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Subject: [Boost-commit] svn:boost r76811 - in sandbox/math: boost/math/special_functions libs/math/test
From: john_at_[hidden]
Date: 2012-01-31 13:04:31


Author: johnmaddock
Date: 2012-01-31 13:04:30 EST (Tue, 31 Jan 2012)
New Revision: 76811
URL: http://svn.boost.org/trac/boost/changeset/76811

Log:
Add forwarding/type promoting/policy enabled functions to owens_t.hpp.
Add test data files.
Update tests to use test data.
Added:
   sandbox/math/libs/math/test/owens_t.ipp (contents, props changed)
   sandbox/math/libs/math/test/owens_t_large_data.ipp (contents, props changed)
Text files modified:
   sandbox/math/boost/math/special_functions/owens_t.hpp | 742 ++++++++++++++++++++-------------------
   sandbox/math/libs/math/test/test_owens_t.cpp | 111 +++++
   2 files changed, 493 insertions(+), 360 deletions(-)

Modified: sandbox/math/boost/math/special_functions/owens_t.hpp
==============================================================================
--- sandbox/math/boost/math/special_functions/owens_t.hpp (original)
+++ sandbox/math/boost/math/special_functions/owens_t.hpp 2012-01-31 13:04:30 EST (Tue, 31 Jan 2012)
@@ -27,370 +27,392 @@
 
 namespace boost
 {
- namespace math
- {
- namespace detail
- {
- // owens_t_znorm1(x) = P(-oo<Z<=x)-0.5 with Z being normally distributed.
- template<typename RealType>
- inline RealType owens_t_znorm1(const RealType x)
- {
- using namespace boost::math::constants;
- return erf(x/root_two<RealType>())*half<RealType>();
- } // RealType owens_t_znorm1(const RealType x)
-
- // owens_t_znorm2(x) = P(x<=Z<oo) with Z being normally distributed.
- template<typename RealType>
- inline RealType owens_t_znorm2(const RealType x)
- {
- using namespace boost::math::constants;
- return erfc(x/root_two<RealType>())*half<RealType>();
- } // RealType owens_t_znorm2(const RealType x)
-
- // Auxiliary function, it computes an array key that is used to determine
- // the specific computation method for Owen's T and the order thereof
- // used in owens_t_dispatch.
- template<typename RealType>
- inline unsigned short owens_t_compute_code(const RealType h, const RealType a)
- {
- static const RealType hrange[] =
- {0.02, 0.06, 0.09, 0.125, 0.26, 0.4, 0.6, 1.6, 1.7, 2.33, 2.4, 3.36, 3.4, 4.8};
-
- static const RealType arange[] = {0.025, 0.09, 0.15, 0.36, 0.5, 0.9, 0.99999};
- /*
- original select array from paper:
- 1, 1, 2,13,13,13,13,13,13,13,13,16,16,16, 9
- 1, 2, 2, 3, 3, 5, 5,14,14,15,15,16,16,16, 9
- 2, 2, 3, 3, 3, 5, 5,15,15,15,15,16,16,16,10
- 2, 2, 3, 5, 5, 5, 5, 7, 7,16,16,16,16,16,10
- 2, 3, 3, 5, 5, 6, 6, 8, 8,17,17,17,12,12,11
- 2, 3, 5, 5, 5, 6, 6, 8, 8,17,17,17,12,12,12
- 2, 3, 4, 4, 6, 6, 8, 8,17,17,17,17,17,12,12
- 2, 3, 4, 4, 6, 6,18,18,18,18,17,17,17,12,12
- */
- // subtract one because the array is written in FORTRAN in mind - in C arrays start @ zero
- static const unsigned short select[] =
- {
- 0, 0 , 1 , 12 ,12 , 12 , 12 , 12 , 12 , 12 , 12 , 15 , 15 , 15 , 8,
- 0 , 1 , 1 , 2 , 2 , 4 , 4 , 13 , 13 , 14 , 14 , 15 , 15 , 15 , 8,
- 1 , 1 , 2 , 2 , 2 , 4 , 4 , 14 , 14 , 14 , 14 , 15 , 15 , 15 , 9,
- 1 , 1 , 2 , 4 , 4 , 4 , 4 , 6 , 6 , 15 , 15 , 15 , 15 , 15 , 9,
- 1 , 2 , 2 , 4 , 4 , 5 , 5 , 7 , 7 , 16 ,16 , 16 , 11 , 11 , 10,
- 1 , 2 , 4 , 4 , 4 , 5 , 5 , 7 , 7 , 16 , 16 , 16 , 11 , 11 , 11,
- 1 , 2 , 3 , 3 , 5 , 5 , 7 , 7 , 16 , 16 , 16 , 16 , 16 , 11 , 11,
- 1 , 2 , 3 , 3 , 5 , 5 , 17 , 17 , 17 , 17 , 16 , 16 , 16 , 11 , 11
- };
-
- unsigned short ihint = 14, iaint = 7;
- for(unsigned short i = 0; i != 14; i++)
- {
- if( h <= hrange[i] )
- {
- ihint = i;
- break;
- }
- } // for(unsigned short i = 0; i != 14; i++)
-
- for(unsigned short i = 0; i != 7; i++)
- {
- if( a <= arange[i] )
- {
- iaint = i;
- break;
- }
- } // for(unsigned short i = 0; i != 7; i++)
-
- // interprete select array as 8x15 matrix
- return select[iaint*15 + ihint];
-
- } // unsigned short owens_t_compute_code(const RealType h, const RealType a)
-
- // compute the value of Owen's T function with method T1 from the reference paper
- template<typename RealType>
- inline RealType owens_t_T1(const RealType h, const RealType a, const unsigned short m)
- {
- using namespace boost::math::constants;
-
- const RealType hs = -h*h*half<RealType>();
- const RealType dhs = exp( hs );
- const RealType as = a*a;
-
- unsigned short j=1;
- RealType jj = 1;
- RealType aj = a / (static_cast<RealType>(2)*pi<RealType>());
- RealType dj = expm1( hs );
- RealType gj = hs*dhs;
-
- RealType val = atan( a ) / (static_cast<RealType>(2)*pi<RealType>());
-
- while( true )
- {
- val += dj*aj/jj;
-
- if( m <= j )
- break;
-
- j++;
- jj += static_cast<RealType>(2);
- aj *= as;
- dj = gj - dj;
- gj *= hs / static_cast<RealType>(j);
- } // while( true )
-
- return val;
- } // RealType owens_t_T1(const RealType h, const RealType a, const unsigned short m)
-
- // compute the value of Owen's T function with method T2 from the reference paper
- template<typename RealType>
- inline RealType owens_t_T2(const RealType h, const RealType a, const unsigned short m, const RealType ah)
- {
- using namespace boost::math::constants;
-
- const unsigned short maxii = m+m+1;
- const RealType hs = h*h;
- const RealType as = -a*a;
- const RealType y = static_cast<RealType>(1) / hs;
-
- unsigned short ii = 1;
- RealType val = 0;
- RealType vi = a * exp( -ah*ah*half<RealType>() ) / root_two_pi<RealType>();
- RealType z = owens_t_znorm1(ah)/h;
-
- while( true )
- {
- val += z;
- if( maxii <= ii )
- {
- val *= exp( -hs*half<RealType>() ) / root_two_pi<RealType>();
- break;
- } // if( maxii <= ii )
- z = y * ( vi - static_cast<RealType>(ii) * z );
- vi *= as;
- ii += 2;
- } // while( true )
-
- return val;
- } // RealType owens_t_T2(const RealType h, const RealType a, const unsigned short m, const RealType ah)
-
- // compute the value of Owen's T function with method T3 from the reference paper
- template<typename RealType>
- inline RealType owens_t_T3(const RealType h, const RealType a, const unsigned short m, const RealType ah)
- {
- using namespace boost::math::constants;
-
- static const RealType c2[] =
- {
- 0.99999999999999987510,
- -0.99999999999988796462, 0.99999999998290743652,
- -0.99999999896282500134, 0.99999996660459362918,
- -0.99999933986272476760, 0.99999125611136965852,
- -0.99991777624463387686, 0.99942835555870132569,
- -0.99697311720723000295, 0.98751448037275303682,
- -0.95915857980572882813, 0.89246305511006708555,
- -0.76893425990463999675, 0.58893528468484693250,
- -0.38380345160440256652, 0.20317601701045299653,
- -0.82813631607004984866E-01, 0.24167984735759576523E-01,
- -0.44676566663971825242E-02, 0.39141169402373836468E-03
- };
-
- const RealType as = a*a;
- const RealType hs = h*h;
- const RealType y = static_cast<RealType>(1)/hs;
-
- RealType ii = 1;
- unsigned short i = 0;
- RealType vi = a * exp( -ah*ah*half<RealType>() ) / root_two_pi<RealType>();
- RealType zi = owens_t_znorm1(ah)/h;
- RealType val = 0;
-
- while( true )
- {
- BOOST_ASSERT(i < 21);
- val += zi*c2[i];
- if( m <= i ) // if( m < i+1 )
- {
- val *= exp( -hs*half<RealType>() ) / root_two_pi<RealType>();
- break;
- } // if( m < i )
- zi = y * (ii*zi - vi);
- vi *= as;
- ii += 2;
- i++;
- } // while( true )
-
- return val;
- } // RealType owens_t_T3(const RealType h, const RealType a, const unsigned short m, const RealType ah)
-
- // compute the value of Owen's T function with method T4 from the reference paper
- template<typename RealType>
- inline RealType owens_t_T4(const RealType h, const RealType a, const unsigned short m)
- {
- using namespace boost::math::constants;
-
- const unsigned short maxii = m+m+1;
- const RealType hs = h*h;
- const RealType as = -a*a;
-
- unsigned short ii = 1;
- RealType ai = a * exp( -hs*(static_cast<RealType>(1)-as)*half<RealType>() ) / (static_cast<RealType>(2)*pi<RealType>());
- RealType yi = 1;
- RealType val = 0;
-
- while( true )
- {
- val += ai*yi;
- if( maxii <= ii )
- break;
- ii += 2;
- yi = (static_cast<RealType>(1)-hs*yi) / static_cast<RealType>(ii);
- ai *= as;
- } // while( true )
-
- return val;
- } // RealType owens_t_T4(const RealType h, const RealType a, const unsigned short m)
-
- // compute the value of Owen's T function with method T5 from the reference paper
- template<typename RealType>
- inline RealType owens_t_T5(const RealType h, const RealType a, const unsigned short m)
- {
- static const RealType pts[] = {0.35082039676451715489E-02,
- 0.31279042338030753740E-01, 0.85266826283219451090E-01,
- 0.16245071730812277011, 0.25851196049125434828,
- 0.36807553840697533536, 0.48501092905604697475,
- 0.60277514152618576821, 0.71477884217753226516,
- 0.81475510988760098605, 0.89711029755948965867,
- 0.95723808085944261843, 0.99178832974629703586};
- static const RealType wts[] = { 0.18831438115323502887E-01,
- 0.18567086243977649478E-01, 0.18042093461223385584E-01,
- 0.17263829606398753364E-01, 0.16243219975989856730E-01,
- 0.14994592034116704829E-01, 0.13535474469662088392E-01,
- 0.11886351605820165233E-01, 0.10070377242777431897E-01,
- 0.81130545742299586629E-02, 0.60419009528470238773E-02,
- 0.38862217010742057883E-02, 0.16793031084546090448E-02};
-
- const RealType as = a*a;
- const RealType hs = -h*h*boost::math::constants::half<RealType>();
-
- RealType val = 0;
- for(unsigned short i = 0; i < m; ++i)
- {
- BOOST_ASSERT(i < 13);
- const RealType r = static_cast<RealType>(1) + as*pts[i];
- val += wts[i] * exp( hs*r ) / r;
- } // for(unsigned short i = 0; i < m; ++i)
-
- return val*a;
- } // RealType owens_t_T5(const RealType h, const RealType a, const unsigned short m)
-
- // compute the value of Owen's T function with method T6 from the reference paper
- template<typename RealType>
- inline RealType owens_t_T6(const RealType h, const RealType a)
- {
- using namespace boost::math::constants;
-
- const RealType normh = owens_t_znorm2( h );
- const RealType y = static_cast<RealType>(1) - a;
- const RealType r = atan2(y, ( static_cast<RealType>(1) + a ) );
-
- RealType val = normh * ( static_cast<RealType>(1) - normh ) * half<RealType>();
-
- if( r != 0 )
- val -= r * exp( -y*h*h*half<RealType>()/r ) / (static_cast<RealType>(2)*pi<RealType>());
-
- return val;
- } // RealType owens_t_T6(const RealType h, const RealType a, const unsigned short m)
-
- // This routine dispatches the call to one of six subroutines, depending on the values
- // of h and a.
- // preconditions: h >= 0, 0<=a<=1, ah=a*h
- template<typename RealType>
- inline RealType owens_t_dispatch(const RealType h, const RealType a, const RealType ah)
- {
- static const unsigned short meth[] = {1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6}; // 18 entries
- static const unsigned short ord[] = {2, 3, 4, 5, 7, 10, 12, 18, 10, 20, 30, 20, 4, 7, 8, 20, 13, 0}; // 18 entries
-
- RealType val = 0; // avoid compiler warnings, 0 will be overwritten in any case
-
- const unsigned short icode = owens_t_compute_code(h,a);
- const unsigned short m = ord[icode];
-
- // determine the appropriate method, T1 ... T6
- switch( meth[icode] )
- {
- case 1: // T1
- val = owens_t_T1(h,a,m);
- break;
- case 2: // T2
- val = owens_t_T2(h,a,m,ah);
- break;
- case 3: // T3
- val = owens_t_T3(h,a,m,ah);
- break;
- case 4: // T4
- val = owens_t_T4(h,a,m);
- break;
- case 5: // T5
- val = owens_t_T5(h,a,m);
- break;
- case 6: // T6
- val = owens_t_T6(h,a);
- break;
- default:
- BOOST_THROW_EXCEPTION(std::logic_error("selection routine in Owen's T function failed"));
- }
- return val;
- } // RealType owens_t_dispatch(RealType h, RealType a, RealType ah)
-
- } // namespace detail
-
- // compute Owen's T function, T(h,a), for arbitrary values of h and a
- template<typename RealType>
- inline RealType owens_t(RealType h, RealType a)
- {
- // exploit that T(-h,a) == T(h,a)
- h = fabs(h);
-
- // Use equation (2) in the paper to remap the arguments
- // such that h>=0 and 0<=a<=1 for the call of the actual
- // computation routine.
-
- const RealType fabs_a = fabs(a);
- const RealType fabs_ah = fabs_a*h;
-
- RealType val = 0.0; // avoid compiler warnings, 0.0 will be overwritten in any case
-
- if(fabs_a <= 1)
- {
- val = detail::owens_t_dispatch(h, fabs_a, fabs_ah);
- } // if(fabs_a <= 1.0)
- else
- {
- if( h <= 0.67 )
- {
- const RealType normh = detail::owens_t_znorm1(h);
- const RealType normah = detail::owens_t_znorm1(fabs_ah);
- val = static_cast<RealType>(1)/static_cast<RealType>(4) - normh*normah -
- detail::owens_t_dispatch(fabs_ah, static_cast<RealType>(1) / fabs_a, h);
- } // if( h <= 0.67 )
- else
- {
- const RealType normh = detail::owens_t_znorm2(h);
- const RealType normah = detail::owens_t_znorm2(fabs_ah);
- val = constants::half<RealType>()*(normh+normah) - normh*normah -
- detail::owens_t_dispatch(fabs_ah, static_cast<RealType>(1) / fabs_a, h);
- } // else [if( h <= 0.67 )]
- } // else [if(fabs_a <= 1)]
+ namespace math
+ {
+ namespace detail
+ {
+ // owens_t_znorm1(x) = P(-oo<Z<=x)-0.5 with Z being normally distributed.
+ template<typename RealType>
+ inline RealType owens_t_znorm1(const RealType x)
+ {
+ using namespace boost::math::constants;
+ return erf(x/root_two<RealType>())*half<RealType>();
+ } // RealType owens_t_znorm1(const RealType x)
+
+ // owens_t_znorm2(x) = P(x<=Z<oo) with Z being normally distributed.
+ template<typename RealType>
+ inline RealType owens_t_znorm2(const RealType x)
+ {
+ using namespace boost::math::constants;
+ return erfc(x/root_two<RealType>())*half<RealType>();
+ } // RealType owens_t_znorm2(const RealType x)
+
+ // Auxiliary function, it computes an array key that is used to determine
+ // the specific computation method for Owen's T and the order thereof
+ // used in owens_t_dispatch.
+ template<typename RealType>
+ inline unsigned short owens_t_compute_code(const RealType h, const RealType a)
+ {
+ static const RealType hrange[] =
+ {0.02, 0.06, 0.09, 0.125, 0.26, 0.4, 0.6, 1.6, 1.7, 2.33, 2.4, 3.36, 3.4, 4.8};
+
+ static const RealType arange[] = {0.025, 0.09, 0.15, 0.36, 0.5, 0.9, 0.99999};
+ /*
+ original select array from paper:
+ 1, 1, 2,13,13,13,13,13,13,13,13,16,16,16, 9
+ 1, 2, 2, 3, 3, 5, 5,14,14,15,15,16,16,16, 9
+ 2, 2, 3, 3, 3, 5, 5,15,15,15,15,16,16,16,10
+ 2, 2, 3, 5, 5, 5, 5, 7, 7,16,16,16,16,16,10
+ 2, 3, 3, 5, 5, 6, 6, 8, 8,17,17,17,12,12,11
+ 2, 3, 5, 5, 5, 6, 6, 8, 8,17,17,17,12,12,12
+ 2, 3, 4, 4, 6, 6, 8, 8,17,17,17,17,17,12,12
+ 2, 3, 4, 4, 6, 6,18,18,18,18,17,17,17,12,12
+ */
+ // subtract one because the array is written in FORTRAN in mind - in C arrays start @ zero
+ static const unsigned short select[] =
+ {
+ 0, 0 , 1 , 12 ,12 , 12 , 12 , 12 , 12 , 12 , 12 , 15 , 15 , 15 , 8,
+ 0 , 1 , 1 , 2 , 2 , 4 , 4 , 13 , 13 , 14 , 14 , 15 , 15 , 15 , 8,
+ 1 , 1 , 2 , 2 , 2 , 4 , 4 , 14 , 14 , 14 , 14 , 15 , 15 , 15 , 9,
+ 1 , 1 , 2 , 4 , 4 , 4 , 4 , 6 , 6 , 15 , 15 , 15 , 15 , 15 , 9,
+ 1 , 2 , 2 , 4 , 4 , 5 , 5 , 7 , 7 , 16 ,16 , 16 , 11 , 11 , 10,
+ 1 , 2 , 4 , 4 , 4 , 5 , 5 , 7 , 7 , 16 , 16 , 16 , 11 , 11 , 11,
+ 1 , 2 , 3 , 3 , 5 , 5 , 7 , 7 , 16 , 16 , 16 , 16 , 16 , 11 , 11,
+ 1 , 2 , 3 , 3 , 5 , 5 , 17 , 17 , 17 , 17 , 16 , 16 , 16 , 11 , 11
+ };
+
+ unsigned short ihint = 14, iaint = 7;
+ for(unsigned short i = 0; i != 14; i++)
+ {
+ if( h <= hrange[i] )
+ {
+ ihint = i;
+ break;
+ }
+ } // for(unsigned short i = 0; i != 14; i++)
+
+ for(unsigned short i = 0; i != 7; i++)
+ {
+ if( a <= arange[i] )
+ {
+ iaint = i;
+ break;
+ }
+ } // for(unsigned short i = 0; i != 7; i++)
+
+ // interprete select array as 8x15 matrix
+ return select[iaint*15 + ihint];
+
+ } // unsigned short owens_t_compute_code(const RealType h, const RealType a)
+
+ // compute the value of Owen's T function with method T1 from the reference paper
+ template<typename RealType>
+ inline RealType owens_t_T1(const RealType h, const RealType a, const unsigned short m)
+ {
+ BOOST_MATH_STD_USING
+ using namespace boost::math::constants;
+
+ const RealType hs = -h*h*half<RealType>();
+ const RealType dhs = exp( hs );
+ const RealType as = a*a;
+
+ unsigned short j=1;
+ RealType jj = 1;
+ RealType aj = a / (static_cast<RealType>(2)*pi<RealType>());
+ RealType dj = expm1( hs );
+ RealType gj = hs*dhs;
+
+ RealType val = atan( a ) / (static_cast<RealType>(2)*pi<RealType>());
+
+ while( true )
+ {
+ val += dj*aj/jj;
+
+ if( m <= j )
+ break;
+
+ j++;
+ jj += static_cast<RealType>(2);
+ aj *= as;
+ dj = gj - dj;
+ gj *= hs / static_cast<RealType>(j);
+ } // while( true )
+
+ return val;
+ } // RealType owens_t_T1(const RealType h, const RealType a, const unsigned short m)
+
+ // compute the value of Owen's T function with method T2 from the reference paper
+ template<typename RealType>
+ inline RealType owens_t_T2(const RealType h, const RealType a, const unsigned short m, const RealType ah)
+ {
+ BOOST_MATH_STD_USING
+ using namespace boost::math::constants;
+
+ const unsigned short maxii = m+m+1;
+ const RealType hs = h*h;
+ const RealType as = -a*a;
+ const RealType y = static_cast<RealType>(1) / hs;
+
+ unsigned short ii = 1;
+ RealType val = 0;
+ RealType vi = a * exp( -ah*ah*half<RealType>() ) / root_two_pi<RealType>();
+ RealType z = owens_t_znorm1(ah)/h;
+
+ while( true )
+ {
+ val += z;
+ if( maxii <= ii )
+ {
+ val *= exp( -hs*half<RealType>() ) / root_two_pi<RealType>();
+ break;
+ } // if( maxii <= ii )
+ z = y * ( vi - static_cast<RealType>(ii) * z );
+ vi *= as;
+ ii += 2;
+ } // while( true )
+
+ return val;
+ } // RealType owens_t_T2(const RealType h, const RealType a, const unsigned short m, const RealType ah)
+
+ // compute the value of Owen's T function with method T3 from the reference paper
+ template<typename RealType>
+ inline RealType owens_t_T3(const RealType h, const RealType a, const unsigned short m, const RealType ah)
+ {
+ BOOST_MATH_STD_USING
+ using namespace boost::math::constants;
+
+ static const RealType c2[] =
+ {
+ 0.99999999999999987510,
+ -0.99999999999988796462, 0.99999999998290743652,
+ -0.99999999896282500134, 0.99999996660459362918,
+ -0.99999933986272476760, 0.99999125611136965852,
+ -0.99991777624463387686, 0.99942835555870132569,
+ -0.99697311720723000295, 0.98751448037275303682,
+ -0.95915857980572882813, 0.89246305511006708555,
+ -0.76893425990463999675, 0.58893528468484693250,
+ -0.38380345160440256652, 0.20317601701045299653,
+ -0.82813631607004984866E-01, 0.24167984735759576523E-01,
+ -0.44676566663971825242E-02, 0.39141169402373836468E-03
+ };
+
+ const RealType as = a*a;
+ const RealType hs = h*h;
+ const RealType y = static_cast<RealType>(1)/hs;
+
+ RealType ii = 1;
+ unsigned short i = 0;
+ RealType vi = a * exp( -ah*ah*half<RealType>() ) / root_two_pi<RealType>();
+ RealType zi = owens_t_znorm1(ah)/h;
+ RealType val = 0;
+
+ while( true )
+ {
+ BOOST_ASSERT(i < 21);
+ val += zi*c2[i];
+ if( m <= i ) // if( m < i+1 )
+ {
+ val *= exp( -hs*half<RealType>() ) / root_two_pi<RealType>();
+ break;
+ } // if( m < i )
+ zi = y * (ii*zi - vi);
+ vi *= as;
+ ii += 2;
+ i++;
+ } // while( true )
+
+ return val;
+ } // RealType owens_t_T3(const RealType h, const RealType a, const unsigned short m, const RealType ah)
+
+ // compute the value of Owen's T function with method T4 from the reference paper
+ template<typename RealType>
+ inline RealType owens_t_T4(const RealType h, const RealType a, const unsigned short m)
+ {
+ BOOST_MATH_STD_USING
+ using namespace boost::math::constants;
+
+ const unsigned short maxii = m+m+1;
+ const RealType hs = h*h;
+ const RealType as = -a*a;
+
+ unsigned short ii = 1;
+ RealType ai = a * exp( -hs*(static_cast<RealType>(1)-as)*half<RealType>() ) / (static_cast<RealType>(2)*pi<RealType>());
+ RealType yi = 1;
+ RealType val = 0;
+
+ while( true )
+ {
+ val += ai*yi;
+ if( maxii <= ii )
+ break;
+ ii += 2;
+ yi = (static_cast<RealType>(1)-hs*yi) / static_cast<RealType>(ii);
+ ai *= as;
+ } // while( true )
+
+ return val;
+ } // RealType owens_t_T4(const RealType h, const RealType a, const unsigned short m)
+
+ // compute the value of Owen's T function with method T5 from the reference paper
+ template<typename RealType>
+ inline RealType owens_t_T5(const RealType h, const RealType a, const unsigned short m)
+ {
+ BOOST_MATH_STD_USING
+ static const RealType pts[] = {0.35082039676451715489E-02,
+ 0.31279042338030753740E-01, 0.85266826283219451090E-01,
+ 0.16245071730812277011, 0.25851196049125434828,
+ 0.36807553840697533536, 0.48501092905604697475,
+ 0.60277514152618576821, 0.71477884217753226516,
+ 0.81475510988760098605, 0.89711029755948965867,
+ 0.95723808085944261843, 0.99178832974629703586};
+ static const RealType wts[] = { 0.18831438115323502887E-01,
+ 0.18567086243977649478E-01, 0.18042093461223385584E-01,
+ 0.17263829606398753364E-01, 0.16243219975989856730E-01,
+ 0.14994592034116704829E-01, 0.13535474469662088392E-01,
+ 0.11886351605820165233E-01, 0.10070377242777431897E-01,
+ 0.81130545742299586629E-02, 0.60419009528470238773E-02,
+ 0.38862217010742057883E-02, 0.16793031084546090448E-02};
+
+ const RealType as = a*a;
+ const RealType hs = -h*h*boost::math::constants::half<RealType>();
+
+ RealType val = 0;
+ for(unsigned short i = 0; i < m; ++i)
+ {
+ BOOST_ASSERT(i < 13);
+ const RealType r = static_cast<RealType>(1) + as*pts[i];
+ val += wts[i] * exp( hs*r ) / r;
+ } // for(unsigned short i = 0; i < m; ++i)
+
+ return val*a;
+ } // RealType owens_t_T5(const RealType h, const RealType a, const unsigned short m)
+
+ // compute the value of Owen's T function with method T6 from the reference paper
+ template<typename RealType>
+ inline RealType owens_t_T6(const RealType h, const RealType a)
+ {
+ BOOST_MATH_STD_USING
+ using namespace boost::math::constants;
+
+ const RealType normh = owens_t_znorm2( h );
+ const RealType y = static_cast<RealType>(1) - a;
+ const RealType r = atan2(y, ( static_cast<RealType>(1) + a ) );
+
+ RealType val = normh * ( static_cast<RealType>(1) - normh ) * half<RealType>();
+
+ if( r != 0 )
+ val -= r * exp( -y*h*h*half<RealType>()/r ) / (static_cast<RealType>(2)*pi<RealType>());
+
+ return val;
+ } // RealType owens_t_T6(const RealType h, const RealType a, const unsigned short m)
+
+ // This routine dispatches the call to one of six subroutines, depending on the values
+ // of h and a.
+ // preconditions: h >= 0, 0<=a<=1, ah=a*h
+ template<typename RealType>
+ inline RealType owens_t_dispatch(const RealType h, const RealType a, const RealType ah)
+ {
+ static const unsigned short meth[] = {1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6}; // 18 entries
+ static const unsigned short ord[] = {2, 3, 4, 5, 7, 10, 12, 18, 10, 20, 30, 20, 4, 7, 8, 20, 13, 0}; // 18 entries
+
+ RealType val = 0; // avoid compiler warnings, 0 will be overwritten in any case
+
+ const unsigned short icode = owens_t_compute_code(h,a);
+ const unsigned short m = ord[icode];
+
+ // determine the appropriate method, T1 ... T6
+ switch( meth[icode] )
+ {
+ case 1: // T1
+ val = owens_t_T1(h,a,m);
+ break;
+ case 2: // T2
+ val = owens_t_T2(h,a,m,ah);
+ break;
+ case 3: // T3
+ val = owens_t_T3(h,a,m,ah);
+ break;
+ case 4: // T4
+ val = owens_t_T4(h,a,m);
+ break;
+ case 5: // T5
+ val = owens_t_T5(h,a,m);
+ break;
+ case 6: // T6
+ val = owens_t_T6(h,a);
+ break;
+ default:
+ BOOST_THROW_EXCEPTION(std::logic_error("selection routine in Owen's T function failed"));
+ }
+ return val;
+ } // RealType owens_t_dispatch(RealType h, RealType a, RealType ah)
+
+ // compute Owen's T function, T(h,a), for arbitrary values of h and a
+ template<typename RealType, class Policy>
+ inline RealType owens_t(RealType h, RealType a, const Policy&)
+ {
+ BOOST_MATH_STD_USING
+ // exploit that T(-h,a) == T(h,a)
+ h = fabs(h);
+
+ // Use equation (2) in the paper to remap the arguments
+ // such that h>=0 and 0<=a<=1 for the call of the actual
+ // computation routine.
+
+ const RealType fabs_a = fabs(a);
+ const RealType fabs_ah = fabs_a*h;
+
+ RealType val = 0.0; // avoid compiler warnings, 0.0 will be overwritten in any case
+
+ if(fabs_a <= 1)
+ {
+ val = detail::owens_t_dispatch(h, fabs_a, fabs_ah);
+ } // if(fabs_a <= 1.0)
+ else
+ {
+ if( h <= 0.67 )
+ {
+ const RealType normh = detail::owens_t_znorm1(h);
+ const RealType normah = detail::owens_t_znorm1(fabs_ah);
+ val = static_cast<RealType>(1)/static_cast<RealType>(4) - normh*normah -
+ detail::owens_t_dispatch(fabs_ah, static_cast<RealType>(1) / fabs_a, h);
+ } // if( h <= 0.67 )
+ else
+ {
+ const RealType normh = detail::owens_t_znorm2(h);
+ const RealType normah = detail::owens_t_znorm2(fabs_ah);
+ val = constants::half<RealType>()*(normh+normah) - normh*normah -
+ detail::owens_t_dispatch(fabs_ah, static_cast<RealType>(1) / fabs_a, h);
+ } // else [if( h <= 0.67 )]
+ } // else [if(fabs_a <= 1)]
+
+ // exploit that T(h,-a) == -T(h,a)
+ if(a < 0)
+ {
+ return -val;
+ } // if(a < 0)
+
+ return val;
+ } // RealType owens_t(RealType h, RealType a)
+
+ } // namespace detail
+
+ template <class T1, class T2, class Policy>
+ inline typename tools::promote_args<T1, T2>::type owens_t(T1 h, T2 a, const Policy& pol)
+ {
+ typedef typename tools::promote_args<T1, T2>::type result_type;
+ typedef typename policies::evaluation<result_type, Policy>::type value_type;
+ return policies::checked_narrowing_cast<result_type, Policy>(detail::owens_t(static_cast<value_type>(h), static_cast<value_type>(a), pol), "boost::math::ellint_2<%1%>(%1%,%1%)");
+ }
 
- // exploit that T(h,-a) == -T(h,a)
- if(a < 0)
+ template <class T1, class T2>
+ inline typename tools::promote_args<T1, T2>::type owens_t(T1 h, T2 a)
       {
- return -val;
- } // if(a < 0)
+ return owens_t(h, a, policies::policy<>());
+ }
 
- return val;
- } // RealType owens_t(RealType h, RealType a)
 
- } // namespace math
+ } // namespace math
 } // namespace boost
 
 #endif

Added: sandbox/math/libs/math/test/owens_t.ipp
==============================================================================
--- (empty file)
+++ sandbox/math/libs/math/test/owens_t.ipp 2012-01-31 13:04:30 EST (Tue, 31 Jan 2012)
@@ -0,0 +1,702 @@
+#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
+ static const boost::array<boost::array<T, 3>, 697> owens_t = {{
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.5404199514595574747570713746494151025268800591428092305565955095004523390337536013741524407418314221e-02) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.0010701992637516727797091369103082532517459271402594814684567286890576012180323913380406945333254433e-02) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.1332906164178518972574268187024803748414239635855039713830116629943727269089917609501812348568158694e-02) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.8838196992874145507812500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.9497732913197441421634738200591428651081744416977299347792633259582138166066492824062953351734971326e-02) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.4461377980649813429967638972049588545984220919222655655272868480482098267541540626951440449763854707e-02) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(2.7849817276000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(4.3026583966923789568091566850723112480516234646844404437974655875339068616168711586396230857873261933e-02) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(4.7352660318684410145760680974409966960109219141006383807963726245025098923727509612529000874631511184e-02) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(5.4688143730163574218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.9251098476838543790821601143696739762450795973840859895623085830366175700706769000382846304280361633e-02) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(5.4722046852111816406250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.9292382299586117783383473429555739957956045336733535906338125361902546243514075488809454811625085285e-02) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.9283929584647226144799992889295414179917167757792005735638292140472312579780590044366800685284035460e-02) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.0821523406287745649878477518754157140491916119181914999067575707174038100475631938611762643046960281e-01) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.1012176965143817702904588209701176814898763587643566685468576162882480229128117340630354221891277393e-01) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.1648114341467215940804062243109356475409194851840898213651470186249284208360095748987438975241388822e-01) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.1713619124964516626938802721777814178031787450149920028696681472639044542115311444575109992914735026e-01) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.5750665664672851562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2085030540700508832319806636930979667852176440430880432068177603501530660917473607825143514812318538e-01) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.6488833427429199218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2145560419832477599298866332576713597432473622794221325235520781098936045711403892028244915177826356e-01) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.6769475936889648437500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2168455230195827965221868712678081976739392846187644779772362776166461208673673048935549721947955859e-01) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2178005538277089893049805952041600236268574922075225252634975599100803378030675848407694602221760153e-01) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.9288129806518554687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2371052143346369692671888813391802442912081675645149747662297040811705590188335291420904538042325169e-01) },
+ { SC_(9.5669686794281005859375000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2399432392897432201783086392594688544536998321447486248480904582836691223164602326779005064741739479e-01) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(2.2942365980155351117754771526378292708740231264960539316842063696200884829628237039895484898529192823e-03) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.9680322689154555657058017082736661495213677947212098762543622722763825563827711568131850564334565506e-03) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.1597654248037660387449520543820166351754668510505531823382492970457382200077558044792256804713386129e-03) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.8838196992874145507812500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(4.3232953135233836153944327583670440589476418747370390302105974330237550687887327299360596774532791101e-03) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.0100550889644229746912561152386170907268949874219104978095620802138249447202878889126283209658742296e-03) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(2.7849817276000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(6.1497543339940146251856615610147485246423382395107105527248575888794201708943383385544040841893167983e-03) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(6.7002307780595028311848002054681870716943983498717211440016321757838493256869247382910637200137362515e-03) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(5.4688143730163574218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.0087628098924846553420452991323128540455257919474718546084030038511341392097627616477463678020520866e-02) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(5.4722046852111816406250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.0091132928374177373986149936548570045661635017241761865456752105413011145950758665503631981469962091e-02) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.0865842961288026187893734175479235962324504288027096290482416005557459196544605743966959957549259912e-02) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.1928879205559397161128411536383665386049060100190891105612351797899324440156577849032776806264950516e-02) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2007404932089150629318599721043926151201252590201116565157838995615594563567446592356739043515060955e-02) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2234231937902890618076422454559854736034641208834938001805660215261543653258044507100832640227607205e-02) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2254641258057330150164973433843452155232009681583050905550399458557126941497853232806334014703269603e-02) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.5750665664672851562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2360475720884925881580539738830093572012024162485856485613974712653546627243019666702904836835836072e-02) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.6488833427429199218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2376176601227851086722830167717452814836846810367599158215995631280835335070487840750421239628452270e-02) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.6769475936889648437500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2382005445939933843659988418503656684093356069262317993257524956338275590041101050569009428193352371e-02) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2384419169235315605535269562348458006973333200556008698543822798769741450130359222839946856017776574e-02) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.9288129806518554687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2431007739121873243331263486394085638096884194270101674004097829060031548768693191305694357247777346e-02) },
+ { SC_(1.9508080482482910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2437508801776841503931807680295142938639719448531279010032010195899482047937342387190771017427394090e-02) },
+ { SC_(2.1972351074218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.3739601263440303226918035390461302916191514347600351110784576857642713755718071769772677041294683025e-03) },
+ { SC_(2.1972351074218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.7755211095666850907050159203733314812578048117130333814997454620344339103547485744436876594592594664e-03) },
+ { SC_(2.1972351074218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.8895218753167505577359746448950163400947078523031794841165877926231799969709191009746042288646494843e-03) },
+ { SC_(2.1972351074218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.8838196992874145507812500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.5781057388815972568580990049167334421131198187178357304675508387536982285102037331036325472901318330e-03) },
+ { SC_(2.1972351074218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.9813127962403681526074696193085471870719700248555413887946766855427144291814792336665831726158573852e-03) },
+ { SC_(2.1972351074218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(2.7849817276000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.6434740055060828092727583311402330706214508315720813400404570952388814404574952574760312539133823596e-03) },
+ { SC_(2.1972351074218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.9594653109748921985832206457831539307912152304126677229221726746777735815292673434685995290780235442e-03) },
+ { SC_(2.1972351074218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(5.4688143730163574218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.8153336572171919066803693532442435338019315969392956239199353497198641315968821241228406724318120012e-03) },
+ { SC_(2.1972351074218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(5.4722046852111816406250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.8171378154102163054041925800547367393270264855863898236145171492893983793004589689890928278905271900e-03) },
+ { SC_(2.1972351074218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(6.2065122685859086676859364417120943815449052990048074531391080808225444823546260066061473660513511280e-03) },
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+ { SC_(1.9411849975585937500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.5319865680966959060729241655561473415594452796773647367493490169395106789231944517144794542634470072e-84) },
+ { SC_(1.9411849975585937500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(2.7849817276000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.5320124385154220850558591717809980528213168544141661229690125089007315401688630744619529339011561526e-84) },
+ { SC_(1.9411849975585937500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.5320125267904777666272502802563625361893429964993506264448452498589240790753552050595135112635103916e-84) },
+ { SC_(1.9411849975585937500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(5.4688143730163574218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.5320125298663196968581147301148732024040618476640305337898585340270160397026130772180441754883028481e-84) },
+ { SC_(1.9411849975585937500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(5.4722046852111816406250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.5320125298663196968581147321359620966184462436004616199798354451310387746032074935127170057510476708e-84) },
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+ { SC_(1.9622192382812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.4987074853782940787622472442318567238925012983676225447676094303428176340917386394929402352015039784e-86) },
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+ { SC_(1.9857620239257812500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.3672831316167632657724475029929234130566491646454665814596085474916464739333870332873695536029518534e-88) },
+ { SC_(1.9857620239257812500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(2.7849817276000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.3673086849227167312500038271366885158855725283973352461790290342204550385443187547817889150752632821e-88) },
+ { SC_(1.9857620239257812500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.3673087529822476518694748438059077395092889307169444313706384386840282580125934385201938096902673118e-88) },
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+ { SC_(1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.6380132109203215953682341142006484163028723876320845280985884437990702987939134369984972274801723921e-89) },
+ { SC_(1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(1.8838196992874145507812500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.6756432225141755716181254364578838398260084711471148446038558395555151245520302395698427479909090188e-89) },
+ { SC_(1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.6765370329975020887578693197006018491279730057642519497656614145617760862881464201058169472650265027e-89) },
+ { SC_(1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(2.7849817276000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.6765940072383066005097652539757437078433621689726193895722238525223712942947787019057651330175067344e-89) },
+ { SC_(1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.6765941529819362163555178434780673589908418376638967134553680595361500546239249492182079654295352261e-89) },
+ { SC_(1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(5.4688143730163574218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.6765941572108102929182392355720017900893213514144857837052426624327588242025916320562922691572615536e-89) },
+ { SC_(1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(5.4722046852111816406250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.6765941572108102929182392359376746516400752338011814009982639136654163659015328286598007640951121062e-89) },
+ { SC_(1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.6765941572108102929182392406617201965462427239939549761682717880384292426173011499264309557470010809e-89) },
+ { SC_(1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.6765941572108102929182392406617202048399346202690008425364176650068311070333103178533019023731342326e-89) },
+ { SC_(1.9929222106933593750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+01), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.6765941572108102929182392406617202048399346202690008425365120016320727925714718349788376825053245493e-89) }
+ }};
+#undef SC_
+

Added: sandbox/math/libs/math/test/owens_t_large_data.ipp
==============================================================================
--- (empty file)
+++ sandbox/math/libs/math/test/owens_t_large_data.ipp 2012-01-31 13:04:30 EST (Tue, 31 Jan 2012)
@@ -0,0 +1,2890 @@
+#define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
+ static const boost::array<boost::array<T, 3>, 2885> owens_t_large_data = {{
+ { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.6268227342739713502703544094063046502970633338286877424177911599011069718129959960042078522658699109e-13) },
+ { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(3.2872192210153061560336359834807763481241672582903121396605264909003831872851684882922331211080601734e-13) },
+ { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(6.9332300317581641024844429921358823776245117187500000000000000000000000000000000000000000000000000000e-12), SC_(1.1034578311474902992468636272154252648543610234328757257960205793906523876580386307388275422538773152e-12) },
+ { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.3351444949627477853937307372689247131347656250000000000000000000000000000000000000000000000000000000e-11), SC_(2.1249484611525346257228097629186708159796465913946169055318511177939349633530037969769274276139249529e-12) },
+ { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.6399812063916385795891983434557914733886718750000000000000000000000000000000000000000000000000000000e-11), SC_(2.6101111557503909742711476058030412732880995582978484322147525417758385679712703088533594824355915075e-12) },
+ { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(5.7301594025283009159466018900275230407714843750000000000000000000000000000000000000000000000000000000e-11), SC_(9.1198319361688071046789440118184467731070635965269094421518899910011944514104971561910485262874291152e-12) },
+ { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.1137313293829720350913703441619873046875000000000000000000000000000000000000000000000000000000000000e-10), SC_(1.7725584634760785388480140752195984232912697160244798887338176755896232118526224180271147757734467490e-11) },
+ { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.4214707189097453010617755353450775146484375000000000000000000000000000000000000000000000000000000000e-10), SC_(2.2623409137487606453332830556671814504569555272894149140529454414660848738045832674961908856994691353e-11) },
+ { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(3.8006320313144215106149204075336456298828125000000000000000000000000000000000000000000000000000000000e-10), SC_(6.0488937465708132722237921513706847494574388931411818594067778081183946081994560850118704738363060651e-11) },
+ { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(6.0916272026645401638234034180641174316406250000000000000000000000000000000000000000000000000000000000e-10), SC_(9.6951258077711646494232518149651621243650487327378994578084503639264935413862733045545737297786642497e-11) },
+ { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.0221641311147777742007747292518615722656250000000000000000000000000000000000000000000000000000000000e-09), SC_(1.6268247411814909909363484092040827319985724336271832553254067384618811831525572720958417469446856329e-10) },
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+ { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(1.1201295256614685058593750000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.8390680869170597699720842613264772464876308721136991295224616093707364354492520675189576497246764167e-1002) },
+ { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(2.3480379581451416015625000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.2049581593479429116154878124318749518939899322084484041245129505130167983236287904514223578285734307e-1002) },
+ { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(4.8987305164337158203125000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(4.7317801448617662832868071022107954108127181201894985492041026822845607257487534458649294162077940279e-1002) },
+ { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(7.5183129310607910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.7854241158894130266294456817686363286501744961515988393632821458276485805990027566919435329662352223e-1002) }
+ }};
+#undef SC_
+

Modified: sandbox/math/libs/math/test/test_owens_t.cpp
==============================================================================
--- sandbox/math/libs/math/test/test_owens_t.cpp (original)
+++ sandbox/math/libs/math/test/test_owens_t.cpp 2012-01-31 13:04:30 EST (Tue, 31 Jan 2012)
@@ -32,6 +32,11 @@
 
 #include <boost/test/test_exec_monitor.hpp> // for test_main.
 #include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE and BOOST_CHECK_CLOSE_fraction.
+#include <boost/array.hpp>
+
+#include "libs/math/test/handle_test_result.hpp"
+#include "libs/math/test/table_type.hpp"
+#include "libs/math/test/functor.hpp"
 
 #include <iostream>
 using std::cout;
@@ -39,6 +44,52 @@
 #include <limits>
 using std::numeric_limits;
 
+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::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
+ {
+ 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
+ "boost::math::owens_t", 10, 5); // test function
+ add_expected_result(
+ ".*", // compiler
+ ".*", // stdlib
+ ".*", // platform
+ "real_concept", // test type(s)
+ ".*", // test data group
+ "boost::math::owens_t", 10, 5); // 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 <class RealType>
 void test_spot(
      RealType h, //
@@ -91,10 +142,61 @@
 
 } // template <class RealType>void test_spots(RealType)
 
+template <class Real, class T>
+void do_test_owens_t(const T& data, const char* type_name, const char* test_name)
+{
+ typedef typename T::value_type row_type;
+ typedef Real value_type;
+
+ typedef value_type (*pg)(value_type, value_type);
+#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
+ pg funcp = boost::math::owens_t<value_type>;
+#else
+ pg funcp = boost::math::owens_t;
+#endif
+
+ boost::math::tools::test_result<value_type> result;
+
+ std::cout << "Testing " << test_name << " with type " << type_name
+ << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
+
+ //
+ // test hermite against data:
+ //
+ result = boost::math::tools::test_hetero<Real>(
+ data,
+ bind_func<Real>(funcp, 0, 1),
+ extract_result<Real>(2));
+ handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::owens_t", test_name);
+
+ std::cout << std::endl;
+}
+
+template <class T>
+void test_owens_t(T, const char* name)
+{
+ //
+ // The actual test data is rather verbose, so it's in a separate file
+ //
+ // The contents are as follows, each row of data contains
+ // three items, input value a, input value b and erf(a, b):
+ //
+# include "owens_t.ipp"
+
+ do_test_owens_t<T>(owens_t, name, "Owens T (medium small values)");
+
+#include "owens_t_large_data.ipp"
+
+ do_test_owens_t<T>(owens_t_large_data, name, "Owens T (large and diverse values)");
+}
+
+
 int test_main(int, char* [])
 {
   BOOST_MATH_CONTROL_FP;
 
+ expected_results();
+
   // Basic sanity-check spot values.
 
   // (Parameter value, arbitrarily zero, only communicates the floating point type).
@@ -106,6 +208,15 @@
   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
 #endif
 #endif
+
+ test_owens_t(0.0F, "float"); // Test float.
+ test_owens_t(0.0, "double"); // Test double.
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+ test_owens_t(0.0L, "long double"); // Test long double.
+#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
+ test_owens_t(boost::math::concepts::real_concept(0.), "real_concept"); // Test real concept.
+#endif
+#endif
   return 0;
 } // int test_main(int, char* [])
 


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