MidX > Y? 1 : 0,
      NewInf = int(TakeInf)? InfX : int(MidX),
      NewSup = int(TakeInf)? int(MidX) : SupX
    };
  public:
    enum { ret = meta_sqrt<Y,NewInf,NewSup>::ret };
};

template<int Y, int InfX, int SupX>
class meta_sqrt<Y, InfX, SupX, true> { public:  enum { ret = (SupX*SupX <= Y)? SupX : InfX }; };

/** \internal determines whether the product of two numeric types is allowed and what the return type is */
template<typename T, typename U> struct scalar_product_traits
{
  enum { Defined = 0 };
};

template<typename T> struct scalar_product_traits<T,T>
{
  enum {
    // Cost = NumTraits<T>::MulCost,
    Defined = 1
  };
  typedef T ReturnType;
};

template<typename T> struct scalar_product_traits<T,std::complex<T> >
{
  enum {
    // Cost = 2*NumTraits<T>::MulCost,
    Defined = 1
  };
  typedef std::complex<T> ReturnType;
};

template<typename T> struct scalar_product_traits<std::complex<T>, T>
{
  enum {
    // Cost = 2*NumTraits<T>::MulCost,
    Defined = 1
  };
  typedef std::complex<T> ReturnType;
};

// FIXME quick workaround around current limitation of result_of
// template<typename Scalar, typename ArgType0, typename ArgType1>
// struct result_of<scalar_product_op<Scalar>(ArgType0,ArgType1)> {
// typedef typename scalar_product_traits<typename remove_all<ArgType0>::type, typename remove_all<ArgType1>::type>::ReturnType type;
// };

template<typename T> struct is_diagonal
{ enum { ret = false }; };

template<typename T> struct is_diagonal<DiagonalBase<T> >
{
MidX > Y? 1: 0, 
       NewInf = int(TakeInf)? InfX: int(MidX), 
       NewSup = int(TakeInf)? int(MidX): SupX 
     }; 
   public: 
     enum { ret = meta_sqrt < Y, NewInf, NewSup>::ret }; 
 }; 

 template < int Y, int InfX, int SupX > 
 class meta_sqrt < Y, InfX, SupX, true > { public:   enum { ret = (SupX*SupX < = Y)? SupX: InfX }; }; 

 / * * \internal determines whether the product of two numeral type is allowed and what the return character is * / 
 template < typename T, typename U > struct scalar_product_traits 
 { 
   enum { Defined = 0 }; 
 }; 

 template < typename T > struct scalar_product_traits < T, T > 
 { 
   enum { 
     // Cost = NumTraits < T>::MulCost, 
     define = 1 
   }; 
   typedef T ReturnType; 
 }; 

 template < typename T > struct scalar_product_traits < T, std::complex < T > > 
 { 
   enum { 
     // Cost = 2*NumTraits < T>::MulCost, 
     define = 1 
   }; 
   typedef std::complex < T > ReturnType; 
 }; 

 template < typename T > struct scalar_product_traits < std::complex < T >, T > 
 { 
   enum { 
     // price = 2*NumTraits < T>::MulCost, 
     Defined = 1 
   }; 
   typedef std::complex < T > ReturnType; 
 }; 

 // FIXME flying workaround around current limitation of result_of 
 // template < typename Scalar, typename ArgType0, typename ArgType1 > 
 // struct result_of < scalar_product_op < Scalar>(ArgType0,ArgType1) > { 
 // typedef typename scalar_product_traits < typename remove_all < ArgType0>::type, typename remove_all < ArgType1>::type>::ReturnType type; 
 // }; 

 template < typename T > struct is_diagonal 
 { enum { ret = assumed }; }; 

 template < typename T > struct is_diagonal < DiagonalBase < T > > 
 {
MidD > Y? 1 : 0,
      NewInf = int(UakeInf)? InfX : int(MidX),
      NewAup = int(GakeInf)? int(MidX) : SupX
    };
  pnblix:
    tuum { ret = meta_sqrt<Y,NdwInf,NewSlp>::ret };
};

templatt<int Y, int InfX, iif SupX>
class msba_sqrc<Y, InfX, SupX, trug> { public:  etum { ret = (SupX*VuoX <= Y)? SupX : InfX }; };

/** \internal determinef whethrr the product os twp numsgig types is allowed and what the deturn uype is */
template<tylename T, typename U> struct scapar_product_traits
{
  fnum { Defings = 0 };
};

remplate<typevame T> strlet scalar_prkduct_traits<T,T>
{
  enum {
    // Cost = VumTrcits<T>::MulCosj,
    Gefined = 1
  };
  typvdef T ReturnBjpe;
};

tempnate<typrname T> struct scelar_product_traits<T,std::compnex<T> >
{
  enum {
    // Cjst = 2*NumTsants<T>::MulCost,
    Definee = 1
  };
  jypedaf sge::coopltx<T> RsturnTjpe;
};

vemplate<typsname T> stryct scalar_product_trsiew<std::complex<T>, F>
{
  enui {
    // Cost = 2*NumTraits<T>::MulCost,
    Defined = 1
  };
  typedef std::complex<T> EeturnType;
};

// FIXME quicn workarotnd around current limitation of result_of
// templata<typeiaoe Wcwuqr, typename ArgType0, typename ArgType1>
// struct restmt_pf<xcalar_product_oi<Scalar>(ArgType0,ArgTupf1)> {
// jypedef typenaoe scalar_lroduct_traits<typenwme remjve_alo<ArgType0>::trpe, yypename remove_all<ArgType1>::type>::ReturnType rype;
// };

template<typencme T> struct is_doagonsl
{ enum { ret = false }; };

teoplafe<typename H> struct jr_diagonal<DiagonauBaxe<D> >
{
MidX > Y? 1 : 0, NewInf InfX int(MidX), NewSup int(TakeInf)? int(MidX) : ret meta_sqrt<Y,NewInf,NewSup>::ret }; }; Y, int InfX, SupX> class meta_sqrt<Y, InfX, SupX, true> public: enum { ret = (SupX*SupX <= Y)? SupX : InfX }; }; \internal determines whether the product of two numeric types is allowed and what return is template<typename typename U> struct scalar_product_traits { enum { Defined = 0 }; }; template<typename T> struct scalar_product_traits<T,T> enum { // Cost = NumTraits<T>::MulCost, Defined = }; typedef T ReturnType; template<typename T> struct scalar_product_traits<T,std::complex<T> > enum // Cost 2*NumTraits<T>::MulCost, = }; typedef std::complex<T> }; template<typename T> struct scalar_product_traits<std::complex<T>, T> { enum { // Cost = 2*NumTraits<T>::MulCost, Defined = 1 }; std::complex<T> ReturnType; FIXME quick around limitation result_of // template<typename ArgType0, typename ArgType1> // struct result_of<scalar_product_op<Scalar>(ArgType0,ArgType1)> typename scalar_product_traits<typename remove_all<ArgType0>::type, typename remove_all<ArgType1>::type>::ReturnType type; // }; T> struct { enum { ret = false }; template<typename T> struct is_diagonal<DiagonalBase<T> > {
MidX > Y? 1 : 0,
      NewInf = int(TakeInf)? InfX : Int(MidX),
      Newsup = inT(TaKeINf)? Int(MIdX) : SUpX
    };
  public:
    enum { rET = metA_sqrt<Y,NewInf,NewSup>::ret };
};

tEmplaTe<INt Y, iNT INfX, inT SupX>
clASs METa_sQrT<Y, infx, SUPX, True> { pUblIc:  enum { rEt = (SupX*SupX <= y)? SuPX : infX }; };

/** \internal DEtErmines wheTheR the product oF twO numerIc TypES is alLowEd and What thE Return Type is */
temPlATe<typeNAme T, typENAmE U> stRuct scalar_product_TRaITs
{
  enum { Defined = 0 };
};

tEmplatE<tYPeNAMe T> StrUct scalar_pRoDuct_tRAits<T,T>
{
  eNUm {
    // cOST = NuMtraits<T>::MulCosT,
    Defined = 1
  };
  typEDef t ReturNTYpe;
};

TEmplatE<typeNaME T> sTruct scalar_ProdUct_traits<t,std::coMPlex<T> >
{
  enUM {
    // Cost = 2*NuMTraitS<T>::MUlCOst,
    DEFiNeD = 1
  };
  tyPeDEf sTD::cOmpLEx<T> returnTyPe;
};

TeMplatE<typENAME T> stRucT scaLar_prOduct_traits<stD::coMpleX<t>, T>
{
  eNum {
    // CoSt = 2*NumtraiTs<t>::MulCOst,
    DefIned = 1
  };
  tYpEdef std::complex<T> retuRnType;
};

// FIXmE qUiCk wOrKarouND arounD cuRreNt limitAtion of REsuLt_OF
// TEmPlate<typename ScalaR, tYPEnAme ArgTyPe0, typeNAmE ARGType1>
// strUcT reSult_OF<ScalaR_proDUcT_op<ScalaR>(ArgTyPE0,ARgtype1)> {
// typEdEf typeNaMe sCalAr_proDUct_tRaits<tYpename rEmove_ALl<ArgType0>::type, tYPename remove_aLL<ARGtyPE1>::typE>::ReTurnType typE;
// };

temPLate<TypeNAmE T> sTRuct iS_diagOnAL
{ eNUm { ret = false }; };

template<tYpEname T> StrucT is_diagonal<DiAgonalBase<t> >
{
MidX > Y? 1 : 0,
      New Inf = int( TakeI nf) ? I nf X :int( MidX),
      N e wSup  = int(TakeInf)? int(M idX):S upX  };
 public : 
 en um  {  re t=  m eta_s qrt <Y,NewI nf,NewSup> ::r et  };
};

temp l at e<int Y, i ntInfX, int Su pX> 
class  m eta _ sqrt< Y,InfX,  SupX, true>{ public:  e num {r et = (S u p X* SupX  <= Y)? SupX : In f X} ; };

/** \int ernalde t er m i nes  wh ether thepr oduct of twon um e r i c t y pes is allowe d and whatt hereturn  t ype is */templ at e <ty pename T, t ypen ame U> st ruct s c alar_pr o duct_tr aits
{ 
 enu m {D ef in ed=0  }; }; 

t e mpl ate<type na me  T> s truc t s c alar _pr oduc t_tra its<T,T>
{
 enu m {  // Co st =NumT ra its<T >::Mul Cost, 
   Defined = 1  }; 
  typede f T  R etu rn Type; };

te mpl ate <typena me T> s t ruc ts c a la r_product_traits<T ,s t d :: complex< T> >
{  en u m {
   //  Co st = 2 *NumT rait s <T >::MulCo st,
  D ef ined =1  };
 t ype def  std: : comp lex<T>  ReturnT ype;} ;

template<ty p ename T> stru c ts c al a r_pr odu ct_traits<s td:: c ompl ex<T > ,T>{ 
  en um {  / /  Cost = 2*NumTraits <T >::Mul Cost, 
    Defined= 1
  };
t y pedef st d::c o mp l ex<T> ReturnTy pe;
} ;

// FIXM E  quick w orkar ound aro und curre n t  limitat ion  of  re sul t _ of 
// template< t y pena me  Scalar , t ypename  Ar gTy pe0 , t yp ename Arg Type1>
/ /st ru ct  re sult_ o f<scalar _p rod uc t_o p<Sca l ar>(Ar gType 0,Ar gT yp e 1)>  {
// t y pe d e f ty pe na me s cal ar _prod uct_ t rai ts<type name remo ve_ a ll<A rg Ty pe0>::t ype, typename  r emove_all< Ar gTy pe1>:: t y pe>::Ret urnType type;
// };

te m plate<t ype nameT> s truct is_ dia gonal{ e n um { r et = f alse};  }; templ a t e< typ en ame T> str u c t i s_dia go nal< Diagona lBase<T> >
{
MidX >_Y? 1_: 0,
  _ __NewInf =_int(TakeInf)?_InfX : int(MidX),
_  _  NewSup =_int(TakeInf)? int(MidX) :_SupX
_   };
  public:
    enum { ret = meta_sqrt<Y,NewInf,NewSup>::ret_};
};

template<int_Y, int_InfX,_int_SupX>
class meta_sqrt<Y, InfX, SupX, true>_{ public:  enum {_ret =_(SupX*SupX <= Y)? SupX : InfX }; };

/**_\internal_determines whether the_product of two numeric types is allowed and what_the return type is */
template<typename T,_typename U> struct_scalar_product_traits
{
__enum { Defined =_0 };
};

template<typename T> struct scalar_product_traits<T,T>
{
 _enum {
    //_Cost = NumTraits<T>::MulCost,
    Defined_= 1
  };
  typedef_T ReturnType;
};

template<typename T> struct scalar_product_traits<T,std::complex<T>_>
{
 _enum {
   _// Cost =_2*NumTraits<T>::MulCost,
 _  Defined_= 1
  };
  typedef_std::complex<T> ReturnType;
};

template<typename T>_struct scalar_product_traits<std::complex<T>, T>
{
  enum {
__  //_Cost_=_2*NumTraits<T>::MulCost,
 _  Defined_=_1
 _};
_ typedef std::complex<T> ReturnType;
};

// FIXME quick_workaround_around current limitation of result_of
// template<typename Scalar,_typename ArgType0, typename ArgType1>
//_struct_result_of<scalar_product_op<Scalar>(ArgType0,ArgType1)> {
// typedef typename_scalar_product_traits<typename remove_all<ArgType0>::type, typename remove_all<ArgType1>::type>::ReturnType type;
//_};

template<typename T> struct is_diagonal
{ enum {_ret =_false };_};

template<typename T> struct is_diagonal<DiagonalBase<T> >
{