[Boost-commit] svn:boost r76811 - in sandbox/math: boost/math/special_functions libs/math/test

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) }, 
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+      { 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) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.8819222563924995483830571174621582031250000000000000000000000000000000000000000000000000000000000000e-09), SC_(4.5867217271141486339160821644641952822866469502517942182085170304446570870359571340281862661719150822e-10) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(4.7627768395841485471464693546295166015625000000000000000000000000000000000000000000000000000000000000e-09), SC_(7.5801947686341227685882762309702938054411038784149146023042003417494939820473296405561032038719889454e-10) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(8.8541334264391480246558785438537597656250000000000000000000000000000000000000000000000000000000000000e-09), SC_(1.4091791016129708241732724442034721450385381018184766427087539851618922556658870815982471576003575230e-09) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.3050326092288742074742913246154785156250000000000000000000000000000000000000000000000000000000000000e-08), SC_(3.6685733374678442905547630599568100040399882655007508893296914136141767754617631724243051933698630378e-09) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(5.9392490925347374286502599716186523437500000000000000000000000000000000000000000000000000000000000000e-08), SC_(9.4526085133095603909118721856358503854476626499102411037769699698190317989894166084062116909539782142e-09) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.1667648891489079687744379043579101562500000000000000000000000000000000000000000000000000000000000000e-07), SC_(1.8569639953411517488091297612639567531883022983393951341450539697233064712011075512034201376828628647e-08) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.3799674409019644372165203094482421875000000000000000000000000000000000000000000000000000000000000000e-07), SC_(3.7878358261730877395051421794730588045150770809795251213724933158772238405360872789923715228029469337e-08) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(4.6846594159433152526617050170898437500000000000000000000000000000000000000000000000000000000000000000e-07), SC_(7.4558670274931543802267138819943653210864790512959655045492450954836395319035456996750660961974241684e-08) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(9.3826997726864647120237350463867187500000000000000000000000000000000000000000000000000000000000000000e-07), SC_(1.4933030483698153840898614143667403799379036154581575136247832301591964873139598339061015450733538355e-07) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.1039855962735600769519805908203125000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.7570476474911921144441299538626312188915932067598479617555134318254957786428235385954716950761042757e-07) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(3.2917760108830407261848449707031250000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(5.2390242368146428947874501624028265360761692434567231765124510248149278979110527591706574294590227084e-07) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(7.5172138167545199394226074218750000000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.1964017371926393297441613587482126199632217781094725701415054395924207290291930046111070520684902141e-06) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.5114666894078254699707031250000000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(2.4055739491967920671996429612374532229773038227218099383160216743783228488120926554820319286082815673e-06) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.9863993404433131217956542968750000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(4.7530021693662914833221511931463311876155764785880196684146073720053904252530631069801624407245081911e-06) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(3.3870281185954809188842773437500000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(5.3906226725957640914509504485915510208687129227956507748428867535738522060193129922760259703067484413e-06) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(9.0660119894891977310180664062500000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(1.4429006183044035895326704209736668301097732573465398206597058152102744877609677189308186968625340495e-05) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.1949532674625515937805175781250000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(3.4933765676221920704801308812665979382828934566008231354705213060170675347901065915029398298535763697e-05) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(4.3952150736004114151000976562500000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(6.9952015987127847173327366561933507956876676553255863100102384467753504280617636800143792341240004065e-05) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(6.3331518322229385375976562500000000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(1.0079522846905594649365880261582083200269373765501479102288668176654328494317944277990390589021351611e-04) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.1151232756674289703369140625000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(1.7747730791498257228724466609010718640474213075672967658862407999244799169006547085676549441195024178e-04) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.9624670967459678649902343750000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(3.1233593813865074092187000076318815815992765797503889021675650309606396130758236641602948938095154247e-04) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(5.5537540465593338012695312500000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(8.8389832159378808809293547216957606519871387206040393639793321109091551227432869376832529237719171445e-04) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(8.6911283433437347412109375000000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(1.3832012105613475616998882811021056691364209978319849568811726856289329149947567331982486012024525700e-03) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.9933363199234008789062500000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(4.7626206103193143738384301857108373117725586408971862272829975917238953196119655638033879930832236044e-03) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(5.1242604851722717285156250000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(8.1483868224095205699782264982954100006346028090824774698826779614053277857684296752070685883885970087e-03) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(1.1201295256614685058593750000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.7753411797371264216252612641814729347033592054673354499571296899305242858735043628726078292990235901e-02) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.3480379581451416015625000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.6705270516178514484770674000065465275074365985299243331678923668415427683613952911548417263422039709e-02) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(4.8987305164337158203125000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.2497189937166102985881853793717432358301440115122694098536922293177672003931038251309026880570812377e-02) }, 
+      { SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(7.5183129310607910156250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.0260275242520624299591122151182172428983045243753202135303342272446124940659802383826019436186264313e-01) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(1.6504814008555523940913190017454326152801513671875000000000000000000000000000000000000000000000000000e-12), SC_(2.6268227342739713502703523842914341937722379610915808469306457991912693990824999870362500844702068812e-13) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(3.2872192210153061560336334492418115066156408908601018800808095526105195084424773361241178860623240932e-13) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(6.9332300317581641024844429921358823776245117187500000000000000000000000000000000000000000000000000000e-12), SC_(1.1034578311474902992468627765189417824553551046424513466987211593038802937973400245202793858062958887e-12) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(1.3351444949627477853937307372689247131347656250000000000000000000000000000000000000000000000000000000e-11), SC_(2.1249484611525346257228081247172530019648393623770113776771874586198520650085035253672046110487273171e-12) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(1.6399812063916385795891983434557914733886718750000000000000000000000000000000000000000000000000000000e-11), SC_(2.6101111557503909742711455935717452336179995122990479274326626789281668681404562922293515795706809440e-12) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(5.7301594025283009159466018900275230407714843750000000000000000000000000000000000000000000000000000000e-11), SC_(9.1198319361688071046789369810024617331627461999030269627612158231525346683126209815490493046601299672e-12) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(1.1137313293829720350913703441619873046875000000000000000000000000000000000000000000000000000000000000e-10), SC_(1.7725584634760785388480127086886725627321695064883626408138079496440358837100932274040947931169331279e-11) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(1.4214707189097453010617755353450775146484375000000000000000000000000000000000000000000000000000000000e-10), SC_(2.2623409137487606453332813115448367269938367067832752055093026600700493984513760088374478804414694397e-11) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(3.8006320313144215106149204075336456298828125000000000000000000000000000000000000000000000000000000000e-10), SC_(6.0488937465708132722237874880546123850477031153928287996846907084754672484540972888536598448051669432e-11) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(6.0916272026645401638234034180641174316406250000000000000000000000000000000000000000000000000000000000e-10), SC_(9.6951258077711646494232443406338385488549616233104452912249488638637126434166879526306999396061267573e-11) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(1.0221641311147777742007747292518615722656250000000000000000000000000000000000000000000000000000000000e-09), SC_(1.6268247411814909909363471550246773204663638191723936326958291371641419238064811369063126080736398839e-10) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(2.8819222563924995483830571174621582031250000000000000000000000000000000000000000000000000000000000000e-09), SC_(4.5867217271141486339160786283906509849826844641131334606887283001931475983583888101765599470933686379e-10) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(4.7627768395841485471464693546295166015625000000000000000000000000000000000000000000000000000000000000e-09), SC_(7.5801947686341227685882703871175866449317338440287185885726007130473110336682195037211062211847247125e-10) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(8.8541334264391480246558785438537597656250000000000000000000000000000000000000000000000000000000000000e-09), SC_(1.4091791016129708241732713578151458304566108967753812978355252666287977243286856036842483063775748705e-09) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(2.3050326092288742074742913246154785156250000000000000000000000000000000000000000000000000000000000000e-08), SC_(3.6685733374678442905547602317178420175541180223525593489788525763188029865911017936123527150363995951e-09) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(5.9392490925347374286502599716186523437500000000000000000000000000000000000000000000000000000000000000e-08), SC_(9.4526085133095603909118648982700852197243857240615102637585441804161218321695484499783176111507131382e-09) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(1.1667648891489079687744379043579101562500000000000000000000000000000000000000000000000000000000000000e-07), SC_(1.8569639953411517488091283296616823396738235315406261551276458083492469542419812312865780260669932006e-08) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(2.3799674409019644372165203094482421875000000000000000000000000000000000000000000000000000000000000000e-07), SC_(3.7878358261730877395051392592902241027370388943962860748022414786622825416096177848511645906064482117e-08) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(4.6846594159433152526617050170898437500000000000000000000000000000000000000000000000000000000000000000e-07), SC_(7.4558670274931543802267081339905154544550453024627854792031160076582446472811373796979013565519201135e-08) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(9.3826997726864647120237350463867187500000000000000000000000000000000000000000000000000000000000000000e-07), SC_(1.4933030483698153840898602631241498940995678063098246842794492632703188913410650000287825256045549415e-07) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(1.1039855962735600769519805908203125000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.7570476474911921144441285992895674906413362924517550724212511878469874716735168397950908171110660654e-07) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(3.2917760108830407261848449707031250000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(5.2390242368146428947874461234451343162394896329847611330551914478464554168409506412061952813400720803e-07) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(7.5172138167545199394226074218750000000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.1964017371926393297441604363978318874304328747007371000551187006896396802687797251773688604363660143e-06) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(1.5114666894078254699707031250000000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(2.4055739491967920671996411066914599553042142935668150814103566491427111231588603323177673692342572183e-06) }, 
+      { SC_(2.0654207510961697380480472929775714874267578125000000000000000000000000000000000000000000000000000000e-12), SC_(2.9863993404433131217956542968750000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(4.7530021693662914833221475288810384564522391506019101601724506416707971559952730605285150599762340613e-06) }, 
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+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(5.9392490925347374286502599716186523437500000000000000000000000000000000000000000000000000000000000000e-08), SC_(5.8009179842184072086002259539527678495404712138210300302523365002410915498256898447602908749915306309e-1006) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(1.1667648891489079687744379043579101562500000000000000000000000000000000000000000000000000000000000000e-07), SC_(1.1378463397282546695048984630798836353649395694787808029001374162083167905784112752674502871482803956e-1005) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(2.3799674409019644372165203094482421875000000000000000000000000000000000000000000000000000000000000000e-07), SC_(2.3230747400043843103752596819096731924880860216842211276343079193497580162195761431992203364026759773e-1005) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(4.6846594159433152526617050170898437500000000000000000000000000000000000000000000000000000000000000000e-07), SC_(4.5757532757662115204361175552766290155068361033174052514009095381131597289173469487257370262476951068e-1005) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(9.3826997726864647120237350463867187500000000000000000000000000000000000000000000000000000000000000000e-07), SC_(9.1605317059224944639894661116484782065866639938208408879130634737373907787990279151018206738489359633e-1005) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(1.1039855962735600769519805908203125000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(1.0768814218233222063480030506816713493693800470371455514736815110210300174643349860393588599050788563e-1004) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(3.2917760108830407261848449707031250000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(3.2136769752166323435836148699860001180309155812016995304119050657422759689800570049354249315705705594e-1004) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(7.5172138167545199394226074218750000000000000000000000000000000000000000000000000000000000000000000000e-06), SC_(7.3356454882500527096853576901949587057277246248054970184194462969987696798106895462017338361619853704e-1004) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(1.5114666894078254699707031250000000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(1.4737716112811031093513535548450737903672668803300177671257651359679024281918877462310018805486067459e-1003) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(2.9863993404433131217956542968750000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(2.9105761901804736696145289292041257415875594003460550768358732197304567257138633561661840000330901009e-1003) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(3.3870281185954809188842773437500000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(3.3039285191173465747559248809382018737608334530620033815243490408529891786233971814388911451060280566e-1003) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(9.0660119894891977310180664062500000000000000000000000000000000000000000000000000000000000000000000000e-05), SC_(8.7773597511376221241243067291498104324597246770507348576300713330073467759372628617387045176627976133e-1003) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(2.1949532674625515937805175781250000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(2.0290279898523452880773798814265236961795552017336023564018764529210455221448023809368071354070726149e-1002) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(4.3952150736004114151000976562500000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(3.4065120339766543984756193317869124773936873029332991508527973607228302412324033596597909820589704662e-1002) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(6.3331518322229385375976562500000000000000000000000000000000000000000000000000000000000000000000000000e-04), SC_(3.7466087318885938500868585922583133975458514178219193590768422410120330433955950135813327838489056619e-1002) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(1.1151232756674289703369140625000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(8.8351207392340792320745851361592195561268721150413293223420354770782032301090005747009228943254904115e-1003) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(5.5537540465593338012695312500000000000000000000000000000000000000000000000000000000000000000000000000e-03), SC_(3.5488351086463247124651053266580965581095385901421239119030770117134205443115650843986970621558455209e-1002) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(2.9933363199234008789062500000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.8927120579447065133147228408843181643250872480757994196816410729138242902995013783459717664831176112e-1002) }, 
+      { SC_(1.5819158323200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+12), SC_(5.1242604851722717285156250000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(4.3768966339971338120402965695449857550017642611752861580137949811132186713175969374250597099922094758e-1002) }, 
+      { 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* [])