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[leishi.git] / draft / en / note / xfdtd_pic / Techniques_scientic_cpp.org

#author Todd Veldhuizen,ʯÀÚ
#date   Aug,2000
#desc 
#title  C++¿Æѧ¼ÆËã¼¼ÇÉ( Techniques of scientic C++)

* <lisp>(setq  Title "C++¿Æѧ¼ÆËã¼¼ÇÉ")</lisp>
 - ×÷Õß:[[mailto:tveldhui@acm.org][ Todd Veldhuizen]]
 - ·­Òë: [[http://stoneszone.net][ʯÀÚ]]
 - ³ö´¦: Indiana University Computer science Technical Report #542 Version 0.4,August 2000
 - °æȨ: תÔØÇë×¢Ã÷³ö´¦
<contents depth="4">

** µÚÒ»ÕÂ
*** 1.1 C++ ±àÒëÆ÷
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  1. Template
  2. STL
  
   Èç¹ûÄãÐèҪд¿ÉÒÔÔÚ²»Í¬Æ½Ì¨Ï¹¤×÷µÄ´úÂ룬´ó²¿·Öʱ¼äÄã»áÔڼ尾Öжȹý¡£ÔÚBlitz++¿âÖУ¬ÎÒ²ÉÓÃÁËÀ©Õ¹µÄÔ¤´¦ÀíKludgesÀ´½â¾ö²»Í¬µÄ±àÒëÆ÷¡£ÀýÈçÏÂÃæÕâ¶Î´úÂë:

<source lang="C">
#include <cmath>

namespace blitz{
    double pow(double x,double y)
    {return std::pow(x,y);}
};
</source>

  Õâ¶Î¼òµ¥µÄ´úÂëÔÚBlitz namespace(Ãû×Ö¿Õ¼ä)Öж¨ÒåÁËÒ»¸öº¯Êýpow,Ëüµ÷ÓÃÁ˱ê×¼µÄpowº¯Êý¡£Ò»Ð©±àÒëÆ÷²»Ö§³Ö<cmath>Í·Îļþ£¬ËùÒÔÐèÒªÌ滻Ϊ<math.h>¡£Ò»Ð©±àÒëÆ÷Ö§³Ö£¬µ«ÊÇC mathº¯Êý²»ÔÚstdµÄnamespaceÖС£ÉõÖÁһЩ±àÒëÆ÷¸ù±¾¾Í²»Ö§³Önamespace¡£ÎÒʹÓõĽâ¾ö·½°¸ÈçÏÂ:

<source lang="C">
#ifdef BZ_MATH_FN_IN_NAMESPACE_STD
  #include <cmath>
#else
  #include <math.h>
#endif

#ifdef BZ_NAMESPACES
double pow(double x,double y)
{
  return BZ_MATHFN_SCOPE(pow)(x,y);
}
#endif
</source>

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**** 1.2.3 ³ÌÐòÊý¾Ý¿â·½·¨-visual age c++

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**** 1.2.4 ¶þ´Î/Èý´Î Ä£°æËã·¨
  ÏñBlitz++µÄ¿âʹÓÃÁË´óÁ¿µÄtemplate¡£Ò»Ð©±àÒëÆ÷ÔÚÄ£°æ¾ÛÏÖÉÏÓÐ×Ô¼ºµÄËã·¨£¬µ«ÊÊÓ¦ÐÔ²»ÊǺܺá£ÀýÈçÏÂÃæµÄ´úÂë:

<source lang="C">
template<int N>
void foo()
{
  for<N-1>();
}

template<>
void foo<0>()
{}

</source>

  Èç¹û¾ÛÏÖfoo<N>,ÄÇôfoo<N-1>±»¾ÛÏÖ£¬Í¬Ñùfoo<N-1>,...,Ö±µ½foo<0>¡£±àÒëÐèÒª¶àÉÙʱ¼ä£¿¾ÛÏֵĺ¯Êý¸öÊýÊÇN¸ö£¬ËùÒÔ±àÒëʱ¼äÓ¦¸ÃËæNÏßÐÔÔö³¤£¬¶ÔÂð£¿

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*** 1.3 ¾²Ì¬¶à̬
**** 1.3.1 Ð麯ÊýÊÇа¶ñµÄÂð£¿
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 - Ä¿Ç°µÄC++ ±àÒëÆ÷²»ÄÜÓÅ»¯Ð麯Êýµ÷ÓÃ: Ëü×èÖ¹ÁËÖ¸Áîscheduling,Êý¾ÝÁ÷·ÖÎö£¬Ñ­»·Õ¹¿ªµÈ¡£

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<source lang="C">
class Matrix{
  public:virtual double operator()(int i,int j)=0;
};

class SymmetricMatrix:public Matrix{
  public:virtual double operator()(int i ,int j);
};

class UpperTriangularMatrix:public Matrix{
  public:virtual double operator()(int i,int j);
};
</source>

  Ð麯Êý·ÖÅÉoperator()À´´Ó¾ØÕóÖжÁÈ¡ÔªËØ£¬Õâ»áÆÆ»µÈκÎÒ»ÖÖ¾ØÕóËã·¨µÄÐÔÄÜ¡£

**** 1.3.2 ½â¾ö·½·¨A: ¼òµ¥ÒýÇæ(simple engines)
  "engines"À´×ÔÔÚLANLµÄPOOMAÍŶӡ£Éè¼ÆģʽÉçÇøÒ²ÓÐÒ»¸öͬÑùµÄÃû³Æ¡£

  Ïë·¨ÊǰѶ¯Ì¬¶à̬£¨Ð麯Êý£©Ì滻Ϊ¾²Ì¬¶à̬(template parameters)¡£ÕâÊÇÒ»¸ö²ÉÓÃÁËÕâÖÖ¼¼ÊõµÄMatrixµÄ¹Ç¼Ü¡£

<source lang="C">
class Symmetric{
//·â×°Õë¶Ô¶Ô³Æ¾ØÕóµÄ´æ´¢ÐÅÏ¢
};

class UpperTriangular{
//·â×°Õë¶ÔÈý½Ç¾ØÕóµÄ´æ´¢ÐÅÏ¢
};

tempalte<class T_engine>
class Matrix{
private:
 T_engine engine;
};

//²ÉÓÃÈκξØÕó½á¹¹µÄº¯Êý
template<class T_engine>
double sum(Matrix<T_engine>& A);

//ʹÓÃÀý×Ó...
Matrix<Symmetric> A;
sum(A);

</source>
  
  ÔÚÉÏÀýÖУ¬¾ØÕó½á¹¹µÄ²»Í¬±ä»¯Òþ²ØÔÚengines SymmetricºÍUpperTriangularÖС£MatrixÀà°Ñengine×÷Ϊtemplate parameter,²¢ÇÒ°üº¬Õâ¸öengineµÄʵÀý×÷Ϊ³ÉÔ±±äÁ¿¡£

  Óû§Ê¹ÓõķûºÅ±äÁË£ºMatrix<Symmetric> ¶ø²»ÊÇÔ­À´µÄSymmetricMatrix£¬²»¹ýÕâ¸ö²»ÊÇÒ»¸ö´óÎÊÌâ¡£ÎÒÃÇ¿ÉÒÔʹÓÃtypedefineÀ´Òþ²ØÕâ¸öϸ½Ú¡£Í¬Ñù£¬ÔÚMatrixÖУ¬´ó²¿·Ö²Ù×÷Òª±»´úÀí¸øenginesÀ´´¦Àí¡£

  ÕâÖÖ½â¾ö·½·¨×îÑÏÖصÄÎÊÌâÊÇËùÓеÄMatrix×ÓÀàÐͶ¼±ØÐëÓÐͬÑùµÄ³ÉÔ±º¯Êý¡£ÀýÈ磬Èç¹ûÎÒÃÇÏëÒªMatrix<Symmetric>ÓÐÒ»¸öisSymmetricPositiveDefinite()µÄ·½·¨£¬µäÐ͵ÄʵÏÖÊÇ£º

<source lang="C">
template<class T_engine>
class Matrix{
public:
  //Delegate to the engine
  bool isSymmetricPositiveDefinite()
  {return engine.isSymmetricPositiveDefinite();}

private:
  T_engine engine;
};

class Symmetric{
public:
  bool isSymmetricPositiveDefinite()
  {
   ...
  }
};
</source>
  
  µ«ÊÇÕⲢûÓÐʹMatrix<UpperTriangular>ÓÐÀíÓÉ°üº¬isSymmetricPositiveDefinite()º¯Êý£¬ÒòΪupper triangular¾ØÕó²»ÄÜΪ¶Ô³Æ¡£´ÓÉÏÀý¿ÉÒÔ¿´³öÕâÖÖ·½·¨Ê¹»ùÀà°üº¬ÁËËùÓÐ×ÓÀàÐÍËùÓµÓеĺ¯Êý¡£ËùÒÔµ¼Ö²úÉúÁ˺ܶàÔÚengineÖлáÅ׳öÒì³£µÄ³ÉÔ±º¯Êý¡£

<source lang="C">

class UpperTriangular{
public:
  bool isSymmetricPositiveDefinite()
  {
    throw makeError("Method isSymmetricPositiveDefinite() is not defined for UpperTriangular¾ØÕó");
    return false;
  }

};

</source>

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  ¿ÉϲµÄÊÇ£¬ÓÐÒ»ÖÖ¸üºÃµÄ½â¾ö·½·¨¡£

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  ÕâÖÖ¼¼Êõ³ÆΪ"Barton and Nackman Trick",ÒòΪ ËûÃÇÔÚËûÃǵĽܳöÖø×÷<<Scientific and Engineering C++>>ÖÐʹÓÃÁËÕâÖÖ¼¼Êõ¡£GeoffÈ¡ÁËÒ»¸ö±È½ÏÓÐÒâÒåµÄÃû×Ö"Curiously Recursive Template Pattern"¡£

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<source lang="C">

//»ùÀàÓÐÒ»¸öÄ£°æ²ÎÊý¡£Õâ¸ö²ÎÊý¶¨ÒåÁ˸ÃÀàÓ¦¸Ã´ÓÄÄÀï¼Ì³Ð¡£
template<class T_leaftype>
class Matrix{
public:
 T_leaftype& asLeaf()
{return static_cast<T_leaftype&>(*this);}

double operator()(int i,int j)
{return asLeaf()(i,j);} //´úÀí¸øleaf

}£»

class SymmetricMatirx : public Matrix<SymmetricMatrix>{
...
};

class UpperTriMatrix: public Matrix<UpperTriMatrix>{
...
};

// ʹÓÃÀý×Ó£¬¿ÉÒÔ½ÓÊÜÈκξØÕóÀà
template<class T_leaftype>
double sum(Matrix<T_leaftype>& A);

//Àý×Ó
SymmetricMatrix A;
sum(A);
</source>

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  ʹÄãµÄ¼Ì³ÐÊ÷¶àÓÚÒ»²ãÊÇ¿ÉÐеģ¬µ«ÐèÒª¶à¼Ó¿¼ÂÇ¡£

*** 1.4 Callback inlining ¼¼Êõ
  Callback ¾­³£»á³öÏÖÔÚ³ÌÐòÖС£Ò»Ð©µäÐ͵ÄÀý×ÓÈçÏÂ
 - ÊýÖµ»ý·Ö:Ò»¸öÒ»°ãÐԵĻý·Ö³ÌÐòʹÓÃCallbackº¯ÊýÀ´¶ÔÐèÒª±»»ý·ÖµÄº¯ÊýÇóÖµ¡£ÔÚC¿âÖУ¬Í¨¹ý´«È뺯ÊýÖ¸ÕëµÄ²ÎÊýʵÏÖ¡£
 - ÓÅ»¯º¯Êý
 - ¶ÔÒ»¸öÈÝÆ÷ÖеÄËùÓбäÁ¿Ó¦ÓÃÒ»¸öº¯Êý¡£
 - ÅÅÐòº¯Êý£¬Èçqsort()ºÍbsearch()ÐèÒªcallbackÀ´±È½Ï±äÁ¿¡£

  ±ê×¼µÄCº¯Êý·½·¨²ÉÓú¯ÊýÖ¸ÕëÀ´ÊµÏÖCallback¡£
<source lang="C">
double integrate(double a,double b,int numSamplePoints,double(*f)(double){
double delta=(b-a)/numSamplePoints-1);
double sum = 0.0;

for(int i=0;i<numSamplePoints;++i)
  sum+=f(a+i*delta);

return sum*(b-a)/numSamplePoints;
}
</source> 

  ÕâÖÖ·½·¨¹¤×÷µÄºÜºÃ£¬µ«ÊǶÔÐÔÄÜÓÐÓ°Ïì:ÔÚÄÚ²¿Ñ­»·Öеĺ¯Êýµ÷ÓûᵼÖ½ϴóµÄÐÔÄÜËðʧ¡£Ò»Ð©ÓÅ»¯±àÒëÆ÷Ò²Ðí»áÖ´ÐÐinter-proceduralºÍÖ¸Õë·ÖÎöÀ´È·¶¨fÖ¸ÏòµÄÈ·Çк¯Êý£¬µ«ÊÇ´ó¶àÊý±àÒëÆ÷²»»á×ö¡£

**** 1.4.1 Callbacks: C++·½Ê½
  ÔÚC++¿âÖУ¬callbacksÒ»°ã²ÉÓÃÐ麯Êý¡£ÐÂÒ»µãµÄ·½Ê½ÊǶ¨ÒåÒ»¸ö»ùÀ࣬ÈçIetegrator£¬¶¨ÒåÒ»¸öÐ麯Êý£¬Ôڼ̳Ð×ÓÀàÖж¨Òåʵ¼ÊÐèÒª±»»ý·ÖµÄº¯Êý¡£

<source lang="C">
class Integrator{
public:

double integrate(double a,double b,int numSamplePoints)
{
double delta=(b-a)/..;
...

for(int i=0;i<numSamplePoints;++i)
  sum+=functionToIntegrate(a+i*delta);
reutrn sum*(b-a)/numSamplePoints;
}

virtual double functionToIntegrate(double x)=0;
};

class IntegrateMyFunction:Integrator{
public:
  virtual double functionToIntegrate(double x)
  {
     return cos(x);
  }
};
</source>

  ͬCÀàËÆ£¬Ð麯Êý·ÖÅÉÔÚÄÚ²¿Ñ­»·»áµ¼ÖÂÐÔÄÜϽµ(Èç¹û¸Ãº¯ÊýÖ´ÐÐʱ¼ä±È½Ï³¤£¬ÔòÐ麯ÊýµÄËðʧ¿ÉÒÔºöÂÔ²»¼Æ)¡£¶ÔÓÚÐÔÄÜ£¬ÐèÒªÔÚ»ý·Öº¯ÊýÖвÉÓÃinline the callbackº¯Êý¡£
  
  ÏÂÃæ¾Í½éÉÜÈýÖÖ·½·¨ÊµÏÖinlined callbacks¡£

 1. Expression templates

   ÕâÊÇÒ»ÖÖ¾«Ï¸£¬¸´ÔӵĽâ¾ö·½·¨¡£ËüÀ©Õ¹ºÍά»¤ÆðÀ´±È½ÏÄÑ¡£Ò»°ã²»±ØÀË·ÑÄãµÄ¾«Á¦È¥Ñ¡ÔñÕâÖÖ·½·¨¡£

 2. stl·ç¸ñµÄº¯Êý¶ÔÏó

   Callbackº¯Êý¿ÉÒÔ±»·â×°ÔÚÒ»¸öÀàÖУ¬´Ó¶ø´´½¨Ò»¸öº¯Êý¶ÔÏó»òÕ߽зº¯Êý¡£

<source lang="C">

class MyFunction{
public:

   //×¢Ò⣺Ϊinline ³ÉÔ±º¯Êý
  double operator()(double x)
  {return 1.0/(1.0+x);}
};

template<class T_function>
double integrate(double a,double b,int numSamplePoints,T_function f)
{
  double delta=(b-a)/(numSamplePoints-a);
  double sum=0;

  for(int i=0;i<numSamplePoints;++i)
    sum+=f(a+i*delta);

  return sum*(b-a)/numSamplePoints;

}

//Ó÷¨
integrate(0.3,0.5,30,MyFunction())£»

</source>

  Ò»¸öMyFunctionµÄ¶ÔÏó×÷Ϊ²ÎÊý´«Èëintegrateº¯Êý¡£C++±àÒëÆ÷»á¾ÛÏÖ»¯integrate, ÓÃMyFunctionÀ´Ìæ»»T_function;ÕâÑù»áµ¼ÖÂMyFunction::operator()±»inlined½øintegrate()µÄÄÚ²¿Ñ­»·ÖС£

  ÕâÖÖ·½·¨µÄȱµãÊÇÓû§±ØÐ뽫ËùÓÐËûÏëµ÷Óõĺ¯Êý·â×°ÔÚÀàÖС£Í¬Ñù£¬Èç¹ûCallbackº¯ÊýÐèÒª²ÎÊý£¬Ôò±ØÐëÌṩ¸øMyFunctionµÄ¹¹Ô캯Êý£¬²¢±£´æΪ³ÉÔ±±äÁ¿¡£

  ×¢Ò⣬Äã¿ÉÒÔÏòÉÏÀýµÄintegrate´«È뺯ÊýÖ¸Õë¡£µ«ÕâºÍC·ç¸ñµÄcallbackº¯ÊýÒ»Ñù£¬²»»áÔÚÑ­»·Öн«Äã´«ÈëµÄº¯ÊýÖ¸Õë½øÐÐinline»¯¡£

  3. º¯ÊýÖ¸Õë×÷Ϊģ°æ²ÎÊý
   µÚÈýÖÖ·½·¨ºÜ¼òµ¥£º

<source lang="C">

double function1(double x)
{
  return 1.0/(1.0+x);
}

template<double T_function(double)>
double integrate(double a,double b,int numSamplePoints)
{

  double delta=(b-a)/(numSamplePoints-1);
  double sum=0.0;
  
  for(int i=0;i<numSamplePoints;++i)
     sum+=T_function(a+i*delta);

  return sum*(b-a)/numSamplePoints;

}

//..
integrate<function1>(1.0,2.0,100);
</source>
    
  integrate()º¯Êý½«Ö¸Ïòcallbackº¯ÊýµÄº¯ÊýÖ¸Õë×÷Ϊģ°æ²ÎÊý¡£ÓÉÓÚÕâ¸öÖ¸ÕëÔÚ±àÒëÆÚ¼ä¾Í¿ÉÒÔÈ·¶¨£¬ËùÒÔfunction1±»inline½øÈëÄÚ²¿Ñ­»·¡£²Î¿¼oon-listµµ°¸µÄSumclass algorithmsÌõÄ¿¡£

*** 1.5 ¿ØÖÆ´úÂëÅòÕÍ
  ´úÂëÅòÕͶÔÓÚ»ùÓÚÄ£°æµÄ¿âÀ´ËµÊÇÒ»¸öÎÊÌâ¡£ÀýÈ磬ÄãʹÓÃqueueµÄһЩʵÀý£º

<source lang="C">
  queue<float>
  queue<int>
  queue<Event>
</source>

  ÄãµÄ³ÌÐò»áÓÐÈý¸ö²»Í¬°æ±¾µÄqueue<>¡£Õâ¶ÔÓÚʹÓûùÓÚÐ麯Êý¶à̬µÄÀÏ·ç¸ñc++¿â²¢²»ÊÇÎÊÌâ¡£

  µ«ÊÇ£¬Êµ¼ÊÖбàÒëÆ÷»áÉú³ÉһЩ»ÄÃýµÄ¶àÓà´úÂëʹµÃÎÊÌâ¸ü¼ÓÑÏÖØ¡£
  - һЩ±àÒëÆ÷ÔÚÿ¸öÄ£¿éÖоÛÏÖÄ£°æ£¬²¢ÇÒÔÚÁ¬½Óʱ±¨Öظ´¶ÔÏó´íÎó¡£
  - һЩ±àÒëÆ÷(ÀϵÄ)¾ÛÏÖÄ£°æµÄÿһ¸ö³ÉÔ±º¯Êý¡£ISO/ANSIµÄ±àÒëÆ÷½ûÖ¹ÕâÖÐ×ö·¨£º±àÒëÆ÷Ó¦¸ÃÖ»¾ÛÏÖÕæÕýʵÓõÄÄ£°æ¡£

  ÕâЩÎÊÌâÒ»²¿·ÖÊÇÎÒÃÇ×Ô¼ºÒýÆðµÄ: ʹÓÃÄ£°æÉú³É´úÂëÌ«ÈÝÒ×ÁË£¬ÒÔÖÁÓÚ³ÌÐòÔ±ºÜÉÙ¿¼ÂÇËüµÄºó¹û¡£ÎÒÇ÷ÏòÓÚÔÚÈκεط½Ê¹ÓÃÄ£°æ£¬ºÜ¶àʱºò¸ü²»²»È¥¿¼ÂÇʹÓÃÐ麯Êý¡£ÎÒ¸öÈËÒ»°ã²»¹ØÐÄ´úÂëÅòÕÍ£¬ÒòΪÎҵijÌÐòÒ»°ã¶¼ºÜС¡£µ«Êǹ¤×÷ÔÚ´óÐͳÌÐòµÄÈ˱ØÐ뿼ÂÇʹÓÃÄ£°æ»¹ÊÇÐ麯Êý¡£

 - ËäȻģ°æ¿ÉÒÔ´øÀ´½ÏºÃµÄÐÔÄÜ£¬µ«ÊÇÒ²Òâζ×Å´ó¶àÊýÇé¿ö´øÀ´½Ï¶àµÄ´úÂë¡£(Èç¹ûÄãÖ»ÓÃÄ£°æÆäÖеÄÒ»¸öʵÀý£¬ËûÃDz»»á¸øÄã¸ü¶àµÄ´úÂë)
 - Ð麯Êý¸øÄã×îÉٵĴúÂ룬µ«ÊÇÈ´ÊǽÏÂýµÄ´úÂë¡£ÕâÖÖÐÔÄÜËðʧÔÚÐ麯Êýº¯Êý¼ÆËãÁ¿½Ï´óµÄʱºòÊÇ¿ÉÒÔºöÂԵģ¬»òÕßÔÚº¯Êýµ÷ÓýÏÉÙµÄʱºò¡£

 µ±È»£¬Ð麯ÊýºÍÄ£°æ²¢²»ÊǶÔÿ¸öÎÊÌⶼÊÇ¿ÉÒÔÑ¡ÔñµÄ¡£Èç¹ûÄãÐèÒª¶¯Ì¬µÄ¶à̬£¬Ä£°æ¾Í²»ÄÜʤÈΡ£ÏÂÃæ¾Í¸ø³öһЩ½µµÍ´úÂëÅòÕ͵Ľ¨Òé¡£

**** 1.5.1 ±ÜÃâkitchen-sinkÄ£°æ²ÎÊý
  ½«ÀàµÄÿ¸öÊôÐÔ¶¼×÷Ϊģ°æ²ÎÊýÊǺÜÓÐÓÕ»óÁ¦µÄ¡£ÏÂÃæ¾ÍÊÇÒ»¸ö¿äÕŵÄÀý×Ó¡£

<source lang="C">
template<typename number_type,int N,intM,bool sparse,typename allocator,bool symmetric,bool banded,int bandwidthIfBanded>
class Matrix;
</source>

  ÿ¸ö¶àÓàµÄÄ£°æ²ÎÊý¶¼Îª´úÂëÅòÕÍÌṩÁË»ú»á¡£Èç¹ûÄãʹÓÃÁ˺ܶàÖÖ"kitchen-sink"µÄÄ£°æÀ࣬ÄãÓ¦¸Ã¿¼ÂÇͨ¹ýÐ麯Êý£¬³ÉԱģ°æµÈ¼õÉÙһЩģ°æ²ÎÊý¡£

  ÀýÈ磬ÎÒÃÇÓÐÒ»¸öÀàlist<>¡£ÎÒÃÇÏëÒªÓû§ÓÐÄÜÁ¦Ìṩ×Ô¼ºµÄÄÚ´æ·ÖÅäÆ÷£¬ËùÒÔÎÒÃÇ¿ÉÒÔ½«Alloctor×÷Ϊһ¸öÄ£°å²ÎÊý:

<source lang="C">
list<double ,allocator<double>> A;
list<double , my_alloctor<double>>B;
</source>

 ÕâÑù»áΪAºÍBÉú³É²»Í¬µÄlist°æ±¾£¬¾¡¹ÜÁ½Õߴ󲿷ֶ¼ÊÇһģһÑùµÄ(±ÈÈçÄãÒª±éÀúlist£¬Äã¾Í²»ÐèÒª¿¼ÂÇËüÔÚÄÚ´æÖÐÊÇÔõô·ÖÅäµÄ)¡£²ÉÓÃalloactor×÷Ϊģ°æ²ÎÊýÓÐʲôºÃ´¦Â𣿼¸ºõûÓÐ-ÄÚ´æ·ÖÅäÊǺÜÂýµÄ£¬ËùÒÔ¸½¼ÓµÄÐ麯ÊýËðʧ¶ÔËûÀ´ËµÊÇ¿ÉÒÔ½ÓÊܵġ£ÏÂÃæµÄ·½·¨¿ÉÒÔ»ñµÃͬÑùÁé»îµÄÉè¼Æ:

<source lang="C">
list<double> A(allocator<double>());
list<double> B(my_allocator<double>());
</source>

  ÆäÖÐallocatorºÍmy_allocatorÊǶà̬µÄ¡£

**** 1.5.2 ½«º¯Êý¶¨ÒåÔÚÄ£°æÍâ
   Äã¿ÉÒÔͨ¹ý½«º¯Êý¶¨ÒåÒƶ¯ÖÁÀඨÒåµÄÍâÃæÀ´±ÜÃâ´´½¨²»ÐèÒªµÄÖظ´³ÉÔ±º¯Êý¡£ÀýÈ磬ÏÂÃæÊÇÒ»¸öArray3DÀàµÄ¿ò¼Ü¡£

<source lang="C">
template<class T_numtype>
class Array3D{
public:
  //È·±£ÏÂÃæµÄarrayÓÐͬÑùµÄ´óС
  template<class T_numtype2>
  bool shapeCheck(Array3D<T_numtype2>&);

private:
  int base[3];              //Æðʼx,y,zµÄindexÖµ
  int extent[3];            //ÿ¸öx,y,zµÄ³¤¶È
};

template<class T_numtype> template<class T_numtype2>
bool Array3D<T_numtype>::shapeCheck(Array3D<T_numtype2>&B)
{
  for(int i=0;i<3;++i)
    if((base[i]!=B.base(i))||(extent[i]!=B.extent(i)))
      return false;

   return true;
}

</source>


  shapeCheck()º¯ÊýÈ·¶¨Á½¸öarrayÊÇ·ñÓÐͬÑùµÄÆðʼindexºÍ³¤¶È¡£Èç¹ûÄãÓкܶàÖÖ²»Í¬µÄarray(Array3D<float>,Array3D<int>,...),Äã»á×îÖÕÓµÓкܶà¸öshapeCheck()º¯ÊýµÄʵÀý¡£µ«ÊÇ£¬ÆäʵÕâЩʵÀýÊÇÍêÈ«Ò»ÑùµÄ£¬ÒòΪshapeCheck()²¢²»Ê¹ÓòÎÊýT_numtypeºÍT_numtype2¡£

  ΪÁ˱ÜÃâ²úÉú¶àÖصÄʵÀý£¬Äã¿ÉÒÔ½«shapeCheck()Òƶ¯ÖÁûÓÐÄ£°æ²ÎÊýµÄ»ùÀ࣬»òÕßÒÆÖÁÈ«¾Öº¯Êý£¬ÈçÏ£º

<source lang="C">
class Array3D_base{

public:
  bool shapeCheck(Array3D_base&);

private:

  int base[3];
  int extent[3];
};

template<class T_numtype>
class Array3D:public Array3D_base{
  ...
};
</source>

ÓÉÓÚshapeCheck()ÏÖÔÚ²»ÔÚÄ£°æÀàÖУ¬ËùÒÔÖ»ÓÐÒ»¸öËüµÄʵÀý¡£Èç¹ûÄãÕýºÃÊÇC++±àÒëÆ÷µÄ×÷Õߣ¬¶Áµ½ÕâÀÄãÓ¦¸Ã×¢Ò⣬Õâ¸öÎÊÌâ¿ÉÒÔͨ¹ý×Ô¶¯µÄ½øÐÐÄ£°æ²ÎÊýÓÐЧÐÔ¼ì²âÀ´±ÜÃâ¡£

**** 1.5.3 Inlining ¼¶±ð
  Ò»°ãÇé¿ö£¬ÎÒÇ÷ÏòÓÚÔÚBlitz++Öн«ºÜ¶à¶«Î÷inline»¯£¬ÒòΪÕâÑù×Ó»áЭÖú±àÒëÆ÷ÓÅ»¯(¶ÔÓÚÄÇЩ²»×öinterprocedural·ÖÎöºÍÇ¿»¯inliningµÄ±àÒëÆ÷)¡£Èç¹ûÓÐÒ»Ì죬ÎҸоõBlitz++ÖеÄinlineÌ«¶àÁË£¬ÕâÓÐÒ»ÖÖ²ßÂÔ¿ÉÒÔ´¦ÀíÕâ¸öÎÊÌâ¡£

<source lang="C">
#if BZ_INLINING_LEVEL==0
  //NO INLINING
  #define _bz_inline1
  #define _bz_inline2
#elif BZ_INLINING_LEVEL==1
  #define _bz_inline1 inline
  #define _bz_inline2
#elif BZ_INLINING_LEVEL==2
  #define _bz_inline1 inline
  #define _bz_iiline2 inline
#endif

_bz_inline void foo(Array<int>&A)
{
  //...
}
</source>

  Óû§Èç¹û²»ÏëÒªÈκεÄinline£¬¿ÉÒÔ-DBZ_INLINING_LEVEL=0À´±àÒë,»¹¿ÉÒÔ¿ØÖÆÆäΪ1,2À´¿ØÖÆINLINEµÄ³Ì¶È¡£

*** 1.6 ÈÝÆ÷
  ÈÝÆ÷Àà¿ÉÒÔ´óÖ·ÖΪÁ½¸ö²¿·Ö:STL·ç¸ñ(»ùÓÚiteratorµÄ)ºÍData/View·ç¸ñµÄ¡£
**** 1.6.1 ·ç¸ñÈÝÆ÷
 - Ò»¸öÈÝÆ÷ÀàÓµÓÐËùÓеÄÊý¾Ý¡£
 - ×ÓÈÝÆ÷ͨ¹ýiterator rangeÀ´Ö¸¶¨£¬Ò»°ã²ÉÓÿª·Å-·â±ÕµÄÇøÓò:[iter1,iter2)¡£
 - ÕâÖÖÉè¼Æ·ç¸ñÀ´×ÔSTL£»Èç¹ûÄãͨ¹ýÕâÖÖ·½·¨Ð´ÈÝÆ÷£¬Äã¿ÉÒÔÈ¡µÃÎÞ·ìµ÷ÓÃSTLËã·¨µÄÓÅÊÆ¡£
 - ÈÝÆ÷ÖÁÉÙÐèÒªÓÐ1-DÐòÁеÄÓïÒå¡£ËùÓеÄ×ÓÈÝÆ÷±ØÐëintervals½øÄǸö1DµÄ˳Ðò¡£Õâ»á¶ÔÓÚ¶àάÊý×é»á²úÉúÎÊÌâ¡£(ÀýÈ磬A(2:6:2,2:6:2)µÄÔªËØÃ÷ÏÔ²»¾ßÓÐ1-DÐòÁеÄÓïÒå)
 - iterator»ùÓÚÖ¸ÕëµÄ¸ÅÄ¶øÖ¸ÕëÓÖÊÇC++ÖÐ×îÈÝÒ×·¸´íÎóµÄµØ·½Ö®Ò»¡£Õâµ¼ÖºܶàÈÝÒ×´íÎóµÄʹÓÃiterator¡£
 - ¶ÔÓÚº¯ÊýÀ´Ëµ£¬½«ÈÝÆ÷×÷ΪֵÀ´·µ»Ø±È½ÏÀ§ÄÑ¡£Ïà·´£¬ÈÝÆ÷¿ÉÒÔÓô«Èë²ÎÊýµÄ·½·¨(argument)À´½ÓÊܽá¹ûÄÚÈÝ¡£

**** 1.6.2 Data/View ÈÝÆ÷
  - ÈÝÆ÷µÄÄÚÈÝ(Êý¾Ý)±£´æÔÚÈÝÆ÷Íⲿ¡£ÈÝÆ÷Ö»ÊÇÒ»¸öÊý¾ÝµÄÇáÁ¿¼¶¾ä±ú¡£
  - ¶à¸öÈÝÆ÷¶ÔÏó¿ÉÒÔË÷Òýͬһ¸öÊý¾ÝÄÚÈÝ£¬µ«ÌṩËüµÄ²»Í¬µÄÊÓͼ¡£
  - ʹÓòο¼¼ÆÊý:ÈÝÆ÷µÄÊý¾ÝÄÚÈÝÔÚ×îºóÒ»¸ö¾ä±úÏú»ÙºóÏú»Ù¡£ÕâÌṩÁËÒ»¸öÀ¬»ø»ØÊÕ»úÖƵÄʵÏÖ(ÇÒÓÐЧÂÊ)¡£
  - ÓÐЩÇé¿ö϶¨Òå×ÓÈÝÆ÷±È½ÏÈÝÒ×(ÀýÈ磬¶àάÊý×éµÄ×ÓÊý×é)¡£
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  - ʹÓÃÒýÓüÆÊýµÄÈÝÆ÷ÐèÒª½ÏΪ¾«Ï¸µÄÉè¼Æ·½·¨¡£
  - ´Óº¯ÊýÖзµ»ØÈÝÆ÷±È½ÏÈÝÒ×£¬²¢ÇÒ¿ÉÒÔ½«ÈÝÆ÷°´Öµ´«µÝ¡£

*** 1.7 AliasigºÍÏÞÖÆ

 Aliasing¶ÔC++¿Æѧ¼ÆËã¿âÀ´ËµÊÇÓ°ÏìÐÔÄܵÄÒ»´óÎÊÌâ¡£ÀýÈ磬¿¼ÂǼÆËã1½×¾ØÕóA <- A+xxT£º

<source lang="C">
void rank1Update(Matrix&A,const Vector&x)
{
  for(int i=0;i<A.rows();++i)
     for(int j=0;j<A.cols();++j)
        A(i,j)+=x(i)*x(j);
}
</source>

 ¶ÔÓںõÄÐÔÄÜ£¬±àÒëÆ÷ÐèÒª±£³Öx(i)ÔڼĴæÆ÷Öжø²»ÊÇÔÚÄÚ²¿Ñ­»·ÀïÖظ´µÄÔØÈëËü¡£¾¡¹ÜÈç´Ë£¬±àÒëÆ÷²»ÄÜÈ·¶¨µÄÊÇÔÚAÖеÄÊý¾Ý²»»á¸²¸Çx(i)ÖеÄÊý¾Ý¡£Õâ¶ÔÓÚ¾ØÕóºÍÏòÁ¿ÀàµÄÉè¼ÆÀ´ËµÊDz»¿ÉÄܲÉÓõģ¬µ«ÊDZàÒëÆ÷²»ÖªµÀÕâЩ¡£AliasingµÄ¿ÉÄÜÐÔµ¼Ö±àÒëÆ÷²úÉúµÍЧÂʵĴúÂë¡£

 ÁíÒ»¸öAliasingµÄ½á¹ûÊÇÖжÏÑ­»·µÄÈí¼þÁ÷Ë®Ïß¡£ ÀýÈ磬һ¸öDAXPY²Ù×÷y <- y + a*x

<source lang="C">
  void daxpy(int n,double a,double*x,double *y)
{
  for(int i=0;i<n;++i)
    y[i]=y[i]+a*x[i];
}

</source>

 ΪÁËÈ¡µÃºÃµÄЧÂÊ£¬Ò»¸öÓÅ»¯±àÒëÆ÷»á²¿·ÖµÄÕ¹¿ªÑ­»·£¬È»ºó½øÐÐÈí¼þÁ÷Ë®ÏßÀ´ÕÒµ½ÓÐЧµÄÄÚ²¿Ñ­»··½·¨¡£Éè¼ÆÕâ¸ö·½·¨¾­³£ÐèÒª¸Ä±äÑ­»·ÖеÄÔØÈëºÍ´æ´¢Ë³Ðò£¬ÀýÈç:

<source lang="C">
  //ÐéÄâµÄÁ÷Ë®»¯DAXPYÑ­»·
  double* xt=x;
  double* yt=y;
  for(;i<n;i+=4)
  £û
     double t0=yt[0]+a*xt[0];
     double t1=yt[1]+a*xt[1];
     yt[0]=t0;
     double t2=yt[2]+a*xt[2];
     double t3=yt[3]+a*xt[3];
     yt[1]=t1
     double t3=yt[3]+a*xt[3];
     i+=4;
     xt+=4;
     yt[2]=t2;
     yt+=4;
     yt[3]=t3;
  }
</source>

  ²»ÐÒµÄÊÇ£¬±àÒëÆ÷ÎÞ·¨¸Ä±äÔØÈëºÍ´æ´¢µÄ˳ÐòÒòΪx,yÖ¸Õë¿ÉÄÜÔÚÄÚ´æÖÐÖصü¡£ÔÚFortran77/90ÖУ¬±àÒëÆ÷¿ÉÒÔ¼ÙÉèÊý×éµØַûÓÐÖصþ¡£¶ÔÓÚÔÚcacheÖеÄÊý×éÕâ»áµ¼ÖÂ20£­50£¥µÄÐÔÄܲîÒì¡£ÕâÒÀÀµÓÚÌض¨µÄÑ­»·/¼Ü¹¹¡£Aliasing¶ÔÓÚout-of-cacheÊý×éÀ´Ëµ²»ÊÇ´óÎÊÌâ¡£

  ÓÅÐãµÄc/c++±àÒëÆ÷»á×öAliasing·ÖÎö£¬Ä¿µÄÊÇÈ·¶¨ÊÇ·ñ¿ÉÒÔÈÏΪָÕë¿É±»ÈÏΪÊÇÖ¸Ïò²»ÖصþÄÚ´æµÄ¡£Alias·ÖÎö¿ÉÒÔ¼õÉÙÐí¶àµÄAliasing¿ÉÄÜÐÔ£¬µ«ÊÇËû²»ÊÇÍêÃÀµÄ¡£ÀýÈ磬·ÖÎöÏñdaxpyº¯ÊýµÄ³ÌÐò±ØÐë×öÈ«¾Ö·ÖÎö¡£±àÒëÆ÷±ØÐëÔÚͬһʱ¼ä¿¼ÂÇÄãÖ´ÐеÄËùÓк¯Êý¡£³ý·ÇÄãµÄ±àÒëÆ÷×öÁËÈ«¾Öalias·ÖÎö(SGI»á),·ñÔòÄã¾Í»áÓÐaliasingÎÊÌâ¡£

  NCEG(Numerical C Extensions Group)Éè¼ÆÁËÒ»¸ö¹Ø¼ü×Örestrict,¿ÉÒÔ±»Ò»Ð©±àÒëÆ÷ʶ±ð£¨KAI,Cray,SGi,Intel,gcc)¡£restrictÊÇÒ»¸ö¿ÉÒÔ¸æËß±àÒëÆ÷¸Ã±äÁ¿Ã»ÓÐAliasingµÄÐÞÊηû¡£ÀýÈ磺

<source lang="C">
  double * restrict a;  //a[0],a[1]..ûÓÐaliasing
  int & restrict b ;    //bûÓÐaliases
</source>

  ÔÚC++ÖÐrestrictµÄÃ÷È·¶¨Òå²¢²»ÊǺÜnailed down¡£µ«Êǵ±restrictʹÓú󣬱àÒëÆ÷¿ÉÒÔ×ÔÓɵÄÓÅ»¯¶ø²»È¥¿¼ÂÇ×°ÔØ£¯´æ´¢Ë³Ðò¡£

  ²»ÐÒµÄÊǽ«restrict¼ÓÈëiso/ansi c++±ê×¼µÄÌáÒé±»·ñ¾öÁË¡£ÎÒÃÇ×îÖյõ½µÄÊÇÒ»¸öÄÜÁ¦ÓÐÕùÒéµÄvalarray¡£valarrayÊý×éÀàÉè¼ÆΪûÓÐaliasing£¬Òò´Ë¿ÉÒÔÔÊÐí±àÒëÆ÷¶ÔÆäÉϵIJÙ×÷½øÐÐÓÅ»¯¡£

  ¾¡¹ÜÈç´Ë£¬restrictÒѾ­±»ansi/iso cÁÐΪ±ê×¼£¬Òò´ËÓпÉÄÜÔÚÏÂÒ»´ÎÖмÓÈëc++±ê×¼¡£µ±¿ÉÒÔʹÓÃrestrictʱ£¬¿ª·¢³ÌÐò¿ÉÒÔʹÓÃÔ¤ÏȱàÒëkludge¡£ÀýÈç,blitz++¶¨ÒåÁËÈçϵĺ꣺

<source lang="C">
 #ifdef BZ_HAS_RESTRICT
  #define _bz_restrict restrict
 #else
  #define _bz_restrict
 #endif


class Vector{
double * _bz_restrict data_;

};
</source>

  ÔÚһЩƽ̨ÉÏ£¬±àÒëÆ÷ÓÐÑ¡Ïî¿ÉÒÔÔÊÐí±àÒëÆ÷¼ÙÉèûÓÐaliasing¡£Õâ¿ÉÒÔµ¼ÖºõÄЧ¹û£¬µ«ÊDZØÐë¸øÓè×¢Òâ¡£ÕâЩѡÏî»á¸Ä±äÄãËùÓгÌÐòÖеÄÖ¸ÕëÓïÒâÒåsemantics of pointers¡£Èç¹ûÄã¶ÔÖ¸Õë×öÁËдÌØÊâ´¦Àí£¬Õâ¿ÉÄܻᵼÖÂÎÊÌâ¡£

*** 1.8 TraitsÝÍÈ¡Æ÷
  Traits¼¼ÊõÊÇÓÉNathan MyersÔÚC++ Report 1995ÄêJune·¢±íµÄ[[http://www.cantrip.org/traits.html][¡¶Traits:a new and useful template technique¡·]]ÖÐ×îÐÂÌá³öµÄ¡£
  TraitÀà±£´æһЩӳÉä¹Øϵ£¬½«Ò»Ð©¸ÅÄîÓ³Éäµ½ÁíһЩÉÏÈ¥¡£Äã¿ÉÒÔ´ÓÒÔ϶«Î÷·¢³öÓ³Éä:
  - ÀàÐÍTypes
  - ±àÒëÆÚ¼äÒÑÖªµÀµÄÖµ(ÀýÈç³£Êý)
  - ÉÏÊöÁ½ÕßµÄTuples
  - ÉÏÊöµÄTuples

  ²¢ÇÒ¿ÉÒÔÓ³Éäµ½¼¸ºõËùÓÐÄãÏëÒªµÄ£¨ÀàÐÍ£¬³£Êý£¬ÔËÐÐÆÚ¼ä±äÁ¿£¬º¯Êý)¡£

**** 1.8.1 Àý×Ó: average()
  ¿¼ÂÇÏÂÃæµÄ´úÂ룬Ëü¼ÆËãÒ»¸öÊý×éµÄƽ¾ùÖµ:

<source lang="C">
template<class T>
T average(const*T data,int numElements)
{
  T sum=0;
  for (int i=0;i<numElements;++i)
      sum+=data[i];
  return sum/numElements;
}

</source>

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 - TÊÇÒ»¸ö×Ö·û:ÇóºÍ²Ù×÷»áÒç³ö¡£

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