(const normal_distribution<RealType>&
{ // Range of supported values for random variable x.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(-max_value(), +max_value()); // - to + infinity.
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + infinity.
}

4
include/boost/math/distributions/poisson.hpp
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@@ -180,7 +180,7 @@ namespace boost
const std::pair<RealType, RealType> range(const poisson_distribution<RealType>& dist)
{ // Range of permissible values for random variable k.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value()); // Max integer?
return std::pair<RealType, RealType>(0, max_value<RealType>()); // Max integer?
}
template <class RealType>
@@ -188,7 +188,7 @@ namespace boost
{ // Range of supported values for random variable k.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value());
return std::pair<RealType, RealType>(0, max_value<RealType>());
}
template <class RealType>

4
include/boost/math/distributions/students_t.hpp
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@@ -62,7 +62,7 @@ template <class RealType>
const std::pair<RealType, RealType> range(const students_t_distribution<RealType>& dist)
{ // Range of permissible values for random variable x.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(-max_value(), +max_value());
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
}
template <class RealType>
@@ -70,7 +70,7 @@ const std::pair<RealType, RealType> support(const students_t_distribution<RealTy
{ // Range of supported values for random variable x.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(-max_value(), +max_value());
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>());
}
template <class RealType>

4
include/boost/math/distributions/uniform.hpp
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@@ -141,7 +141,7 @@ namespace boost{ namespace math
const std::pair<RealType, RealType> range(const uniform_distribution<RealType>& dist)
{ // Range of permissible values for random variable x.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(-max_value(), +max_value()); // - to + infinity
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + infinity
}
template <class RealType>
@@ -149,7 +149,7 @@ namespace boost{ namespace math
{ // Range of supported values for random variable x.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(dist.lower(), dist.upper());
return std::pair<RealType, RealType>(dist.lower(), dist.upper());
}
template <class RealType>

4
include/boost/math/distributions/weibull.hpp
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@@ -100,7 +100,7 @@ template <class RealType>
const std::pair<RealType, RealType> range(const weibull_distribution<RealType>& dist)
{ // Range of permissible values for random variable x.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value());
return std::pair<RealType, RealType>(0, max_value<RealType>());
}
template <class RealType>
@@ -108,7 +108,7 @@ const std::pair<RealType, RealType> support(const weibull_distribution<RealType>
{ // Range of supported values for random variable x.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
using boost::math::tools::max_value;
return const std::pair<RealType, RealType>(0, +max_value());
return std::pair<RealType, RealType>(0, max_value<RealType>());
}
template <class RealType>

135
include/boost/math/special_functions/ellint_1.hpp Normal file
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@@ -0,0 +1,135 @@
// Copyright (c) 2006 Xiaogang Zhang
// Copyright (c) 2006 John Maddock
// 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)
//
// History:
// XZ wrote the original of this file as part of the Google
// Summer of Code 2006. JM modified it to fit into the
// Boost.Math conceptual framework better, and to ensure
// that the code continues to work no matter how many digits
// type T has.
#ifndef BOOST_MATH_ELLINT_1_HPP
#define BOOST_MATH_ELLINT_1_HPP
#include <boost/math/special_functions/ellint_rf.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/math/tools/error_handling.hpp>
#include <boost/math/tools/evaluation_type.hpp>
// Elliptic integrals (complete and incomplete) of the first kind
// Carlson, Numerische Mathematik, vol 33, 1 (1979)
namespace boost { namespace math {
namespace detail{
// Elliptic integral (Legendre form) of the first kind
template <typename T>
T ellint_f_imp(T phi, T k)
{
using namespace std;
using namespace boost::math::tools;
using namespace boost::math::constants;
if (abs(k) > 1)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Got k = %1%, function requires |k| <= 1", k);
}
bool invert = false;
if(phi < 0)
{
phi = fabs(phi);
invert = true;
}
T result;
if(phi >= tools::max_value<T>())
{
// Need to handle infinity as a special case:
result = tools::overflow_error<T>(BOOST_CURRENT_FUNCTION, 0);
}
else if(phi > 1 / tools::epsilon<T>())
{
// Phi is so large that phi%pi is necessarily zero (or garbage),
// just return the second part of the duplication formula:
result = 2 * phi * ellint_k_imp(k) / constants::pi<T>();
}
else
{
// Carlson's algorithm works only for |phi| <= pi/2,
// use the integrand's periodicity to normalize phi
//
// Xiaogang's original code used a cast to long long here
// but that fails if T has more digits than a long long,
// so rewritten to use fmod instead:
//
T rphi = fmod(phi, constants::pi<T>() / 2);
T m = 2 * (phi - rphi) / constants::pi<T>();
int s = 1;
if(fmod(m, T(2)) > 0.5)
{
m += 1;
s = -1;
rphi = constants::pi<T>() / 2 - rphi;
}
T sinp = sin(rphi);
T cosp = cos(rphi);
result = s * sinp * ellint_rf_imp(cosp * cosp, 1 - k * k * sinp * sinp, T(1));
if(m != 0)
result += m * ellint_k_imp(k);
}
return invert ? -result : result;
}
// Complete elliptic integral (Legendre form) of the first kind
template <typename T>
T ellint_k_imp(T k)
{
using namespace std;
using namespace boost::math::tools;
if (abs(k) > 1)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Got k = %1%, function requires |k| <= 1", k);
}
if (abs(k) == 1)
{
return overflow_error<T>(BOOST_CURRENT_FUNCTION, 0);
}
T x = 0;
T y = 1 - k * k;
T z = 1;
T value = ellint_rf_imp(x, y, z);
return value;
}
}
// Complete elliptic integral (Legendre form) of the first kind
template <typename T>
inline T ellint_1(T k)
{
typedef typename tools::evaluation<typename remove_cv<T>::type>::type value_type;
return tools::checked_narrowing_cast<typename remove_cv<T>::type>(detail::ellint_k_imp(static_cast<value_type>(k)), BOOST_CURRENT_FUNCTION);
}
// Elliptic integral (Legendre form) of the first kind
template <typename T>
inline T ellint_1(T phi, T k)
{
typedef typename tools::evaluation<typename remove_cv<T>::type>::type value_type;
return tools::checked_narrowing_cast<typename remove_cv<T>::type>(detail::ellint_f_imp(static_cast<value_type>(phi), static_cast<value_type>(k)), BOOST_CURRENT_FUNCTION);
}
}} // namespaces
#endif // BOOST_MATH_ELLINT_1_HPP

136
include/boost/math/special_functions/ellint_2.hpp Normal file
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@@ -0,0 +1,136 @@
// Copyright (c) 2006 Xiaogang Zhang
// Copyright (c) 2006 John Maddock
// 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)
//
// History:
// XZ wrote the original of this file as part of the Google
// Summer of Code 2006. JM modified it to fit into the
// Boost.Math conceptual framework better, and to ensure
// that the code continues to work no matter how many digits
// type T has.
#ifndef BOOST_MATH_ELLINT_2_HPP
#define BOOST_MATH_ELLINT_2_HPP
#include <boost/math/special_functions/ellint_rf.hpp>
#include <boost/math/special_functions/ellint_rd.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/math/tools/error_handling.hpp>
#include <boost/math/tools/evaluation_type.hpp>
// Elliptic integrals (complete and incomplete) of the second kind
// Carlson, Numerische Mathematik, vol 33, 1 (1979)
namespace boost { namespace math { namespace detail{
template <typename T>
T ellint_e_imp(T k);
// Elliptic integral (Legendre form) of the second kind
template <typename T>
T ellint_e_imp(T phi, T k)
{
using namespace std;
using namespace boost::math::tools;
using namespace boost::math::constants;
bool invert = false;
if(phi < 0)
{
phi = fabs(phi);
invert = true;
}
T result;
if(phi >= tools::max_value<T>())
{
// Need to handle infinity as a special case:
result = tools::overflow_error<T>(BOOST_CURRENT_FUNCTION, 0);
}
else if(phi > 1 / tools::epsilon<T>())
{
// Phi is so large that phi%pi is necessarily zero (or garbage),
// just return the second part of the duplication formula:
result = 2 * phi * ellint_e_imp(k) / constants::pi<T>();
}
else
{
// Carlson's algorithm works only for |phi| <= pi/2,
// use the integrand's periodicity to normalize phi
//
// Xiaogang's original code used a cast to long long here
// but that fails if T has more digits than a long long,
// so rewritten to use fmod instead:
//
T rphi = fmod(phi, constants::pi<T>() / 2);
T m = 2 * (phi - rphi) / constants::pi<T>();
int s = 1;
if(fmod(m, T(2)) > 0.5)
{
m += 1;
s = -1;
rphi = constants::pi<T>() / 2 - rphi;
}
T sinp = sin(rphi);
T cosp = cos(rphi);
T x = cosp * cosp;
T t = k * k * sinp * sinp;
T y = 1 - t;
T z = 1;
result = s * sinp * (ellint_rf_imp(x, y, z) - t * ellint_rd_imp(x, y, z) / 3);
if(m != 0)
result += m * ellint_e_imp(k);
}
return invert ? -result : result;
}
// Complete elliptic integral (Legendre form) of the second kind
template <typename T>
T ellint_e_imp(T k)
{
using namespace std;
using namespace boost::math::tools;
if (abs(k) > 1)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Got k = %1%, function requires |k| <= 1", k);
}
if (abs(k) == 1)
{
return static_cast<T>(1);
}
T x = 0;
T t = k * k;
T y = 1 - t;
T z = 1;
T value = ellint_rf_imp(x, y, z) - t * ellint_rd_imp(x, y, z) / 3;
return value;
}
} // detail
// Complete elliptic integral (Legendre form) of the second kind
template <typename T>
inline T ellint_2(T k)
{
typedef typename tools::evaluation<typename remove_cv<T>::type>::type value_type;
return tools::checked_narrowing_cast<typename remove_cv<T>::type>(detail::ellint_e_imp(static_cast<value_type>(k)), BOOST_CURRENT_FUNCTION);
}
// Elliptic integral (Legendre form) of the second kind
template <typename T>
inline T ellint_2(T phi, T k)
{
typedef typename tools::evaluation<typename remove_cv<T>::type>::type value_type;
return tools::checked_narrowing_cast<typename remove_cv<T>::type>(detail::ellint_e_imp(static_cast<value_type>(phi), static_cast<value_type>(k)), BOOST_CURRENT_FUNCTION);
}
}} // namespaces
#endif // BOOST_MATH_ELLINT_2_HPP

275
include/boost/math/special_functions/ellint_3.hpp Normal file
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@@ -0,0 +1,275 @@
// Copyright (c) 2006 Xiaogang Zhang
// 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)
//
// History:
// XZ wrote the original of this file as part of the Google
// Summer of Code 2006. JM modified it to fit into the
// Boost.Math conceptual framework better, and to correctly
// handle the various corner cases.
//
#ifndef BOOST_MATH_ELLINT_3_HPP
#define BOOST_MATH_ELLINT_3_HPP
#include <boost/math/special_functions/ellint_rf.hpp>
#include <boost/math/special_functions/ellint_rj.hpp>
#include <boost/math/special_functions/ellint_1.hpp>
#include <boost/math/special_functions/ellint_2.hpp>
#include <boost/math/special_functions/log1p.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/math/tools/error_handling.hpp>
// Elliptic integrals (complete and incomplete) of the third kind
// Carlson, Numerische Mathematik, vol 33, 1 (1979)
namespace boost { namespace math { namespace detail{
template <typename T>
T ellint_pi_imp(T v, T k, T vc);
// Elliptic integral (Legendre form) of the third kind
template <typename T>
T ellint_pi_imp(T v, T phi, T k, T vc)
{
// Note vc = 1-v presumably without cancellation error.
T value, x, y, z, p, t;
using namespace std;
using namespace boost::math::tools;
using namespace boost::math::constants;
if (abs(k) > 1)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Got k = %1%, function requires |k| <= 1", k);
}
T sphi = sin(fabs(phi));
if(v > 1 / (sphi * sphi))
{
// Complex result is a domain error:
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Got v = %1%, but result is complex for v > 1 / sin^2(phi)", v);
}
// Special cases first:
if(v == 0)
{
// A&S 17.7.18 & 19
return (k == 0) ? phi : ellint_f_imp(phi, k);
}
if(phi == constants::pi<T>() / 2)
{
// Have to filter this case out before the next
// special case, otherwise we might get an infinity from
// tan(phi).
// Also note that since we can't represent PI/2 exactly
// in a T, this is a bit of a guess as to the users true
// intent...
//
return ellint_pi_imp(v, k, vc);
}
if(k == 0)
{
// A&S 17.7.20:
if(v < 1)
{
T vcr = sqrt(vc);
return atan(vcr * tan(phi)) / vcr;
}
else if(v == 1)
{
return tan(phi);
}
else
{
// v > 1:
T vcr = sqrt(-vc);
T arg = vcr * tan(phi);
return (boost::math::log1p(arg) - boost::math::log1p(-arg)) / (2 * vcr);
}
}
if(v < 0)
{
//
// If we don't shift to 0 <= v <= 1 we get
// cancellation errors later on. Use
// A&S 17.7.15/16 to shift to v > 0:
//
T k2 = k * k;
T N = (k2 - v) / (1 - v);
T Nm1 = (1 - k2) / (1 - v);
T p2 = sqrt(-v * (k2 - v) / (1 - v));
T delta = sqrt(1 - k2 * sphi * sphi);
T result = ellint_pi_imp(N, phi, k, Nm1);
result *= sqrt(Nm1 * (1 - k2 / N));
result += ellint_f_imp(phi, k) * k2 / p2;
result += atan((p2/2) * sin(2 * phi) / delta);
result /= sqrt((1 - v) * (1 - k2 / v));
return result;
}
#if 0 // disabled but retained for future reference: see below.
if(v > 1)
{
//
// If v > 1 we can use the identity in A&S 17.7.7/8
// to shift to 0 <= v <= 1. Unfortunately this
// identity appears only to function correctly when
// 0 <= phi <= PI/2, but it's when phi is outside that
// range that we really need it: That's when
// Carlson's formula fails, and the periodicity
// reduction used below on phi doesn't work when v > 1.
// So we're stuck... the code is archived here in case
// some bright spart can figure out the fix.
//
T k2 = k * k;
T N = k2 / v;
T Nm1 = (v - k2) / v;
T p1 = sqrt((-vc) * (1 - k2 / v));
T delta = sqrt(1 - k2 * sphi * sphi);
T result = -ellint_pi_imp(N, phi, k, Nm1);
result += ellint_f_imp(phi, k);
result += log((delta + p1 * tan(phi)) / (delta - p1 * tan(phi))) / (2 * p1);
return result;
}
#endif
// Carlson's algorithm works only for |phi| <= pi/2,
// use the integrand's periodicity to normalize phi
//
// Xiaogang's original code used a cast to long long here
// but that fails if T has more digits than a long long,
// so rewritten to use fmod instead:
//
if(fabs(phi) > 1 / tools::epsilon<T>())
{
if(v > 1)
return tools::domain_error<T>(
BOOST_CURRENT_FUNCTION,
"Got v = %1%, but this is only supported for 0 <= phi <= pi/2", v);
//
// Phi is so large that phi%pi is necessarily zero (or garbage),
// just return the second part of the duplication formula:
//
value = 2 * fabs(phi) * ellint_pi_imp(v, k, vc) / constants::pi<T>();
}
else
{
T rphi = fmod(fabs(phi), constants::pi<T>() / 2);
T m = 2 * (fabs(phi) - rphi) / constants::pi<T>();
int sign = 1;
if(fmod(m, T(2)) > 0.5)
{
m += 1;
sign = -1;
rphi = constants::pi<T>() / 2 - rphi;
}
if((m > 0) && (v > 1))
return tools::domain_error<T>(
BOOST_CURRENT_FUNCTION,
"Got v = %1%, but this is only supported for 0 <= phi <= pi/2", v);
T sinp = sin(rphi);
T cosp = cos(rphi);
x = cosp * cosp;
t = sinp * sinp;
y = 1 - k * k * t;
z = 1;
if(v * t < 0.5)
p = 1 - v * t;
else
p = x + vc * t;
value = sign * sinp * (ellint_rf_imp(x, y, z) + v * t * ellint_rj_imp(x, y, z, p) / 3);
if(m > 0)
value += m * ellint_pi_imp(v, k, vc);
}
if (phi < 0)
{
value = -value; // odd function
}
return value;
}
// Complete elliptic integral (Legendre form) of the third kind
template <typename T>
T ellint_pi_imp(T v, T k, T vc)
{
// Note arg vc = 1-v, possibly without cancellation errors
using namespace std;
using namespace boost::math::tools;
if (abs(k) >= 1)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Got k = %1%, function requires |k| <= 1", k);
}
if(vc <= 0)
{
// Result is complex:
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Got v = %1%, function requires v < 1", v);
}
if(v == 0)
{
return (k == 0) ? boost::math::constants::pi<T>() / 2 : ellint_k_imp(k);
}
if(v < 0)
{
T k2 = k * k;
T N = (k2 - v) / (1 - v);
T Nm1 = (1 - k2) / (1 - v);
T p2 = sqrt(-v * (k2 - v) / (1 - v));
T result = boost::math::detail::ellint_pi_imp(N, k, Nm1);
result *= sqrt(Nm1 * (1 - k2 / N));
result += ellint_k_imp(k) * k2 / p2;
result /= sqrt((1 - v) * (1 - k2 / v));
return result;
}
T x = 0;
T y = 1 - k * k;
T z = 1;
T p = vc;
T value = ellint_rf_imp(x, y, z) + v * ellint_rj_imp(x, y, z, p) / 3;
return value;
}
} // namespace detail
template <typename T>
inline T ellint_3(T v, T phi, T k)
{
typedef typename tools::evaluation<typename remove_cv<T>::type>::type value_type;
return tools::checked_narrowing_cast<typename remove_cv<T>::type>(
detail::ellint_pi_imp(
static_cast<value_type>(v),
static_cast<value_type>(phi),
static_cast<value_type>(k),
static_cast<value_type>(1-v)), BOOST_CURRENT_FUNCTION);
}
template <typename T>
inline T ellint_3(T v, T k)
{
typedef typename tools::evaluation<typename remove_cv<T>::type>::type value_type;
return tools::checked_narrowing_cast<typename remove_cv<T>::type>(
detail::ellint_pi_imp(
static_cast<value_type>(v),
static_cast<value_type>(k),
static_cast<value_type>(1-v)), BOOST_CURRENT_FUNCTION);
}
}} // namespaces
#endif // BOOST_MATH_ELLINT_3_HPP

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// Copyright (c) 2006 Xiaogang Zhang
// 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)
//
// History:
// XZ wrote the original of this file as part of the Google
// Summer of Code 2006. JM modified it to fit into the
// Boost.Math conceptual framework better, and to correctly
// handle the y < 0 case.
//
#ifndef BOOST_MATH_ELLINT_RC_HPP
#define BOOST_MATH_ELLINT_RC_HPP
#include <boost/math/tools/error_handling.hpp>
#include <boost/math/tools/evaluation_type.hpp>
// Carlson's degenerate elliptic integral
// R_C(x, y) = R_F(x, y, y) = 0.5 * \int_{0}^{\infty} (t+x)^{-1/2} (t+y)^{-1} dt
// Carlson, Numerische Mathematik, vol 33, 1 (1979)
namespace boost { namespace math { namespace detail{
template <typename T>
T ellint_rc_imp(T x, T y)
{
T value, S, u, lambda, tolerance, prefix;
int k;
using namespace std;
using namespace boost::math::tools;
if(x < 0)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Argument x must be non-negative but got %1%", x);
}
if(y == 0)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Argument y must not be zero but got %1%", y);
}
// error scales as the 6th power of tolerance
tolerance = pow(4 * tools::epsilon<T>(), T(1) / 6);
// for y < 0, the integral is singular, return Cauchy principal value
if (y < 0)
{
prefix = sqrt(x / (x - y));
x = x - y;
y = -y;
}
else
prefix = 1;
// duplication
for (k = 1; k < BOOST_MATH_MAX_ITER; k++)
{
u = (x + y + y) / 3;
S = y / u - 1; // 1 - x / u = 2 * S
if (2 * abs(S) < tolerance)
break;
T sx = sqrt(x);
T sy = sqrt(y);
lambda = 2 * sx * sy + y;
x = (x + lambda) / 4;
y = (y + lambda) / 4;
}
// Check to see if we gave up too soon:
tools::check_series_iterations(BOOST_CURRENT_FUNCTION, k);
// Taylor series expansion to the 5th order
value = (1 + S * S * (T(3) / 10 + S * (T(1) / 7 + S * (T(3) / 8 + S * T(9) / 22)))) / sqrt(u);
return value * prefix;
}
} // namespace detail
template <typename T>
inline T ellint_rc(T x, T y)
{
typedef typename tools::evaluation<typename remove_cv<T>::type>::type value_type;
return tools::checked_narrowing_cast<typename remove_cv<T>::type>(
detail::ellint_rc_imp(
static_cast<value_type>(x),
static_cast<value_type>(y)), BOOST_CURRENT_FUNCTION);
}
}} // namespaces
#endif // BOOST_MATH_ELLINT_RC_HPP

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// Copyright (c) 2006 Xiaogang Zhang
// 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)
//
// History:
// XZ wrote the original of this file as part of the Google
// Summer of Code 2006. JM modified it slightly to fit into the
// Boost.Math conceptual framework better.
#ifndef BOOST_MATH_ELLINT_RD_HPP
#define BOOST_MATH_ELLINT_RD_HPP
#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/math/tools/config.hpp>
#include <boost/math/tools/error_handling.hpp>
#include <boost/math/tools/evaluation_type.hpp>
// Carlson's elliptic integral of the second kind
// R_D(x, y, z) = R_J(x, y, z, z) = 1.5 * \int_{0}^{\infty} [(t+x)(t+y)]^{-1/2} (t+z)^{-3/2} dt
// Carlson, Numerische Mathematik, vol 33, 1 (1979)
namespace boost { namespace math { namespace detail{
template <typename T>
T ellint_rd_imp(T x, T y, T z)
{
T value, u, lambda, sigma, factor, tolerance;
T X, Y, Z, EA, EB, EC, ED, EE, S1, S2;
int k;
using namespace std;
using namespace boost::math::tools;
if (x < 0)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Argument x must be >= 0, but got %1%", x);
}
if (y < 0)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Argument y must be >= 0, but got %1%", y);
}
if (z <= 0)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Argument z must be > 0, but got %1%", z);
}
if (x + y == 0)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"At most one argument can be zero, but got, x + y = %1%", x+y);
}
// error scales as the 6th power of tolerance
tolerance = pow(tools::epsilon<T>() / 3, T(1)/6);
// duplication
sigma = 0;
factor = 1;
for (k = 1; k < BOOST_MATH_MAX_ITER; k++)
{
u = (x + y + z + z + z) / 5;
X = (u - x) / u;
Y = (u - y) / u;
Z = (u - z) / u;
if ((tools::max)(abs(X), abs(Y), abs(Z)) < tolerance)
break;
T sx = sqrt(x);
T sy = sqrt(y);
T sz = sqrt(z);
lambda = sy * (sx + sz) + sz * sx; //sqrt(x * y) + sqrt(y * z) + sqrt(z * x);
sigma += factor / (sz * (z + lambda));
factor /= 4;
x = (x + lambda) / 4;
y = (y + lambda) / 4;
z = (z + lambda) / 4;
}
// Check to see if we gave up too soon:
tools::check_series_iterations(BOOST_CURRENT_FUNCTION, k);
// Taylor series expansion to the 5th order
EA = X * Y;
EB = Z * Z;
EC = EA - EB;
ED = EA - 6 * EB;
EE = ED + EC + EC;
S1 = ED * (ED * T(9) / 88 - Z * EE * T(9) / 52 - T(3) / 14);
S2 = Z * (EE / 6 + Z * (-EC * T(9) / 22 + Z * EA * T(3) / 26));
value = 3 * sigma + factor * (1 + S1 + S2) / (u * sqrt(u));
return value;
}
} // namespace detail
template <typename T>
inline T ellint_rd(T x, T y, T z)
{
typedef typename tools::evaluation<typename remove_cv<T>::type>::type value_type;
return tools::checked_narrowing_cast<typename remove_cv<T>::type>(
detail::ellint_rd_imp(
static_cast<value_type>(x),
static_cast<value_type>(y),
static_cast<value_type>(z)), BOOST_CURRENT_FUNCTION);
}
}} // namespaces
#endif // BOOST_MATH_ELLINT_RD_HPP

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// Copyright (c) 2006 Xiaogang Zhang
// 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)
//
// History:
// XZ wrote the original of this file as part of the Google
// Summer of Code 2006. JM modified it to fit into the
// Boost.Math conceptual framework better, and to handle
// types longer than 80-bit reals.
//
#ifndef BOOST_MATH_ELLINT_RF_HPP
#define BOOST_MATH_ELLINT_RF_HPP
#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/math/tools/config.hpp>
#include <boost/math/tools/error_handling.hpp>
#include <boost/math/tools/evaluation_type.hpp>
// Carlson's elliptic integral of the first kind
// R_F(x, y, z) = 0.5 * \int_{0}^{\infty} [(t+x)(t+y)(t+z)]^{-1/2} dt
// Carlson, Numerische Mathematik, vol 33, 1 (1979)
namespace boost { namespace math { namespace detail{
template <typename T>
T ellint_rf_imp(T x, T y, T z)
{
T value, X, Y, Z, E2, E3, u, lambda, tolerance;
int k;
using namespace std;
using namespace boost::math::tools;
if (x < 0 || y < 0 || z < 0)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"domain error, all arguments must be non-negative, "
"only sensible result is %1%.",
std::numeric_limits<T>::quiet_NaN());
}
if (x + y == 0 || y + z == 0 || z + x == 0)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"domain error, at most one argument can be zero, "
"only sensible result is %1%.",
std::numeric_limits<T>::quiet_NaN());
}
// Carlson scales error as the 6th power of tolerance,
// but this seems not to work for types larger than
// 80-bit reals, this heuristic seems to work OK:
if(tools::digits<T>() > 64)
{
tolerance = pow(tools::epsilon<T>(), T(1)/4.25f);
}
else
{
tolerance = pow(4*tools::epsilon<T>(), T(1)/6);
}
// duplication
for (k = 1; k < BOOST_MATH_MAX_ITER; k++)
{
u = (x + y + z) / 3;
X = (u - x) / u;
Y = (u - y) / u;
Z = (u - z) / u;
// Termination condition:
if ((tools::max)(abs(X), abs(Y), abs(Z)) < tolerance)
break;
T sx = sqrt(x);
T sy = sqrt(y);
T sz = sqrt(z);
lambda = sy * (sx + sz) + sz * sx;
x = (x + lambda) / 4;
y = (y + lambda) / 4;
z = (z + lambda) / 4;
}
// Check to see if we gave up too soon:
tools::check_series_iterations(BOOST_CURRENT_FUNCTION, k);
// Taylor series expansion to the 5th order
E2 = X * Y - Z * Z;
E3 = X * Y * Z;
value = (1 + E2*(E2/24 - E3*T(3)/44 - T(0.1)) + E3/14) / sqrt(u);
return value;
}
} // namespace detail
template <typename T>
inline T ellint_rf(T x, T y, T z)
{
typedef typename tools::evaluation<typename remove_cv<T>::type>::type value_type;
return tools::checked_narrowing_cast<typename remove_cv<T>::type>(
detail::ellint_rf_imp(
static_cast<value_type>(x),
static_cast<value_type>(y),
static_cast<value_type>(z)), BOOST_CURRENT_FUNCTION);
}
}} // namespaces
#endif // BOOST_MATH_ELLINT_RF_HPP

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// Copyright (c) 2006 Xiaogang Zhang
// 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)
//
// History:
// XZ wrote the original of this file as part of the Google
// Summer of Code 2006. JM modified it to fit into the
// Boost.Math conceptual framework better, and to correctly
// handle the p < 0 case.
//
#ifndef BOOST_MATH_ELLINT_RJ_HPP
#define BOOST_MATH_ELLINT_RJ_HPP
#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/math/tools/config.hpp>
#include <boost/math/tools/error_handling.hpp>
#include <boost/math/tools/evaluation_type.hpp>
#include <boost/math/special_functions/ellint_rc.hpp>
// Carlson's elliptic integral of the third kind
// R_J(x, y, z, p) = 1.5 * \int_{0}^{\infty} (t+p)^{-1} [(t+x)(t+y)(t+z)]^{-1/2} dt
// Carlson, Numerische Mathematik, vol 33, 1 (1979)
namespace boost { namespace math { namespace detail{
template <typename T>
T ellint_rj_imp(T x, T y, T z, T p)
{
T value, u, lambda, alpha, beta, sigma, factor, tolerance;
T X, Y, Z, P, EA, EB, EC, E2, E3, S1, S2, S3;
int k;
using namespace std;
using namespace boost::math::tools;
if (x < 0)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Argument x must be non-negative, but got x = %1%", x);
}
if(y < 0)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Argument y must be non-negative, but got y = %1%", y);
}
if(z < 0)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Argument z must be non-negative, but got z = %1%", z);
}
if(p == 0)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"Argument p must not be zero, but got p = %1%", p);
}
if (x + y == 0 || y + z == 0 || z + x == 0)
{
return domain_error<T>(BOOST_CURRENT_FUNCTION,
"At most one argument can be zero, "
"only possible result is %1%.", std::numeric_limits<T>::quiet_NaN());
}
// error scales as the 6th power of tolerance
tolerance = pow(T(1) * tools::epsilon<T>() / 3, T(1) / 6);
// for p < 0, the integral is singular, return Cauchy principal value
if (p < 0)
{
T q = -p;
T pmy = (z - y) * (y - x) / (y + q); // p - y
if(pmy < 0)
{
//
// TODO, FIXME if you can.... (JM Dec. 2006)
//
// The logic breaks down here, we can go into
// an infinite recursion unless we bail out right away!!
//
// This may be fixable by permuting x, y, and z, but may not
// be worth the hassle, fix this if you care about this use case!
//
return tools::domain_error<T>(
BOOST_CURRENT_FUNCTION,
"Unable to compute Cauchy principle value, p had the value %1% "
"and (z-y)(y-x) was negative. Identity formula could not be applied!",
p);
}
T p = pmy + y;
value = ellint_rj(x, y, z, p);
value *= pmy;
value -= 3 * ellint_rf(x, y, z);
value += 3 * sqrt((x * y * z) / (x * z + p * q)) * ellint_rc(x * z + p * q, p * q);
value /= (y + q);
return value;
}
// duplication
sigma = 0;
factor = 1;
for (k = 1; k < BOOST_MATH_MAX_ITER; k++)
{
u = (x + y + z + p + p) / 5;
X = (u - x) / u;
Y = (u - y) / u;
Z = (u - z) / u;
P = (u - p) / u;
if ((tools::max)(abs(X), abs(Y), abs(Z), abs(P)) < tolerance)
break;
T sx = sqrt(x);
T sy = sqrt(y);
T sz = sqrt(z);
lambda = sy * (sx + sz) + sz * sx;
alpha = p * (sx + sy + sz) + sx * sy * sz;
alpha *= alpha;
beta = p * (p + lambda) * (p + lambda);
sigma += factor * ellint_rc(alpha, beta);
factor /= 4;
x = (x + lambda) / 4;
y = (y + lambda) / 4;
z = (z + lambda) / 4;
p = (p + lambda) / 4;
}
// Check to see if we gave up too soon:
tools::check_series_iterations(BOOST_CURRENT_FUNCTION, k);
// Taylor series expansion to the 5th order
EA = X * Y + Y * Z + Z * X;
EB = X * Y * Z;
EC = P * P;
E2 = EA - 3 * EC;
E3 = EB + 2 * P * (EA - EC);
S1 = 1 + E2 * (E2 * T(9) / 88 - E3 * T(9) / 52 - T(3) / 14);
S2 = EB * (T(1) / 6 + P * (T(-6) / 22 + P * T(3) / 26));
S3 = P * ((EA - EC) / 3 - P * EA * T(3) / 22);
value = 3 * sigma + factor * (S1 + S2 + S3) / (u * sqrt(u));
return value;
}
} // namespace detail
template <typename T>
inline T ellint_rj(T x, T y, T z, T p)
{
typedef typename tools::evaluation<typename remove_cv<T>::type>::type value_type;
return tools::checked_narrowing_cast<typename remove_cv<T>::type>(
detail::ellint_rj_imp(
static_cast<value_type>(x),
static_cast<value_type>(y),
static_cast<value_type>(z),
static_cast<value_type>(p)), BOOST_CURRENT_FUNCTION);
}
}} // namespaces
#endif // BOOST_MATH_ELLINT_RJ_HPP

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include/boost/math/tools/config.hpp
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@@ -10,6 +10,18 @@ namespace boost{ namespace math{
namespace tools
{
template <class T>
inline T max BOOST_PREVENT_MACRO_SUBSTITUTION(T a, T b, T c)
{
return (std::max)((std::max)(a, b), c);
}
template <class T>
inline T max BOOST_PREVENT_MACRO_SUBSTITUTION(T a, T b, T c, T d)
{
return (std::max)((std::max)(a, b), (std::max)(c, d));
}
inline void check_series_iterations(const char* function, boost::uintmax_t max_iter)
{
if(max_iter >= BOOST_MATH_MAX_ITER)

29
include/boost/math/tools/ntl.hpp
View File

@@ -292,12 +292,39 @@ namespace NTL{
{
return boost::math::tools::newton_raphson_iterate(
asin_root(z),
NTL::RR(0),
NTL::RR(std::asin(boost::math::tools::real_cast<double>(z))),
NTL::RR(-boost::math::constants::pi<NTL::RR>()/2),
NTL::RR(boost::math::constants::pi<NTL::RR>()/2),
boost::math::tools::digits<NTL::RR>());
}
struct atan_root
{
atan_root(NTL::RR const& target) : t(target){}
std::tr1::tuple<NTL::RR, NTL::RR, NTL::RR> operator()(NTL::RR const& p)
{
NTL::RR c = cos(p);
NTL::RR ta = tan(p);
NTL::RR f0 = ta - t;
NTL::RR f1 = 1 / (c * c);
NTL::RR f2 = 2 * ta / (c * c);
return std::tr1::make_tuple(f0, f1, f2);
}
private:
NTL::RR t;
};
inline NTL::RR atan(NTL::RR z)
{
return boost::math::tools::halley_iterate(
atan_root(z),
NTL::RR(std::atan(boost::math::tools::real_cast<double>(z))),
-boost::math::constants::pi<NTL::RR>()/2,
boost::math::constants::pi<NTL::RR>()/2,
boost::math::tools::digits<NTL::RR>());
}
inline NTL::RR fmod(NTL::RR x, NTL::RR y)
{
// This is a really crummy version of fmod, we rely on lots

18
test/Jamfile.v2
View File

@@ -18,12 +18,16 @@ run test_beta.cpp ;
run test_beta_dist.cpp ;
run test_binomial.cpp ;
run test_binomial_coeff.cpp ;
run test_carlson.cpp ;
run test_cauchy.cpp ;
run test_cbrt.cpp ;
run test_chi_squared.cpp ;
run test_classify.cpp ;
run test_digamma.cpp ;
run test_dist_overloads.cpp ;
run test_ellint_1.cpp ;
run test_ellint_2.cpp ;
run test_ellint_3.cpp ;
run test_erf.cpp ;
run test_error_handling.cpp ;
run test_exponential_dist.cpp ;
@@ -39,6 +43,7 @@ run test_ibeta_inv_ab.cpp ;
run test_igamma.cpp ;
run test_igamma_inv.cpp ;
run test_igamma_inva.cpp ;
run test_instantiate1.cpp test_instantiate2.cpp ;
run test_laguerre.cpp ;
run test_legendre.cpp ;
run test_lognormal.cpp ;
@@ -52,8 +57,8 @@ run test_roots.cpp ;
run test_spherical_harmonic.cpp ;
run test_students_t.cpp ;
run test_tgamma_ratio.cpp ;
run test_triangular.cpp ;
run test_toms748_solve.cpp ;
run test_triangular.cpp ;
run test_uniform.cpp ;
run test_weibull.cpp ;
@@ -61,14 +66,3 @@ compile distribution_concept_check.cpp ;
compile std_real_concept_check.cpp ;

525
test/ellint_e2_data.ipp Normal file
View File

@@ -0,0 +1,525 @@
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 3>, 520> ellint_e2_data = {
SC_(0.177219114266335964202880859375e-2), SC_(-0.804919183254241943359375e0), SC_(0.17721905416489978459933452744691987573693030723399e-2),
SC_(0.177219114266335964202880859375e-2), SC_(-0.74602639675140380859375e0), SC_(0.17721906263793616232304803862551613935165980878975e-2),
SC_(0.177219114266335964202880859375e-2), SC_(-0.72904598712921142578125e0), SC_(0.17721906496143189532808590572077500756745196250994e-2),
SC_(0.177219114266335964202880859375e-2), SC_(-0.62323606014251708984375e0), SC_(0.17721907823458326176536911566374461949290266081915e-2),
SC_(0.177219114266335964202880859375e-2), SC_(-0.5579319000244140625e0), SC_(0.17721908538996504890695781731051446713497872352528e-2),
SC_(0.177219114266335964202880859375e-2), SC_(-0.44300353527069091796875e0), SC_(0.1772190960611723703532438177387763930589137687723e-2),
SC_(0.177219114266335964202880859375e-2), SC_(-0.38366591930389404296875e0), SC_(0.17721910061149527140815880383922381002724195459473e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.9376299381256103515625e-1), SC_(0.17721911345080004258530792787497396150296565903888e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.944411754608154296875e-1), SC_(0.17721911343895994071624688564628016634872782068401e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.264718532562255859375e0), SC_(0.17721910776580442894609156234461709334349303324512e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.62944734096527099609375e0), SC_(0.17721907751280664212690267651483481595911639313105e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.67001712322235107421875e0), SC_(0.17721907262237245229946682518231598438599636326697e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.81158387660980224609375e0), SC_(0.1772190531655048767532217861236813247332269413991e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.826751708984375e0), SC_(0.17721905086031437581845682018005163376219526346493e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.91501367092132568359375e0), SC_(0.17721903659952045902730471028534006712649156285481e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.92977702617645263671875e0), SC_(0.17721903407305898397789671421686956699622188608929e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.93538987636566162109375e0), SC_(0.17721903310191937273874074422793996165770412692148e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.93773555755615234375e0), SC_(0.17721903269433608619814655577621926258964232521032e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.98576259613037109375e0), SC_(0.17721902412478400771222500977665176615786698940728e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.99292266368865966796875e0), SC_(0.17721902281054485597950865679003652002775579957175e-2),
SC_(0.22177286446094512939453125e-2), SC_(-0.804919183254241943359375e0), SC_(0.22177274667911356404114891574256878749693907344194e-2),
SC_(0.22177286446094512939453125e-2), SC_(-0.74602639675140380859375e0), SC_(0.22177276328387303450482024510234767179030032679487e-2),
SC_(0.22177286446094512939453125e-2), SC_(-0.72904598712921142578125e0), SC_(0.2217727678372686367339028586754168902231177349864e-2),
SC_(0.22177286446094512939453125e-2), SC_(-0.62323606014251708984375e0), SC_(0.22177279384889650054782811230773624538568740820856e-2),
SC_(0.22177286446094512939453125e-2), SC_(-0.5579319000244140625e0), SC_(0.22177280787142304325383561406780984188050064485493e-2),
SC_(0.22177286446094512939453125e-2), SC_(-0.44300353527069091796875e0), SC_(0.22177282878397316166435787421159323409852657193959e-2),
SC_(0.22177286446094512939453125e-2), SC_(-0.38366591930389404296875e0), SC_(0.22177283770131950245199600240560529548081991406878e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.9376299381256103515625e-1), SC_(0.2217728628627254479372625258375135600386491716262e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.944411754608154296875e-1), SC_(0.2217728628395221979258299938047197957597496164853e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.264718532562255859375e0), SC_(0.22177285172174219060847672057602083161874684079641e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.62944734096527099609375e0), SC_(0.22177279243441823271547938764610382865435171389572e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.67001712322235107421875e0), SC_(0.22177278285054864598218183902335374842302009015249e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.81158387660980224609375e0), SC_(0.22177274472058160774429082218212375574848674857853e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.826751708984375e0), SC_(0.22177274020305878581113108501360596469572415665098e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.91501367092132568359375e0), SC_(0.22177271225592599152503205364411936997104330819552e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.92977702617645263671875e0), SC_(0.22177270730477403168508453406178297939782452362205e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.93538987636566162109375e0), SC_(0.22177270540161426246190034172682702788389529386352e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.93773555755615234375e0), SC_(0.22177270460286595928412185481890644744187621951273e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.98576259613037109375e0), SC_(0.22177268780896006483002343116598140190281467534408e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.99292266368865966796875e0), SC_(0.22177268523342180309535844744234619982692618957978e-2),
SC_(0.7444499991834163665771484375e-2), SC_(-0.804919183254241943359375e0), SC_(0.74444554408367041960081599572734384580648039601292e-2),
SC_(0.7444499991834163665771484375e-2), SC_(-0.74602639675140380859375e0), SC_(0.74444617216162272729935658343672599710823129917136e-2),
SC_(0.7444499991834163665771484375e-2), SC_(-0.72904598712921142578125e0), SC_(0.7444463443944617202862815487638272084421484282213e-2),
SC_(0.7444499991834163665771484375e-2), SC_(-0.62323606014251708984375e0), SC_(0.74444732828674762841832446009298546988014342845109e-2),
SC_(0.7444499991834163665771484375e-2), SC_(-0.5579319000244140625e0), SC_(0.74444785868925647373677427756541386357216267403116e-2),
SC_(0.7444499991834163665771484375e-2), SC_(-0.44300353527069091796875e0), SC_(0.7444486497059729002932025822805836773020204604622e-2),
SC_(0.7444499991834163665771484375e-2), SC_(-0.38366591930389404296875e0), SC_(0.7444489870039692628767038225671358877887084418318e-2),
SC_(0.7444499991834163665771484375e-2), SC_(0.9376299381256103515625e-1), SC_(0.74444993873102289959003988480526261034186232298732e-2),
SC_(0.7444499991834163665771484375e-2), SC_(0.944411754608154296875e-1), SC_(0.74444993785336377021615551123021090095012183365455e-2),
SC_(0.7444499991834163665771484375e-2), SC_(0.264718532562255859375e0), SC_(0.74444951732496163285321657924324274340742574731183e-2),
SC_(0.7444499991834163665771484375e-2), SC_(0.62944734096527099609375e0), SC_(0.74444727478402810869648210185177744717615995463001e-2),
SC_(0.7444499991834163665771484375e-2), SC_(0.67001712322235107421875e0), SC_(0.74444691227345931676783343972213308719772501191675e-2),
SC_(0.7444499991834163665771484375e-2), SC_(0.81158387660980224609375e0), SC_(0.74444547000179682301220146799104273617595274550494e-2),
SC_(0.7444499991834163665771484375e-2), SC_(0.826751708984375e0), SC_(0.74444529912552191587668074107636437041675982253389e-2),
SC_(0.7444499991834163665771484375e-2), SC_(0.91501367092132568359375e0), SC_(0.74444424201776730075960207569226490521597156912434e-2),
SC_(0.7444499991834163665771484375e-2), SC_(0.92977702617645263671875e0), SC_(0.74444405473886664282906533654411935648151688362809e-2),
SC_(0.7444499991834163665771484375e-2), SC_(0.93538987636566162109375e0), SC_(0.74444398275122133283989327309245789244705679180104e-2),
SC_(0.7444499991834163665771484375e-2), SC_(0.93773555755615234375e0), SC_(0.74444395253830019766374648366268259171697141665571e-2),
SC_(0.7444499991834163665771484375e-2), SC_(0.98576259613037109375e0), SC_(0.74444331730273938555860696278431505938817087276882e-2),
SC_(0.7444499991834163665771484375e-2), SC_(0.99292266368865966796875e0), SC_(0.74444321988199504330861521619247593689621297824599e-2),
SC_(0.1433600485324859619140625e-1), SC_(-0.804919183254241943359375e0), SC_(0.14335686705725696407060645727945600655565741414147e-1),
SC_(0.1433600485324859619140625e-1), SC_(-0.74602639675140380859375e0), SC_(0.14335731558581990142476732612631387140359085570156e-1),
SC_(0.1433600485324859619140625e-1), SC_(-0.72904598712921142578125e0), SC_(0.14335743858193055553888894193489743522839559243509e-1),
SC_(0.1433600485324859619140625e-1), SC_(-0.62323606014251708984375e0), SC_(0.14335814120326027832379597580040828122216388507481e-1),
SC_(0.1433600485324859619140625e-1), SC_(-0.5579319000244140625e0), SC_(0.14335851997467008238725204894793026916257019753693e-1),
SC_(0.1433600485324859619140625e-1), SC_(-0.44300353527069091796875e0), SC_(0.14335908485363563424533546850245012850090360873434e-1),
SC_(0.1433600485324859619140625e-1), SC_(-0.38366591930389404296875e0), SC_(0.14335932572318417439388238927592963489979339519294e-1),
SC_(0.1433600485324859619140625e-1), SC_(0.9376299381256103515625e-1), SC_(0.14336000536285207953459760778071938813620926376329e-1),
SC_(0.1433600485324859619140625e-1), SC_(0.944411754608154296875e-1), SC_(0.14336000473610715309472432563583032814457494094135e-1),
SC_(0.1433600485324859619140625e-1), SC_(0.264718532562255859375e0), SC_(0.14335970443226789444113931927418674846075665585412e-1),
SC_(0.1433600485324859619140625e-1), SC_(0.62944734096527099609375e0), SC_(0.14335810299578782495392921047255424568664286939309e-1),
SC_(0.1433600485324859619140625e-1), SC_(0.67001712322235107421875e0), SC_(0.14335784411863985146631166860519228538944451465492e-1),
SC_(0.1433600485324859619140625e-1), SC_(0.81158387660980224609375e0), SC_(0.14335681415313482527267826975008547916557671973967e-1),
SC_(0.1433600485324859619140625e-1), SC_(0.826751708984375e0), SC_(0.14335669212508490437041994345359491275578416731562e-1),
SC_(0.1433600485324859619140625e-1), SC_(0.91501367092132568359375e0), SC_(0.1433559372086014461936976066148820437936563510921e-1),
SC_(0.1433600485324859619140625e-1), SC_(0.92977702617645263671875e0), SC_(0.14335580346584476426767024206037631424851951301064e-1),
SC_(0.1433600485324859619140625e-1), SC_(0.93538987636566162109375e0), SC_(0.14335575205677374246197434850917518154812470284912e-1),
SC_(0.1433600485324859619140625e-1), SC_(0.93773555755615234375e0), SC_(0.14335573048058908550764743332104831817119331680375e-1),
SC_(0.1433600485324859619140625e-1), SC_(0.98576259613037109375e0), SC_(0.14335527683396662777675860041375777953747610473763e-1),
SC_(0.1433600485324859619140625e-1), SC_(0.99292266368865966796875e0), SC_(0.14335520726182617060139852455489440586802090752734e-1),
SC_(0.1760916970670223236083984375e-1), SC_(-0.804919183254241943359375e0), SC_(0.17608580108574407596974329704841169956949700562955e-1),
SC_(0.1760916970670223236083984375e-1), SC_(-0.74602639675140380859375e0), SC_(0.17608663231619667706144284604540728747274691033403e-1),
SC_(0.1760916970670223236083984375e-1), SC_(-0.72904598712921142578125e0), SC_(0.17608686025692226081166910626170820785576222384032e-1),
SC_(0.1760916970670223236083984375e-1), SC_(-0.62323606014251708984375e0), SC_(0.17608816237609089248262489588718703344935310646926e-1),
SC_(0.1760916970670223236083984375e-1), SC_(-0.5579319000244140625e0), SC_(0.17608886432433642683152813125927533432394416093985e-1),
SC_(0.1760916970670223236083984375e-1), SC_(-0.44300353527069091796875e0), SC_(0.17608991116840504430604382009436726055680942592846e-1),
SC_(0.1760916970670223236083984375e-1), SC_(-0.38366591930389404296875e0), SC_(0.176090357551125362347926995427228626500868394589e-1),
SC_(0.1760916970670223236083984375e-1), SC_(0.9376299381256103515625e-1), SC_(0.17609161706489009824375122022213121549814666772137e-1),
SC_(0.1760916970670223236083984375e-1), SC_(0.944411754608154296875e-1), SC_(0.17609161590340381771438539655887170786578607686625e-1),
SC_(0.1760916970670223236083984375e-1), SC_(0.264718532562255859375e0), SC_(0.17609105937855647197851193299561879969853300958653e-1),
SC_(0.1760916970670223236083984375e-1), SC_(0.62944734096527099609375e0), SC_(0.17608809156899384005720536484472837230830065065362e-1),
SC_(0.1760916970670223236083984375e-1), SC_(0.67001712322235107421875e0), SC_(0.17608761181057073227708699591125844960940811676035e-1),
SC_(0.1760916970670223236083984375e-1), SC_(0.81158387660980224609375e0), SC_(0.17608570304162501463076154868058948699689399732159e-1),
SC_(0.1760916970670223236083984375e-1), SC_(0.826751708984375e0), SC_(0.17608547689404223463630864650669183425712473803568e-1),
SC_(0.1760916970670223236083984375e-1), SC_(0.91501367092132568359375e0), SC_(0.17608407784672239506239468119798486189473586582955e-1),
SC_(0.1760916970670223236083984375e-1), SC_(0.92977702617645263671875e0), SC_(0.17608382998754781901869199398720568129229579547611e-1),
SC_(0.1760916970670223236083984375e-1), SC_(0.93538987636566162109375e0), SC_(0.17608373471347270582239268505690054737704285676384e-1),
SC_(0.1760916970670223236083984375e-1), SC_(0.93773555755615234375e0), SC_(0.17608369472730925070207638812129721785547912618809e-1),
SC_(0.1760916970670223236083984375e-1), SC_(0.98576259613037109375e0), SC_(0.1760828540033432824714172980056450648102099021249e-1),
SC_(0.1760916970670223236083984375e-1), SC_(0.99292266368865966796875e0), SC_(0.1760827250680427232498457772793807499892371857118e-1),
SC_(0.6152711808681488037109375e-1), SC_(-0.804919183254241943359375e0), SC_(0.61501977006950685147287768516293323208160579222561e-1),
SC_(0.6152711808681488037109375e-1), SC_(-0.74602639675140380859375e0), SC_(0.61505522489025659599931604724877390313025548257308e-1),
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SC_(0.10074598388671875e4), SC_(-0.72904598712921142578125e0), SC_(0.85590189104276483616202632098287025738931943507153e3),
SC_(0.10074598388671875e4), SC_(-0.62323606014251708984375e0), SC_(0.9009738212363659705854642096463530651141689117269e3),
SC_(0.10074598388671875e4), SC_(-0.5579319000244140625e0), SC_(0.92372203670774325404806275709264270484304517663929e3),
SC_(0.10074598388671875e4), SC_(-0.44300353527069091796875e0), SC_(0.95602114692228459835045237318476147078694497472822e3),
SC_(0.10074598388671875e4), SC_(-0.38366591930389404296875e0), SC_(0.96927625305559748266490795989045893214495805831554e3),
SC_(0.10074598388671875e4), SC_(0.9376299381256103515625e-1), SC_(0.10052408954500277585485462407617932594289289210602e4),
SC_(0.10074598388671875e4), SC_(0.944411754608154296875e-1), SC_(0.10052086262210379665209822645440559289291237665647e4),
SC_(0.10074598388671875e4), SC_(0.264718532562255859375e0), SC_(0.98956304231616558867754941531972183396056332288818e3),
SC_(0.10074598388671875e4), SC_(0.62944734096527099609375e0), SC_(0.89862442644009820675218558218153173632055069943683e3),
SC_(0.10074598388671875e4), SC_(0.67001712322235107421875e0), SC_(0.88241671832232838738799982334634993277048716392487e3),
SC_(0.10074598388671875e4), SC_(0.81158387660980224609375e0), SC_(0.81173128112196665137058131884505478065505214589458e3),
SC_(0.10074598388671875e4), SC_(0.826751708984375e0), SC_(0.80250834127587356001580304856418261116625810606362e3),
SC_(0.10074598388671875e4), SC_(0.91501367092132568359375e0), SC_(0.73912196799060491702381369566485537415592290789722e3),
SC_(0.10074598388671875e4), SC_(0.92977702617645263671875e0), SC_(0.7262884386240235721342337367344044620971138470138e3),
SC_(0.10074598388671875e4), SC_(0.93538987636566162109375e0), SC_(0.72116757185358740018078031894015653763422120624137e3),
SC_(0.10074598388671875e4), SC_(0.93773555755615234375e0), SC_(0.71898356440546660369364312811873716877046903540745e3),
SC_(0.10074598388671875e4), SC_(0.98576259613037109375e0), SC_(0.66558630336818747011593267003329852836650815741705e3),
SC_(0.10074598388671875e4), SC_(0.99292266368865966796875e0), SC_(0.6548786829121203110560807170365229948244134922981e3),
SC_(0.1185395751953125e4), SC_(-0.804919183254241943359375e0), SC_(0.95992720290264897479760554571647114770157610887996e3),
SC_(0.1185395751953125e4), SC_(-0.74602639675140380859375e0), SC_(0.99741366529362017349163653479322848619622124868772e3),
SC_(0.1185395751953125e4), SC_(-0.72904598712921142578125e0), SC_(0.10072278878934483167286843735137660835902486784055e4),
SC_(0.1185395751953125e4), SC_(-0.62323606014251708984375e0), SC_(0.10602110806127832608392589101187996342688647189112e4),
SC_(0.1185395751953125e4), SC_(-0.5579319000244140625e0), SC_(0.10869529954610434278852140581154818972542686423743e4),
SC_(0.1185395751953125e4), SC_(-0.44300353527069091796875e0), SC_(0.11249233882184205470868187837372292890877647671181e4),
SC_(0.1185395751953125e4), SC_(-0.38366591930389404296875e0), SC_(0.11405061649275106998721240053724233425466223964298e4),
SC_(0.1185395751953125e4), SC_(0.9376299381256103515625e-1), SC_(0.11827870772689532014486419251476519345293661688085e4),
SC_(0.1185395751953125e4), SC_(0.944411754608154296875e-1), SC_(0.11827491403552705968358829702474865775810482378628e4),
SC_(0.1185395751953125e4), SC_(0.264718532562255859375e0), SC_(0.11643556929058415420471543503560945498245581125436e4),
SC_(0.1185395751953125e4), SC_(0.62944734096527099609375e0), SC_(0.10574492529652112224851625390587579547328457881061e4),
SC_(0.1185395751953125e4), SC_(0.67001712322235107421875e0), SC_(0.1038396462932344155293121667046538419874167990145e4),
SC_(0.1185395751953125e4), SC_(0.81158387660980224609375e0), SC_(0.9553066699471665679840089770219957164232252629554e3),
SC_(0.1185395751953125e4), SC_(0.826751708984375e0), SC_(0.94446573985220084327197598058015000573173775032994e3),
SC_(0.1185395751953125e4), SC_(0.91501367092132568359375e0), SC_(0.86996356635663675306873109547180307652983494815843e3),
SC_(0.1185395751953125e4), SC_(0.92977702617645263671875e0), SC_(0.85488052815230820219522803855058047921692647892349e3),
SC_(0.1185395751953125e4), SC_(0.93538987636566162109375e0), SC_(0.84886217610355647741057825617131638665389927335333e3),
SC_(0.1185395751953125e4), SC_(0.93773555755615234375e0), SC_(0.84629542044995161715099588574641450818752524118888e3),
SC_(0.1185395751953125e4), SC_(0.98576259613037109375e0), SC_(0.78354531056875687291420826162420650224843893529921e3),
SC_(0.1185395751953125e4), SC_(0.99292266368865966796875e0), SC_(0.77096378731739644110407751882818742444499646261653e3),
};
#undef SC_

105
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#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 2>, 100> ellint_e_data = {
SC_(-0.990433037281036376953125e0), SC_(0.10274527688571687030049782227296053357094496206279e1),
SC_(-0.936334311962127685546875e0), SC_(0.11232874555917022066938321555637623562213676975972e1),
SC_(-0.931107819080352783203125e0), SC_(0.1130760221755419903369153157619439589360779303926e1),
SC_(-0.928576648235321044921875e0), SC_(0.11343097282371636644057123410674810478126636794066e1),
SC_(-0.92711746692657470703125e0), SC_(0.11363362574688624051162518398981635242155496915255e1),
SC_(-0.907657206058502197265625e0), SC_(0.11621185270599645325148449388373607697900140479452e1),
SC_(-0.89756715297698974609375e0), SC_(0.11746803765109846934010357339330910078574216811115e1),
SC_(-0.80573642253875732421875e0), SC_(0.12711544492641534140326897830960020400731161482408e1),
SC_(-0.804919183254241943359375e0), SC_(0.1271899578518333585916968732627512791380932403316e1),
SC_(-0.780276477336883544921875e0), SC_(0.12936183519259955902237796585053994588791953787341e1),
SC_(-0.775070965290069580078125e0), SC_(0.12980290901572191577411456044089492043970943779076e1),
SC_(-0.7496345043182373046875e0), SC_(0.13187607273206970520631617642065752154074679201729e1),
SC_(-0.74820673465728759765625e0), SC_(0.13198856849340247002745787630036800286336929689325e1),
SC_(-0.74602639675140380859375e0), SC_(0.13215959480936459650266993732312887701493706168114e1),
SC_(-0.72904598712921142578125e0), SC_(0.1334606672267782799453143920126631207219848911468e1),
SC_(-0.7162272930145263671875e0), SC_(0.13440793050791416705713681443513787752467694981452e1),
SC_(-0.701772034168243408203125e0), SC_(0.13544180205342472921449637366285993011101451511219e1),
SC_(-0.68477380275726318359375e0), SC_(0.13661308406125643621284019270477708148951227020526e1),
SC_(-0.657626628875732421875e0), SC_(0.13838947645626975911149829417421592164301145093627e1),
SC_(-0.652269661426544189453125e0), SC_(0.13872692599655636614951215534059306447757898114989e1),
SC_(-0.6262547969818115234375e0), SC_(0.14030728449607783731169275509403934977874920947839e1),
SC_(-0.62323606014251708984375e0), SC_(0.14048456682760981684618618684460963872624120364616e1),
SC_(-0.57958185672760009765625e0), SC_(0.14291386904685383227954283815576245068501134204508e1),
SC_(-0.576151371002197265625e0), SC_(0.14309448152636963724388781094697116200713399276732e1),
SC_(-0.5579319000244140625e0), SC_(0.14402965087704791609397947280292073414645780530405e1),
SC_(-0.446154057979583740234375e0), SC_(0.14894386503626442042107428737827539093660806612699e1),
SC_(-0.44300353527069091796875e0), SC_(0.14906320545924202935802686800501318065294882015735e1),
SC_(-0.40594112873077392578125e0), SC_(0.15039335802932226988591218103108193186540888213994e1),
SC_(-0.396173775196075439453125e0), SC_(0.15072169743011592499372913974729141564215181659934e1),
SC_(-0.38366591930389404296875e0), SC_(0.15112892448422190697630083347423467639448624581727e1),
SC_(-0.36689913272857666015625e0), SC_(0.15165180033802033267632053479981021035471425681416e1),
SC_(-0.365801036357879638671875e0), SC_(0.15168513413633160947387236074965552423019640205414e1),
SC_(-0.277411997318267822265625e0), SC_(0.15401245425176709136660196900048700278424091275112e1),
SC_(-0.236883103847503662109375e0), SC_(0.15485231276601733576918931368003657825692622988276e1),
SC_(-0.215545952320098876953125e0), SC_(0.15523894121876553934587790103948024781080753117537e1),
SC_(-0.202522933483123779296875e0), SC_(0.15545635291592032109785456524323662491832287557881e1),
SC_(-0.18253767490386962890625e0), SC_(0.15576286893796261035306290689920363346745725969978e1),
SC_(-0.156477451324462890625e0), SC_(0.15611364139446355493431072334668884516455428910749e1),
SC_(-0.1558246612548828125e0), SC_(0.15612172160025555618286865486857507482242942668515e1),
SC_(-0.12251126766204833984375e0), SC_(0.15648856105816674567926606395168937481071020785374e1),
SC_(-0.1088275909423828125e0), SC_(0.15661350376732836367309274463594953937245200605844e1),
SC_(-0.8402168750762939453125e-1), SC_(0.15680203305860144668144643526811660961420870159842e1),
SC_(-0.5048263072967529296875e-1), SC_(0.15697950560238758069422088665702687900822920595852e1),
SC_(-0.29248714447021484375e-1), SC_(0.15704603238122883636275639829068215175843565484093e1),
SC_(-0.2486217021942138671875e-1), SC_(0.1570553560549795220596952208506368318845323442966e1),
SC_(-0.2047121524810791015625e-1), SC_(0.15706317452006442392207295085961102343692070947481e1),
SC_(-0.18821895122528076171875e-1), SC_(0.15706571985088185541190068658162634466459956376283e1),
SC_(0.73254108428955078125e-2), SC_(0.15707752537045378829148682574129984681356739471373e1),
SC_(0.9376299381256103515625e-1), SC_(0.15673382012803800695565201533706558176677595081402e1),
SC_(0.944411754608154296875e-1), SC_(0.15672879111272468454088900653008917791981439593238e1),
SC_(0.264718532562255859375e0), SC_(0.15429050287765040115345161487328955754762740575513e1),
SC_(0.27952671051025390625e0), SC_(0.15396478942459482760618960796407428547408640525839e1),
SC_(0.29262602329254150390625e0), SC_(0.15366093920760526747388381843200711024138982306603e1),
SC_(0.3109557628631591796875e0), SC_(0.15321071618558340305908384979951601020818799999842e1),
SC_(0.31148135662078857421875e0), SC_(0.15319737203884180398267043979026904916868658518393e1),
SC_(0.32721102237701416015625e0), SC_(0.1527867114331003738198228458599913043176805971218e1),
SC_(0.3574702739715576171875e0), SC_(0.15193440688380299383044814920714973708033404406654e1),
SC_(0.362719058990478515625e0), SC_(0.15177809660808721467844113827968123756890771957761e1),
SC_(0.3896572589874267578125e0), SC_(0.15093570468318824817504413386396057198219992161732e1),
SC_(0.4120922088623046875e0), SC_(0.15018188427341099768691902236893549315641407909401e1),
SC_(0.41872966289520263671875e0), SC_(0.14994958178213154496366968552961386017760898588045e1),
SC_(0.45167791843414306640625e0), SC_(0.1487322085908655313535535255202869925685698085035e1),
SC_(0.48129451274871826171875e0), SC_(0.14754407459744073247384176419011374260929941397226e1),
SC_(0.4862649440765380859375e0), SC_(0.14733570928853164419583523432188100088746641413847e1),
SC_(0.50937330722808837890625e0), SC_(0.14633222267462579060234013375472616462719440305596e1),
SC_(0.5154802799224853515625e0), SC_(0.14605730543776299802897695844262830217129367088168e1),
SC_(0.52750003337860107421875e0), SC_(0.1455040905739579018637680781037806414611373457245e1),
SC_(0.53103363513946533203125e0), SC_(0.14533836180900849164859243315111429017381139244939e1),
SC_(0.58441460132598876953125e0), SC_(0.14265695055008370758871995090190851074198707889523e1),
SC_(0.5879499912261962890625e0), SC_(0.14246715204117826383644822612160764733188324494824e1),
SC_(0.59039986133575439453125e0), SC_(0.14233470653300894642788935610227647487095507501819e1),
SC_(0.59455978870391845703125e0), SC_(0.14210806804871026734537311084007732025147240364441e1),
SC_(0.59585726261138916015625e0), SC_(0.14203692855345104085630580991694310940176283484347e1),
SC_(0.5962116718292236328125e0), SC_(0.14201745910377376893163001298577620388569425640087e1),
SC_(0.6005609035491943359375e0), SC_(0.14177721978271857966949913233824083454479033587509e1),
SC_(0.6150619983673095703125e0), SC_(0.1409584186264459097822607166118300162769330850531e1),
SC_(0.62944734096527099609375e0), SC_(0.14011843899700989964492170135501929645905818746914e1),
SC_(0.64380657672882080078125e0), SC_(0.13925155171987190379716348493447778489398983557681e1),
SC_(0.6469156742095947265625e0), SC_(0.13906001623565653310360026300062173208737677732474e1),
SC_(0.67001712322235107421875e0), SC_(0.13759265375091920908763740804480465836032745124162e1),
SC_(0.6982586383819580078125e0), SC_(0.13568776608794218001220481427238400798591422244367e1),
SC_(0.74485766887664794921875e0), SC_(0.13225089163569380724816605958889295619432742743828e1),
SC_(0.75686132907867431640625e0), SC_(0.13130049536402767623871717650724612640189448665164e1),
SC_(0.81158387660980224609375e0), SC_(0.1265774005474254141411822958784348996686269275959e1),
SC_(0.826751708984375e0), SC_(0.1251401815196169298547115798872087290243528044558e1),
SC_(0.83147108554840087890625e0), SC_(0.12468018231406093242228210016848902253352539970597e1),
SC_(0.84174954891204833984375e0), SC_(0.12365605223473625325793146444569526624443067779814e1),
SC_(0.8679864406585693359375e0), SC_(0.12089081947735379320176271312129936213684657310011e1),
SC_(0.90044414997100830078125e0), SC_(0.11711493603723543295821235205304820794673798105369e1),
SC_(0.91433393955230712890625e0), SC_(0.11535184098186861192678956506006329721663192849427e1),
SC_(0.91501367092132568359375e0), SC_(0.11526291690338582866360141839353650400854743647163e1),
SC_(0.918984889984130859375e0), SC_(0.11473810486945145917917969281137061723789053926309e1),
SC_(0.92977702617645263671875e0), SC_(0.11326318918571500732674050143237850082646730427556e1),
SC_(0.93538987636566162109375e0), SC_(0.11246526120138518224375085002257139975074424198895e1),
SC_(0.93773555755615234375e0), SC_(0.11212495302257932905970525402254900901444230096575e1),
SC_(0.94118559360504150390625e0), SC_(0.11161664223439311396943776225269812587817500317889e1),
SC_(0.96221935749053955078125e0), SC_(0.10828018699366994143027254777963854661530573064246e1),
SC_(0.98576259613037109375e0), SC_(0.10380503716235214587344268369403753352254592216066e1),
SC_(0.9881370067596435546875e0), SC_(0.10327762472475272053177375153237179387280796303267e1),
SC_(0.99292266368865966796875e0), SC_(0.10213677605130466359178501196768639821158116338631e1),
};
#undef SC_

616
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#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 3>, 610> ellint_f_data = {
SC_(0.177219114266335964202880859375e-2), SC_(0.12698681652545928955078125e0), SC_(0.17721911576221833285284471505772299979929420100157e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.135477006435394287109375e0), SC_(0.17721911596893097495385621130075639520810631802367e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.22103404998779296875e0), SC_(0.17721911879842626333735727252300568988042608181058e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.308167040348052978515625e0), SC_(0.17721912307586304284414392153484736630244171106967e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.6323592662811279296875e0), SC_(0.17721915136072145749706721763844561838990574996748e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.814723670482635498046875e0), SC_(0.17721917584088468746420484903332375635064689539385e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.835008561611175537109375e0), SC_(0.17721917894520936923412246849940510596766888342397e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.905791938304901123046875e0), SC_(0.17721919037560789892218093103766859258846695998999e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.9133758544921875e0), SC_(0.17721919165542367899383364723376572314588337429883e-2),
SC_(0.177219114266335964202880859375e-2), SC_(0.968867778778076171875e0), SC_(0.1772192013446002825503764323931321827613955432354e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.12698681652545928955078125e0), SC_(0.22177286739245139979235205992077921703857874992614e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.135477006435394287109375e0), SC_(0.22177286779754970704335950293621400375492832466137e-2),
SC_(0.22177286446094512939453125e-2), SC_(0.22103404998779296875e0), SC_(0.22177287334256025917867525959622978930360537074924e-2),
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SC_(0.19929225921630859375e2), SC_(0.97540400922298431396484375e-1), SC_(0.19975886328405901668305093050689660120707141316602e2),
SC_(0.19929225921630859375e2), SC_(0.12698681652545928955078125e0), SC_(0.20008605915303070801582050926154802900088794048964e2),
SC_(0.19929225921630859375e2), SC_(0.135477006435394287109375e0), SC_(0.20019688942140272434266047438835346018341741915511e2),
SC_(0.19929225921630859375e2), SC_(0.188381969928741455078125e0), SC_(0.20105850846081957007436768267527465156969052735547e2),
SC_(0.19929225921630859375e2), SC_(0.22103404998779296875e0), SC_(0.20174266422647172012150979392231829627779414396837e2),
SC_(0.19929225921630859375e2), SC_(0.278498232364654541015625e0), SC_(0.20324849469295553710957519872007277741843364722133e2),
SC_(0.19929225921630859375e2), SC_(0.308167040348052978515625e0), SC_(0.20418709708488624812924232071906879942886525542029e2),
SC_(0.19929225921630859375e2), SC_(0.546881496906280517578125e0), SC_(0.21696140642124331439508133866139932201302076151348e2),
SC_(0.19929225921630859375e2), SC_(0.54722058773040771484375e0), SC_(0.21698820879919996353144760914681524104995035006532e2),
SC_(0.19929225921630859375e2), SC_(0.6323592662811279296875e0), SC_(0.2248785248670487339037134222906002093786314923977e2),
SC_(0.19929225921630859375e2), SC_(0.814723670482635498046875e0), SC_(0.25534059615544403238480102528913553132379413621289e2),
SC_(0.19929225921630859375e2), SC_(0.835008561611175537109375e0), SC_(0.26099050398865334629533525410109890297302254597982e2),
SC_(0.19929225921630859375e2), SC_(0.905791938304901123046875e0), SC_(0.28967243162656729801455052134450446896264393672653e2),
SC_(0.19929225921630859375e2), SC_(0.9133758544921875e0), SC_(0.29412943361256553874561548032106119373059225314887e2),
SC_(0.19929225921630859375e2), SC_(0.957506835460662841796875e0), SC_(0.33316451349895040185793214377890308351033763723109e2),
SC_(0.19929225921630859375e2), SC_(0.964888513088226318359375e0), SC_(0.34391265339548473169790956472595433220957162008448e2),
SC_(0.19929225921630859375e2), SC_(0.967694938182830810546875e0), SC_(0.34863504351466085585554980530563512546455300394261e2),
SC_(0.19929225921630859375e2), SC_(0.968867778778076171875e0), SC_(0.35073684228035671034339162557868963087508664681989e2),
SC_(0.19929225921630859375e2), SC_(0.992881298065185546875e0), SC_(0.43650868172850778393525355531550453773052652935489e2),
SC_(0.19929225921630859375e2), SC_(0.996461331844329833984375e0), SC_(0.47791504341919311227161099998742414152705210735222e2),
SC_(0.24750102996826171875e2), SC_(0.12698681652545928955078125e0), SC_(0.24852206550898319978190983067100514776615377727473e2),
SC_(0.24750102996826171875e2), SC_(0.135477006435394287109375e0), SC_(0.24866464070855511040663338301964479223598462797236e2),
SC_(0.24750102996826171875e2), SC_(0.22103404998779296875e0), SC_(0.25065363656732084822750387055815189187723429657877e2),
SC_(0.24750102996826171875e2), SC_(0.308167040348052978515625e0), SC_(0.25380073970395947922582583397566279723752708041733e2),
SC_(0.24750102996826171875e2), SC_(0.6323592662811279296875e0), SC_(0.2805260001123830228051193977609968789435237527768e2),
SC_(0.24750102996826171875e2), SC_(0.814723670482635498046875e0), SC_(0.32013812288161230383507254058691739835624677000322e2),
SC_(0.24750102996826171875e2), SC_(0.835008561611175537109375e0), SC_(0.32751766781102618452555944128390146420838932359409e2),
SC_(0.24750102996826171875e2), SC_(0.905791938304901123046875e0), SC_(0.36511896764707420590932811629213597607442192208936e2),
SC_(0.24750102996826171875e2), SC_(0.9133758544921875e0), SC_(0.37098090138580051103542727188386673865227695373655e2),
SC_(0.24750102996826171875e2), SC_(0.968867778778076171875e0), SC_(0.44576670431026372474999805087999761032786564151124e2),
SC_(0.637722015380859375e2), SC_(0.12698681652545928955078125e0), SC_(0.64029707052819358798026202945496034201051376675713e2),
SC_(0.637722015380859375e2), SC_(0.135477006435394287109375e0), SC_(0.64065662867329731510905167206470426348000579756421e2),
SC_(0.637722015380859375e2), SC_(0.22103404998779296875e0), SC_(0.64567221477870510803896006565094849896791667291395e2),
SC_(0.637722015380859375e2), SC_(0.308167040348052978515625e0), SC_(0.65360653914250445223499712404078058345986158088873e2),
SC_(0.637722015380859375e2), SC_(0.6323592662811279296875e0), SC_(0.72091068969413354768470555979894375250854883743041e2),
SC_(0.637722015380859375e2), SC_(0.814723670482635498046875e0), SC_(0.82046315600696025842317036872213782774465494655701e2),
SC_(0.637722015380859375e2), SC_(0.835008561611175537109375e0), SC_(0.83898717232428299594870923028741701777220145751954e2),
SC_(0.637722015380859375e2), SC_(0.905791938304901123046875e0), SC_(0.93328998463557747079788635557387681634136121872602e2),
SC_(0.637722015380859375e2), SC_(0.9133758544921875e0), SC_(0.94798090083448401328383552423060476950786086617102e2),
SC_(0.637722015380859375e2), SC_(0.968867778778076171875e0), SC_(0.11352388177887899862769270203556217867987795179232e3),
SC_(0.1252804412841796875e3), SC_(0.12698681652545928955078125e0), SC_(0.12579154382331624849995504971737598053587224775121e3),
SC_(0.1252804412841796875e3), SC_(0.135477006435394287109375e0), SC_(0.1258629123249332796639091198974708149109486889059e3),
SC_(0.1252804412841796875e3), SC_(0.22103404998779296875e0), SC_(0.12685851994596818963211475589675243092409541745734e3),
SC_(0.1252804412841796875e3), SC_(0.308167040348052978515625e0), SC_(0.12843375727132041082283110776238893197168320725174e3),
SC_(0.1252804412841796875e3), SC_(0.6323592662811279296875e0), SC_(0.14180779137123412498124168609891981092056098817107e3),
SC_(0.1252804412841796875e3), SC_(0.814723670482635498046875e0), SC_(0.16162410252299947507128901048395142821231251884648e3),
SC_(0.1252804412841796875e3), SC_(0.835008561611175537109375e0), SC_(0.1653152013141215856944195913668621513903319809522e3),
SC_(0.1252804412841796875e3), SC_(0.905791938304901123046875e0), SC_(0.18412078840911869664652903874125802301205742425445e3),
SC_(0.1252804412841796875e3), SC_(0.9133758544921875e0), SC_(0.18705231339830243358318239275545179927816644574167e3),
SC_(0.1252804412841796875e3), SC_(0.968867778778076171875e0), SC_(0.22444947582863925345693507386186458537730111006249e3),
SC_(0.25554705810546875e3), SC_(0.12698681652545928955078125e0), SC_(0.25658502090244978090877141970893960506917422719394e3),
SC_(0.25554705810546875e3), SC_(0.135477006435394287109375e0), SC_(0.25672995659370167636074162037295145926099041806219e3),
SC_(0.25554705810546875e3), SC_(0.22103404998779296875e0), SC_(0.25875180174660371624905238703656604914656092031662e3),
SC_(0.25554705810546875e3), SC_(0.308167040348052978515625e0), SC_(0.26195057844009785727683464893701821156596484750488e3),
SC_(0.25554705810546875e3), SC_(0.6323592662811279296875e0), SC_(0.2891011463129193460573977573707949150504396644584e3),
SC_(0.25554705810546875e3), SC_(0.814723670482635498046875e0), SC_(0.32930739590633854381605546287467793111283231579432e3),
SC_(0.25554705810546875e3), SC_(0.835008561611175537109375e0), SC_(0.33679375763609597539308592356025124507335101594018e3),
SC_(0.25554705810546875e3), SC_(0.905791938304901123046875e0), SC_(0.37492445861810085142108868488536553926419178382588e3),
SC_(0.25554705810546875e3), SC_(0.9133758544921875e0), SC_(0.38086699090058068271279985054050727201708494031721e3),
SC_(0.25554705810546875e3), SC_(0.968867778778076171875e0), SC_(0.45664903993544502840751750992103769324314215524713e3),
SC_(0.503011474609375e3), SC_(0.12698681652545928955078125e0), SC_(0.50505659203440279938830010253440085323070647638583e3),
SC_(0.503011474609375e3), SC_(0.135477006435394287109375e0), SC_(0.50534216388830445980335135399460817135115935936356e3),
SC_(0.503011474609375e3), SC_(0.22103404998779296875e0), SC_(0.50932593644875965893234599959022743691202259918901e3),
SC_(0.503011474609375e3), SC_(0.308167040348052978515625e0), SC_(0.51562892434896885100439228418671454505533824895074e3),
SC_(0.503011474609375e3), SC_(0.6323592662811279296875e0), SC_(0.5691388458382702939253765036826448847256790383481e3),
SC_(0.503011474609375e3), SC_(0.814723670482635498046875e0), SC_(0.64841647174915260562168094112340451126659760019193e3),
SC_(0.503011474609375e3), SC_(0.835008561611175537109375e0), SC_(0.66318246845203780675903083663338059471936088994611e3),
SC_(0.503011474609375e3), SC_(0.905791938304901123046875e0), SC_(0.73841077722591654304210596796019202721941795711926e3),
SC_(0.503011474609375e3), SC_(0.9133758544921875e0), SC_(0.75013755084726454965881401907276391709101666410419e3),
SC_(0.503011474609375e3), SC_(0.968867778778076171875e0), SC_(0.89973134282710925452142048450157816262200221102697e3),
SC_(0.10074598388671875e4), SC_(0.12698681652545928955078125e0), SC_(0.10115604555368949483687471890824497026532038567019e4),
SC_(0.10074598388671875e4), SC_(0.135477006435394287109375e0), SC_(0.1012133050497275830780347173002131083103600802088e4),
SC_(0.10074598388671875e4), SC_(0.22103404998779296875e0), SC_(0.1020120880922149604989950464445671598395259388161e4),
SC_(0.10074598388671875e4), SC_(0.308167040348052978515625e0), SC_(0.10327591029439108059157922326032636145569231829932e4),
SC_(0.10074598388671875e4), SC_(0.6323592662811279296875e0), SC_(0.11400597837237931811476044006089184883421460101765e4),
SC_(0.10074598388671875e4), SC_(0.814723670482635498046875e0), SC_(0.12990515604873895842003339764405472011586481003657e4),
SC_(0.10074598388671875e4), SC_(0.835008561611175537109375e0), SC_(0.13286671610382179011061935562304250712176020940221e4),
SC_(0.10074598388671875e4), SC_(0.905791938304901123046875e0), SC_(0.14795587929982445488758894910099973156560147854256e4),
SC_(0.10074598388671875e4), SC_(0.9133758544921875e0), SC_(0.15030813318756246891355137019045501942292731438192e4),
SC_(0.10074598388671875e4), SC_(0.968867778778076171875e0), SC_(0.18031683136020447255217816635153572296860929726591e4),
SC_(0.1185395751953125e4), SC_(0.12698681652545928955078125e0), SC_(0.11902165793870267987435741776753047875920265751213e4),
SC_(0.1185395751953125e4), SC_(0.135477006435394287109375e0), SC_(0.11908897391528240120679535097563994079186387409261e4),
SC_(0.1185395751953125e4), SC_(0.22103404998779296875e0), SC_(0.12002804010608050581829575008183192405062961123642e4),
SC_(0.1185395751953125e4), SC_(0.308167040348052978515625e0), SC_(0.12151378934996375824220394156626328228788742423087e4),
SC_(0.1185395751953125e4), SC_(0.6323592662811279296875e0), SC_(0.13412676685915296881822755838145300215000346890517e4),
SC_(0.1185395751953125e4), SC_(0.814723670482635498046875e0), SC_(0.15281201627814349911219322982937563560261834041215e4),
SC_(0.1185395751953125e4), SC_(0.835008561611175537109375e0), SC_(0.15629208273736966018850653753226433255433492941276e4),
SC_(0.1185395751953125e4), SC_(0.905791938304901123046875e0), SC_(0.17402117426998289313370860215974579190403457757437e4),
SC_(0.1185395751953125e4), SC_(0.9133758544921875e0), SC_(0.17678472099706618291007501715448169066167629554269e4),
SC_(0.1185395751953125e4), SC_(0.968867778778076171875e0), SC_(0.2120363403215687272189669275949606957433496693392e4),
};
#undef SC_

105
test/ellint_k_data.ipp Normal file
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@@ -0,0 +1,105 @@
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 2>, 100> ellint_k_data = {
SC_(-0.99042308330535888671875e0), SC_(0.3377711175347896212115917173531827081735908096628e1),
SC_(-0.936324596405029296875e0), SC_(0.24799928378892127263868582279024816073017669022263e1),
SC_(-0.931098163127899169921875e0), SC_(0.24445366497109921574142184681825951967450363552834e1),
SC_(-0.928566992282867431640625e0), SC_(0.24283992440860978354078883091691713688375646750641e1),
SC_(-0.927107870578765869140625e0), SC_(0.24193766718674199444433297470157473721017375354321e1),
SC_(-0.907647669315338134765625e0), SC_(0.23150567546618192429964125282245930582572797978818e1),
SC_(-0.89755761623382568359375e0), SC_(0.22701438887345149877132302334749426657376446371554e1),
SC_(-0.805727422237396240234375e0), SC_(0.20065967275502056522161145711205880615166307631054e1),
SC_(-0.804910182952880859375e0), SC_(0.20049607901713509576649915223436597681197065440791e1),
SC_(-0.78026759624481201171875e0), SC_(0.19592100556166276984041617991618803394021101627948e1),
SC_(-0.775062084197998046875e0), SC_(0.19503477481367618080344709104861737619417735663137e1),
SC_(-0.749625742435455322265625e0), SC_(0.19104400630324162677555937926672404286027386161554e1),
SC_(-0.748197972774505615234375e0), SC_(0.19083524493958065222471464174677965403570194813599e1),
SC_(-0.746017634868621826171875e0), SC_(0.19051932837924025803305082607208317930893376343866e1),
SC_(-0.729037344455718994140625e0), SC_(0.18817193270349712906579552152250851402884979195389e1),
SC_(-0.7162187099456787109375e0), SC_(0.18652211443514110895753017730892076794376353163691e1),
SC_(-0.70176351070404052734375e0), SC_(0.18477488779057501703815851124765277365377561449605e1),
SC_(-0.684765398502349853515625e0), SC_(0.18285893795597042965531449099985329446409496660036e1),
SC_(-0.657618343830108642578125e0), SC_(0.18007288418337930091030357471813257042005823390856e1),
SC_(-0.65226137638092041015625e0), SC_(0.17955901766989373531455842967467859457919280319805e1),
SC_(-0.626246631145477294921875e0), SC_(0.17721381024097650892501675317068276777213166539113e1),
SC_(-0.62322795391082763671875e0), SC_(0.17695682119254878963375370515480337143290717650699e1),
SC_(-0.579573929309844970703125e0), SC_(0.17355084423179730268283500692922635797002148145716e1),
SC_(-0.576143443584442138671875e0), SC_(0.17330585071273208935299581419876214110701077039073e1),
SC_(-0.557924091815948486328125e0), SC_(0.17205458226692737403200667710314658175352937313565e1),
SC_(-0.4461468160152435302734375e0), SC_(0.1659143428704545241870880533420140506147522333952e1),
SC_(-0.442996323108673095703125e0), SC_(0.16577357283229169972381488150848899831930773096426e1),
SC_(-0.4059340953826904296875e0), SC_(0.16422906110493949856538834271333672987146221978421e1),
SC_(-0.3961667716503143310546875e0), SC_(0.16385456546730544519392193048583469346592283426711e1),
SC_(-0.38365900516510009765625e0), SC_(0.16339371135272803257688801436358682987064021339502e1),
SC_(-0.366892278194427490234375e0), SC_(0.16280775355945302002930914045811739595274403877109e1),
SC_(-0.3657942116260528564453125e0), SC_(0.16277061660792581984612626919271028055659130917587e1),
SC_(-0.2774055898189544677734375e0), SC_(0.16023984430282800438657607498499405531471989727973e1),
SC_(-0.236876904964447021484375e0), SC_(0.15935547153447952975660160168795914210559129958763e1),
SC_(-0.215539872646331787109375e0), SC_(0.1589532821488995266987321628138860611930750500013e1),
SC_(-0.20251691341400146484375e0), SC_(0.15872846186561139876915281752585049624892405264006e1),
SC_(-0.18253175914287567138671875e0), SC_(0.15841312442860499386355917744088632471227360101517e1),
SC_(-0.15647165477275848388671875e0), SC_(0.15805456328241604119645385355233009390341499402715e1),
SC_(-0.155818879604339599609375e0), SC_(0.15804633259546865645050516399359359956031398166357e1),
SC_(-0.12250564992427825927734375e0), SC_(0.15767400871102419514183615836102806382524229776023e1),
SC_(-0.108822040259838104248046875e0), SC_(0.15754779970087063716770992170704593788694293192204e1),
SC_(-0.84016263484954833984375e-1), SC_(0.15735793449827667079522175566532496627258499829808e1),
SC_(-0.5047737061977386474609375e-1), SC_(0.15717983468978644730669790777144243904901266418816e1),
SC_(-0.2924356050789356231689453125e-1), SC_(0.15711323191301626906143245522892930046111479139043e1),
SC_(-0.2485703863203525543212890625e-1), SC_(0.15710390490728134946675992373238514306032071520432e1),
SC_(-0.2046610601246356964111328125e-1), SC_(0.15709608520853443438268600756375428033257896081621e1),
SC_(-0.1881679333746433258056640625e-1), SC_(0.15709353981303437885151982749950681277334084182671e1),
SC_(0.73303808458149433135986328125e-2), SC_(0.15708174289149913873348609319163921760640886342517e1),
SC_(0.93767531216144561767578125e-1), SC_(0.15742662557451933000168330868057640508121413022011e1),
SC_(0.94445712864398956298828125e-1), SC_(0.15743168849992435161106319232000048329301973530501e1),
SC_(0.26472222805023193359375e0), SC_(0.15994564178224078022860215956833860720177728374035e1),
SC_(0.2795303165912628173828125e0), SC_(0.16029072336719100270539575574782330640458373122935e1),
SC_(0.2926295697689056396484375e0), SC_(0.16061468472007804719214570477294979509859730905091e1),
SC_(0.31095921993255615234375e0), SC_(0.1610983807838740712761368067192691405393131953881e1),
SC_(0.311484813690185546875e0), SC_(0.16111278469143224539903626000312660918785264354958e1),
SC_(0.3272143900394439697265625e0), SC_(0.16155797975233104967915214233565515716306532094698e1),
SC_(0.35747349262237548828125e0), SC_(0.16249404264362997324992641484372408858215631632002e1),
SC_(0.3627222478389739990234375e0), SC_(0.16266751570835125835068247288118651474745966539618e1),
SC_(0.3896603286266326904296875e0), SC_(0.16361224926513534404184731359873689992038364400691e1),
SC_(0.4120951592922210693359375e0), SC_(0.16447205720518345410219553921960387345221364427466e1),
SC_(0.418732583522796630859375e0), SC_(0.16473983100889105980743072684285213201961112169823e1),
SC_(0.451680660247802734375e0), SC_(0.16616537578199064695178688197080983284328919711812e1),
SC_(0.4812971055507659912109375e0), SC_(0.16759409027443021223185102539476096588592566487743e1),
SC_(0.486267507076263427734375e0), SC_(0.16784859353297838419400330721985671192135840854661e1),
SC_(0.509375751018524169921875e0), SC_(0.16909133957115563796676413045863923443879243171298e1),
SC_(0.515482723712921142578125e0), SC_(0.16943684153133994180565117266182132481147687142707e1),
SC_(0.52750241756439208984375e0), SC_(0.17013882771778724726932964262059466393678608760062e1),
SC_(0.531035959720611572265625e0), SC_(0.17035089955832848907265521472430416089318818612814e1),
SC_(0.584416687488555908203125e0), SC_(0.17390197327988114565246996689229900966075086201035e1),
SC_(0.587952077388763427734375e0), SC_(0.17416228307854377082064181076439075579393688159215e1),
SC_(0.5904018878936767578125e0), SC_(0.17434466233796448758342732941787231810206075234501e1),
SC_(0.5945618152618408203125e0), SC_(0.17465816562648604997075231101739061981996142156151e1),
SC_(0.5958592891693115234375e0), SC_(0.17475694098213745790315441260074496951659216831348e1),
SC_(0.59621369838714599609375e0), SC_(0.17478400476807070940242210641459121619833657136515e1),
SC_(0.60056293010711669921875e0), SC_(0.17511905345983286033588753251945176786720874355107e1),
SC_(0.6150639057159423828125e0), SC_(0.17627654245195403785778656645694141888969985612575e1),
SC_(0.629449188709259033203125e0), SC_(0.17748975492324966654441702323788071861970996989102e1),
SC_(0.6438083648681640625e0), SC_(0.17877036110717852208569994416480820233927146151031e1),
SC_(0.64691746234893798828125e0), SC_(0.17905734108284599293495949910396246976486037925061e1),
SC_(0.67001879215240478515625e0), SC_(0.18130645541261783392588745817521015225200222756122e1),
SC_(0.698260128498077392578125e0), SC_(0.18436823516091780453599478590327018132893271380223e1),
SC_(0.744858920574188232421875e0), SC_(0.1903528375308813580432291088034833377552119409638e1),
SC_(0.75686252117156982421875e0), SC_(0.1921257878508255118587957424341444494608703851379e1),
SC_(0.81158483028411865234375e0), SC_(0.20185697260071845965032147456371482208660801062775e1),
SC_(0.826752603054046630859375e0), SC_(0.20517631918180497335416092658794507587336758082983e1),
SC_(0.831471920013427734375e0), SC_(0.20628007317688811564201523487885011440347375983853e1),
SC_(0.841750323772430419921875e0), SC_(0.20881524894194487687984856759006121206951763482194e1),
SC_(0.867987096309661865234375e0), SC_(0.21626553443645542835585774105841427525784980815445e1),
SC_(0.90044462680816650390625e0), SC_(0.22824738454300952253057616561926426370482782713694e1),
SC_(0.914334356784820556640625e0), SC_(0.23479275233217975943026959240752324894340069192044e1),
SC_(0.915014088153839111328125e0), SC_(0.23514264944956428937368978831156074286111428698483e1),
SC_(0.918985307216644287109375e0), SC_(0.23725035893866734721028942202359170270846633736916e1),
SC_(0.9297773838043212890625e0), SC_(0.2436037207911617888011813888250469085423814242563e1),
SC_(0.935390174388885498046875e0), SC_(0.24734276363166698887860324191541438396367793619322e1),
SC_(0.937735855579376220703125e0), SC_(0.24901081139855480473523004657581668979713789812992e1),
SC_(0.941185891628265380859375e0), SC_(0.25159148953544058237986278218012688105174747190388e1),
SC_(0.962219536304473876953125e0), SC_(0.27197444631906795382660830171523843323266857162631e1),
SC_(0.985762655735015869140625e0), SC_(0.31847978937935282927541645440535551111318175394252e1),
SC_(0.988137066364288330078125e0), SC_(0.32733547952035871434783118403258690613147460127497e1),
SC_(0.992922723293304443359375e0), SC_(0.35258676303484017878276559590157568137293088406988e1),
};
#undef SC_

505
test/ellint_pi2_data.ipp Normal file
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@@ -0,0 +1,505 @@
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 3>, 500> ellint_pi2_data = {
SC_(-0.871743316650390625e2), SC_(0.12698681652545928955078125e0), SC_(0.1674125184786922275852201144520277497358358213892e0),
SC_(-0.871743316650390625e2), SC_(0.135477006435394287109375e0), SC_(0.16743071541243053183466547814319460702264753849723e0),
SC_(-0.871743316650390625e2), SC_(0.22103404998779296875e0), SC_(0.16768328087467940131221559947745677007068360020936e0),
SC_(-0.871743316650390625e2), SC_(0.308167040348052978515625e0), SC_(0.16807808560619590184466399113136263382376022541855e0),
SC_(-0.871743316650390625e2), SC_(0.6323592662811279296875e0), SC_(0.17122026715243530525631538196923732076962513344995e0),
SC_(-0.871743316650390625e2), SC_(0.814723670482635498046875e0), SC_(0.17534141630242782956646324755267751416323066482835e0),
SC_(-0.871743316650390625e2), SC_(0.835008561611175537109375e0), SC_(0.17605554592184937069060075230541493581360045985831e0),
SC_(-0.871743316650390625e2), SC_(0.905791938304901123046875e0), SC_(0.17950085945970126738588840411224305832081644195523e0),
SC_(-0.871743316650390625e2), SC_(0.9133758544921875e0), SC_(0.18001354683126288823677625533339788309413921715434e0),
SC_(-0.871743316650390625e2), SC_(0.968867778778076171875e0), SC_(0.1861623643134889055406196973715380337805086459718e0),
SC_(-0.8631682586669921875e2), SC_(0.12698681652545928955078125e0), SC_(0.16823313926270090905448439997177323604952165614363e0),
SC_(-0.8631682586669921875e2), SC_(0.135477006435394287109375e0), SC_(0.16825150634432729564119302859989272874459890613116e0),
SC_(-0.8631682586669921875e2), SC_(0.22103404998779296875e0), SC_(0.1685064347403877889119812191305941553416022238658e0),
SC_(-0.8631682586669921875e2), SC_(0.308167040348052978515625e0), SC_(0.16890493817434378352408134048753732273764880942954e0),
SC_(-0.8631682586669921875e2), SC_(0.6323592662811279296875e0), SC_(0.17207676229429286979803490409285729827120332255809e0),
SC_(-0.8631682586669921875e2), SC_(0.814723670482635498046875e0), SC_(0.17623726816880267488571098227884869828610508117243e0),
SC_(-0.8631682586669921875e2), SC_(0.835008561611175537109375e0), SC_(0.17695826377184426719315773208991477000910029521482e0),
SC_(-0.8631682586669921875e2), SC_(0.905791938304901123046875e0), SC_(0.18043685472666137350386874269852689421871499307432e0),
SC_(-0.8631682586669921875e2), SC_(0.9133758544921875e0), SC_(0.18095451269215495642582809340040493458719660291695e0),
SC_(-0.8631682586669921875e2), SC_(0.968867778778076171875e0), SC_(0.18716320978769236210159810482536135896363176742343e0),
SC_(-0.7767555999755859375e2), SC_(0.12698681652545928955078125e0), SC_(0.17723805469497005138970658754479684034139004976308e0),
SC_(-0.7767555999755859375e2), SC_(0.135477006435394287109375e0), SC_(0.17725833547565335175365419889134424107345532565877e0),
SC_(-0.7767555999755859375e2), SC_(0.22103404998779296875e0), SC_(0.17753984165266644170812805305717146395671420094776e0),
SC_(-0.7767555999755859375e2), SC_(0.308167040348052978515625e0), SC_(0.17797995186642175489596380169052339842058010566152e0),
SC_(-0.7767555999755859375e2), SC_(0.6323592662811279296875e0), SC_(0.18148541433576540744902539513186881476311716728227e0),
SC_(-0.7767555999755859375e2), SC_(0.814723670482635498046875e0), SC_(0.18608934162792226467645945802477829030064897877359e0),
SC_(-0.7767555999755859375e2), SC_(0.835008561611175537109375e0), SC_(0.18688773786015825638183632881144496436170974248241e0),
SC_(-0.7767555999755859375e2), SC_(0.905791938304901123046875e0), SC_(0.19074161304026152406747562924366026789550786287803e0),
SC_(-0.7767555999755859375e2), SC_(0.9133758544921875e0), SC_(0.19131534459003262670423020772987735547496828534479e0),
SC_(-0.7767555999755859375e2), SC_(0.968867778778076171875e0), SC_(0.19819980751100172478383698040644955494927942439633e0),
SC_(-0.6887512969970703125e2), SC_(0.12698681652545928955078125e0), SC_(0.18807673277332863572439323149240003591140207896313e0),
SC_(-0.6887512969970703125e2), SC_(0.135477006435394287109375e0), SC_(0.18809942894445066895052818190744724738603008664113e0),
SC_(-0.6887512969970703125e2), SC_(0.22103404998779296875e0), SC_(0.18841448356519705070217464671784444233160761372693e0),
SC_(-0.6887512969970703125e2), SC_(0.308167040348052978515625e0), SC_(0.1889071243831848858362782229683818449975108831782e0),
SC_(-0.6887512969970703125e2), SC_(0.6323592662811279296875e0), SC_(0.19283429586558276570559152326779096606423284809356e0),
SC_(-0.6887512969970703125e2), SC_(0.814723670482635498046875e0), SC_(0.19799982175435638480350130578229601669520072124985e0),
SC_(-0.6887512969970703125e2), SC_(0.835008561611175537109375e0), SC_(0.19889635678180396557867565231805298960791065374116e0),
SC_(-0.6887512969970703125e2), SC_(0.905791938304901123046875e0), SC_(0.20322643729961523231468602423697484017124986208135e0),
SC_(-0.6887512969970703125e2), SC_(0.9133758544921875e0), SC_(0.20387136735607637387480442251720783691354881786227e0),
SC_(-0.6887512969970703125e2), SC_(0.968867778778076171875e0), SC_(0.21161453485391920919877033907030403099202567227684e0),
SC_(-0.361317138671875e2), SC_(0.12698681652545928955078125e0), SC_(0.25807395141922622129192766140410293065730739479983e0),
SC_(-0.361317138671875e2), SC_(0.135477006435394287109375e0), SC_(0.25811504785027394933935002408996823143204300773286e0),
SC_(-0.361317138671875e2), SC_(0.22103404998779296875e0), SC_(0.25868576719992802882962788582860568063380617782066e0),
SC_(-0.361317138671875e2), SC_(0.308167040348052978515625e0), SC_(0.25957908488371220675239650970681566250728634199314e0),
SC_(-0.361317138671875e2), SC_(0.6323592662811279296875e0), SC_(0.26673759528219383447347331664283586398767715711549e0),
SC_(-0.361317138671875e2), SC_(0.814723670482635498046875e0), SC_(0.27624188294753047128196814230568161804652916161863e0),
SC_(-0.361317138671875e2), SC_(0.835008561611175537109375e0), SC_(0.27790012081814387436020029758750215255750597263172e0),
SC_(-0.361317138671875e2), SC_(0.905791938304901123046875e0), SC_(0.2859382172923565009441543467819242355142627417165e0),
SC_(-0.361317138671875e2), SC_(0.9133758544921875e0), SC_(0.28713902465022766561269528868552426093781301498377e0),
SC_(-0.361317138671875e2), SC_(0.968867778778076171875e0), SC_(0.30160824142871788586221637018441354445836038223767e0),
SC_(-0.17712909698486328125e2), SC_(0.12698681652545928955078125e0), SC_(0.3636729206179323089584368881165294845044180186145e0),
SC_(-0.17712909698486328125e2), SC_(0.135477006435394287109375e0), SC_(0.36375007260253424844068666864895304741725434790239e0),
SC_(-0.17712909698486328125e2), SC_(0.22103404998779296875e0), SC_(0.36482213460485031933513677664348491484058391598753e0),
SC_(-0.17712909698486328125e2), SC_(0.308167040348052978515625e0), SC_(0.3665025099771102643902474028243205860953862778759e0),
SC_(-0.17712909698486328125e2), SC_(0.6323592662811279296875e0), SC_(0.38006573775283109160868693734996149636084699279112e0),
SC_(-0.17712909698486328125e2), SC_(0.814723670482635498046875e0), SC_(0.39831093780271045079340378355274398784600363650505e0),
SC_(-0.17712909698486328125e2), SC_(0.835008561611175537109375e0), SC_(0.40151794120384245966685931317645917709530730447343e0),
SC_(-0.17712909698486328125e2), SC_(0.905791938304901123046875e0), SC_(0.41714508520694688780251187692727469785205563133695e0),
SC_(-0.17712909698486328125e2), SC_(0.9133758544921875e0), SC_(0.41948979991844566329448196311636376356543866861521e0),
SC_(-0.17712909698486328125e2), SC_(0.968867778778076171875e0), SC_(0.44789348577906501674071047048613668162470396490226e0),
SC_(-0.15664134979248046875e2), SC_(0.12698681652545928955078125e0), SC_(0.38540911235754062027100516500243302844112919081157e0),
SC_(-0.15664134979248046875e2), SC_(0.135477006435394287109375e0), SC_(0.38549479957369784596836782557901855735579578476386e0),
SC_(-0.15664134979248046875e2), SC_(0.22103404998779296875e0), SC_(0.38668559678037966531615532383662693169751820619251e0),
SC_(-0.15664134979248046875e2), SC_(0.308167040348052978515625e0), SC_(0.38855258005908474248043155982604199055563647089976e0),
SC_(-0.15664134979248046875e2), SC_(0.6323592662811279296875e0), SC_(0.4036431452565898907217581801534326597925982641061e0),
SC_(-0.15664134979248046875e2), SC_(0.814723670482635498046875e0), SC_(0.42399489399858261609254890113247088932413060034193e0),
SC_(-0.15664134979248046875e2), SC_(0.835008561611175537109375e0), SC_(0.42757740157245514965345992590002825014839199992751e0),
SC_(-0.15664134979248046875e2), SC_(0.905791938304901123046875e0), SC_(0.44505252332215040025742915418095282301447922985417e0),
SC_(-0.15664134979248046875e2), SC_(0.9133758544921875e0), SC_(0.44767679456118756417042666801411008888573438377822e0),
SC_(-0.15664134979248046875e2), SC_(0.968867778778076171875e0), SC_(0.47950133312940792812445326014374908427710586619841e0),
SC_(-0.85150146484375e1), SC_(0.12698681652545928955078125e0), SC_(0.51024420337071918152663377907810133020609909421411e0),
SC_(-0.85150146484375e1), SC_(0.135477006435394287109375e0), SC_(0.51038538213980156116084936888558434244159146142024e0),
SC_(-0.85150146484375e1), SC_(0.22103404998779296875e0), SC_(0.51234852907158154983060025475260748897671531226719e0),
SC_(-0.85150146484375e1), SC_(0.308167040348052978515625e0), SC_(0.51543084244645024279702031896115309018656014885961e0),
SC_(-0.85150146484375e1), SC_(0.6323592662811279296875e0), SC_(0.54053307124193505250530229329510213640826062354041e0),
SC_(-0.85150146484375e1), SC_(0.814723670482635498046875e0), SC_(0.57485945052545126554066528283220704394725671520491e0),
SC_(-0.85150146484375e1), SC_(0.835008561611175537109375e0), SC_(0.58095036613926759413831871317625984920620978697546e0),
SC_(-0.85150146484375e1), SC_(0.905791938304901123046875e0), SC_(0.6108332503553336432615891037745891649411427341433e0),
SC_(-0.85150146484375e1), SC_(0.9133758544921875e0), SC_(0.61534259474950438497700068371964480496721253218291e0),
SC_(-0.85150146484375e1), SC_(0.968867778778076171875e0), SC_(0.67036117324955476789547801395426121216314167238235e0),
SC_(-0.77490386962890625e1), SC_(0.12698681652545928955078125e0), SC_(0.53214537749930974923530793848098446673924558763616e0),
SC_(-0.77490386962890625e1), SC_(0.135477006435394287109375e0), SC_(0.53229733769976224201856173461401623455938844211535e0),
SC_(-0.77490386962890625e1), SC_(0.22103404998779296875e0), SC_(0.53441061264437586894262479620958694286810111069806e0),
SC_(-0.77490386962890625e1), SC_(0.308167040348052978515625e0), SC_(0.5377294161924223676286300166620738439919478705884e0),
SC_(-0.77490386962890625e1), SC_(0.6323592662811279296875e0), SC_(0.56479107742731414101881346070741395143895861655694e0),
SC_(-0.77490386962890625e1), SC_(0.814723670482635498046875e0), SC_(0.601881967717377378801568953100251074711843156646e0),
SC_(-0.77490386962890625e1), SC_(0.835008561611175537109375e0), SC_(0.6084722098461551401225157616926834919686419666249e0),
SC_(-0.77490386962890625e1), SC_(0.905791938304901123046875e0), SC_(0.6408364334233277447605831932496202047571760069003e0),
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SC_(0.992881298065185546875e0), SC_(0.135477006435394287109375e0), SC_(0.18777093567206457027427679959699782319685742366512e2),
SC_(0.992881298065185546875e0), SC_(0.188381969928741455078125e0), SC_(0.18930084599083729385128059668237675166261690632749e2),
SC_(0.992881298065185546875e0), SC_(0.22103404998779296875e0), SC_(0.19052199240193895593945310055717452371775388831154e2),
SC_(0.992881298065185546875e0), SC_(0.278498232364654541015625e0), SC_(0.19322964997802663294514050078545249868423535988744e2),
SC_(0.992881298065185546875e0), SC_(0.308167040348052978515625e0), SC_(0.19493130642004336551317918485444554537583720971045e2),
SC_(0.992881298065185546875e0), SC_(0.546881496906280517578125e0), SC_(0.21918916261281206367305171092343155433491434321112e2),
SC_(0.992881298065185546875e0), SC_(0.54722058773040771484375e0), SC_(0.21924227186423693776610203715720022304704645216433e2),
SC_(0.992881298065185546875e0), SC_(0.6323592662811279296875e0), SC_(0.23529707797658380333063244192127188223302192558852e2),
SC_(0.992881298065185546875e0), SC_(0.814723670482635498046875e0), SC_(0.30575859801875799739375471862054166647512113645807e2),
SC_(0.992881298065185546875e0), SC_(0.835008561611175537109375e0), SC_(0.32043676668849497954006889709974841705829962521726e2),
SC_(0.992881298065185546875e0), SC_(0.905791938304901123046875e0), SC_(0.40366423262962757965206220506997277916388787599754e2),
SC_(0.992881298065185546875e0), SC_(0.9133758544921875e0), SC_(0.41799032567813402312687064507199400755567816106555e2),
SC_(0.992881298065185546875e0), SC_(0.957506835460662841796875e0), SC_(0.56128172471137549389344415739570835037807068562013e2),
SC_(0.992881298065185546875e0), SC_(0.964888513088226318359375e0), SC_(0.60675965176721448584035543697674959062919562854532e2),
SC_(0.992881298065185546875e0), SC_(0.967694938182830810546875e0), SC_(0.6276157259900044417409413119621359487406867750706e2),
SC_(0.992881298065185546875e0), SC_(0.968867778778076171875e0), SC_(0.63707286094632152287529888037895307035240586536621e2),
SC_(0.992881298065185546875e0), SC_(0.992881298065185546875e0), SC_(0.1120903461776478755543567802910659613184060305846e3),
SC_(0.992881298065185546875e0), SC_(0.996461331844329833984375e0), SC_(0.14251487713932698105862123589172439943765575331836e3),
SC_(0.996461331844329833984375e0), SC_(0.97540400922298431396484375e-1), SC_(0.26525228363305081889178508646675136190937635090909e2),
SC_(0.996461331844329833984375e0), SC_(0.12698681652545928955078125e0), SC_(0.26609183579980223193874498139758348544252737042937e2),
SC_(0.996461331844329833984375e0), SC_(0.135477006435394287109375e0), SC_(0.26637665635242177149342425025355691196208309182209e2),
SC_(0.996461331844329833984375e0), SC_(0.188381969928741455078125e0), SC_(0.26859854936512317034208182700195391532482709459344e2),
SC_(0.996461331844329833984375e0), SC_(0.22103404998779296875e0), SC_(0.27037248327624528229706950425004550527856127233531e2),
SC_(0.996461331844329833984375e0), SC_(0.278498232364654541015625e0), SC_(0.27430729276514554098633382905293142866236072404168e2),
SC_(0.996461331844329833984375e0), SC_(0.308167040348052978515625e0), SC_(0.27678118753104768841544241662525580388107866876282e2),
SC_(0.996461331844329833984375e0), SC_(0.546881496906280517578125e0), SC_(0.31213240738021743521644147864390542809845218224843e2),
SC_(0.996461331844329833984375e0), SC_(0.54722058773040771484375e0), SC_(0.31220997617474390630713051844594666758716918064286e2),
SC_(0.996461331844329833984375e0), SC_(0.6323592662811279296875e0), SC_(0.33569286497756543464285670293321380122426984476525e2),
SC_(0.996461331844329833984375e0), SC_(0.814723670482635498046875e0), SC_(0.4395386723690573604089341802484590769216982250272e2),
SC_(0.996461331844329833984375e0), SC_(0.835008561611175537109375e0), SC_(0.46132844280074174499202090082014892744405520616437e2),
SC_(0.996461331844329833984375e0), SC_(0.905791938304901123046875e0), SC_(0.58587652855298148334031858334558601606458070313074e2),
SC_(0.996461331844329833984375e0), SC_(0.9133758544921875e0), SC_(0.60748367915375862531255830821598900720628098154312e2),
SC_(0.996461331844329833984375e0), SC_(0.957506835460662841796875e0), SC_(0.82625470558383026944908893678685038814065230848324e2),
SC_(0.996461331844329833984375e0), SC_(0.964888513088226318359375e0), SC_(0.89667844444233284890246553088819296424506047104969e2),
SC_(0.996461331844329833984375e0), SC_(0.967694938182830810546875e0), SC_(0.92913130201351090779050947500643074594936139585892e2),
SC_(0.996461331844329833984375e0), SC_(0.968867778778076171875e0), SC_(0.94387923495063103062113556546657899915314134335375e2),
SC_(0.996461331844329833984375e0), SC_(0.992881298065185546875e0), SC_(0.17241273531195384234344983626787913729253040033677e3),
SC_(0.996461331844329833984375e0), SC_(0.996461331844329833984375e0), SC_(0.22388123241793230536309311882526020237726710081432e3),
};
#undef SC_

405
test/ellint_pi3_data.ipp Normal file
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@@ -0,0 +1,405 @@
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 4>, 400> ellint_pi3_data = {
SC_(0.97540400922298431396484375e-1), SC_(0.15321610867977142333984375e0), SC_(0.814723670482635498046875e0), SC_(0.15373203842748125370338546651780574888816846402842e0),
SC_(0.97540400922298431396484375e-1), SC_(0.1994704306125640869140625e0), SC_(0.135477006435394287109375e0), SC_(0.19975117232566753482238350513231879856319046077755e0),
SC_(0.97540400922298431396484375e-1), SC_(0.2128067910671234130859375e0), SC_(0.905791938304901123046875e0), SC_(0.21444962146028791552496083456124507126701014421723e0),
SC_(0.97540400922298431396484375e-1), SC_(0.295909702777862548828125e0), SC_(0.835008561611175537109375e0), SC_(0.2997980220798275355640498732995940042091456814389e0),
SC_(0.97540400922298431396484375e-1), SC_(0.3471994698047637939453125e0), SC_(0.12698681652545928955078125e0), SC_(0.3486476485633547682857103272510437125962758824058e0),
SC_(0.97540400922298431396484375e-1), SC_(0.4374639987945556640625e0), SC_(0.968867778778076171875e0), SC_(0.45394401267101670348318068398554096043112056011139e0),
SC_(0.97540400922298431396484375e-1), SC_(0.4840676784515380859375e0), SC_(0.9133758544921875e0), SC_(0.50429356834860180919136192213432534063086058053706e0),
SC_(0.97540400922298431396484375e-1), SC_(0.859039485454559326171875e0), SC_(0.22103404998779296875e0), SC_(0.88214398516284753446093152446515519356116616485632e0),
SC_(0.97540400922298431396484375e-1), SC_(0.859572112560272216796875e0), SC_(0.6323592662811279296875e0), SC_(0.92068616339339750141383142107393122316780108757901e0),
SC_(0.97540400922298431396484375e-1), SC_(0.993307650089263916015625e0), SC_(0.308167040348052978515625e0), SC_(0.10344161605846899329010060099405650089702846030678e1),
SC_(0.97540400922298431396484375e-1), SC_(0.127976500988006591796875e1), SC_(0.97540400922298431396484375e-1), SC_(0.13345405612458198850035058621296608418958648996025e1),
SC_(0.97540400922298431396484375e-1), SC_(0.131162846088409423828125e1), SC_(0.54722058773040771484375e0), SC_(0.1467211661750789199498096403270216766602112811216e1),
SC_(0.97540400922298431396484375e-1), SC_(0.142281472682952880859375e1), SC_(0.278498232364654541015625e0), SC_(0.1517376955674343715832681461618162299318704226245e1),
SC_(0.97540400922298431396484375e-1), SC_(0.14347274303436279296875e1), SC_(0.188381969928741455078125e0), SC_(0.15154584947701684136724391750741680569501800622377e1),
SC_(0.97540400922298431396484375e-1), SC_(0.150404822826385498046875e1), SC_(0.546881496906280517578125e0), SC_(0.17193768372540183459266121250638009185486028760609e1),
SC_(0.97540400922298431396484375e-1), SC_(0.15156433582305908203125e1), SC_(0.992881298065185546875e0), SC_(0.32971643837652261637854814203821825514327178475199e1),
SC_(0.97540400922298431396484375e-1), SC_(0.15200517177581787109375e1), SC_(0.957506835460662841796875e0), SC_(0.26533602409619323321869623248304538129999833091585e1),
SC_(0.97540400922298431396484375e-1), SC_(0.1521893978118896484375e1), SC_(0.996461331844329833984375e0), SC_(0.3561780644579714064351594651991953922505125185799e1),
SC_(0.97540400922298431396484375e-1), SC_(0.155961430072784423828125e1), SC_(0.964888513088226318359375e0), SC_(0.28980698413581142714910692917445567690962125009838e1),
SC_(0.97540400922298431396484375e-1), SC_(0.156523787975311279296875e1), SC_(0.967694938182830810546875e0), SC_(0.2963846383355250968965561470164902664673523718254e1),
SC_(0.12698681652545928955078125e0), SC_(0.15321610867977142333984375e0), SC_(0.15761308372020721435546875e0), SC_(0.15338276528480469307645524589925911983842933545318e0),
SC_(0.12698681652545928955078125e0), SC_(0.1994704306125640869140625e0), SC_(0.725838959217071533203125e0), SC_(0.20050472017966223244832559958930749817872953420574e0),
SC_(0.12698681652545928955078125e0), SC_(0.2128067910671234130859375e0), SC_(0.970592796802520751953125e0), SC_(0.21474633975859950860058990149085299903493818118173e0),
SC_(0.12698681652545928955078125e0), SC_(0.295909702777862548828125e0), SC_(0.981109678745269775390625e0), SC_(0.30126622877564752427416022416319928001205083826745e0),
SC_(0.12698681652545928955078125e0), SC_(0.3471994698047637939453125e0), SC_(0.957166969776153564453125e0), SC_(0.35556281810161664845441307089338900623226704681013e0),
SC_(0.12698681652545928955078125e0), SC_(0.4374639987945556640625e0), SC_(0.109861753880977630615234375e0), SC_(0.44108704490870617851306791784352122043342900288043e0),
SC_(0.12698681652545928955078125e0), SC_(0.4840676784515380859375e0), SC_(0.4853756427764892578125e0), SC_(0.4931534053333340013873746669080440363943172483071e0),
SC_(0.12698681652545928955078125e0), SC_(0.859039485454559326171875e0), SC_(0.79810583591461181640625e0), SC_(0.95793555582395747656127633027011309520362186574239e0),
SC_(0.12698681652545928955078125e0), SC_(0.859572112560272216796875e0), SC_(0.80028045177459716796875e0), SC_(0.95916493478176953527039854676450394699681072398641e0),
SC_(0.12698681652545928955078125e0), SC_(0.993307650089263916015625e0), SC_(0.297029435634613037109375e0), SC_(0.10423576221417789616871878908198112649827548095731e1),
SC_(0.12698681652545928955078125e0), SC_(0.127976500988006591796875e1), SC_(0.14188633859157562255859375e0), SC_(0.13546856275247299959686911377471236914557130492097e1),
SC_(0.12698681652545928955078125e0), SC_(0.131162846088409423828125e1), SC_(0.47834846191108226776123046875e-2), SC_(0.13852508127489059545144640536254575613018719622883e1),
SC_(0.12698681652545928955078125e0), SC_(0.142281472682952880859375e1), SC_(0.4217612743377685546875e0), SC_(0.1580806460730606927026951555195055758185719667744e1),
SC_(0.12698681652545928955078125e0), SC_(0.14347274303436279296875e1), SC_(0.1124645173549652099609375e0), SC_(0.15299877934449998899665605808479497934876736447949e1),
SC_(0.12698681652545928955078125e0), SC_(0.150404822826385498046875e1), SC_(0.915735542774200439453125e0), SC_(0.23689609442676919170416815484427154520853373075881e1),
SC_(0.12698681652545928955078125e0), SC_(0.15156433582305908203125e1), SC_(0.639763355255126953125e0), SC_(0.1835738109897334786523262319533878046183264001931e1),
SC_(0.12698681652545928955078125e0), SC_(0.15200517177581787109375e1), SC_(0.792207300662994384765625e0), SC_(0.20421897283663486226184747704649952019905530832883e1),
SC_(0.12698681652545928955078125e0), SC_(0.1521893978118896484375e1), SC_(0.878430664539337158203125e0), SC_(0.22634516501807612485356151537759920819079714452558e1),
SC_(0.12698681652545928955078125e0), SC_(0.155961430072784423828125e1), SC_(0.9594924449920654296875e0), SC_(0.28887516554719816744397706140122177270738385968024e1),
SC_(0.12698681652545928955078125e0), SC_(0.156523787975311279296875e1), SC_(0.50366270542144775390625e0), SC_(0.18034472925184640376371577046428385276285373444411e1),
SC_(0.135477006435394287109375e0), SC_(0.15321610867977142333984375e0), SC_(0.655740678310394287109375e0), SC_(0.15363629557196132980883089360225522896492220958322e0),
SC_(0.135477006435394287109375e0), SC_(0.1994704306125640869140625e0), SC_(0.797928631305694580078125e0), SC_(0.20067494179979137242421676287559757328741739620642e0),
SC_(0.135477006435394287109375e0), SC_(0.2128067910671234130859375e0), SC_(0.357116796076297760009765625e-1), SC_(0.21324169024677035294223198881641105042673468575295e0),
SC_(0.135477006435394287109375e0), SC_(0.295909702777862548828125e0), SC_(0.3612940013408660888671875e0), SC_(0.29762814633345360441629373229306400484051906392213e0),
SC_(0.135477006435394287109375e0), SC_(0.3471994698047637939453125e0), SC_(0.84912931919097900390625e0), SC_(0.35421678576166500134526995976876470429367721514915e0),
SC_(0.135477006435394287109375e0), SC_(0.4374639987945556640625e0), SC_(0.21192432940006256103515625e0), SC_(0.44177167179472452041878404853114448084677945000124e0),
SC_(0.135477006435394287109375e0), SC_(0.4840676784515380859375e0), SC_(0.93399322032928466796875e0), SC_(0.50663380674601173483407086537779743434452929228299e0),
SC_(0.135477006435394287109375e0), SC_(0.859039485454559326171875e0), SC_(0.6813595294952392578125e0), SC_(0.93627839278165512585472067471532220087472706511487e0),
SC_(0.135477006435394287109375e0), SC_(0.859572112560272216796875e0), SC_(0.67873513698577880859375e0), SC_(0.93649514133220802251023716495055301794222292469291e0),
SC_(0.135477006435394287109375e0), SC_(0.993307650089263916015625e0), SC_(0.3987385332584381103515625e0), SC_(0.10560205210680177542821652194191329203962951766098e1),
SC_(0.135477006435394287109375e0), SC_(0.127976500988006591796875e1), SC_(0.75774013996124267578125e0), SC_(0.15792362576660079817584588221413499564813109220967e1),
SC_(0.135477006435394287109375e0), SC_(0.131162846088409423828125e1), SC_(0.740647256374359130859375e0), SC_(0.16166573009327473944412502794295013421915138113773e1),
SC_(0.135477006435394287109375e0), SC_(0.142281472682952880859375e1), SC_(0.74313247203826904296875e0), SC_(0.18051149573204353151046319086097224034327358735037e1),
SC_(0.135477006435394287109375e0), SC_(0.14347274303436279296875e1), SC_(0.474758684635162353515625e0), SC_(0.16246331859624891584468937862242197255022663725014e1),
SC_(0.135477006435394287109375e0), SC_(0.150404822826385498046875e1), SC_(0.3922270238399505615234375e0), SC_(0.16794499146710961167059977468015447083859789387452e1),
SC_(0.135477006435394287109375e0), SC_(0.15156433582305908203125e1), SC_(0.42208766937255859375e0), SC_(0.17060778738061936719641657840144566082201208057621e1),
SC_(0.135477006435394287109375e0), SC_(0.15200517177581787109375e1), SC_(0.65547788143157958984375e0), SC_(0.18666567615959102360545655098338303883335250287837e1),
SC_(0.135477006435394287109375e0), SC_(0.1521893978118896484375e1), SC_(0.1738651692867279052734375e0), SC_(0.16454282072183386718850345865233706115846811877772e1),
SC_(0.135477006435394287109375e0), SC_(0.155961430072784423828125e1), SC_(0.1711866855621337890625e0), SC_(0.16893141542034271144719727903810757021076763554868e1),
SC_(0.135477006435394287109375e0), SC_(0.156523787975311279296875e1), SC_(0.3019131124019622802734375e0), SC_(0.17247629437572107835994205744033158553091594172942e1),
SC_(0.188381969928741455078125e0), SC_(0.15321610867977142333984375e0), SC_(0.70604610443115234375e0), SC_(0.15374129235371893318320391783184832151469294397024e0),
SC_(0.188381969928741455078125e0), SC_(0.1994704306125640869140625e0), SC_(0.797279894351959228515625e0), SC_(0.2008145356675702347171190965342317709807636891598e0),
SC_(0.188381969928741455078125e0), SC_(0.2128067910671234130859375e0), SC_(0.318328440189361572265625e-1), SC_(0.21341117056965599965495209080176878817755967511103e0),
SC_(0.188381969928741455078125e0), SC_(0.295909702777862548828125e0), SC_(0.316550433635711669921875e0), SC_(0.29795513263165928606457135223504215685844085773217e0),
SC_(0.188381969928741455078125e0), SC_(0.3471994698047637939453125e0), SC_(0.2769229710102081298828125e0), SC_(0.35033068412795226925211701071698054849499734821317e0),
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SC_(0.992881298065185546875e0), SC_(0.1994704306125640869140625e0), SC_(0.71846997737884521484375e0), SC_(0.20283934930431330261325692288358107410442895192458e0),
SC_(0.992881298065185546875e0), SC_(0.2128067910671234130859375e0), SC_(0.29632079601287841796875e0), SC_(0.21619844220527214635649026415392786440017796933018e0),
SC_(0.992881298065185546875e0), SC_(0.295909702777862548828125e0), SC_(0.2878049910068511962890625e0), SC_(0.3051647326285145064763788149974065042939649411249e0),
SC_(0.992881298065185546875e0), SC_(0.3471994698047637939453125e0), SC_(0.74469280242919921875e0), SC_(0.36593269361963920740660627814234613035125736530233e0),
SC_(0.992881298065185546875e0), SC_(0.4374639987945556640625e0), SC_(0.623435556888580322265625e0), SC_(0.47351038005245946606485569936799511854047412964646e0),
SC_(0.992881298065185546875e0), SC_(0.4840676784515380859375e0), SC_(0.188955008983612060546875e0), SC_(0.52619421119616314908557198345534215266757025628341e0),
SC_(0.992881298065185546875e0), SC_(0.859039485454559326171875e0), SC_(0.811873972415924072265625e0), SC_(0.12796147420322316976041013515903300942049403300717e1),
SC_(0.992881298065185546875e0), SC_(0.859572112560272216796875e0), SC_(0.6867754459381103515625e0), SC_(0.12394269966981472546595377372621649553539498692944e1),
SC_(0.992881298065185546875e0), SC_(0.993307650089263916015625e0), SC_(0.31250798702239990234375e0), SC_(0.15534506456507100564291157167033185308229885626081e1),
SC_(0.992881298065185546875e0), SC_(0.127976500988006591796875e1), SC_(0.18351115286350250244140625e0), SC_(0.32883134974911278663257207579294642984195789886813e1),
SC_(0.992881298065185546875e0), SC_(0.131162846088409423828125e1), SC_(0.3857105076313018798828125e0), SC_(0.3843930070475687905185740186007796682476313279295e1),
SC_(0.992881298065185546875e0), SC_(0.142281472682952880859375e1), SC_(0.3684845864772796630859375e0), SC_(0.64560281183013155713676475264767841267885661014251e1),
SC_(0.992881298065185546875e0), SC_(0.14347274303436279296875e1), SC_(0.3439297378063201904296875e0), SC_(0.68762448789590812867204741141193446919124297531292e1),
SC_(0.992881298065185546875e0), SC_(0.150404822826385498046875e1), SC_(0.62561857700347900390625e0), SC_(0.13204500086777579559121699778257730234656273348984e2),
SC_(0.992881298065185546875e0), SC_(0.15156433582305908203125e1), SC_(0.81576907634735107421875e0), SC_(0.18782686397271619660785945631793130083787364064634e2),
SC_(0.992881298065185546875e0), SC_(0.15200517177581787109375e1), SC_(0.7802274227142333984375e0), SC_(0.18302545936290427541117117730722002834553061125842e2),
SC_(0.992881298065185546875e0), SC_(0.1521893978118896484375e1), SC_(0.669285118579864501953125e0), SC_(0.16059155876792932443850017386340255003749606531065e2),
SC_(0.992881298065185546875e0), SC_(0.155961430072784423828125e1), SC_(0.811257660388946533203125e-1), SC_(0.17107262415330151383028878013437636789944479173721e2),
SC_(0.992881298065185546875e0), SC_(0.156523787975311279296875e1), SC_(0.379418849945068359375e0), SC_(0.19155786972659388496036522827203540528048007161044e2),
SC_(0.996461331844329833984375e0), SC_(0.15321610867977142333984375e0), SC_(0.929385960102081298828125e0), SC_(0.15494953789788259980228066836666586023123819724425e0),
SC_(0.996461331844329833984375e0), SC_(0.1994704306125640869140625e0), SC_(0.4584968984127044677734375e0), SC_(0.20243262749758402603750294407634188860785303898664e0),
SC_(0.996461331844329833984375e0), SC_(0.2128067910671234130859375e0), SC_(0.775712668895721435546875e0), SC_(0.21706303863374380621352712917030134681912729698606e0),
SC_(0.996461331844329833984375e0), SC_(0.295909702777862548828125e0), SC_(0.303613960742950439453125e0), SC_(0.30524071829572125811103009319660245769811854653147e0),
SC_(0.996461331844329833984375e0), SC_(0.3471994698047637939453125e0), SC_(0.4867916405200958251953125e0), SC_(0.36356073608058866564834344897710010972287253451556e0),
SC_(0.996461331844329833984375e0), SC_(0.4374639987945556640625e0), SC_(0.910564959049224853515625e0), SC_(0.48104301408957402493870044558559339292659904746407e0),
SC_(0.996461331844329833984375e0), SC_(0.4840676784515380859375e0), SC_(0.4358585774898529052734375e0), SC_(0.5296599894432982217860267176354900496432490384687e0),
SC_(0.996461331844329833984375e0), SC_(0.859039485454559326171875e0), SC_(0.488617718219757080078125e0), SC_(0.11959816962457412713215082894885440106679306405223e1),
SC_(0.996461331844329833984375e0), SC_(0.859572112560272216796875e0), SC_(0.4467837512493133544921875e0), SC_(0.11905815264303277217419460505969483267592093504852e1),
SC_(0.996461331844329833984375e0), SC_(0.993307650089263916015625e0), SC_(0.75578987598419189453125e0), SC_(0.17303829899385816376582825125863049753469531971278e1),
SC_(0.996461331844329833984375e0), SC_(0.127976500988006591796875e1), SC_(0.3063494861125946044921875e0), SC_(0.33959201984939021366299708945798000348464210899788e1),
SC_(0.996461331844329833984375e0), SC_(0.131162846088409423828125e1), SC_(0.108061917126178741455078125e0), SC_(0.37244311575010030859404652598599661337479280352413e1),
SC_(0.996461331844329833984375e0), SC_(0.142281472682952880859375e1), SC_(0.5085086822509765625e0), SC_(0.71622395151588347106386969682257760699123684023386e1),
SC_(0.996461331844329833984375e0), SC_(0.14347274303436279296875e1), SC_(0.39358985424041748046875e0), SC_(0.73636293852590201326616972102360781065664379097234e1),
SC_(0.996461331844329833984375e0), SC_(0.150404822826385498046875e1), SC_(0.510771572589874267578125e0), SC_(0.13953417098210141831895151114277855224069335314941e2),
SC_(0.996461331844329833984375e0), SC_(0.15156433582305908203125e1), SC_(0.870186746120452880859375e0), SC_(0.2556857706461314333232853600430574327145004073045e2),
SC_(0.996461331844329833984375e0), SC_(0.15200517177581787109375e1), SC_(0.817627727985382080078125e0), SC_(0.23625019083977016071256452688852096136119845707138e2),
SC_(0.996461331844329833984375e0), SC_(0.1521893978118896484375e1), SC_(0.36086070537567138671875e0), SC_(0.15792458525021165627427857010031529171479777626611e2),
SC_(0.996461331844329833984375e0), SC_(0.155961430072784423828125e1), SC_(0.79483139514923095703125e0), SC_(0.36995201253231850772712106938485439098332159356711e2),
SC_(0.996461331844329833984375e0), SC_(0.156523787975311279296875e1), SC_(0.917117893695831298828125e0), SC_(0.57989207945838172546694589268843963845498536168854e2),
};
#undef SC_

385
test/ellint_pi3_large_data.ipp Normal file
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@@ -0,0 +1,385 @@
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 4>, 380> ellint_pi3_large_data = {
SC_(-0.882951507568359375e2), SC_(-0.80491924285888671875e1), SC_(0.814723670482635498046875e0), SC_(-0.87472421400728425336727040442604900083192977041785e0),
SC_(-0.882951507568359375e2), SC_(-0.7460263729095458984375e1), SC_(0.135477006435394287109375e0), SC_(-0.82718880423302271609361236805097048706326618138613e0),
SC_(-0.882951507568359375e2), SC_(-0.729045963287353515625e1), SC_(0.905791938304901123046875e0), SC_(-0.87747551276758882959544200152954525505618423971659e0),
SC_(-0.882951507568359375e2), SC_(-0.623236083984375e1), SC_(0.835008561611175537109375e0), SC_(-0.65215237953434450934522345100560800793657047297229e0),
SC_(-0.882951507568359375e2), SC_(-0.5579319000244140625e1), SC_(0.12698681652545928955078125e0), SC_(-0.5122762429234107157399593560830350036728566184486e0),
SC_(-0.882951507568359375e2), SC_(-0.443003559112548828125e1), SC_(0.968867778778076171875e0), SC_(-0.54332403292257364440317808333720203684254160082478e0),
SC_(-0.882951507568359375e2), SC_(-0.38366591930389404296875e1), SC_(0.9133758544921875e0), SC_(-0.51338947010848800530828929008203919356014977411471e0),
SC_(-0.882951507568359375e2), SC_(0.9376299381256103515625e0), SC_(0.22103404998779296875e0), SC_(0.15824345778373739469179000212986130442374553398e0),
SC_(-0.882951507568359375e2), SC_(0.944411754608154296875e0), SC_(0.6323592662811279296875e0), SC_(0.16010110842241419282972789586647601062389080124406e0),
SC_(-0.882951507568359375e2), SC_(0.264718532562255859375e1), SC_(0.308167040348052978515625e0), SC_(0.18812698999986759709990325160594334177917367010501e0),
SC_(-0.882951507568359375e2), SC_(0.62944736480712890625e1), SC_(0.97540400922298431396484375e-1), SC_(0.6764648718685968528811245633241126898305817526621e0),
SC_(-0.882951507568359375e2), SC_(0.670017147064208984375e1), SC_(0.54722058773040771484375e0), SC_(0.81778541776042463995319059339588552698088433898419e0),
SC_(-0.882951507568359375e2), SC_(0.81158390045166015625e1), SC_(0.278498232364654541015625e0), SC_(0.83745249382380518272911191808287678555946548573727e0),
SC_(-0.882951507568359375e2), SC_(0.826751708984375e1), SC_(0.188381969928741455078125e0), SC_(0.83757094918096990315704827205570637800372489102387e0),
SC_(-0.882951507568359375e2), SC_(0.91501369476318359375e1), SC_(0.546881496906280517578125e0), SC_(0.88536530789452037214536364734769886885031477691156e0),
SC_(-0.882951507568359375e2), SC_(0.929777050018310546875e1), SC_(0.992881298065185546875e0), SC_(0.10670104592156217618232174187269358103233999652509e1),
SC_(-0.882951507568359375e2), SC_(0.93538990020751953125e1), SC_(0.957506835460662841796875e0), SC_(0.10357277056795963385227029717982264964969263725296e1),
SC_(-0.882951507568359375e2), SC_(0.93773555755615234375e1), SC_(0.996461331844329833984375e0), SC_(0.11393287366513926492075339545953276894721889046337e1),
SC_(-0.882951507568359375e2), SC_(0.98576259613037109375e1), SC_(0.964888513088226318359375e0), SC_(0.12490646709828734017662810793035855992633603697925e1),
SC_(-0.882951507568359375e2), SC_(0.992922687530517578125e1), SC_(0.967694938182830810546875e0), SC_(0.12562075694306417376583251897842403492180529464883e1),
SC_(-0.8681658935546875e2), SC_(-0.80491924285888671875e1), SC_(0.15761308372020721435546875e0), SC_(-0.84140469773208335456919923830249117896698295285825e0),
SC_(-0.8681658935546875e2), SC_(-0.7460263729095458984375e1), SC_(0.725838959217071533203125e0), SC_(-0.85987671052370888277919669524246227679947360493402e0),
SC_(-0.8681658935546875e2), SC_(-0.729045963287353515625e1), SC_(0.970592796802520751953125e0), SC_(-0.91443922525100421734210147418874666650910614494338e0),
SC_(-0.8681658935546875e2), SC_(-0.623236083984375e1), SC_(0.981109678745269775390625e0), SC_(-0.7106272156738935312370492307790173553201815649551e0),
SC_(-0.8681658935546875e2), SC_(-0.5579319000244140625e1), SC_(0.957166969776153564453125e0), SC_(-0.58106009812366507614405013631862001052582083043834e0),
SC_(-0.8681658935546875e2), SC_(-0.443003559112548828125e1), SC_(0.109861753880977630615234375e0), SC_(-0.49983870530384115095256605303312645824352714073227e0),
SC_(-0.8681658935546875e2), SC_(-0.38366591930389404296875e1), SC_(0.4853756427764892578125e0), SC_(-0.49428566816516318921025209597689924685446558273393e0),
SC_(-0.8681658935546875e2), SC_(0.9376299381256103515625e0), SC_(0.79810583591461181640625e0), SC_(0.16264406175756977733142719519534386130654412249944e0),
SC_(-0.8681658935546875e2), SC_(0.944411754608154296875e0), SC_(0.80028045177459716796875e0), SC_(0.16282022749627678393354605008370427957677491731307e0),
SC_(-0.8681658935546875e2), SC_(0.264718532562255859375e1), SC_(0.297029435634613037109375e0), SC_(0.18977993070188281230059741069586097466083740104406e0),
SC_(-0.8681658935546875e2), SC_(0.62944736480712890625e1), SC_(0.14188633859157562255859375e0), SC_(0.68239209777614933756004515248637654641240799137633e0),
SC_(-0.8681658935546875e2), SC_(0.670017147064208984375e1), SC_(0.47834846191108226776123046875e-2), SC_(0.81288526517388767163902468894469430412802255190882e0),
SC_(-0.8681658935546875e2), SC_(0.81158390045166015625e1), SC_(0.4217612743377685546875e0), SC_(0.84924877776215008160678238935268625874487764674281e0),
SC_(-0.8681658935546875e2), SC_(0.826751708984375e1), SC_(0.1124645173549652099609375e0), SC_(0.8436484863509619135739901228550661577676789921708e0),
SC_(-0.8681658935546875e2), SC_(0.91501369476318359375e1), SC_(0.915735542774200439453125e0), SC_(0.95373283829252902405087581062925853275855864089375e0),
SC_(-0.8681658935546875e2), SC_(0.929777050018310546875e1), SC_(0.639763355255126953125e0), SC_(0.93674317644311585360231935232845892831637346827973e0),
SC_(-0.8681658935546875e2), SC_(0.93538990020751953125e1), SC_(0.792207300662994384765625e0), SC_(0.98735879657086553764434857657877232118368138213484e0),
SC_(-0.8681658935546875e2), SC_(0.93773555755615234375e1), SC_(0.878430664539337158203125e0), SC_(0.1025248511731665221473972396370335124655052772948e1),
SC_(-0.8681658935546875e2), SC_(0.98576259613037109375e1), SC_(0.9594924449920654296875e0), SC_(0.12550759972155121101731042438144441861148487473869e1),
SC_(-0.8681658935546875e2), SC_(0.992922687530517578125e1), SC_(0.50366270542144775390625e0), SC_(0.11673484395886820589854473845868240195541869146431e1),
SC_(-0.847615814208984375e2), SC_(-0.80491924285888671875e1), SC_(0.655740678310394287109375e0), SC_(-0.87330537529798589363707267477409442925913183364478e0),
SC_(-0.847615814208984375e2), SC_(-0.7460263729095458984375e1), SC_(0.797928631305694580078125e0), SC_(-0.87904389668569057123243043710903035434038423609968e0),
SC_(-0.847615814208984375e2), SC_(-0.729045963287353515625e1), SC_(0.357116796076297760009765625e-1), SC_(-0.84078525712373178220947745986249080780651559495176e0),
SC_(-0.847615814208984375e2), SC_(-0.623236083984375e1), SC_(0.3612940013408660888671875e0), SC_(-0.63550174673913486415783145741809241052044800786891e0),
SC_(-0.847615814208984375e2), SC_(-0.5579319000244140625e1), SC_(0.84912931919097900390625e0), SC_(-0.55823097207697128640129681058469928375758518851429e0),
SC_(-0.847615814208984375e2), SC_(-0.443003559112548828125e1), SC_(0.21192432940006256103515625e0), SC_(-0.50653264566656418790206483978766196380143408274079e0),
SC_(-0.847615814208984375e2), SC_(-0.38366591930389404296875e1), SC_(0.93399322032928466796875e0), SC_(-0.52768082863143565944979426054840570548981898393827e0),
SC_(-0.847615814208984375e2), SC_(0.9376299381256103515625e0), SC_(0.6813595294952392578125e0), SC_(0.16345840597997446286580518084575460850493778657533e0),
SC_(-0.847615814208984375e2), SC_(0.944411754608154296875e0), SC_(0.67873513698577880859375e0), SC_(0.16358167818281164666410027933856064945511994225518e0),
SC_(-0.847615814208984375e2), SC_(0.264718532562255859375e1), SC_(0.3987385332584381103515625e0), SC_(0.19345780441354699416180322379934184345689867702227e0),
SC_(-0.847615814208984375e2), SC_(0.62944736480712890625e1), SC_(0.75774013996124267578125e0), SC_(0.71608605816567507682817792208387170386687198164273e0),
SC_(-0.847615814208984375e2), SC_(0.670017147064208984375e1), SC_(0.740647256374359130859375e0), SC_(0.8478488690134601561699988304099457366052743530796e0),
SC_(-0.847615814208984375e2), SC_(0.81158390045166015625e1), SC_(0.74313247203826904296875e0), SC_(0.88382693905031403996710245196053643566630916949913e0),
SC_(-0.847615814208984375e2), SC_(0.826751708984375e1), SC_(0.474758684635162353515625e0), SC_(0.86418097073779732383859343034185666552250993263043e0),
SC_(-0.847615814208984375e2), SC_(0.91501369476318359375e1), SC_(0.3922270238399505615234375e0), SC_(0.89564552708012969117963354018008675677974201436592e0),
SC_(-0.847615814208984375e2), SC_(0.929777050018310546875e1), SC_(0.42208766937255859375e0), SC_(0.9334232677038391406419076040839712278510329146248e0),
SC_(-0.847615814208984375e2), SC_(0.93538990020751953125e1), SC_(0.65547788143157958984375e0), SC_(0.98146659133251440967385843955400661406021307071047e0),
SC_(-0.847615814208984375e2), SC_(0.93773555755615234375e1), SC_(0.1738651692867279052734375e0), SC_(0.97451533127978846620711239186218485925497514027631e0),
SC_(-0.847615814208984375e2), SC_(0.98576259613037109375e1), SC_(0.1711866855621337890625e0), SC_(0.11640615124862612845435426946332017761732520618732e1),
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SC_(-0.2233159542083740234375e1), SC_(0.93773555755615234375e1), SC_(0.493326842784881591796875e0), SC_(0.5455958348692104517652116375856606963768856463546e1),
SC_(-0.2233159542083740234375e1), SC_(0.98576259613037109375e1), SC_(0.4509237110614776611328125e0), SC_(0.58425715884572127603208314559986328209865929040183e1),
SC_(-0.2233159542083740234375e1), SC_(0.992922687530517578125e1), SC_(0.3785004317760467529296875e0), SC_(0.58235654495321593144993439337365609617712620177635e1),
SC_(0.201027393341064453125e0), SC_(-0.80491924285888671875e1), SC_(0.54700887203216552734375e0), SC_(-0.99225565272299265057474332033452451298257411758289e1),
SC_(0.201027393341064453125e0), SC_(-0.7460263729095458984375e1), SC_(0.71846997737884521484375e0), SC_(-0.98733924062829495855268464439174693001319340908722e1),
SC_(0.201027393341064453125e0), SC_(-0.729045963287353515625e1), SC_(0.29632079601287841796875e0), SC_(-0.82838310087004006715984395376110573887564954006723e1),
SC_(0.201027393341064453125e0), SC_(-0.623236083984375e1), SC_(0.2878049910068511962890625e0), SC_(-0.71399649768593994233565781388330571566404664291638e1),
SC_(0.201027393341064453125e0), SC_(-0.5579319000244140625e1), SC_(0.74469280242919921875e0), SC_(-0.7852838275875078318898768277396954817312338949233e1),
SC_(0.201027393341064453125e0), SC_(-0.443003559112548828125e1), SC_(0.623435556888580322265625e0), SC_(-0.55353469466832669055948998690680459923127869705195e1),
SC_(0.201027393341064453125e0), SC_(-0.38366591930389404296875e1), SC_(0.188955008983612060546875e0), SC_(-0.42670151795740926550616070898142650427001824200856e1),
SC_(0.201027393341064453125e0), SC_(0.9376299381256103515625e0), SC_(0.811873972415924072265625e0), SC_(0.10948999881609283534865564650155039154841364221285e1),
SC_(0.201027393341064453125e0), SC_(0.944411754608154296875e0), SC_(0.6867754459381103515625e0), SC_(0.10678437743348588891519840198915283249591294529495e1),
SC_(0.201027393341064453125e0), SC_(0.264718532562255859375e1), SC_(0.31250798702239990234375e0), SC_(0.31064483566488608931281755219427099993121689654282e1),
SC_(0.201027393341064453125e0), SC_(0.62944736480712890625e1), SC_(0.18351115286350250244140625e0), SC_(0.71043510436913445771405941909028349861445575844728e1),
SC_(0.201027393341064453125e0), SC_(0.670017147064208984375e1), SC_(0.3857105076313018798828125e0), SC_(0.77553041204136176774038756662263769147319302501976e1),
SC_(0.201027393341064453125e0), SC_(0.81158390045166015625e1), SC_(0.3684845864772796630859375e0), SC_(0.94787138653519013648251654059066285072949428515173e1),
SC_(0.201027393341064453125e0), SC_(0.826751708984375e1), SC_(0.3439297378063201904296875e0), SC_(0.96231456672706330197751945234594804514605578493294e1),
SC_(0.201027393341064453125e0), SC_(0.91501369476318359375e1), SC_(0.62561857700347900390625e0), SC_(0.11697431340770649519046006010297689812160093617617e2),
SC_(0.201027393341064453125e0), SC_(0.929777050018310546875e1), SC_(0.81576907634735107421875e0), SC_(0.13689559632918850897185479014035065907489555706468e2),
SC_(0.201027393341064453125e0), SC_(0.93538990020751953125e1), SC_(0.7802274227142333984375e0), SC_(0.13252477031585661466687278470237361058228506710271e2),
SC_(0.201027393341064453125e0), SC_(0.93773555755615234375e1), SC_(0.669285118579864501953125e0), SC_(0.12219207125307825999387228477920190151422215626939e2),
SC_(0.201027393341064453125e0), SC_(0.98576259613037109375e1), SC_(0.811257660388946533203125e-1), SC_(0.11000670184663049479533855890007560504469595099336e2),
SC_(0.201027393341064453125e0), SC_(0.992922687530517578125e1), SC_(0.379418849945068359375e0), SC_(0.11497477476964669120779679338120232828710984170976e2),
};
#undef SC_

207
test/ellint_rc_data.ipp Normal file
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@@ -0,0 +1,207 @@
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 3>, 201> ellint_rc_data = {
SC_(0.11698430441812742785454260394458960094979845402414e-30), SC_(0.1429457475085533184e20), SC_(0.41546482167023371731518451342517736095263780557582e-9),
SC_(0.60682196926171104626767727515008970841312337712241e-30), SC_(0.20031258624e11), SC_(0.11098537606275153066313383027431717728910787699004e-4),
SC_(0.75974287571611502022633594876763844865744160884209e-30), SC_(0.20657736771171195551744e23), SC_(0.10928951720653730370271800759007590309935803177545e-10),
SC_(0.10711124272997777587041261201942927950011067906889e-29), SC_(0.47946235e7), SC_(0.71736902777915132997000781571354752397421561836787e-3),
SC_(0.22148209406780902835423848339554340607932845033396e-29), SC_(0.19855378956352178823888896e26), SC_(0.35251758550831167800571476411635458611576128740787e-12),
SC_(0.41366469991877353664505423235416110752209856263632e-29), SC_(0.1080339869874636584075679427013641468012674864323e-29), SC_(0.73882898278016317196709226502699714371366335165311e15),
SC_(0.44767214645416419053919245787147718165594030426536e-29), SC_(0.26553176031232e14), SC_(0.30483276103299498395114390375939883603035900740311e-6),
SC_(0.60078474312334545656635060929362382794743178141472e-29), SC_(0.37131016039637643189053051173686981201171875e-8), SC_(0.25778133019186154518263488635604654249614963342631e5),
SC_(0.61834249098451553748337548320711315606925672313013e-29), SC_(0.15125532639232e16), SC_(0.40389133730438812928090167163598082343384172921425e-7),
SC_(0.15386248307178551019952166983379913769903023636025e-28), SC_(0.11083928e9), SC_(0.14920144492544889019454092007748150269559896140113e-3),
SC_(0.19696330564073048658818435820590984305819001943432e-28), SC_(0.32238440243425309843308409068705787565729120602853e-24), SC_(0.27528315706771612956183484092479935495449666128525e13),
SC_(0.3000732163818651513042917353020530062720192427143e-28), SC_(0.28816120624542236328125e1), SC_(0.92534167116491481810744772274112199743911312596723e0),
SC_(0.47155488899394500240213479534565823420775918905622e-28), SC_(0.4463543296e10), SC_(0.23511481798013935669754503155612804985989597208762e-4),
SC_(0.65104581211365760324995297566040105840304400052279e-28), SC_(0.700861590985368820838630199432373046875e-9), SC_(0.59334016337111736885565181305039468621938956693965e5),
SC_(0.3949284499458758322165682321378970124179942071882e-27), SC_(0.670079424e9), SC_(0.60681559827956246896673839347875883912858354314319e-4),
SC_(0.55263283825603576259688637477087526891102295303199e-27), SC_(0.14570690537170526341649579027404115549870766699314e-16), SC_(0.41150783369497640278522169895393702894524362953078e9),
SC_(0.56127809703514701593677302775789618452802567406812e-27), SC_(0.9228809556838246663801328395493328571319580078125e-11), SC_(0.51706725181069699755346169652670461023196225991383e6),
SC_(0.12941088853490731622934705547460304161866623869764e-26), SC_(0.51905646303429040628284185654450766378431580960751e-16), SC_(0.21802745983479448951816941696856049925016007329412e9),
SC_(0.13705567485615801022446745431989965211687137938007e-26), SC_(0.5078582763671875e0), SC_(0.22041878790098954794667581190100145257683475089988e1),
SC_(0.16793731632787596740420928687663819571897812904515e-26), SC_(0.3518738464768e13), SC_(0.8373873246615759174577066128415186701403437615454e-6),
SC_(0.38344456302173223195286237326130017242619817813276e-26), SC_(0.1287535325337014953720268054032123824574619620157e-27), SC_(0.39122934559161731153423283680987267387840851196098e14),
SC_(0.39915753210320770987303899714279126384431587576396e-26), SC_(0.21695373623974084952946051325821291927687106275468e-28), SC_(0.52362555864098150198972240138118002904488963483036e14),
SC_(0.4719122320543576863524228422930565122003386188676e-26), SC_(0.13622372113626680630865559552e29), SC_(0.13458402336127820973876482234542361593374249767564e-13),
SC_(0.60865414403362585004788968196643994088311036341765e-26), SC_(0.123742392e9), SC_(0.14120842972598363583851550459968997099008965981731e-3),
SC_(0.10912435391066719332460695603753930316446923640128e-25), SC_(0.701712293691392e16), SC_(0.18751686532816272762803237369940986207556087504473e-7),
SC_(0.11837831633021164326650292224515978315498715423004e-25), SC_(0.27219574150194603134877979755401611328125e-7), SC_(0.95209265255492104735446619994567552559697239051341e4),
SC_(0.27826294978205525521980137859608542144911232096849e-25), SC_(0.87440356429873925658498856170228582591246249688943e-25), SC_(0.39786583496854506510922922833320145505046484128036e13),
SC_(0.34919368622379363366113344149995795887854964367758e-25), SC_(0.253342638931968e15), SC_(0.9868831456740266966933448023215284826954206363932e-7),
SC_(0.43573388456807634241895548780677530339229715228289e-25), SC_(0.4951682e8), SC_(0.22322534554145528116293051775479117197834119520022e-3),
SC_(0.60515264161661452673922225736467336588411333742066e-25), SC_(0.787468255232e13), SC_(0.55976191846459760569727531324370941602465103140201e-6),
SC_(0.14044194233643483429544463937103636612564738772591e-24), SC_(0.11511007425024644135191920213401317596435546875e-10), SC_(0.4629810115470076825533605597799208284244799296532e6),
SC_(0.14235380836999617679740726134029336127093459674064e-24), SC_(0.13978527726259656235898667313173260930711863658793e-24), SC_(0.26665402305818478969438170708975555299492041941187e13),
SC_(0.63171350201374448567926894124993295043246632758382e-24), SC_(0.34594001439795600424927311319582115491182941913878e-27), SC_(0.55978470361004464102520617099230932588604458370896e13),
SC_(0.1809900535358029636909945199492450026643175498009e-23), SC_(0.4521496521192602813243865966796875e-5), SC_(0.73871816148130469176849633363812844159103317042416e3),
SC_(0.63795086741914598182229839666991088459324643622494e-23), SC_(0.19953517994584643852448181812338140391502663839596e-24), SC_(0.97252851335184218861516452118643565455819826848263e12),
SC_(0.12701055793371805794043341177064064973639689881679e-22), SC_(0.2068948375e7), SC_(0.10920563536493094936157694716029214151487193559361e-2),
SC_(0.25335998731998849030698736206528910198942927678445e-22), SC_(0.99404931640625e3), SC_(0.49821398201934740455232191323883688893256512444693e-1),
SC_(0.71863877935764437100797607417958061393203905709015e-22), SC_(0.174722980453023744e19), SC_(0.11883513458141578715964474656644636676047017752235e-8),
SC_(0.33895318467300131244893458519885746926814107382597e-21), SC_(0.108193802361711277626454830169677734375e-6), SC_(0.47754980229555933492229104255715482771563363261078e4),
SC_(0.96362472102334232055222076765519517715929964651878e-21), SC_(0.229194643907248973846435546875e-3), SC_(0.1037570568888513512672421917866018283061872751937e3),
SC_(0.24141449950396592978032251394348434159198291126813e-20), SC_(0.18448819419086848e17), SC_(0.11564732376740008952525889248768816116526843336083e-7),
SC_(0.27589042212186362242123678200494962808875243354123e-20), SC_(0.16342684e8), SC_(0.3885600849080471885427919126603669380019521916121e-3),
SC_(0.32517390764125836699536241120728208287005145393778e-20), SC_(0.32148523727519219712e22), SC_(0.27703801044419253206437768255298726473435062914505e-10),
SC_(0.13713993780991436762807365477498389161326031171484e-19), SC_(0.805980574786256896e18), SC_(0.17496758182365486418837119046398196242651995908202e-8),
SC_(0.48988976909583188869227858043553514022505623870529e-19), SC_(0.20838384443777613341808319091796875e-4), SC_(0.34410251008331861623295558733232180042927229855377e3),
SC_(0.59220483766176692878700381014733800100202643079683e-19), SC_(0.170295034922225631232e22), SC_(0.38064390844573575145663807454900781472238386155909e-10),
SC_(0.82997499668329372719087076888666576479636205476709e-19), SC_(0.13155479315039595949803718770027355301939497866925e-23), SC_(0.21587999863350804994131547408624282253340872631383e11),
SC_(0.94969911521617292598785838378394608128019171999767e-19), SC_(0.16011657277825719347674748860299587249755859375e-10), SC_(0.39253685794445481713501328838333615978147538487421e6),
SC_(0.20581069188704517551523841788208013525718342862092e-18), SC_(0.79597584432992412060764095271814255738718202337623e-18), SC_(0.1350343783064271491301645561749747948509003384249e10),
SC_(0.22622955483503716568203720238550147314526839181781e-18), SC_(0.85913526136044117637383110697157917456934228539467e-16), SC_(0.16414615605631462414018849697787131696542279589859e9),
SC_(0.30420727664434581210352358596193944606511649908498e-18), SC_(0.28656053473241627216339111328125e-4), SC_(0.29343482785228047725924696469302777739683607703434e3),
SC_(0.5065993732313771067901500902430633743733778828755e-18), SC_(0.1568245533434264871175400912761688232421875e-11), SC_(0.12538793439957801193747997519423750597372445322011e7),
SC_(0.1269279595243605041993096779751049041351507185027e-17), SC_(0.33297255999405977634352134242323728585688513703644e-17), SC_(0.6307182542731725660001150747369468435224945316479e9),
SC_(0.12784377253954858878954355810853016350847610738128e-17), SC_(0.687874899968e12), SC_(0.1893935330545222150970846791789958509229989435048e-5),
SC_(0.29343589097392396787046010830923847834128537215292e-17), SC_(0.988066171875e5), SC_(0.49972014999347714801287931360926030236802518594537e-2),
SC_(0.46871312598868006987253009842930850936681963503361e-17), SC_(0.3093168493023691324522496e26), SC_(0.28243472271946788164939900071622955356799263239731e-12),
SC_(0.152616857880340486461855087352290638591512106359e-16), SC_(0.2803833618070566221119488e25), SC_(0.93808838274358563783082952025021048853623300403696e-12),
SC_(0.27022364375023134885640124780437076879024971276522e-16), SC_(0.27506543358959030582888269221280574638246675400223e-29), SC_(0.30108032875150741383088202176437518530075493145293e10),
SC_(0.55460104261295954577309919031335994077380746603012e-16), SC_(0.154132149174272e16), SC_(0.4001043378763428887183412693378271572857296764857e-7),
SC_(0.13209346463532805303342509972708285204134881496429e-15), SC_(0.3125807523929324815981090068817138671875e-7), SC_(0.8884250355437972613883213327503914013438652227259e4),
SC_(0.31354745663454523796342954256033408455550670623779e-15), SC_(0.18973853599391077295877039432525634765625e-8), SC_(0.3605203076290095918464079777019357642842666108285e5),
SC_(0.40558081566683637682324548023871102486737072467804e-15), SC_(0.208714828125e6), SC_(0.3438295704906441724421284923146054131214779732901e-2),
SC_(0.86986000872677090266227306614155168063007295131683e-15), SC_(0.6724360036363488659828113408e28), SC_(0.19155539931271849389875536772683217400458105317664e-13),
SC_(0.92657114094649205629505850367877428652718663215637e-15), SC_(0.32666126748015500425026402808725833892822265625e-10), SC_(0.27390641716269741695214339048257696917547990788968e6),
SC_(0.1327809695148788465823841420387907419353723526001e-14), SC_(0.54374770505732477601443242143375300656771287322044e-16), SC_(0.63904369494942025897253747392585085351726876366063e8),
SC_(0.16682115902222024485246354430501014576293528079987e-14), SC_(0.40149480284466451673885956097365124151110649108887e-13), SC_(0.69610251923240433370059407687180639587649479389139e7),
SC_(0.62660384591791979530528422515089914668351411819458e-14), SC_(0.199429788239058325416408479213714599609375e-7), SC_(0.11119107448133471075560965516334728421690408075844e5),
SC_(0.63024210653626119155168439078806841280311346054077e-14), SC_(0.83430262439221944230360872296614616061560809612274e-15), SC_(0.22574681584731394754127234813389452607870443810549e8),
SC_(0.10676147262794234704674778413391322828829288482666e-13), SC_(0.43214794983836329352138753913566138198376620493946e-21), SC_(0.89081662541541586914322012810403516608773228196705e8),
SC_(0.11175146230483004594624674155056709423661231994629e-13), SC_(0.13292268387650598312620966562043814396254504117678e-22), SC_(0.10375337151147634989665344794895368826014425089457e9),
SC_(0.14452686009774895481427847698796540498733520507813e-13), SC_(0.669478515625e5), SC_(0.6070878688152193299924869338064352690120583642415e-2),
SC_(0.15741248433312655941040958396115456707775592803955e-13), SC_(0.55817784918415767502848e23), SC_(0.66486516347017242385736020715678344161218353890444e-11),
SC_(0.20907895301679711719256005153511068783700466156006e-13), SC_(0.893892793119022144310292787849903106689453125e-9), SC_(0.52377290723662340541539667066133146373413622848047e5),
SC_(0.39424006729538510485078006695403018966317176818848e-13), SC_(0.57692237126522896384e20), SC_(0.2068050725918743676865501216749142009296095185495e-9),
SC_(0.5554841051654164918449652077470091171562671661377e-13), SC_(0.12544762676037794895951386908716784773787367157638e-18), SC_(0.30521794362592775449474387740993552064903872666301e8),
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SC_(0.292186842467552253181952e24), SC_(0.8000304500511383121995759616e28), SC_(0.17494456350937238152051998129209403413657779766045e-13),
SC_(0.404188410838900933656576e24), SC_(0.15307389070737408e17), SC_(0.14530172405497225203148631842861632557097281219397e-10),
SC_(0.432213410600102056165376e24), SC_(0.1959631583933896656101239768660304818581607833039e-18), SC_(0.75206449301552958256440392567562049430798996389352e-10),
SC_(0.48688847917066659823616e24), SC_(0.12212552573408426924125600686592708205013835254249e-21), SC_(0.76232145024480748870634232091696723820904729119412e-10),
SC_(0.1611108507323484384264192e25), SC_(0.11971012087915599989354498156046702206367626786232e-15), SC_(0.3694442785175160419076949350029585599009031148763e-10),
SC_(0.1626183676572159287754752e26), SC_(0.18501463382170069138510370976291596889495849609375e-11), SC_(0.10719260914536354712818827718038676299273171700718e-10),
SC_(0.18820064668587267094216704e26), SC_(0.302210201308383830109960399568080902099609375e-9), SC_(0.93936394693848721355885906623218887308774325852727e-11),
SC_(0.24925849334950778558742528e26), SC_(0.31317834636651731435069138009717243018286553235541e-24), SC_(0.11646010681447365669777654446715227593887198721003e-10),
SC_(0.9036469625899950631026688e26), SC_(0.690641880035400390625e1), SC_(0.31148497090217722784373888164259764652317411281318e-11),
SC_(0.7376334675354954747676196864e28), SC_(0.3832167254355459644063744e25), SC_(0.52109798218409315418287118331564136634721278594953e-13),
SC_(0.19445130267235161963321360384e29), SC_(0.27158976561908717618255837411567199524142779409885e-16), SC_(0.37530178368631060137545101809988924309836018928577e-12),
};
#undef SC_

207
test/ellint_rd_data.ipp Normal file
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@@ -0,0 +1,207 @@
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 4>, 201> ellint_rd_data = {
SC_(0.60682196926171104626767727515008970841312337712241e-30), SC_(0.20031258624e11), SC_(0.10313978271484375e4), SC_(0.20551372495384815463856604017047221545095240191057e-7),
SC_(0.13810928266794127506964991575307193802925529863273e-29), SC_(0.2529551275074481964111328125e-3), SC_(0.7030536597341097149183042347431182861328125e-8), SC_(0.26827491422802771467722943731540343461246213838861e11),
SC_(0.44767214645416419053919245787147718165594030426536e-29), SC_(0.26553176031232e14), SC_(0.2085586588137791946752e23), SC_(0.10585138723496739834534066073267118675522211779171e-31),
SC_(0.60078474312334545656635060929362382794743178141472e-29), SC_(0.37131016039637643189053051173686981201171875e-8), SC_(0.32517390764125836699536241120728208287005145393778e-20), SC_(0.15139742233407639223792275679902886417433224652453e26),
SC_(0.61834249098451553748337548320711315606925672313013e-29), SC_(0.15125532639232e16), SC_(0.11666782739894188125617802143096923828125e-6), SC_(0.66117253645648417600031762235375783237535720054585e0),
SC_(0.80490202086679616440767211156605911864354431197377e-29), SC_(0.263248904192e12), SC_(0.297980882347216843954978816e27), SC_(0.10333434770883940055455846219131687005742728721005e-37),
SC_(0.15386248307178551019952166983379913769903023636025e-28), SC_(0.11083928e9), SC_(0.210290006361901760101318359375e-2), SC_(0.13550514102538012513935665942320904977981297554257e0),
SC_(0.27790564235134654243337661318427908127768828411199e-28), SC_(0.21656921296023725949679903214975529301966616912978e-20), SC_(0.16200692698475904762744903564453125e-4), SC_(0.85856403820113222790454310518632166416049096576362e9),
SC_(0.75787209056271355952485380019348769132814133643247e-28), SC_(0.3443290234375e5), SC_(0.87738095954812459262649215691458087947041111220869e-24), SC_(0.18256962837089036695688975681087926934231777165353e23),
SC_(0.83892250504513065845701871993405683214864787598623e-28), SC_(0.1116302655645995400846004486083984375e-5), SC_(0.5191992844812585795584e22), SC_(0.25853043071836854153543603031360043116599575432972e-30),
SC_(0.1287535325337014953720268054032123824574619620157e-27), SC_(0.13705567485615801022446745431989965211687137938007e-26), SC_(0.5078582763671875e0), SC_(0.25453721736248252436275234446728359554220261644493e3),
SC_(0.55263283825603576259688637477087526891102295303199e-27), SC_(0.14570690537170526341649579027404115549870766699314e-16), SC_(0.12941088853490731622934705547460304161866623869764e-26), SC_(0.36729174819285901249546490822632941293048355712711e36),
SC_(0.56127809703514701593677302775789618452802567406812e-27), SC_(0.9228809556838246663801328395493328571319580078125e-11), SC_(0.86422194270699415064029835775727406144142150878906e-12), SC_(0.10781910269701214744433782310389927085727282773814e19),
SC_(0.11649136528196886067987694424015483218044894522109e-26), SC_(0.36767340167168e14), SC_(0.4968523085117340087890625e0), SC_(0.99577870866168728614595399908281899687867831139901e-6),
SC_(0.25172518744793432127678756566548684645107602196601e-26), SC_(0.432213410600102056165376e24), SC_(0.1959631583933896656101239768660304818581607833039e-18), SC_(0.23283511871909436551998718906785080640182682915363e8),
SC_(0.28601321158264026057365024112938563807684451932578e-26), SC_(0.40558081566683637682324548023871102486737072467804e-15), SC_(0.208714828125e6), SC_(0.76237261396619453885730994908723652541092525168043e-6),
SC_(0.73955594308673193523198369636584653936223991005372e-26), SC_(0.15995684594580228399252064264146611094474792480469e-12), SC_(0.170420291286861873152e22), SC_(0.1687006236430131643441016712281856878753726523535e-29),
SC_(0.25325901731494375978251987705874090841683295149966e-25), SC_(0.2247014312744140625e3), SC_(0.275117858615052709715247104e27), SC_(0.18485690522734605390476411600907452658544362635922e-37),
SC_(0.34857664908449107348958795506280082952452713251912e-25), SC_(0.4151866912841796875e2), SC_(0.84098145009994339684283693509730169685090217512879e-22), SC_(0.54257544703354289137242893169458880766652554745316e22),
SC_(0.34919368622379363366113344149995795887854964367758e-25), SC_(0.253342638931968e15), SC_(0.7562174072265625e3), SC_(0.249241547815296223838694888499925239323224138633e-9),
SC_(0.43573388456807634241895548780677530339229715228289e-25), SC_(0.4951682e8), SC_(0.27826294978205525521980137859608542144911232096849e-25), SC_(0.68052511685869677076187126812000404571638179018885e22),
SC_(0.79820903020739723608895214436397557193018231780357e-25), SC_(0.64729720161775472443612539086288393264112528413534e-17), SC_(0.68450550546432e14), SC_(0.19125532541215326384896730405964498227631338694385e-18),
SC_(0.87440356429873925658498856170228582591246249688943e-25), SC_(0.897631640625e4), SC_(0.386145068359375e4), SC_(0.70431488067233168809120506088634745460689092194161e-5),
SC_(0.94440849851249091320281320378524601844016927998382e-25), SC_(0.339495296e9), SC_(0.27455182077952e14), SC_(0.12588696277491280442424745508482566976425259261561e-18),
SC_(0.14235380836999617679740726134029336127093459674064e-24), SC_(0.13978527726259656235898667313173260930711863658793e-24), SC_(0.2028485946357250213623046875e-1), SC_(0.27366411869676160015961055866442893198667542321359e5),
SC_(0.19953517994584643852448181812338140391502663839596e-24), SC_(0.20741449842688e14), SC_(0.4743499375e6), SC_(0.13886820075171731514726499953757541277555907027004e-11),
SC_(0.24754359063412526643006257824154938047573476511687e-24), SC_(0.542938704356835328e18), SC_(0.44974670432440498891960159215184658369128360699829e-26), SC_(0.10752772537029819829836280199737653161290081988757e18),
SC_(0.31317834636651731435069138009717243018286553235541e-24), SC_(0.446171086848e12), SC_(0.49623249953612003082525916397571563720703125e-9), SC_(0.90507658227268922734361508605808168072270615976688e4),
SC_(0.49794778812580822691949943719295546451682199506905e-24), SC_(0.1241846768099137683456e22), SC_(0.16907547929525060340181807204941172504655995389999e-25), SC_(0.78343915398198934519415679862427240727586271564883e15),
SC_(0.56225779987930131445265275562229206527363467582603e-24), SC_(0.59220483766176692878700381014733800100202643079683e-19), SC_(0.170295034922225631232e22), SC_(0.20048163240230817674563773499193885173665982026089e-29),
SC_(0.63171350201374448567926894124993295043246632758382e-24), SC_(0.34594001439795600424927311319582115491182941913878e-27), SC_(0.63795086741914598182229839666991088459324643622494e-23), SC_(0.30128244387255120033790929863955407018683622956366e36),
SC_(0.13769532587968157644195235343886302517048270122046e-23), SC_(0.2007315487162486533634364604949951171875e-6), SC_(0.484821384427736035149791860021650791168212890625e-10), SC_(0.13804448026385854623972866111304415486550268685946e15),
SC_(0.1809900535358029636909945199492450026643175498009e-23), SC_(0.4521496521192602813243865966796875e-5), SC_(0.8669365225699721122509799897670745849609375e-10), SC_(0.16273113459057256254769276696724703797987842259227e14),
SC_(0.23768503319901658006414734019219381138884883419848e-23), SC_(0.545301093941248e15), SC_(0.1237108193663516431115567684173583984375e-9), SC_(0.10384732803004085499895888503014146907429299054875e4),
SC_(0.30307608021550191165014175615417981032514993522398e-23), SC_(0.112407951746718026697635650634765625e-5), SC_(0.2082685879058432e16), SC_(0.78504137547976820009624215245629935490941195781392e-21),
SC_(0.62520772668534154026944814518561754825703991045316e-23), SC_(0.19445130267235161963321360384e29), SC_(0.27158976561908717618255837411567199524142779409885e-16), SC_(0.79176099627370786959440226480012961415298742955765e3),
SC_(0.13102694856934221302627057835335012189043046859638e-22), SC_(0.557648090759990083584e22), SC_(0.511986668338959560742296162061393260955810546875e-10), SC_(0.78466137092077764354738487755677479556614922112935e0),
SC_(0.22752379870925977520487843277428559665698237779452e-22), SC_(0.169495918280704e15), SC_(0.106314858496e12), SC_(0.21650121297190654998249828534683860885914030587266e-17),
SC_(0.25335998731998849030698736206528910198942927678445e-22), SC_(0.99404931640625e3), SC_(0.204871795654296875e3), SC_(0.42132166564785080959023378471888313620164092769291e-3),
SC_(0.34646067293379381351152691325339738961930358129848e-22), SC_(0.26973976499394821796760860105960760360263583912399e-23), SC_(0.238645943284598871514390339143574237823486328125e-10), SC_(0.35432548942737632785957707186626141058866961729541e18),
SC_(0.71863877935764437100797607417958061393203905709015e-22), SC_(0.174722980453023744e19), SC_(0.13073324703744e14), SC_(0.1736004266338139270794293208784155064732837114576e-21),
SC_(0.96362472102334232055222076765519517715929964651878e-21), SC_(0.229194643907248973846435546875e-3), SC_(0.354709317473833607436972670257091522216796875e-9), SC_(0.55865475580945127826780252757531774517543358031385e12),
SC_(0.27589042212186362242123678200494962808875243354123e-20), SC_(0.16342684e8), SC_(0.10564504593401150001064081607182743027806282043457e-12), SC_(0.70232843197284835279286086968072241001475849391442e10),
SC_(0.10233203223084091273258880352287070181205308472272e-19), SC_(0.85809811133878005628972118756792042404413223266602e-13), SC_(0.231948544e9), SC_(0.21282358830663000454676497251299241238551176927446e-10),
SC_(0.18673345450030310831705831391483241255002667458029e-19), SC_(0.16140768350376832622251404282443946390469477480956e-24), SC_(0.35751782069791464758326094786154009108614104661683e-22), SC_(0.57362515961254887975882907105995424791809261862104e33),
SC_(0.21109476364529939751075359117074570214356299402425e-19), SC_(0.8756801014807582267041677127782781970980266472715e-25), SC_(0.19232578752860259808180970650021732008816410797181e-22), SC_(0.10040849239749431240730130421363049484424180456536e34),
SC_(0.48988976909583188869227858043553514022505623870529e-19), SC_(0.20838384443777613341808319091796875e-4), SC_(0.15278292e8), SC_(0.70563639547351817695354788729725173202298905165509e-9),
SC_(0.82997499668329372719087076888666576479636205476709e-19), SC_(0.13155479315039595949803718770027355301939497866925e-23), SC_(0.1327809695148788465823841420387907419353723526001e-14), SC_(0.32382452643409713657086228689471450756020929884496e24),
SC_(0.16677509527778160624086499150275919589603290660307e-18), SC_(0.50082130538252574789989333416135111329551950562359e-29), SC_(0.27393523857242675896004658903787332135948417999316e-20), SC_(0.26379890286497467800536742716267974869467674676907e31),
SC_(0.30420727664434581210352358596193944606511649908498e-18), SC_(0.28656053473241627216339111328125e-4), SC_(0.94969911521617292598785838378394608128019171999767e-19), SC_(0.21152520435266024826733886337057191990575481859773e22),
SC_(0.75868695590633990953827528458397466692986199632287e-18), SC_(0.930611462144e12), SC_(0.18147922618313051311153033283257685840533790511131e-24), SC_(0.83768344778024722769204816337111831433373325848511e16),
SC_(0.79597584432992412060764095271814255738718202337623e-18), SC_(0.75974287571611502022633594876763844865744160884209e-30), SC_(0.20657736771171195551744e23), SC_(0.47403170903497016250215067728483228381506772219895e-31),
SC_(0.12784377253954858878954355810853016350847610738128e-17), SC_(0.687874899968e12), SC_(0.2496727752685546875e2), SC_(0.14487562897240575462420431915733354323986381404974e-6),
SC_(0.22468750405760049766485005051652734664457966573536e-17), SC_(0.20721947294077835977077484130859375e-4), SC_(0.33333534375e6), SC_(0.1891939096717128299814570834532131624242218004607e-6),
SC_(0.33297255999405977634352134242323728585688513703644e-17), SC_(0.31191365320704e14), SC_(0.2293932139873504638671875e0), SC_(0.23416581491449832804939246015659888605843645930834e-5),
SC_(0.35736448257653877024582131372021365223190514370799e-17), SC_(0.1626183676572159287754752e26), SC_(0.18501463382170069138510370976291596889495849609375e-11), SC_(0.40153851788485548350521938534047362493332593188358e0),
SC_(0.46871312598868006987253009842930850936681963503361e-17), SC_(0.3093168493023691324522496e26), SC_(0.16793731632787596740420928687663819571897812904515e-26), SC_(0.60797270634828688834833132685695209121001352766598e10),
SC_(0.57842544071306897015280826246375056598481023684144e-17), SC_(0.29870528793496387010009129880927503108978271484375e-12), SC_(0.2262512535863296e17), SC_(0.29646119268293442517889863887012770015886764481583e-22),
SC_(0.152616857880340486461855087352290638591512106359e-16), SC_(0.2803833618070566221119488e25), SC_(0.130162216009921394288539886474609375e-4), SC_(0.13764477533975189296577420989460030210624358668897e-6),
SC_(0.27022364375023134885640124780437076879024971276522e-16), SC_(0.27506543358959030582888269221280574638246675400223e-29), SC_(0.10302131894484992e19), SC_(0.11533202298793762115879808476821158493089208267767e-24),
SC_(0.51905646303429040628284185654450766378431580960751e-16), SC_(0.15583587e8), SC_(0.46741176605224609375e2), SC_(0.16258625638384341129980088810715602413277009050755e-4),
SC_(0.54374770505732477601443242143375300656771287322044e-16), SC_(0.4562802734375e3), SC_(0.10197021348467909816516131089894163913918803398168e-29), SC_(0.18861228040658158783485684274667884467513804993808e23),
SC_(0.60475637804894883005346617466102543403394520282745e-16), SC_(0.56145323516737172227849140410116390853545453865081e-18), SC_(0.64836257251954521052539348602294921875e-7), SC_(0.19426856083161503849129240968279840607620575171493e13),
SC_(0.17055543082513291604229710429763144929893314838409e-15), SC_(0.6943710148334503173828125e-1), SC_(0.61840874921367523613102701318666731822304427623749e-15), SC_(0.12070723069489973584177449356829135215953130632198e17),
SC_(0.31354745663454523796342954256033408455550670623779e-15), SC_(0.18973853599391077295877039432525634765625e-8), SC_(0.15741248433312655941040958396115456707775592803955e-13), SC_(0.38340329268483399676355291918194933462116017467071e19),
SC_(0.92657114094649205629505850367877428652718663215637e-15), SC_(0.32666126748015500425026402808725833892822265625e-10), SC_(0.62660384591791979530528422515089914668351411819458e-14), SC_(0.60469431091148756507917001500985998650828444618344e20),
SC_(0.10318525717298732830018437311991874594241380691528e-14), SC_(0.14367766698608619435617583803832530975341796875e-9), SC_(0.5059831664766534231603145599365234375e-6), SC_(0.37240456346135514582020163258162977421115936310552e11),
SC_(0.63024210653626119155168439078806841280311346054077e-14), SC_(0.83430262439221944230360872296614616061560809612274e-15), SC_(0.38344456302173223195286237326130017242619817813276e-26), SC_(0.21127757229591123502084107843796645070269626006089e29),
SC_(0.68559452379320356268932457055598206352442502975464e-14), SC_(0.322791595458984375e3), SC_(0.86205957643638764405225050069248027284629642963409e-15), SC_(0.5070464522925097491100578039956621014507338348222e14),
SC_(0.96442290460109492133966568871983326971530914306641e-14), SC_(0.9353629648877212663808e22), SC_(0.52655215867828667928533109554578572897298727184534e-17), SC_(0.13450724270522347382379901409784950912908729078726e6),
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SC_(0.41172763385266176e17), SC_(0.69560673828125e4), SC_(0.747194576263427734375e1), SC_(0.62793115296093377148750971856138022413722904539364e-10),
SC_(0.59877638017122304e17), SC_(0.53512100536178474827209150532780768116936087608337e-15), SC_(0.60865414403362585004788968196643994088311036341765e-26), SC_(0.67932276518492118905647587709216361710433902821356e13),
SC_(0.11384566732292096e18), SC_(0.58757351632535552e19), SC_(0.273440826416015625e3), SC_(0.2218197410675072553866425364806973969075261727874e-18),
SC_(0.128395461743607808e18), SC_(0.206836903384823477636694016e27), SC_(0.53310077419155277311801910400390625e-5), SC_(0.25213187167619695580929289478697105906035912959449e-18),
SC_(0.245924553149120512e18), SC_(0.12432241406593107741605394588021265875441186132822e-25), SC_(0.11698430441812742785454260394458960094979845402414e-30), SC_(0.15814359980865698013833243813020147773628412638471e21),
SC_(0.304309702915784704e18), SC_(0.530327327997952e15), SC_(0.10366431646728266850195727608041629252966231433675e-18), SC_(0.73346046074259210722247465233594194982314902683682e-6),
SC_(0.351564170056957952e18), SC_(0.39915753210320770987303899714279126384431587576396e-26), SC_(0.21695373623974084952946051325821291927687106275468e-28), SC_(0.16012914574357507234163722206932362300988672115721e20),
SC_(0.805980574786256896e18), SC_(0.7298279296875e4), SC_(0.135008262029312e15), SC_(0.24742374685179778771251059396546742229781662198914e-22),
SC_(0.1429457475085533184e20), SC_(0.14041162752e11), SC_(0.16802999673239973138530304e26), SC_(0.32121431604673931143271876891436876644565038320042e-36),
SC_(0.221162365880631296e20), SC_(0.4426536e8), SC_(0.89961878334825112180062577083017316681434749625623e-18), SC_(0.10108911246070441761891693525755853616606808949316e-3),
SC_(0.38083625921602912256e20), SC_(0.14043506688e11), SC_(0.13209346463532805303342509972708285204134881496429e-15), SC_(0.35692228203582006473843647627664557137685858827968e-6),
SC_(0.57692237126522896384e20), SC_(0.63429242800339125096797943115234375e-5), SC_(0.31824542466005171886425636864e29), SC_(0.55222293820695175519018810756922011735863676741191e-41),
SC_(0.6036870791327383552e20), SC_(0.7191220191232e13), SC_(0.68897207938789506442844867706298828125e-6), SC_(0.17346553888445511526875601632160113537907688737997e-12),
SC_(0.113674073964877447168e21), SC_(0.183615109375e6), SC_(0.404058591811917722225189208984375e-4), SC_(0.10330175955957541532693528313466256772187391201874e-9),
SC_(0.140771054246300745728e21), SC_(0.4364620208740234375e2), SC_(0.10711124272997777587041261201942927950011067906889e-29), SC_(0.36980588192743195268081186143904811424184826509079e5),
SC_(0.486625867239520206848e21), SC_(0.2663514463837359985504355062296832912238642165903e-19), SC_(0.4719122320543576863524228422930565122003386188676e-26), SC_(0.12125027886646699970512476707156771853870273067952e14),
SC_(0.1146824826980038344704e22), SC_(0.123134608e9), SC_(0.36464645756234167146109012677852867501115952109103e-20), SC_(0.13220462423972425935917229500420846663825040326569e-3),
SC_(0.317074383652647862272e22), SC_(0.89612589356621110444032e24), SC_(0.2342108211970048e16), SC_(0.11619224315234818923589971905969099280156494799642e-29),
SC_(0.32148523727519219712e22), SC_(0.60515264161661452673922225736467336588411333742066e-25), SC_(0.787468255232e13), SC_(0.67190469656717598102688231195715810897773628309487e-23),
SC_(0.13571258581209030066176e23), SC_(0.2301062643527984619140625e-1), SC_(0.14359374149799930542314996273489668965339660644531e-11), SC_(0.14166931188327778230186785722742287698171547666982e-3),
SC_(0.20821377315431516209152e23), SC_(0.31614863423832064e17), SC_(0.64014885e7), SC_(0.4621406894160877827384001215215505228565154941349e-22),
SC_(0.55817784918415767502848e23), SC_(0.229345916576958775296e21), SC_(0.181080293376e13), SC_(0.62303863493181421011759609358700084332302564282572e-27),
SC_(0.210179409744077661405184e24), SC_(0.775467603201754089842406683474462128114628768627e-26), SC_(0.1351436267417501696e19), SC_(0.48419735649202961080115073168670433174544124355214e-29),
SC_(0.277204771630374352584704e24), SC_(0.178649388253688812255859375e-1), SC_(0.1626075136e10), SC_(0.35041190711483516523923271898554740595024898229225e-20),
SC_(0.286204729096914532827136e24), SC_(0.18205785323743839398957788944244384765625e-7), SC_(0.6443661400749065109504e22), SC_(0.85231956001222048244789008910270023125100724496553e-33),
SC_(0.292186842467552253181952e24), SC_(0.8000304500511383121995759616e28), SC_(0.12346179962158203125e2), SC_(0.17659213899312742611429666455779433659781019844976e-25),
SC_(0.393077021751861389033472e24), SC_(0.85326592849126535957377352366076878413243909232699e-28), SC_(0.11113272845378330266896682587685063481330871582031e-11), SC_(0.43056670697313120117799317169619739766527357451448e1),
SC_(0.48688847917066659823616e24), SC_(0.12212552573408426924125600686592708205013835254249e-21), SC_(0.1269279595243605041993096779751049041351507185027e-17), SC_(0.33543623251839576830546760936703173774870805103267e7),
SC_(0.6959596827501176488460288e25), SC_(0.56396991515163736959758100092886750224006554485772e-29), SC_(0.164767579074269378772992e24), SC_(0.67539896107197358427396075668773079100885280216386e-35),
SC_(0.18820064668587267094216704e26), SC_(0.302210201308383830109960399568080902099609375e-9), SC_(0.33895318467300131244893458519885746926814107382597e-21), SC_(0.21606569536016446005127644096871253975571307187249e4),
SC_(0.66192871423119660955992064e26), SC_(0.65104581211365760324995297566040105840304400052279e-28), SC_(0.700861590985368820838630199432373046875e-9), SC_(0.5261182706092194133617741726329224767119336720926e-3),
SC_(0.9036469625899950631026688e26), SC_(0.690641880035400390625e1), SC_(0.1238969862461090087890625e0), SC_(0.3008677996342580895031853541445446250478520113248e-12),
SC_(0.351293559140227787146657792e27), SC_(0.92746285056e12), SC_(0.7325884342193603515625e1), SC_(0.61405412064015393151121436181259576895276598600887e-19),
SC_(0.48555353730121618377670656e27), SC_(0.41366469991877353664505423235416110752209856263632e-29), SC_(0.1080339869874636584075679427013641468012674864323e-29), SC_(0.42620833187540100646142696579397880259804927864477e17),
SC_(0.3196617981363007079661436928e28), SC_(0.357227936120807498809881508350372314453125e-8), SC_(0.190531306287766710738651454448699951171875e-7), SC_(0.19434029391873011348314670331341701583590531402094e-5),
SC_(0.4932620110638545248192561152e28), SC_(0.39087764918804168701171875e-1), SC_(0.37496308203098109226999139757157200603110425163322e-21), SC_(0.11157521852141686174291251786184006118424156415823e-1),
SC_(0.516425012058796509045456896e28), SC_(0.3000732163818651513042917353020530062720192427143e-28), SC_(0.28816120624542236328125e1), SC_(0.14487121655367107180122470700505306007568660707101e-13),
SC_(0.6724360036363488659828113408e28), SC_(0.39914275e7), SC_(0.5617260831058956682682037353515625e-4), SC_(0.24432489934783656632287527852861417375460919006681e-14),
SC_(0.7376334675354954747676196864e28), SC_(0.3832167254355459644063744e25), SC_(0.86986000872677090266227306614155168063007295131683e-15), SC_(0.60499813791534240550577796444003132563462392194689e-18),
SC_(0.1240879712420966629044649984e29), SC_(0.35030939907262229474824187104684165838808240778235e-22), SC_(0.23553908385443359223970771765266363217961043119431e-16), SC_(0.11419947735685798535870442055414653068651348519666e4),
SC_(0.13622372113626680630865559552e29), SC_(0.5065993732313771067901500902430633743733778828755e-18), SC_(0.1568245533434264871175400912761688232421875e-11), SC_(0.1638076044611111663076389515306947175644793927095e-1),
SC_(0.21413030105610117647127543808e29), SC_(0.56796892335439872e17), SC_(0.44545595303495604738852208133448318250202646595426e-19), SC_(0.40758436912717219001309081424162965116278950127384e-12),
SC_(0.240611655851932728105631744e29), SC_(0.15126033260477136128765155826087636266509091563425e-30), SC_(0.147685372829437255859375e1), SC_(0.13095601170876630580259197493117307804833462447144e-13),
SC_(0.61731988312258099732254031872e29), SC_(0.47155488899394500240213479534565823420775918905622e-28), SC_(0.4463543296e10), SC_(0.27051189723173151307626070067360099122375990020391e-23),
};
#undef SC_

406
test/ellint_rf_data.ipp Normal file
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@@ -0,0 +1,406 @@
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 4>, 401> ellint_rf_data = {
SC_(0.60682196926171104626767727515008970841312337712241e-30), SC_(0.20031258624e11), SC_(0.10313978271484375e4), SC_(0.69081557947567857896297308369623231790841946303168e-4),
SC_(0.13810928266794127506964991575307193802925529863273e-29), SC_(0.2529551275074481964111328125e-3), SC_(0.7030536597341097149183042347431182861328125e-8), SC_(0.41696748464385961137940994051143282877208328256968e3),
SC_(0.14532352659780781796355564562931230420316401288775e-29), SC_(0.62687453931329231730011467674071804187172354186889e-30), SC_(0.26256847716031594952568184453411959111690521240234e-12), SC_(0.40492940437281068910143789937423107620726714449588e8),
SC_(0.21161119528926488937912315394561157356168786172334e-29), SC_(0.142681614079265273176133632659912109375e-6), SC_(0.1414351724088191986083984375e-1), SC_(0.60023495609336663619731475310462707680628111629781e2),
SC_(0.43727979838159528482554219689363356095561935561375e-29), SC_(0.7798122348544e13), SC_(0.8588943201947652980736e22), SC_(0.12728379993876013222161727164717897397898227135914e-9),
SC_(0.44767214645416419053919245787147718165594030426536e-29), SC_(0.26553176031232e14), SC_(0.2085586588137791946752e23), SC_(0.80511870764678968189176930995818394321307940480734e-10),
SC_(0.60078474312334545656635060929362382794743178141472e-29), SC_(0.37131016039637643189053051173686981201171875e-8), SC_(0.32517390764125836699536241120728208287005145393778e-20), SC_(0.25056280362165428100075135368904610528487634651412e6),
SC_(0.61834249098451553748337548320711315606925672313013e-29), SC_(0.15125532639232e16), SC_(0.11666782739894188125617802143096923828125e-6), SC_(0.69024104942927043057057398977626412595781610122053e-6),
SC_(0.80490202086679616440767211156605911864354431197377e-29), SC_(0.263248904192e12), SC_(0.297980882347216843954978816e27), SC_(0.10843189731083616299141336159195842305986739069878e-11),
SC_(0.15386248307178551019952166983379913769903023636025e-28), SC_(0.11083928e9), SC_(0.210290006361901760101318359375e-2), SC_(0.13041677890491263355196952840107362001464424225232e-2),
SC_(0.21260283480045472585820552908849842179312334994757e-28), SC_(0.117237625e7), SC_(0.28658838e8), SC_(0.56137169413466917815737398640168522533687819147944e-3),
SC_(0.23067565607429071342632211210292164463707216326199e-28), SC_(0.44169701635837554931640625e-1), SC_(0.14622103125e6), SC_(0.23255376087386493123620791606540418922162034060246e-1),
SC_(0.27790564235134654243337661318427908127768828411199e-28), SC_(0.21656921296023725949679903214975529301966616912978e-20), SC_(0.16200692698475904762744903564453125e-4), SC_(0.48848907341566731317828094161181483220489237197822e4),
SC_(0.3576658041416457175462348437019377323527317041928e-28), SC_(0.182191292416e12), SC_(0.355224928e9), SC_(0.1056145023109440334189908118197725710820599937924e-4),
SC_(0.45190074381881787947113833644192369803258850957835e-28), SC_(0.903221837196690095865856e24), SC_(0.197033285648384e15), SC_(0.1316234260403974959059386181123491622884455028604e-10),
SC_(0.75787209056271355952485380019348769132814133643247e-28), SC_(0.3443290234375e5), SC_(0.87738095954812459262649215691458087947041111220869e-24), SC_(0.18482788150207164039886687903794355893352157342876e0),
SC_(0.83892250504513065845701871993405683214864787598623e-28), SC_(0.1116302655645995400846004486083984375e-5), SC_(0.5191992844812585795584e22), SC_(0.46130757625625887687399713890619646292026008752597e-9),
SC_(0.10848934303015863927446282468623299997624646840919e-27), SC_(0.62221619626030569058053553009209074892000950850727e-30), SC_(0.343400804652490021666816e24), SC_(0.10342135228893151111628599880598474090206795712037e-9),
SC_(0.1287535325337014953720268054032123824574619620157e-27), SC_(0.13705567485615801022446745431989965211687137938007e-26), SC_(0.5078582763671875e0), SC_(0.44492840412794216795211644099170510281671666177003e2),
SC_(0.20347543751535935665284243442334458135561822645851e-27), SC_(0.440987377729536e16), SC_(0.287391328125e5), SC_(0.21480602601200030281855562249446563848311273705777e-6),
SC_(0.22256795142604778055852756615936599983521384333793e-27), SC_(0.18143533359633255599212774654416246988830607733689e-18), SC_(0.21148944142623804509639739990234375e-5), SC_(0.11297576663225845000545238152727773376633249003903e5),
SC_(0.27311316429626442094674415847188181871613594240214e-27), SC_(0.10845691548033613824e20), SC_(0.400673984e9), SC_(0.40680160276715551282981129022255804380967818080019e-8),
SC_(0.55263283825603576259688637477087526891102295303199e-27), SC_(0.14570690537170526341649579027404115549870766699314e-16), SC_(0.12941088853490731622934705547460304161866623869764e-26), SC_(0.3263066756541685311171843349919704700385781288154e10),
SC_(0.56127809703514701593677302775789618452802567406812e-27), SC_(0.9228809556838246663801328395493328571319580078125e-11), SC_(0.86422194270699415064029835775727406144142150878906e-12), SC_(0.85882928958216539680438351403609321208964637689442e6),
SC_(0.88887406204705208581375488864563298833942634608052e-27), SC_(0.5811525927157390469801612198352813720703125e-8), SC_(0.32174132911148321865672794483970164947095327079296e-17), SC_(0.15798257631853654027208341257989620757183444492979e6),
SC_(0.11649136528196886067987694424015483218044894522109e-26), SC_(0.36767340167168e14), SC_(0.4968523085117340087890625e0), SC_(0.28619662675577147008545299820464843681562410993599e-5),
SC_(0.12708737924245050134296546672544059482912572403568e-26), SC_(0.903024183216244059537408e24), SC_(0.15518063165544166788813746673722175600112280614926e-28), SC_(0.62957032534216916589353715070316990128108284888469e-10),
SC_(0.25172518744793432127678756566548684645107602196601e-26), SC_(0.432213410600102056165376e24), SC_(0.1959631583933896656101239768660304818581607833039e-18), SC_(0.76260606376287472971690034770273684734039141637871e-10),
SC_(0.28601321158264026057365024112938563807684451932578e-26), SC_(0.40558081566683637682324548023871102486737072467804e-15), SC_(0.208714828125e6), SC_(0.5522837672610515535667805214004803961305903914157e-1),
SC_(0.42244364291200267661460233749011480646438909669627e-26), SC_(0.477498138427734375e3), SC_(0.17728046030944125033074269511337850424581574770855e-19), SC_(0.12451945453260696576552580190880249825955248401269e1),
SC_(0.48457483625271488463909528606996389233426292958429e-26), SC_(0.34402809559391418553704811749276853293953368218006e-26), SC_(0.3426654976e10), SC_(0.71831384058159540985490355058964459192302194019864e-3),
SC_(0.51977933341075693398899317919762114747383096799438e-26), SC_(0.266911591494591876579813490688e30), SC_(0.53580234866956732986409406294114887714385986328125e-11), SC_(0.93375161793411865686174480682610243788243937917932e-13),
SC_(0.73955594308673193523198369636584653936223991005372e-26), SC_(0.15995684594580228399252064264146611094474792480469e-12), SC_(0.170420291286861873152e22), SC_(0.98255728430318667072571074195808505094006175327076e-9),
SC_(0.16358995318300954765782308898640009098138844295667e-25), SC_(0.98936341703850100293138325469044502824544906616211e-13), SC_(0.17837596956010162360661830405206274008378386497498e-14), SC_(0.10825479757466109087874722747675913053273852855701e8),
SC_(0.19129386995031684168433400267318972464065419958335e-25), SC_(0.74098306733179406810366224487118565210547929972832e-30), SC_(0.40798337829960889676546298421300207337480969727039e-16), SC_(0.18975656681089523246977362390571886102543681656904e10),
SC_(0.20621651441981357349985057544616166528433660182218e-25), SC_(0.37752524088656425060861465681227855384349822998047e-12), SC_(0.20065922661601206578897704790875877733924426138401e-16), SC_(0.1026562701139222168152586002247636059939894265944e8),
SC_(0.21288901426793981534691419438692370107505096726852e-25), SC_(0.5289344906157640122368e23), SC_(0.11510209314816e14), SC_(0.54396628344807662681292826103022096566324190444093e-10),
SC_(0.25325901731494375978251987705874090841683295149966e-25), SC_(0.2247014312744140625e3), SC_(0.275117858615052709715247104e27), SC_(0.1755537214869906012774193839638577210495131605845e-11),
SC_(0.34857664908449107348958795506280082952452713251912e-25), SC_(0.4151866912841796875e2), SC_(0.84098145009994339684283693509730169685090217512879e-22), SC_(0.44454486362140376311920208456593332541577968986099e1),
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SC_(0.34176589422481911700258816e26), SC_(0.2594374745967797935009002685546875e-4), SC_(0.32639631015324299667668128677178174257278442382813e-11), SC_(0.61686726715099850869664269896236478457721173132798e-11),
SC_(0.66192871423119660955992064e26), SC_(0.65104581211365760324995297566040105840304400052279e-28), SC_(0.700861590985368820838630199432373046875e-9), SC_(0.51196495026574394146099382874482062017583142405701e-11),
SC_(0.8845430532586596087103488e26), SC_(0.19398925304412841796875e1), SC_(0.41011344364960677921772003173828125e-6), SC_(0.32883289253336466203877579763959792657158933119763e-11),
SC_(0.9036469625899950631026688e26), SC_(0.690641880035400390625e1), SC_(0.1238969862461090087890625e0), SC_(0.31745434338722854630828915646448539066116092136479e-11),
SC_(0.26160499139176195703177216e27), SC_(0.25551566240720070127823149164214555639773607254028e-14), SC_(0.2455513858048e13), SC_(0.10841986934216006931865443143259911799200916785229e-11),
SC_(0.351293559140227787146657792e27), SC_(0.92746285056e12), SC_(0.7325884342193603515625e1), SC_(0.96945165287587645794032553087381848752888109990602e-12),
SC_(0.48555353730121618377670656e27), SC_(0.41366469991877353664505423235416110752209856263632e-29), SC_(0.1080339869874636584075679427013641468012674864323e-29), SC_(0.29736856860648111150067984819515308053148330813485e-11),
SC_(0.576385747842019784963129344e27), SC_(0.42413690615195065447551314719021320343017578125e-10), SC_(0.429480374875002013368430198170244693756103515625e-10), SC_(0.18094440824622577258491088407553210906682687995255e-11),
SC_(0.861307183935277657013354496e27), SC_(0.13938332907855510711669921875e-1), SC_(0.68459855298386769923242872813539959368599538368623e-30), SC_(0.11766749224716932927375683670462877212205767926654e-11),
SC_(0.105505156605401800151924736e28), SC_(0.36789907058298876307844693656079471111297607421875e-11), SC_(0.10516135122406685860405589982143287428734135247055e-23), SC_(0.14057878532181048238381113039649629348002517816159e-11),
SC_(0.3196617981363007079661436928e28), SC_(0.357227936120807498809881508350372314453125e-8), SC_(0.190531306287766710738651454448699951171875e-7), SC_(0.73543482163433806936996915244342283274029549975336e-12),
SC_(0.4932620110638545248192561152e28), SC_(0.39087764918804168701171875e-1), SC_(0.37496308203098109226999139757157200603110425163322e-21), SC_(0.49677918885669315094834554588390832782238505953762e-12),
SC_(0.516425012058796509045456896e28), SC_(0.3000732163818651513042917353020530062720192427143e-28), SC_(0.28816120624542236328125e1), SC_(0.45590953716748809622767271344568834414324208839861e-12),
SC_(0.6724360036363488659828113408e28), SC_(0.39914275e7), SC_(0.5617260831058956682682037353515625e-4), SC_(0.3149211786161963517965091650354250566920868130489e-12),
SC_(0.7376334675354954747676196864e28), SC_(0.3832167254355459644063744e25), SC_(0.86986000872677090266227306614155168063007295131683e-15), SC_(0.60174664703890956134939928112815630373518374796924e-13),
SC_(0.1240879712420966629044649984e29), SC_(0.35030939907262229474824187104684165838808240778235e-22), SC_(0.23553908385443359223970771765266363217961043119431e-16), SC_(0.47464339774120723669000561802171052279059315153073e-12),
SC_(0.13622372113626680630865559552e29), SC_(0.5065993732313771067901500902430633743733778828755e-18), SC_(0.1568245533434264871175400912761688232421875e-11), SC_(0.40583512551936497170672012442547588122036553493224e-12),
SC_(0.21413030105610117647127543808e29), SC_(0.56796892335439872e17), SC_(0.44545595303495604738852208133448318250202646595426e-19), SC_(0.10055266250578662063485344934342287093203087991764e-12),
SC_(0.240611655851932728105631744e29), SC_(0.15126033260477136128765155826087636266509091563425e-30), SC_(0.147685372829437255859375e1), SC_(0.21832951144880765009500199074282822236333957933832e-12),
SC_(0.61731988312258099732254031872e29), SC_(0.47155488899394500240213479534565823420775918905622e-28), SC_(0.4463543296e10), SC_(0.94272971828494080864224866724511415301020102514649e-13),
SC_(0.74469943825056746033385570304e29), SC_(0.25381451890023692523876122624e29), SC_(0.353061568e9), SC_(0.73993207202984769111475156231178550093712585836288e-14),
SC_(0.117661009908837424815142862848e30), SC_(0.434518829345703125e3), SC_(0.429355800151824951171875e0), SC_(0.9266881807310148034392861576649650379030278607074e-13),
SC_(0.593089902380358100434877939712e30), SC_(0.6506956228718475954142519412926048971712589263916e-14), SC_(0.61562469482421875e2), SC_(0.43634363152950073747311554335524072760111106270713e-13),
SC_(0.1138966491359350198995104301056e31), SC_(0.16628866613248e14), SC_(0.83722254681922700089433337836521478725337885862245e-21), SC_(0.19460821722924338220942178264562269988472467417183e-13),
};
#undef SC_

401
test/ellint_rj_data.ipp Normal file
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@@ -0,0 +1,401 @@
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 5>, 395> ellint_rj_data = {
SC_(0.34628584803331255547073953716003532083475191421235e-30), SC_(0.303861990424576e15), SC_(0.4400977e7), SC_(0.8120083456e10), SC_(0.94406118682435306969091503176397574982473232273954e-16),
SC_(0.62687453931329231730011467674071804187172354186889e-30), SC_(0.26256847716031594952568184453411959111690521240234e-12), SC_(0.1063940752263547436662784e25), SC_(-0.136451337486336e15), SC_(-0.67037231980991720071044018087634320636670369191284e-24),
SC_(0.68459855298386769923242872813539959368599538368623e-30), SC_(0.3576658041416457175462348437019377323527317041928e-28), SC_(0.182191292416e12), SC_(-0.363291968e9), SC_(-0.83523497967218414236437029496187282518142685409801e-12),
SC_(0.91680349711592282765605796247359202706042027867974e-30), SC_(0.734585367784587264e18), SC_(0.1052182232419898336993917357499253478604839479385e-26), SC_(0.2412866171048483705123448575434206360597333418383e-23), SC_(0.65770139664720747088672501472576668594088104855097e16),
SC_(0.11714106834475308811660531464919355963339235126279e-29), SC_(0.24252292633056640625e2), SC_(0.367521736353615183872e22), SC_(-0.4790649536162908709687890753434018342726830042011e-21), SC_(0.22701967082264264796089141494292880179559115582815e-4),
SC_(0.15170719443124775223923085751802832491502232570833e-29), SC_(0.5680430348320442135445773601531982421875e-8), SC_(0.264763527397376e15), SC_(0.13735858601648942567408084869384765625e-5), SC_(0.46218215900161368547332976532325866494807961652724e0),
SC_(0.16414311592283418833973460759110207528131746805707e-29), SC_(0.2019777626058022108969416021903358834932440402099e-21), SC_(0.2589416226816e13), SC_(-0.8526492879801228497171905473805963993072509765625e-11), SC_(-0.28262895694754696636159676198309944171160827781306e7),
SC_(0.27727679237026680624547360688641283050751007274628e-29), SC_(0.574552528560161590576171875e-1), SC_(0.599083490669727325439453125e-1), SC_(0.326562033434624e15), SC_(0.59574348217068678836770193704601663452299198297862e-13),
SC_(0.43727979838159528482554219689363356095561935561375e-29), SC_(0.7798122348544e13), SC_(0.8588943201947652980736e22), SC_(-0.45831213261398661135397416775299529474035908904739e-23), SC_(0.52890106746769770489956114049541553965288744960747e-8),
SC_(0.44767214645416419053919245787147718165594030426536e-29), SC_(0.26553176031232e14), SC_(0.2085586588137791946752e23), SC_(0.790340763648e12), SC_(0.64331758941919291277431102504836936943662726638851e-23),
SC_(0.71060984495908924431726061148159195715493970237986e-29), SC_(0.61842984e8), SC_(0.3555642664432525634765625e0), SC_(0.133759144e9), SC_(0.28834216749836541937606611695450951218706212147855e-10),
SC_(0.80490202086679616440767211156605911864354431197377e-29), SC_(0.263248904192e12), SC_(0.297980882347216843954978816e27), SC_(0.140897846221923828125e1), SC_(0.44824022549527823491543784090039049377556207542239e-18),
SC_(0.93229513968235881657927660254990574951111859851663e-29), SC_(0.366241894662380218505859375e-1), SC_(0.4340599750656e13), SC_(0.105478806095575292710985138176e30), SC_(0.24012124307552155152973805705552466780637562428371e-33),
SC_(0.98984072271443418184618106348812926220946298945177e-29), SC_(0.96973053952e11), SC_(0.1032632680728338890752e22), SC_(-0.34396671690046787261962890625e-2), SC_(-0.96271364111058320397683919234948561206704260148431e-21),
SC_(0.14087878121271588812030448853437982084687159586205e-28), SC_(0.53508747383344354605481852928e29), SC_(0.62704322937005693765167776976277025369199691340327e-17), SC_(0.235499138513371136e18), SC_(0.22302880199358479320924395693872038333122707229792e-29),
SC_(0.19696330564073048658818435820590984305819001943432e-28), SC_(0.32238440243425309843308409068705787565729120602853e-24), SC_(0.292186842467552253181952e24), SC_(-0.3806432217839128513100120064e28), SC_(-0.82513020195805722794885738700643372535526082646992e-37),
SC_(0.20092729076345475268161641680692456393259236283608e-28), SC_(0.5697601591236889362335205078125e-4), SC_(0.1162191569964638329110528e26), SC_(-0.16412856978298360348657569008246504688175448904985e-21), SC_(0.31839738515206016513063561009026484616216098410256e-2),
SC_(0.20426069933899679481125376462984716200236491481616e-28), SC_(0.3943929741312e13), SC_(0.23412235260009765625e2), SC_(0.10193842560436084643201024e26), SC_(0.21207853870411859766389282691659616682682417758342e-29),
SC_(0.38307908170359829668907275664710825900011835075561e-28), SC_(0.14482298173190688572731232852675020694732666015625e-10), SC_(0.28193880243627888738304e23), SC_(0.589604375e6), SC_(0.60047466992965579411135347476169935325115071814017e-15),
SC_(0.44431992244584514654678755926404518943295031559691e-28), SC_(0.48174394645500255940076463501836601110994706687052e-19), SC_(0.111553230384106831872e21), SC_(0.26075669569036418811408302358884491864634006858979e-29), SC_(0.41939587045610674859432459314508206490215441802069e15),
SC_(0.45190074381881787947113833644192369803258850957835e-28), SC_(0.903221837196690095865856e24), SC_(0.197033285648384e15), SC_(0.32623424794930855341590358875691890716552734375e-10), SC_(0.61845676096363676818434676933016847521984818056106e-13),
SC_(0.72950579063556310785863719706888276620113808904403e-28), SC_(0.590493896484375e4), SC_(0.99392208896e11), SC_(-0.19527980804443359375e2), SC_(-0.16079545628777305110796074754669542322724883666308e-8),
SC_(0.94777901458212457182664258521518150736237789261152e-28), SC_(0.4428201e7), SC_(0.2530101420741656313673562390278253679619336276427e-31), SC_(0.26171386241912841796875e1), SC_(0.18205396527964645652297231995003573026647291521867e-1),
SC_(0.11153434660579423094016106021221904046901687488323e-27), SC_(0.750879536326465313322842121124267578125e-7), SC_(0.9310612177071408979145417106337845325469970703125e-12), SC_(0.31839368781345048800513961029245990630442975088954e-17), SC_(0.99763610438792567414792334839900304053722628109961e19),
SC_(0.11969815900999513257745596351318014772377229309672e-27), SC_(0.1668161242237629641861967998969556656319035425895e-21), SC_(0.2847195703125e5), SC_(-0.12113708519078755261729959946670476256258552893996e-18), SC_(-0.58469912606844089535572230231066119898125245972777e18),
SC_(0.14718026449967740426353456716434433271883469801847e-27), SC_(0.14995603510614981277719965857381914152826921874523e-28), SC_(0.1111803961616105472e19), SC_(0.508679587341021033353172242641448974609375e-8), SC_(0.12814521532382957625567079334028430774339053692899e2),
SC_(0.15284006704962108878625465914339150556459706251089e-27), SC_(0.1302969292737543582916259765625e-2), SC_(0.354480992801311143493632e24), SC_(0.37605104e9), SC_(0.18607859430748510805274307470148837042692731526225e-18),
SC_(0.18215559766104924690332214579658583558792903588607e-27), SC_(0.214253668673336505889892578125e-4), SC_(0.7301043754462531075178496e25), SC_(0.1068455829996046990704172685582307167351245880127e-12), SC_(0.11526214590948729311397784489864538809888995731212e-2),
SC_(0.24529570625501572181775218266146503325173309053089e-27), SC_(0.25641463683753128890529908445738982436523656360805e-17), SC_(0.48869192600250244140625e-1), SC_(0.58277403084650757214336531275763466589806549578157e-23), SC_(0.54865012310632304234244856782916104369657655425137e22),
SC_(0.39141497594833019784983821157723932951078514835136e-27), SC_(0.357364711819011162112e22), SC_(0.667275905609130859375e1), SC_(0.1113973178760695906304e22), SC_(0.10731044892019837510186483399833963183503696610428e-29),
SC_(0.70854346356424203118456450594757848872274827445317e-27), SC_(0.17661992750974924766497868057479880832261187606491e-19), SC_(0.13503679168512e14), SC_(0.99978050734272746818492337364912077787941683637389e-28), SC_(0.40708318789691990117035501094747887529655008140322e18),
SC_(0.95094302859126114224783559857815715520763821290429e-27), SC_(0.24968204839583968605398571483089398270749370567501e-17), SC_(0.9045842452906072139739990234375e-3), SC_(-0.3141900802028363415274725412018597126007080078125e-11), SC_(-0.2449539203496388975798784873357620168741296674017e15),
SC_(0.16793731632787596740420928687663819571897812904515e-26), SC_(0.3518738464768e13), SC_(0.98092148011034996368806559985387139022350311279297e-13), SC_(0.7575111198086004736e19), SC_(0.65039496025983965665832815009530617268807417944382e-23),
SC_(0.21755331614817437617422269623130535179188855751664e-26), SC_(0.2500394162552321830617074738256633281707763671875e-10), SC_(0.72982407463299740342380286062361920775211799206766e-27), SC_(0.247376342155264e15), SC_(0.4709775015194030811246957863705675568998476920662e-7),
SC_(0.21971093546487139650040130832038324586684679279314e-26), SC_(0.63975672837429094514688e23), SC_(0.4539182297546489856e19), SC_(0.84259974327325996997237890661914493965691137777885e-26), SC_(0.72996868550237370924565332261049662117667604966241e-7),
SC_(0.22982227952519826732488902867652779863117686563745e-26), SC_(0.33525770516606100656031852480509769520722329616547e-15), SC_(0.2606888e9), SC_(-0.99916063843772263862794266384148578197255119448528e-19), SC_(-0.54923986434781063090698390941147979292728868719051e12),
SC_(0.51977933341075693398899317919762114747383096799438e-26), SC_(0.266911591494591876579813490688e30), SC_(0.53580234866956732986409406294114887714385986328125e-11), SC_(0.254200357322752e15), SC_(0.69110368402320022163407013192490694398911620896064e-27),
SC_(0.77196710997203362544532626020513746761754665659527e-26), SC_(0.9461145951093060124066579601815525318148601685575e-25), SC_(0.12432433352443051997396992e26), SC_(-0.5228e6), SC_(-0.58320270863535593455030526710289059054679659475945e-16),
SC_(0.11635736870608811874540057457479948586226165679891e-25), SC_(0.17671186639527258161297881214290347985361303510387e-28), SC_(0.22745186078595230213685116928e29), SC_(0.15040896827392e14), SC_(0.60417643323129282335411977676602262754782289036307e-25),
SC_(0.11837831633021164326650292224515978315498715423004e-25), SC_(0.27219574150194603134877979755401611328125e-7), SC_(0.15386248307178551019952166983379913769903023636025e-28), SC_(0.87460832e8), SC_(0.46759013370870059772614259918741759451044911410075e-2),
SC_(0.17550213803783570336671080151775868003491756774714e-25), SC_(0.5815067891204096e17), SC_(0.8830627750050583805952e22), SC_(-0.11121447374743291820226533572930904814057839757879e-20), SC_(0.15769698742831680011244511894063175456041078597779e-10),
SC_(0.21288901426793981534691419438692370107505096726852e-25), SC_(0.5289344906157640122368e23), SC_(0.11510209314816e14), SC_(0.4249272918701171875e2), SC_(0.92648999418099558750700023051939135561434274409392e-18),
SC_(0.27826294978205525521980137859608542144911232096849e-25), SC_(0.87440356429873925658498856170228582591246249688943e-25), SC_(0.897631640625e4), SC_(0.36269013671875e4), SC_(0.28820549055264756824493461253302827935710287805982e-3),
SC_(0.40640597744934306582748730017532743697978442343199e-25), SC_(0.143180119991302490234375e1), SC_(0.7372973065411514426159556023776531219482421875e-10), SC_(0.25642714125858165256502331187864603249699103210135e-25), SC_(0.16806840183003004103311088621594719873834403266311e19),
SC_(0.66556817034054791977215246744979717646037778444601e-25), SC_(0.3026203967488e14), SC_(0.89236039341428712414264201591151959291892126202583e-16), SC_(0.12883867020718753337860107421875e-3), SC_(0.62189172419008455881321301576823244222445688480495e-1),
SC_(0.85862603804552791851901750144015928773062740209099e-25), SC_(0.100811407958566250167576559616e30), SC_(0.4642501040129231797912992205090709774140123045072e-18), SC_(0.6697769276797771453857421875e-3), SC_(0.25597760155920837386398004521369053843545906300128e-9),
SC_(0.10332494589906572792043563946857459391668980497325e-24), SC_(0.363202080623525101568e21), SC_(0.31611702310388430456632212831036277123075706185773e-19), SC_(0.3834788709626559462375424e25), SC_(0.19494480412558630536765884383661183190812241864799e-32),
SC_(0.11061723157371115940205422633821341626969569915673e-24), SC_(0.46915519457248313591588473499272016198347046156414e-19), SC_(0.292094455289770849049091339111328125e-6), SC_(0.155271419401486900365614907392e30), SC_(0.57608762536920856390418378494213938082655486152011e-24),
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SC_(0.593089902380358100434877939712e30), SC_(0.6506956228718475954142519412926048971712589263916e-14), SC_(0.61562469482421875e2), SC_(0.2321270964224e13), SC_(0.21597485998566959444034291971333852159947917872266e-25),
SC_(0.90054999923278052824918786048e30), SC_(0.5752800417419362304e19), SC_(0.23091611800228823082094034944e29), SC_(0.437946654856204986572265625e-1), SC_(0.20691242362670718543784273355620160692479713280658e-36),
SC_(0.1138966491359350198995104301056e31), SC_(0.16628866613248e14), SC_(0.83722254681922700089433337836521478725337885862245e-21), SC_(0.351686295552e12), SC_(0.16740484414913831836071532979123766364786418157375e-26),
};
#undef SC_

116
test/instantiate.hpp Normal file
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@@ -0,0 +1,116 @@
#ifndef BOOST_LIBS_MATH_TEST_INSTANTIATE_HPP
#define BOOST_LIBS_MATH_TEST_INSTANTIATE_HPP
#include <boost/math/distributions/normal.hpp>
#include <boost/math/distributions/students_t.hpp>
#include <boost/math/distributions/binomial.hpp>
#include <boost/math/distributions/cauchy.hpp>
#include <boost/math/distributions/chi_squared.hpp>
#include <boost/math/distributions/exponential.hpp>
#include <boost/math/distributions/extreme_value.hpp>
#include <boost/math/distributions/fisher_f.hpp>
#include <boost/math/distributions/weibull.hpp>
#include <boost/math/distributions/lognormal.hpp>
#include <boost/math/special_functions/digamma.hpp>
#include <boost/math/special_functions/cbrt.hpp>
#include <boost/math/special_functions/legendre.hpp>
#include <boost/math/special_functions/laguerre.hpp>
#include <boost/math/special_functions/hermite.hpp>
#include <boost/math/special_functions/spherical_harmonic.hpp>
#include <boost/math/special_functions/ellint_1.hpp>
#include <boost/math/special_functions/ellint_2.hpp>
#include <boost/math/special_functions/ellint_3.hpp>
#include <boost/math/concepts/distributions.hpp>
template <class RealType>
void instantiate(RealType)
{
using namespace boost;
using namespace boost::math;
using namespace boost::math::concepts;
function_requires<DistributionConcept<normal_distribution<RealType> > >();
function_requires<DistributionConcept<binomial_distribution<RealType> > >();
function_requires<DistributionConcept<cauchy_distribution<RealType> > >();
function_requires<DistributionConcept<chi_squared_distribution<RealType> > >();
function_requires<DistributionConcept<exponential_distribution<RealType> > >();
function_requires<DistributionConcept<extreme_value_distribution<RealType> > >();
function_requires<DistributionConcept<fisher_f_distribution<RealType> > >();
function_requires<DistributionConcept<students_t_distribution<RealType> > >();
function_requires<DistributionConcept<weibull_distribution<RealType> > >();
function_requires<DistributionConcept<lognormal_distribution<RealType> > >();
int i;
RealType v1(0.5), v2(0.5), v3(0.5);
boost::math::tgamma(v1);
boost::math::tgamma1pm1(v1);
boost::math::lgamma(v1);
boost::math::lgamma(v1, &i);
boost::math::digamma(v1);
boost::math::tgamma_ratio(v1, v2);
boost::math::tgamma_delta_ratio(v1, v2);
boost::math::factorial<RealType>(i);
boost::math::unchecked_factorial<RealType>(i);
i = boost::math::max_factorial<RealType>::value;
boost::math::double_factorial<RealType>(i);
boost::math::rising_factorial(v1, i);
boost::math::falling_factorial(v1, i);
boost::math::tgamma(v1, v2);
boost::math::tgamma_lower(v1, v2);
boost::math::gamma_P(v1, v2);
boost::math::gamma_Q(v1, v2);
boost::math::gamma_P_inv(v1, v2);
boost::math::gamma_Q_inv(v1, v2);
boost::math::gamma_P_inva(v1, v2);
boost::math::gamma_Q_inva(v1, v2);
boost::math::erf(v1);
boost::math::erfc(v1);
boost::math::erf_inv(v1);
boost::math::erfc_inv(v1);
boost::math::beta(v1, v2);
boost::math::beta(v1, v2, v3);
boost::math::betac(v1, v2, v3);
boost::math::ibeta(v1, v2, v3);
boost::math::ibetac(v1, v2, v3);
boost::math::ibeta_inv(v1, v2, v3);
boost::math::ibetac_inv(v1, v2, v3);
boost::math::ibeta_inva(v1, v2, v3);
boost::math::ibetac_inva(v1, v2, v3);
boost::math::ibeta_invb(v1, v2, v3);
boost::math::ibetac_invb(v1, v2, v3);
boost::math::gamma_P_derivative(v2, v3);
boost::math::ibeta_derivative(v1, v2, v3);
boost::math::fpclassify(v1);
boost::math::isfinite(v1);
boost::math::isnormal(v1);
boost::math::isnan(v1);
boost::math::isinf(v1);
boost::math::log1p(v1);
boost::math::expm1(v1);
boost::math::cbrt(v1);
boost::math::sqrt1pm1(v1);
boost::math::powm1(v1, v2);
boost::math::legendre_p(1, v1);
boost::math::legendre_p(1, 0, v1);
boost::math::legendre_q(1, v1);
boost::math::legendre_next(2, v1, v2, v3);
boost::math::legendre_next(2, 2, v1, v2, v3);
boost::math::laguerre(1, v1);
boost::math::laguerre(2, 1, v1);
boost::math::laguerre_next(2, v1, v2, v3);
boost::math::laguerre_next(2, 1, v1, v2, v3);
boost::math::hermite(1, v1);
boost::math::hermite_next(2, v1, v2, v3);
boost::math::spherical_harmonic_r(2, 1, v1, v2);
boost::math::spherical_harmonic_i(2, 1, v1, v2);
boost::math::ellint_1(v1);
boost::math::ellint_1(v1, v2);
boost::math::ellint_2(v1);
boost::math::ellint_2(v1, v2);
boost::math::ellint_3(v1, v2);
boost::math::ellint_3(v1, v2, v3);
}
#endif // BOOST_LIBS_MATH_TEST_INSTANTIATE_HPP

103
test/std_real_concept_check.cpp
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@@ -6,22 +6,7 @@
#include <boost/math/concepts/std_real_concept.hpp>
#include <boost/math/concepts/distributions.hpp>
#include <boost/math/distributions/normal.hpp>
#include <boost/math/distributions/students_t.hpp>
#include <boost/math/distributions/binomial.hpp>
#include <boost/math/distributions/cauchy.hpp>
#include <boost/math/distributions/chi_squared.hpp>
#include <boost/math/distributions/exponential.hpp>
#include <boost/math/distributions/extreme_value.hpp>
#include <boost/math/distributions/fisher_f.hpp>
#include <boost/math/distributions/weibull.hpp>
#include <boost/math/distributions/lognormal.hpp>
#include <boost/math/special_functions/digamma.hpp>
#include <boost/math/special_functions/cbrt.hpp>
#include <boost/math/special_functions/legendre.hpp>
#include <boost/math/special_functions/laguerre.hpp>
#include <boost/math/special_functions/hermite.hpp>
#include <boost/math/special_functions/spherical_harmonic.hpp>
#include "instantiate.hpp"
//
// The purpose of this test is to verify that our code compiles
@@ -202,92 +187,6 @@ struct numeric_limits<boost::math::concepts::std_real_concept>
}
#endif
template <class RealType>
void instantiate(RealType)
{
using namespace boost;
using namespace boost::math;
using namespace boost::math::concepts;
function_requires<DistributionConcept<normal_distribution<RealType> > >();
function_requires<DistributionConcept<binomial_distribution<RealType> > >();
function_requires<DistributionConcept<cauchy_distribution<RealType> > >();
function_requires<DistributionConcept<chi_squared_distribution<RealType> > >();
function_requires<DistributionConcept<exponential_distribution<RealType> > >();
function_requires<DistributionConcept<extreme_value_distribution<RealType> > >();
function_requires<DistributionConcept<fisher_f_distribution<RealType> > >();
function_requires<DistributionConcept<students_t_distribution<RealType> > >();
function_requires<DistributionConcept<weibull_distribution<RealType> > >();
function_requires<DistributionConcept<lognormal_distribution<RealType> > >();
}
void test_functions()
{
int i;
boost::math::concepts::std_real_concept v1(0.5), v2(0.5), v3(0.5);
boost::math::tgamma(v1);
boost::math::tgamma1pm1(v1);
boost::math::lgamma(v1);
boost::math::lgamma(v1, &i);
boost::math::digamma(v1);
boost::math::tgamma_ratio(v1, v2);
boost::math::tgamma_delta_ratio(v1, v2);
boost::math::factorial<boost::math::concepts::std_real_concept>(i);
boost::math::unchecked_factorial<boost::math::concepts::std_real_concept>(i);
i = boost::math::max_factorial<boost::math::concepts::std_real_concept>::value;
boost::math::double_factorial<boost::math::concepts::std_real_concept>(i);
boost::math::rising_factorial(v1, i);
boost::math::falling_factorial(v1, i);
boost::math::tgamma(v1, v2);
boost::math::tgamma_lower(v1, v2);
boost::math::gamma_P(v1, v2);
boost::math::gamma_Q(v1, v2);
boost::math::gamma_P_inv(v1, v2);
boost::math::gamma_Q_inv(v1, v2);
boost::math::gamma_P_inva(v1, v2);
boost::math::gamma_Q_inva(v1, v2);
boost::math::erf(v1);
boost::math::erfc(v1);
boost::math::erf_inv(v1);
boost::math::erfc_inv(v1);
boost::math::beta(v1, v2);
boost::math::beta(v1, v2, v3);
boost::math::betac(v1, v2, v3);
boost::math::ibeta(v1, v2, v3);
boost::math::ibetac(v1, v2, v3);
boost::math::ibeta_inv(v1, v2, v3);
boost::math::ibetac_inv(v1, v2, v3);
boost::math::ibeta_inva(v1, v2, v3);
boost::math::ibetac_inva(v1, v2, v3);
boost::math::ibeta_invb(v1, v2, v3);
boost::math::ibetac_invb(v1, v2, v3);
boost::math::gamma_P_derivative(v2, v3);
boost::math::ibeta_derivative(v1, v2, v3);
boost::math::fpclassify(v1);
boost::math::isfinite(v1);
boost::math::isnormal(v1);
boost::math::isnan(v1);
boost::math::isinf(v1);
boost::math::log1p(v1);
boost::math::expm1(v1);
boost::math::cbrt(v1);
boost::math::sqrt1pm1(v1);
boost::math::powm1(v1, v2);
boost::math::legendre_p(1, v1);
boost::math::legendre_p(1, 0, v1);
boost::math::legendre_q(1, v1);
boost::math::legendre_next(2, v1, v2, v3);
boost::math::legendre_next(2, 2, v1, v2, v3);
boost::math::laguerre(1, v1);
boost::math::laguerre(2, 1, v1);
boost::math::laguerre_next(2, v1, v2, v3);
boost::math::laguerre_next(2, 1, v1, v2, v3);
boost::math::hermite(1, v1);
boost::math::hermite_next(2, v1, v2, v3);
boost::math::spherical_harmonic_r(2, 1, v1, v2);
boost::math::spherical_harmonic_i(2, 1, v1, v2);
}
int main()

325
test/test_carlson.cpp Normal file
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@@ -0,0 +1,325 @@
// Copyright (c) 2006 Xiaogang Zhang
// 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)
#define BOOST_MATH_THROW_ON_DOMAIN_ERROR
#define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
#include <boost/math/concepts/real_concept.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/ellint_rf.hpp>
#include <boost/math/special_functions/ellint_rc.hpp>
#include <boost/math/special_functions/ellint_rj.hpp>
#include <boost/math/special_functions/ellint_rd.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/array.hpp>
#include <boost/lambda/lambda.hpp>
#include <boost/lambda/bind.hpp>
#include <boost/tr1/random.hpp>
#include "handle_test_result.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the Carlson Elliptic Integrals.
// There are two sets of tests, spot
// tests which compare our results with the published test values,
// in Numerical Computation of Real or Complex Elliptic Integrals,
// B. C. Carlson: http://arxiv.org/abs/math.CA/9409227
// However, the bulk of the accuracy tests
// use values generated with NTL::RR at 1000-bit precision
// and our generic versions of these functions.
//
// Note that when this file is first run on a new platform many of
// these tests will fail: the default accuracy is 1 epsilon which
// is too tight for most platforms. In this situation you will
// need to cast a human eye over the error rates reported and make
// a judgement as to whether they are acceptable. Either way please
// report the results to the Boost mailing list. Acceptable rates of
// error are marked up below as a series of regular expressions that
// identify the compiler/stdlib/platform/data-type/test-data/test-function
// along with the maximum expected peek and RMS mean errors for that
// test.
//
void expected_results()
{
//
// Define the max and mean errors expected for
// various compilers and platforms.
//
const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
if(boost::math::tools::digits<double>() == boost::math::tools::digits<long double>())
{
largest_type = "(long\\s+)?double";
}
else
{
largest_type = "long double";
}
#else
largest_type = "(long\\s+)?double";
#endif
//
// HP-UX:
//
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
largest_type, // test type(s)
".*RJ.*", // test data group
".*", 250, 50); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
"HP-UX", // platform
"real_concept", // test type(s)
".*RJ.*", // test data group
".*", 250, 50); // test function
//
// Catch all cases come last:
//
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*RJ.*", // test data group
".*", 150, 50); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*RJ.*", // test data group
".*", 150, 50); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*", // test data group
".*", 15, 8); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*", // test data group
".*", 15, 8); // test function
//
// Finish off by printing out the compiler/stdlib/platform names,
// we do this to make it easier to mark up expected error rates.
//
std::cout << "Tests run with " << BOOST_COMPILER << ", "
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
template <typename T>
void do_test_ellint_rf(T& data, const char* type_name, const char* test)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
std::cout << "Testing: " << test << std::endl;
value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rf;
boost::math::tools::test_result<value_type> result;
result = boost::math::tools::test(
data,
boost::lambda::bind(fp,
boost::lambda::ret<value_type>(boost::lambda::_1[0]),
boost::lambda::ret<value_type>(boost::lambda::_1[1]),
boost::lambda::ret<value_type>(boost::lambda::_1[2])),
boost::lambda::ret<value_type>(boost::lambda::_1[3]));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_rf", test);
std::cout << std::endl;
}
template <typename T>
void do_test_ellint_rc(T& data, const char* type_name, const char* test)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
std::cout << "Testing: " << test << std::endl;
value_type (*fp)(value_type, value_type) = boost::math::ellint_rc;
boost::math::tools::test_result<value_type> result;
result = boost::math::tools::test(
data,
boost::lambda::bind(fp,
boost::lambda::ret<value_type>(boost::lambda::_1[0]),
boost::lambda::ret<value_type>(boost::lambda::_1[1])),
boost::lambda::ret<value_type>(boost::lambda::_1[2]));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_rc", test);
std::cout << std::endl;
}
template <typename T>
void do_test_ellint_rj(T& data, const char* type_name, const char* test)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
std::cout << "Testing: " << test << std::endl;
value_type (*fp)(value_type, value_type, value_type, value_type) = boost::math::ellint_rj;
boost::math::tools::test_result<value_type> result;
result = boost::math::tools::test(
data,
boost::lambda::bind(fp,
boost::lambda::ret<value_type>(boost::lambda::_1[0]),
boost::lambda::ret<value_type>(boost::lambda::_1[1]),
boost::lambda::ret<value_type>(boost::lambda::_1[2]),
boost::lambda::ret<value_type>(boost::lambda::_1[3])),
boost::lambda::ret<value_type>(boost::lambda::_1[4]));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_rf", test);
std::cout << std::endl;
}
template <typename T>
void do_test_ellint_rd(T& data, const char* type_name, const char* test)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
std::cout << "Testing: " << test << std::endl;
value_type (*fp)(value_type, value_type, value_type) = boost::math::ellint_rd;
boost::math::tools::test_result<value_type> result;
result = boost::math::tools::test(
data,
boost::lambda::bind(fp,
boost::lambda::ret<value_type>(boost::lambda::_1[0]),
boost::lambda::ret<value_type>(boost::lambda::_1[1]),
boost::lambda::ret<value_type>(boost::lambda::_1[2])),
boost::lambda::ret<value_type>(boost::lambda::_1[3]));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_rd", test);
std::cout << std::endl;
}
template <typename T>
void test_spots(T, const char* type_name)
{
using namespace boost::math;
using namespace std;
// Spot values from Numerical Computation of Real or Complex
// Elliptic Integrals, B. C. Carlson: http://arxiv.org/abs/math.CA/9409227
// RF:
T tolerance = (std::max)(T(1e-13f), tools::epsilon<T>() * 5) * 100; // Note 5eps expressed as a persentage!!!
T eps2 = 2 * tools::epsilon<T>();
BOOST_CHECK_CLOSE(ellint_rf(T(1), T(2), T(0)), T(1.3110287771461), tolerance);
BOOST_CHECK_CLOSE(ellint_rf(T(0.5), T(1), T(0)), T(1.8540746773014), tolerance);
BOOST_CHECK_CLOSE(ellint_rf(T(2), T(3), T(4)), T(0.58408284167715), tolerance);
// RC:
BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(0), T(1)/4), boost::math::constants::pi<T>(), eps2);
BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(9)/4, T(2)), log(T(2)), eps2);
BOOST_CHECK_CLOSE_FRACTION(ellint_rc(T(1)/4, T(-2)), log(T(2))/3, eps2);
// RJ:
BOOST_CHECK_CLOSE(ellint_rj(T(0), T(1), T(2), T(3)), T(0.77688623778582), tolerance);
BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(5)), T(0.14297579667157), tolerance);
BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(-0.5)), T(0.24723819703052), tolerance);
BOOST_CHECK_CLOSE(ellint_rj(T(2), T(3), T(4), T(-5)), T(-0.12711230042964), tolerance);
// RD:
BOOST_CHECK_CLOSE(ellint_rd(T(0), T(2), T(1)), T(1.7972103521034), tolerance);
BOOST_CHECK_CLOSE(ellint_rd(T(2), T(3), T(4)), T(0.16510527294261), tolerance);
// Sanity/consistency checks from Numerical Computation of Real or Complex
// Elliptic Integrals, B. C. Carlson: http://arxiv.org/abs/math.CA/9409227
std::tr1::mt19937 ran;
std::tr1::uniform_real<float> ur(0, 1000);
T eps40 = 40 * tools::epsilon<T>();
for(unsigned i = 0; i < 1000; ++i)
{
T x = ur(ran);
T y = ur(ran);
T z = ur(ran);
T lambda = ur(ran);
T mu = x * y / lambda;
// RF, eq 49:
T s1 = ellint_rf(x+lambda, y+lambda, lambda) +
ellint_rf(x + mu, y + mu, mu);
T s2 = ellint_rf(x, y, T(0));
BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
// RC is degenerate case of RF:
s1 = ellint_rc(x, y);
s2 = ellint_rf(x, y, y);
BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
// RC, eq 50 (Note have to assume y = x):
T mu2 = x * x / lambda;
s1 = ellint_rc(lambda, x+lambda)
+ ellint_rc(mu2, x + mu2);
s2 = ellint_rc(T(0), x);
BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
/*
T p = ????; // no closed form for a, b and p???
s1 = ellint_rj(x+lambda, y+lambda, lambda, p+lambda)
+ ellint_rj(x+mu, y+mu, mu, p+mu);
s2 = ellint_rj(x, y, T(0), p)
- 3 * ellint_rc(a, b);
*/
// RD, eq 53:
s1 = ellint_rd(lambda, x+lambda, y+lambda)
+ ellint_rd(mu, x+mu, y+mu);
s2 = ellint_rd(T(0), x, y)
- 3 / (y * sqrt(x+y+lambda+mu));
BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
// RD is degenerate case of RJ:
s1 = ellint_rd(x, y, z);
s2 = ellint_rj(x, y, z, z);
BOOST_CHECK_CLOSE_FRACTION(s1, s2, eps40);
}
//
// Now random spot values:
//
#include "ellint_rf_data.ipp"
do_test_ellint_rf(ellint_rf_data, type_name, "RF: Random data");
#include "ellint_rc_data.ipp"
do_test_ellint_rc(ellint_rc_data, type_name, "RC: Random data");
#include "ellint_rj_data.ipp"
do_test_ellint_rj(ellint_rj_data, type_name, "RJ: Random data");
#include "ellint_rd_data.ipp"
do_test_ellint_rd(ellint_rd_data, type_name, "RD: Random data");
}
int test_main(int, char* [])
{
expected_results();
test_spots(0.0F, "float");
test_spots(0.0, "double");
test_spots(0.0L, "long double");
test_spots(boost::math::concepts::real_concept(0), "real_concept");
return 0;
}

199
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// Copyright (c) 2006 Xiaogang Zhang
//
// 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)
#include <boost/math/concepts/real_concept.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/ellint_1.hpp>
#include <boost/array.hpp>
#include <boost/lambda/lambda.hpp>
#include <boost/lambda/bind.hpp>
#include "handle_test_result.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the Elliptic Integrals of the first kind.
// There are two sets of tests, spot
// tests which compare our results with selected values computed
// using the online special function calculator at
// functions.wolfram.com, while the bulk of the accuracy tests
// use values generated with NTL::RR at 1000-bit precision
// and our generic versions of these functions.
//
// Note that when this file is first run on a new platform many of
// these tests will fail: the default accuracy is 1 epsilon which
// is too tight for most platforms. In this situation you will
// need to cast a human eye over the error rates reported and make
// a judgement as to whether they are acceptable. Either way please
// report the results to the Boost mailing list. Acceptable rates of
// error are marked up below as a series of regular expressions that
// identify the compiler/stdlib/platform/data-type/test-data/test-function
// along with the maximum expected peek and RMS mean errors for that
// test.
//
void expected_results()
{
//
// Define the max and mean errors expected for
// various compilers and platforms.
//
const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
if(boost::math::tools::digits<double>() == boost::math::tools::digits<long double>())
{
largest_type = "(long\\s+)?double";
}
else
{
largest_type = "long double";
}
#else
largest_type = "(long\\s+)?double";
#endif
//
// Catch all cases come last:
//
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*", // test data group
".*", 5, 3); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*", // test data group
".*", 5, 3); // test function
//
// Finish off by printing out the compiler/stdlib/platform names,
// we do this to make it easier to mark up expected error rates.
//
std::cout << "Tests run with " << BOOST_COMPILER << ", "
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
template <typename T>
void do_test_ellint_f(T& data, const char* type_name, const char* test)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
std::cout << "Testing: " << test << std::endl;
value_type (*fp2)(value_type, value_type) = boost::math::ellint_1;
boost::math::tools::test_result<value_type> result;
result = boost::math::tools::test(
data,
boost::lambda::bind(fp2,
boost::lambda::ret<value_type>(boost::lambda::_1[0]),
boost::lambda::ret<value_type>(boost::lambda::_1[1])),
boost::lambda::ret<value_type>(boost::lambda::_1[2]));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_1", test);
std::cout << std::endl;
}
template <typename T>
void do_test_ellint_k(T& data, const char* type_name, const char* test)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
boost::math::tools::test_result<value_type> result;
std::cout << "Testing: " << test << std::endl;
value_type (*fp1)(value_type) = boost::math::ellint_1;
result = boost::math::tools::test(
data,
boost::lambda::bind(fp1,
boost::lambda::ret<value_type>(boost::lambda::_1[0])),
boost::lambda::ret<value_type>(boost::lambda::_1[1]));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_1", test);
std::cout << std::endl;
}
template <typename T>
void test_spots(T, const char* type_name)
{
// Function values calculated on http://functions.wolfram.com/
// Note that Mathematica's EllipticF accepts k^2 as the second parameter.
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 3>, 19> data1 = {
SC_(0), SC_(0), SC_(0),
SC_(-10), SC_(0), SC_(-10),
SC_(-1), SC_(-1), SC_(-1.2261911708835170708130609674719067527242483502207),
SC_(-4), SC_(0.875), SC_(-5.3190556182262405182189463092940736859067548232647),
SC_(8), SC_(-0.625), SC_(9.0419973860310100524448893214394562615252527557062),
SC_(1e-05), SC_(0.875), SC_(0.000010000000000127604166668510945638036143355898993088),
SC_(1e+05), SC_(10)/1024, SC_(100002.38431454899771096037307519328741455615271038),
SC_(1e-20), SC_(1), SC_(1.0000000000000000000000000000000000000000166666667e-20),
SC_(1e-20), SC_(1e-20), SC_(1.000000000000000e-20),
SC_(1e+20), SC_(400)/1024, SC_(1.0418143796499216839719289963154558027005142709763e20),
SC_(1e+50), SC_(0.875), SC_(1.3913251718238765549409892714295358043696028445944e50),
SC_(2), SC_(0.5), SC_(2.1765877052210673672479877957388515321497888026770),
SC_(4), SC_(0.5), SC_(4.2543274975235836861894752787874633017836785640477),
SC_(6), SC_(0.5), SC_(6.4588766202317746302999080620490579800463614807916),
SC_(10), SC_(0.5), SC_(10.697409951222544858346795279378531495869386960090),
SC_(-2), SC_(0.5), SC_(-2.1765877052210673672479877957388515321497888026770),
SC_(-4), SC_(0.5), SC_(-4.2543274975235836861894752787874633017836785640477),
SC_(-6), SC_(0.5), SC_(-6.4588766202317746302999080620490579800463614807916),
SC_(-10), SC_(0.5), SC_(-10.697409951222544858346795279378531495869386960090),
};
#undef SC_
do_test_ellint_f(data1, type_name, "Elliptic Integral F: Mathworld Data");
#include "ellint_f_data.ipp"
do_test_ellint_f(ellint_f_data, type_name, "Elliptic Integral F: Random Data");
// Function values calculated on http://functions.wolfram.com/
// Note that Mathematica's EllipticK accepts k^2 as the second parameter.
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 2>, 9> data2 = {
SC_(0), SC_(1.5707963267948966192313216916397514420985846996876),
SC_(0.125), SC_(1.5769867712158131421244030532288080803822271060839),
SC_(0.25), SC_(1.5962422221317835101489690714979498795055744578951),
SC_(300)/1024, SC_(1.6062331054696636704261124078746600894998873503208),
SC_(400)/1024, SC_(1.6364782007562008756208066125715722889067992997614),
SC_(-0.5), SC_(1.6857503548125960428712036577990769895008008941411),
SC_(-0.75), SC_(1.9109897807518291965531482187613425592531451316788),
1-SC_(1)/8, SC_(2.185488469278223686913080323730158689730428415766),
1-SC_(1)/1024, SC_(4.5074135978990422666372495313621124487894807327687),
};
#undef SC_
do_test_ellint_k(data2, type_name, "Elliptic Integral K: Mathworld Data");
#include "ellint_k_data.ipp"
do_test_ellint_k(ellint_k_data, type_name, "Elliptic Integral K: Random Data");
}
int test_main(int, char* [])
{
expected_results();
test_spots(0.0F, "float");
test_spots(0.0, "double");
test_spots(0.0L, "long double");
test_spots(boost::math::concepts::real_concept(0), "real_concept");
return 0;
}

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// Copyright (c) 2006 Xiaogang Zhang
// 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)
#include <boost/math/concepts/real_concept.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/ellint_2.hpp>
#include <boost/array.hpp>
#include <boost/lambda/lambda.hpp>
#include <boost/lambda/bind.hpp>
#include "handle_test_result.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the Elliptic Integrals of the second kind.
// There are two sets of tests, spot
// tests which compare our results with selected values computed
// using the online special function calculator at
// functions.wolfram.com, while the bulk of the accuracy tests
// use values generated with NTL::RR at 1000-bit precision
// and our generic versions of these functions.
//
// Note that when this file is first run on a new platform many of
// these tests will fail: the default accuracy is 1 epsilon which
// is too tight for most platforms. In this situation you will
// need to cast a human eye over the error rates reported and make
// a judgement as to whether they are acceptable. Either way please
// report the results to the Boost mailing list. Acceptable rates of
// error are marked up below as a series of regular expressions that
// identify the compiler/stdlib/platform/data-type/test-data/test-function
// along with the maximum expected peek and RMS mean errors for that
// test.
//
void expected_results()
{
//
// Define the max and mean errors expected for
// various compilers and platforms.
//
const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
if(boost::math::tools::digits<double>() == boost::math::tools::digits<long double>())
{
largest_type = "(long\\s+)?double";
}
else
{
largest_type = "long double";
}
#else
largest_type = "(long\\s+)?double";
#endif
//
// Catch all cases come last:
//
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*", // test data group
".*", 15, 6); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*", // test data group
".*", 15, 6); // test function
//
// Finish off by printing out the compiler/stdlib/platform names,
// we do this to make it easier to mark up expected error rates.
//
std::cout << "Tests run with " << BOOST_COMPILER << ", "
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
template <typename T>
void do_test_ellint_e2(const T& data, const char* type_name, const char* test)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
std::cout << "Testing: " << test << std::endl;
value_type (*fp2)(value_type, value_type) = boost::math::ellint_2;
boost::math::tools::test_result<value_type> result;
result = boost::math::tools::test(
data,
boost::lambda::bind(fp2,
boost::lambda::ret<value_type>(boost::lambda::_1[0]),
boost::lambda::ret<value_type>(boost::lambda::_1[1])),
boost::lambda::ret<value_type>(boost::lambda::_1[2]));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_2", test);
std::cout << std::endl;
}
template <typename T>
void do_test_ellint_e1(T& data, const char* type_name, const char* test)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
boost::math::tools::test_result<value_type> result;
std::cout << "Testing: " << test << std::endl;
value_type (*fp1)(value_type) = boost::math::ellint_2;
result = boost::math::tools::test(
data,
boost::lambda::bind(fp1,
boost::lambda::ret<value_type>(boost::lambda::_1[0])),
boost::lambda::ret<value_type>(boost::lambda::_1[1]));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_2", test);
std::cout << std::endl;
}
template <typename T>
void test_spots(T, const char* type_name)
{
// Function values calculated on http://functions.wolfram.com/
// Note that Mathematica's EllipticE accepts k^2 as the second parameter.
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 3>, 10> data1 = {
SC_(0), SC_(0), SC_(0),
SC_(-10), SC_(0), SC_(-10),
SC_(-1), SC_(-1), SC_(-0.84147098480789650665250232163029899962256306079837),
SC_(-4), SC_(900) / 1024, SC_(-3.1756145986492562317862928524528520686391383168377),
SC_(8), SC_(-600) / 1024, SC_(7.2473147180505693037677015377802777959345489333465),
SC_(1e-05), SC_(800) / 1024, SC_(9.999999999898274739584436515967055859383969942432E-6),
SC_(1e+05), SC_(100) / 1024, SC_(99761.153306972066658135668386691227343323331995888),
SC_(1e+10), SC_(-0.5), SC_(9.3421545766487137036576748555295222252286528414669e9),
ldexp(SC_(1), 66), SC_(400) / 1024, SC_(7.0886102721911705466476846969992069994308167515242e19),
ldexp(SC_(1), 166), SC_(900) / 1024, SC_(7.1259011068364515942912094521783688927118026465790e49),
};
#undef SC_
do_test_ellint_e2(data1, type_name, "Elliptic Integral E: Mathworld Data");
#include "ellint_e2_data.ipp"
do_test_ellint_e2(ellint_e2_data, type_name, "Elliptic Integral E: Random Data");
// Function values calculated on http://functions.wolfram.com/
// Note that Mathematica's EllipticE accepts k^2 as the second parameter.
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 2>, 10> data2 = {
SC_(-1), SC_(1),
SC_(0), SC_(1.5707963267948966192313216916397514420985846996876),
SC_(100) / 1024, SC_(1.5670445330545086723323795143598956428788609133377),
SC_(200) / 1024, SC_(1.5557071588766556854463404816624361127847775545087),
SC_(300) / 1024, SC_(1.5365278991162754883035625322482669608948678755743),
SC_(400) / 1024, SC_(1.5090417763083482272165682786143770446401437564021),
SC_(-0.5), SC_(1.4674622093394271554597952669909161360253617523272),
SC_(-600) / 1024, SC_(1.4257538571071297192428217218834579920545946473778),
SC_(-800) / 1024, SC_(1.2927868476159125056958680222998765985004489572909),
SC_(-900) / 1024, SC_(1.1966864890248739524112920627353824133420353430982),
};
#undef SC_
do_test_ellint_e1(data2, type_name, "Elliptic Integral E: Mathworld Data");
#include "ellint_e_data.ipp"
do_test_ellint_e1(ellint_e_data, type_name, "Elliptic Integral E: Random Data");
}
int test_main(int, char* [])
{
expected_results();
test_spots(0.0F, "float");
test_spots(0.0, "double");
test_spots(0.0L, "long double");
test_spots(boost::math::concepts::real_concept(0), "real_concept");
return 0;
}

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// Copyright (c) 2006 Xiaogang Zhang
// 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)
#define BOOST_MATH_THROW_ON_DOMAIN_ERROR
#define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
#include <boost/math/concepts/real_concept.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/ellint_3.hpp>
#include <boost/array.hpp>
#include <boost/lambda/lambda.hpp>
#include <boost/lambda/bind.hpp>
#include "handle_test_result.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the Elliptic Integrals of the third kind.
// There are two sets of tests, spot
// tests which compare our results with selected values computed
// using the online special function calculator at
// functions.wolfram.com, while the bulk of the accuracy tests
// use values generated with NTL::RR at 1000-bit precision
// and our generic versions of these functions.
//
// Note that when this file is first run on a new platform many of
// these tests will fail: the default accuracy is 1 epsilon which
// is too tight for most platforms. In this situation you will
// need to cast a human eye over the error rates reported and make
// a judgement as to whether they are acceptable. Either way please
// report the results to the Boost mailing list. Acceptable rates of
// error are marked up below as a series of regular expressions that
// identify the compiler/stdlib/platform/data-type/test-data/test-function
// along with the maximum expected peek and RMS mean errors for that
// test.
//
void expected_results()
{
//
// Define the max and mean errors expected for
// various compilers and platforms.
//
const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
if(boost::math::tools::digits<double>() == boost::math::tools::digits<long double>())
{
largest_type = "(long\\s+)?double";
}
else
{
largest_type = "long double";
}
#else
largest_type = "(long\\s+)?double";
#endif
//
// Catch all cases come last:
//
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*Large.*", // test data group
".*", 50, 20); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*Large.*", // test data group
".*", 50, 20); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
largest_type, // test type(s)
".*", // test data group
".*", 15, 8); // test function
add_expected_result(
".*", // compiler
".*", // stdlib
".*", // platform
"real_concept", // test type(s)
".*", // test data group
".*", 15, 8); // test function
//
// Finish off by printing out the compiler/stdlib/platform names,
// we do this to make it easier to mark up expected error rates.
//
std::cout << "Tests run with " << BOOST_COMPILER << ", "
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}
template <typename T>
void do_test_ellint_pi3(T& data, const char* type_name, const char* test)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
std::cout << "Testing: " << test << std::endl;
value_type (*fp2)(value_type, value_type, value_type) = boost::math::ellint_3;
boost::math::tools::test_result<value_type> result;
result = boost::math::tools::test(
data,
boost::lambda::bind(fp2,
boost::lambda::ret<value_type>(boost::lambda::_1[0]),
boost::lambda::ret<value_type>(boost::lambda::_1[1]),
boost::lambda::ret<value_type>(boost::lambda::_1[2])),
boost::lambda::ret<value_type>(boost::lambda::_1[3]));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_3", test);
std::cout << std::endl;
}
template <typename T>
void do_test_ellint_pi2(T& data, const char* type_name, const char* test)
{
typedef typename T::value_type row_type;
typedef typename row_type::value_type value_type;
std::cout << "Testing: " << test << std::endl;
value_type (*fp2)(value_type, value_type) = boost::math::ellint_3;
boost::math::tools::test_result<value_type> result;
result = boost::math::tools::test(
data,
boost::lambda::bind(fp2,
boost::lambda::ret<value_type>(boost::lambda::_1[0]),
boost::lambda::ret<value_type>(boost::lambda::_1[1])),
boost::lambda::ret<value_type>(boost::lambda::_1[2]));
handle_test_result(result, data[result.worst()], result.worst(),
type_name, "boost::math::ellint_3", test);
std::cout << std::endl;
}
template <typename T>
void test_spots(T, const char* type_name)
{
// function values calculated on http://functions.wolfram.com/
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 4>, 21> data1 = {
SC_(1), SC_(-1), SC_(0), SC_(-1.557407724654902230506974807458360173087),
SC_(0), SC_(-4), SC_(0.4), SC_(-4.153623371196831087495427530365430979011),
SC_(0), SC_(8), SC_(-0.6), SC_(8.935930619078575123490612395578518914416),
SC_(0), SC_(0.5), SC_(0.25), SC_(0.501246705365439492445236118603525029757890291780157969500480),
SC_(0), SC_(0.5), SC_(0), SC_(0.5),
SC_(-2), SC_(0.5), SC_(0), SC_(0.437501067017546278595664813509803743009132067629603474488486),
SC_(0.25), SC_(0.5), SC_(0), SC_(0.510269830229213412212501938035914557628394166585442994564135),
SC_(0.75), SC_(0.5), SC_(0), SC_(0.533293253875952645421201146925578536430596894471541312806165),
SC_(0.75), SC_(0.75), SC_(0), SC_(0.871827580412760575085768367421866079353646112288567703061975),
SC_(1), SC_(0.25), SC_(0), SC_(0.255341921221036266504482236490473678204201638800822621740476),
SC_(2), SC_(0.25), SC_(0), SC_(0.261119051639220165094943572468224137699644963125853641716219),
SC_(1023)/1024, SC_(1.5), SC_(0), SC_(13.2821612239764190363647953338544569682942329604483733197131),
SC_(0.5), SC_(-1), SC_(0.5), SC_(-1.228014414316220642611298946293865487807),
SC_(0.5), SC_(1e+10), SC_(0.5), SC_(1.536591003599172091573590441336982730551e+10),
SC_(-1e+05), SC_(10), SC_(0.75), SC_(0.0347926099493147087821620459290460547131012904008557007934290),
SC_(-1e+10), SC_(10), SC_(0.875), SC_(0.000109956202759561502329123384755016959364346382187364656768212),
SC_(-1e+10), SC_(1e+20), SC_(0.875), SC_(1.00000626665567332602765201107198822183913978895904937646809e15),
SC_(-1e+10), SC_(1608)/1024, SC_(0.875), SC_(0.0000157080616044072676127333183571107873332593142625043567690379),
1-SC_(1) / 1024, SC_(1e+20), SC_(0.875), SC_(6.43274293944380717581167058274600202023334985100499739678963e21),
SC_(50), SC_(0.1), SC_(0.25), SC_(0.124573770342749525407523258569507331686458866564082916835900),
SC_(1.125), SC_(1), SC_(0.25), SC_(1.77299767784815770192352979665283069318388205110727241629752),
//SC_(1.125), SC_(10), SC_(0.25), SC_(0.662467818678976949597336360256848770217429434745967677192487),
//SC_(1.125), SC_(3), SC_(0.25), SC_(-0.142697285116693775525461312178015106079842313950476205580178),
};
#undef SC_
do_test_ellint_pi3(data1, type_name, "Elliptic Integral PI: Mathworld Data");
#include "ellint_pi3_data.ipp"
do_test_ellint_pi3(ellint_pi3_data, type_name, "Elliptic Integral PI: Random Data");
#include "ellint_pi3_large_data.ipp"
do_test_ellint_pi3(ellint_pi3_large_data, type_name, "Elliptic Integral PI: Large Random Data");
// function values calculated on http://functions.wolfram.com/
#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
static const boost::array<boost::array<T, 3>, 9> data2 = {
SC_(0), SC_(0.2), SC_(1.586867847454166237308008033828114192951),
SC_(0), SC_(0.4), SC_(1.639999865864511206865258329748601457626),
SC_(0), SC_(0), SC_(1.57079632679489661923132169163975144209858469968755291048747),
SC_(0.5), SC_(0), SC_(2.221441469079183123507940495030346849307),
SC_(-4), SC_(0.3), SC_(0.712708870925620061597924858162260293305195624270730660081949),
SC_(-1e+05), SC_(-0.5), SC_(0.00496944596485066055800109163256108604615568144080386919012831),
SC_(-1e+10), SC_(-0.75), SC_(0.0000157080225184890546939710019277357161497407143903832703317801),
SC_(1) / 1024, SC_(-0.875), SC_(2.18674503176462374414944618968850352696579451638002110619287),
SC_(1023)/1024, SC_(-0.875), SC_(101.045289804941384100960063898569538919135722087486350366997),
};
#undef SC_
do_test_ellint_pi2(data2, type_name, "Complete Elliptic Integral PI: Mathworld Data");
#include "ellint_pi2_data.ipp"
do_test_ellint_pi2(ellint_pi2_data, type_name, "Complete Elliptic Integral PI: Random Data");
// Special cases, exceptions etc:
BOOST_CHECK_THROW(boost::math::ellint_3(T(-1), T(0), T(1.0001)), std::domain_error);
BOOST_CHECK_THROW(boost::math::ellint_3(T(20), T(1.5), T(0.5)), std::domain_error);
BOOST_CHECK_THROW(boost::math::ellint_3(T(-1), T(1.0001)), std::domain_error);
BOOST_CHECK_THROW(boost::math::ellint_3(T(1), T(0.5)), std::domain_error);
BOOST_CHECK_THROW(boost::math::ellint_3(T(2), T(0.5)), std::domain_error);
}
int test_main(int, char* [])
{
expected_results();
test_spots(0.0F, "float");
test_spots(0.0, "double");
test_spots(0.0L, "long double");
test_spots(boost::math::concepts::real_concept(0), "real_concept");
return 0;
}

3
test/test_gamma_dist.cpp
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@@ -265,4 +265,5 @@ Tolerance for type class boost::math::concepts::real_concept is 0.001 %
*** No errors detected
*/
*/

18
test/test_instantiate1.cpp Normal file
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@@ -0,0 +1,18 @@
// Copyright John Maddock 2006.
// 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)
#include "instantiate.hpp"
extern void other_test();
int main(int argc, char* argv[])
{
if(argc > 10000)
{
instantiate(double(0));
other_test();
}
}

12
test/test_instantiate2.cpp Normal file
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@@ -0,0 +1,12 @@
// Copyright John Maddock 2006.
// 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)
#include "instantiate.hpp"
void other_test()
{
instantiate(double(0));
}

148
tools/carlson_ellint_data.cpp Normal file
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#define BOOST_MATH_THROW_ON_DOMAIN_ERROR
#define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
#include <boost/math/tools/ntl.hpp>
#include <boost/math/tools/dual_precision.hpp>
#include <boost/math/tools/test_data.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/math/special_functions/ellint_3.hpp>
#include <fstream>
#include <boost/math/tools/test_data.hpp>
#include <boost/tr1/random.hpp>
float extern_val;
// confuse the compilers optimiser, and force a truncation to float precision:
float truncate_to_float(float const * pf)
{
extern_val = *pf;
return *pf;
}
std::tr1::tuple<NTL::RR, NTL::RR, NTL::RR, NTL::RR> generate_rf_data(NTL::RR n)
{
static std::tr1::mt19937 r;
std::tr1::uniform_real<float> ur(0, 1);
std::tr1::uniform_int<int> ui(-100, 100);
float x = ur(r);
x = ldexp(x, ui(r));
NTL::RR xr(truncate_to_float(&x));
float y = ur(r);
y = ldexp(y, ui(r));
NTL::RR yr(truncate_to_float(&y));
float z = ur(r);
z = ldexp(z, ui(r));
NTL::RR zr(truncate_to_float(&z));
NTL::RR result = boost::math::ellint_rf(xr, yr, zr);
return std::tr1::make_tuple(xr, yr, zr, result);
}
std::tr1::tuple<NTL::RR, NTL::RR, NTL::RR> generate_rc_data(NTL::RR n)
{
static std::tr1::mt19937 r;
std::tr1::uniform_real<float> ur(0, 1);
std::tr1::uniform_int<int> ui(-100, 100);
float x = ur(r);
x = ldexp(x, ui(r));
NTL::RR xr(truncate_to_float(&x));
float y = ur(r);
y = ldexp(y, ui(r));
NTL::RR yr(truncate_to_float(&y));
NTL::RR result = boost::math::ellint_rc(xr, yr);
return std::tr1::make_tuple(xr, yr, result);
}
std::tr1::tuple<NTL::RR, NTL::RR, NTL::RR, NTL::RR, NTL::RR> generate_rj_data(NTL::RR n)
{
static std::tr1::mt19937 r;
std::tr1::uniform_real<float> ur(0, 1);
std::tr1::uniform_real<float> nur(-1, 1);
std::tr1::uniform_int<int> ui(-100, 100);
float x = ur(r);
x = ldexp(x, ui(r));
NTL::RR xr(truncate_to_float(&x));
float y = ur(r);
y = ldexp(y, ui(r));
NTL::RR yr(truncate_to_float(&y));
float z = ur(r);
z = ldexp(z, ui(r));
NTL::RR zr(truncate_to_float(&z));
float p = nur(r);
p = ldexp(p, ui(r));
NTL::RR pr(truncate_to_float(&p));
boost::math::ellint_rj(x, y, z, p);
NTL::RR result = boost::math::ellint_rj(xr, yr, zr, pr);
return std::tr1::make_tuple(xr, yr, zr, pr, result);
}
std::tr1::tuple<NTL::RR, NTL::RR, NTL::RR, NTL::RR> generate_rd_data(NTL::RR n)
{
static std::tr1::mt19937 r;
std::tr1::uniform_real<float> ur(0, 1);
std::tr1::uniform_int<int> ui(-100, 100);
float x = ur(r);
x = ldexp(x, ui(r));
NTL::RR xr(truncate_to_float(&x));
float y = ur(r);
y = ldexp(y, ui(r));
NTL::RR yr(truncate_to_float(&y));
float z = ur(r);
z = ldexp(z, ui(r));
NTL::RR zr(truncate_to_float(&z));
NTL::RR result = boost::math::ellint_rd(xr, yr, zr);
return std::tr1::make_tuple(xr, yr, zr, result);
}
int test_main(int argc, char*argv [])
{
using namespace boost::math::tools;
NTL::RR::SetOutputPrecision(50);
NTL::RR::SetPrecision(1000);
parameter_info<NTL::RR> arg1, arg2;
test_data<NTL::RR> data;
bool cont;
std::string line;
if(argc < 1)
return 1;
do{
int count;
std::cout << "Number of points: ";
std::cin >> count;
arg1 = make_periodic_param(NTL::RR(0), NTL::RR(1), count);
arg1.type |= dummy_param;
//
// Change this next line to get the R variant you want:
//
data.insert(&generate_rd_data, arg1);
std::cout << "Any more data [y/n]?";
std::getline(std::cin, line);
boost::algorithm::trim(line);
cont = (line == "y");
}while(cont);
std::cout << "Enter name of test data file [default=ellint_rf_data.ipp]";
std::getline(std::cin, line);
boost::algorithm::trim(line);
if(line == "")
line = "ellint_rf_data.ipp";
std::ofstream ofs(line.c_str());
line.erase(line.find('.'));
ofs << std::scientific;
write_code(ofs, data, line.c_str());
return 0;
}

59
tools/ellint_e_data.cpp Normal file
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@@ -0,0 +1,59 @@
#include <boost/math/tools/ntl.hpp>
#include <boost/math/tools/test_data.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/math/special_functions/ellint_2.hpp>
#include <fstream>
#include <boost/math/tools/test_data.hpp>
#include <boost/tr1/random.hpp>
using namespace boost::math::tools;
using namespace boost::math;
using namespace std;
template<class T>
T ellint_e_data(T k)
{
return ellint_2(k);
}
int test_main(int argc, char*argv [])
{
using namespace boost::math::tools;
NTL::RR::SetOutputPrecision(50);
NTL::RR::SetPrecision(1000);
parameter_info<NTL::RR> arg1;
test_data<NTL::RR> data;
bool cont;
std::string line;
if(argc < 1)
return 1;
do{
if(0 == get_user_parameter_info(arg1, "phi"))
return 1;
data.insert(&ellint_e_data<NTL::RR>, arg1);
std::cout << "Any more data [y/n]?";
std::getline(std::cin, line);
boost::algorithm::trim(line);
cont = (line == "y");
}while(cont);
std::cout << "Enter name of test data file [default=ellint_e_data.ipp]";
std::getline(std::cin, line);
boost::algorithm::trim(line);
if(line == "")
line = "ellint_e_data.ipp";
std::ofstream ofs(line.c_str());
line.erase(line.find('.'));
ofs << std::scientific;
write_code(ofs, data, line.c_str());
return 0;
}

71
tools/ellint_f_data.cpp Normal file
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@@ -0,0 +1,71 @@
#include <boost/math/tools/ntl.hpp>
#include <boost/math/tools/test_data.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/math/special_functions/ellint_1.hpp>
#include <fstream>
#include <boost/math/tools/test_data.hpp>
#include <boost/tr1/random.hpp>
using namespace boost::math::tools;
using namespace boost::math;
using namespace std;
float extern_val;
// confuse the compilers optimiser, and force a truncation to float precision:
float truncate_to_float(float const * pf)
{
extern_val = *pf;
return *pf;
}
template<class T>
T ellint_f_data(T phi, T k)
{
return ellint_1(phi, k);
}
int test_main(int argc, char*argv [])
{
using namespace boost::math::tools;
NTL::RR::SetOutputPrecision(50);
NTL::RR::SetPrecision(1000);
parameter_info<NTL::RR> arg1, arg2;
test_data<NTL::RR> data;
bool cont;
std::string line;
if(argc < 1)
return 1;
do{
if(0 == get_user_parameter_info(arg1, "phi"))
return 1;
if(0 == get_user_parameter_info(arg2, "k"))
return 1;
data.insert(&ellint_f_data<NTL::RR>, arg1, arg2);
std::cout << "Any more data [y/n]?";
std::getline(std::cin, line);
boost::algorithm::trim(line);
cont = (line == "y");
}while(cont);
std::cout << "Enter name of test data file [default=ellint_f.ipp]";
std::getline(std::cin, line);
boost::algorithm::trim(line);
if(line == "")
line = "ellint_f.ipp";
std::ofstream ofs(line.c_str());
line.erase(line.find('.'));
ofs << std::scientific;
write_code(ofs, data, line.c_str());
return 0;
}

59
tools/ellint_k_data.cpp Normal file
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@@ -0,0 +1,59 @@
#include <boost/math/tools/ntl.hpp>
#include <boost/math/tools/test_data.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/math/special_functions/ellint_1.hpp>
#include <fstream>
#include <boost/math/tools/test_data.hpp>
#include <boost/tr1/random.hpp>
using namespace boost::math::tools;
using namespace boost::math;
using namespace std;
template<class T>
T ellint_k_data(T k)
{
return ellint_1(k);
}
int test_main(int argc, char*argv [])
{
using namespace boost::math::tools;
NTL::RR::SetOutputPrecision(50);
NTL::RR::SetPrecision(1000);
parameter_info<NTL::RR> arg1;
test_data<NTL::RR> data;
bool cont;
std::string line;
if(argc < 1)
return 1;
do{
if(0 == get_user_parameter_info(arg1, "phi"))
return 1;
data.insert(&ellint_k_data<NTL::RR>, arg1);
std::cout << "Any more data [y/n]?";
std::getline(std::cin, line);
boost::algorithm::trim(line);
cont = (line == "y");
}while(cont);
std::cout << "Enter name of test data file [default=ellint_k_data.ipp]";
std::getline(std::cin, line);
boost::algorithm::trim(line);
if(line == "")
line = "ellint_k_data.ipp";
std::ofstream ofs(line.c_str());
line.erase(line.find('.'));
ofs << std::scientific;
write_code(ofs, data, line.c_str());
return 0;
}

61
tools/ellint_pi2_data.cpp Normal file
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@@ -0,0 +1,61 @@
#define BOOST_MATH_THROW_ON_DOMAIN_ERROR
#define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
#include <boost/math/tools/ntl.hpp>
#include <boost/math/tools/dual_precision.hpp>
#include <boost/math/tools/test_data.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/math/special_functions/ellint_2.hpp>
#include <boost/math/special_functions/ellint_3.hpp>
#include <fstream>
#include <boost/math/tools/test_data.hpp>
#include <boost/tr1/random.hpp>
using namespace boost::math::tools;
using namespace boost::math;
using namespace std;
int test_main(int argc, char*argv [])
{
using namespace boost::math::tools;
NTL::RR::SetOutputPrecision(50);
NTL::RR::SetPrecision(1000);
parameter_info<NTL::RR> arg1, arg2;
test_data<NTL::RR> data;
bool cont;
std::string line;
if(argc < 1)
return 1;
do{
if(0 == get_user_parameter_info(arg1, "n"))
return 1;
if(0 == get_user_parameter_info(arg2, "k"))
return 1;
NTL::RR (*fp)(NTL::RR, NTL::RR) = &ellint_3;
data.insert(fp, arg1, arg2);
std::cout << "Any more data [y/n]?";
std::getline(std::cin, line);
boost::algorithm::trim(line);
cont = (line == "y");
}while(cont);
std::cout << "Enter name of test data file [default=ellint_pi2_data.ipp]";
std::getline(std::cin, line);
boost::algorithm::trim(line);
if(line == "")
line = "ellint_pi2_data.ipp";
std::ofstream ofs(line.c_str());
line.erase(line.find('.'));
ofs << std::scientific;
write_code(ofs, data, line.c_str());
return 0;
}

74
tools/ellint_pi3_data.cpp Normal file
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@@ -0,0 +1,74 @@
#define BOOST_MATH_THROW_ON_DOMAIN_ERROR
#define BOOST_MATH_THROW_ON_OVERFLOW_ERROR
#include <boost/math/tools/ntl.hpp>
#include <boost/math/tools/dual_precision.hpp>
#include <boost/math/tools/test_data.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/math/special_functions/ellint_3.hpp>
#include <fstream>
#include <boost/math/tools/test_data.hpp>
#include <boost/tr1/random.hpp>
float extern_val;
// confuse the compilers optimiser, and force a truncation to float precision:
float truncate_to_float(float const * pf)
{
extern_val = *pf;
return *pf;
}
std::tr1::tuple<NTL::RR, NTL::RR> generate_data(NTL::RR n, NTL::RR phi)
{
static std::tr1::mt19937 r;
std::tr1::uniform_real<float> ui(0, 1);
float k = ui(r);
NTL::RR kr(truncate_to_float(&k));
NTL::RR result = boost::math::ellint_3(n, phi, kr);
return std::tr1::make_tuple(kr, result);
}
int test_main(int argc, char*argv [])
{
using namespace boost::math::tools;
NTL::RR::SetOutputPrecision(50);
NTL::RR::SetPrecision(1000);
parameter_info<NTL::RR> arg1, arg2;
test_data<NTL::RR> data;
bool cont;
std::string line;
if(argc < 1)
return 1;
do{
if(0 == get_user_parameter_info(arg1, "n"))
return 1;
if(0 == get_user_parameter_info(arg2, "phi"))
return 1;
data.insert(&generate_data, arg1, arg2);
std::cout << "Any more data [y/n]?";
std::getline(std::cin, line);
boost::algorithm::trim(line);
cont = (line == "y");
}while(cont);
std::cout << "Enter name of test data file [default=ellint_pi3_data.ipp]";
std::getline(std::cin, line);
boost::algorithm::trim(line);
if(line == "")
line = "ellint_pi3_data.ipp";
std::ofstream ofs(line.c_str());
line.erase(line.find('.'));
ofs << std::scientific;
write_code(ofs, data, line.c_str());
return 0;
}