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Windreamer Is Not a DREAMER
main(){main(puts("Hello,stranger!"));}

2006年3月21日

發(fā)件人: Andrei Alexandrescu (See Website For Email) ?
日期: 2006年3月18日(星期六) 下午12時13分
電子郵件: "Andrei Alexandrescu (See Website For Email)" <SeeWebsiteForEm...@erdani.org>
論壇: comp.lang.c++.moderated

The recent thread "Can GC be beneficial" was quite beneficial :o) - to
me at least. I've reached a number of conclusions that allow me to
better place the conciliation between garbage collection and
deterministic finalization in the language design space - in C++ and in
general.

The following discussion focuses on C++-centric considerations, with
occasional escapes into "the right thing to do if we could break away
with the past.

Basic Tenets, Constraints, and Desiderata
=========================================

Garbage collection is desirable because:

(1) It automates a routine and error-prone task

(2) Reduces client code

(3) Improves type safety

(3) Can improve performance, particularly in multithreaded environments

On the other hand, C++ idioms based on constructors and destructors,
including, but not limited to, scoped resource management, have shown to
be highly useful. The large applicability of such idioms might actually
be the single most important reason for which C++ programmers shy away
from migrating to a garbage-collected C++ environment.

It follows that a set of principled methods that reconcile C++-style
programming based on object lifetime, with garbage collection, would be
highly desirable for fully exploiting garbage collection's advantages
within C++. This article discusses the challenges and to suggests
possible designs to address the challenges.

The constraints include compatibility with existing C++ code and styles
of coding, a preference for type safety at least when it doesn't
adversely incur a performance hit, and the functioning of today's
garbage collection algorithms.

A Causal Design
===============

Claim #1: The lifetime management of objects of a class is a decision of
the class implementer, not of the class user.

In support of this claim we come with the following examples:

a) A class such as complex<double> is oblivious to destruction
timeliness because it does not allocate scarce resource that need timely
release;

b) A class such as string doesn't need to worry about destruction
timeliness within a GC (Garbage Collected) environment;

c) A class such as temporary_file does need to worry about destruction
timeliness because it allocates scarce resources that transcend both the
lifetime of the object (a file handle) and the lifetime of the program
(the file on disk that presumably temporary_file needs to delete after
usage).

In all of these examples, the context in which the objects are used is
largely irrelevant (barring ill-designed types that employ logical
coupling to do entirely different actions depending on their state).
There is, therefore, a strong argument that the implementer of a class
decides entirely what the destruction regime of the class shall be. This
claim will guide design considerations below.

We'll therefore assume a C++ extension that allows a class definition to
include its destruction regime:

?

// ?garbage?collected??
?
class?[collected]?Widget?{...};?
//?deterministically?destroyed??
?
class?[deterministic]?Midget?{...};?


?

These two possible choices could be naturally complemented by the other
allowed storage classes of a class:

?

// ?garbage?collected?or?on?stack??
??
class?[collected,?auto]?Widget?{...};?
//?deterministically?destroyed,?stack,?or?static?storage??
??
class?[deterministic,?auto,?static]?Midget?{...};?

It is illegal, however, that a class specifies both collected and
deterministic regime:

?

// ?illegal??
??
class?[collected,?deterministic]?Wrong?{...};?


?

Claim #2: Collected types cannot define a destruction-time action.

This proposal makes this claim in wake of negative experience with
Java's finalizers.

Claim #3: Collected types can transitively only embed fields of
collected types (or pointers thereof of any depth), and can only derive
from such types.

If a collected type would have a field of a non-collected type, that
type could not be destroyed (as per Claim #2).

If a collected type would have a field of pointer to a non-collected
type, one of two things happens:

a) A dangling pointer access might occur;

b) The resource is kept alive indeterminately and as such cannot be
destroyed (as per claim #2).

If a collected type would have a field of pointer to pointer to (notice
the double indirection) deterministic type, inevitably that pointer's
destination would have to be somehow accessible to the garbage-collected
object. This implies that at the some place in the points-to chain, a
"jump" must exist from the collected realm to the uncollected realm (be
it automatic, static, or deterministic) that would trigger either
post-destruction access, or would prevent the destructor to be called.

Design fork #1: Weak pointers could be supported. A collected type could
hold fields of type weak pointer to non-collected types. The weak
pointers are tracked and are zeroed automatically during destruction of
the resource that they point to. Further dereference attempts accesses
from the collected realm become hard errors.

Claim #4: Deterministic types must track all pointers to their
respective objects (via a precise mechanism such as reference counting
or reference linking).

If deterministic types did allow untracked pointer copying, then
post-destruction access via dangling pointers might occur. The recent
discussion in the thread "Can GC be beneficial" has shown that it is
undesirable to define post-destruction access, and it's best to leave it
as a hard run-time error.

Design branch #2: For type safety reasons, disallow type-erasing
conversions from/to pointers to deterministic types:

?

???
???class?[deterministic]?Widget?{...};?
???Widget?
*?p?=?new?Widget;?
???void?*?p1?=?p;?//?error??
???
p?=?static_cast<Widget?*>(p1);?//?error,?too?

Or: For compatibility reasons, allow type-erasing conversion and incur
the risk of dangling pointer access.

Design branch #3: For purpose of having a type that stands in as a
pointer to any deterministic type (a sort of "deterministic void*"), all
deterministic classes could be thought as (or required to) inherit a
class std::deterministic.

Design branch #3.1: std::deterministic may or may not define virtuals,
and as such confines or not all deterministic classes to have virtuals
(and be suitable for dynamic_cast among other things).

Claim #5: When an object of deterministic type is constructed in
automatic or static storage, its destructor will automatically issue a
hard error if there are any outstanding pointers to it (e.g., the
reference count is greater than one).

If that didn't happen, dangling accesses to expired stack variables
might occur:

?

?class?[deterministic]?Widget?{...};?
?Widget?
*?p;?
int?Fun()?{?
????Widget?w;?
????p?
=?&w;?
????
//?hard?runtime?error?upon?exiting?this?scope?



}
?



?

Discussion of the basic design
==============================

The desiderata set up and the constraints of the current C++ language
created a causal chain that narrowly guided the possible design of an
integrated garbage collection + deterministic destruction in C++:

* The class author decides whether the class is deterministic or garbage
collected

* As a natural extension, the class author can decide whether objects of
that type are allowed to sit on the stack or in static storage. (The
regime of automatic and static storage will be discussed below.)

* Depending on whether a type is deterministic versus collected, the
compiler generates different code for copying pointers to the object.
Basically the compiler automates usage of smart pointers, a
widely-followed semiautomatic discipline in C++.

* The heap is conceptually segregated into two realms. You can hold
unrestricted pointers to objects in the garbage-collected realm, but the
garbage-collected realm cannot hold pointers outside of itself.

* The operations allowed on pointers to deterministic objects are
restricted.

Regime of Automatic Storage
===========================

Claim 6: Pointers to either deterministic or collected objects that are
actually stack allocated should not escape the scope in which their
pointee object exists.

This obvious claim prompts a search in look for an efficient solution to
a class of problems. Here is an example:

?

?class?[auto,?collected]?Widget?{...};?
void?Midgetize(Widget?&?obj)?{?
????obj.Midgetize();?


}
?


void?Foo()?{?
????Widget?giantWidget;?
????Midgetize(giantWidget);?


}
?



?

To make the example above work, Foo is forced to heap-allocate the
Widget object even though the Midgetize function works on it
transitorily and stack allocation would suffice.

To address this problem a pointer/reference modifier, "auto", can be
defined. Its semantics allow only "downward copying": an
pointer/reference to auto can only be copied to lesser scope, never to
object of larger scope. Examples:

?

void?foo()?{?
????Widget?w;?
????Widget?
*auto?p1?=?&w1;?//?fine,?p1?has?lesser?scope?
????{?
??????Widget?
*auto?p2?=?&w;?//?fine?
??????p2?=?p1;?//?fine?
??????p1?=?p2;?//?error!?Escaping?assignment!?
????}
?



}
?



?

Then the example above can be made modularly typesafe and efficient like
this:

?

?class?[auto,?collected]?Widget?{...};?
void?Midgetize(Widget?&auto?obj)?{?
????obj.Midgetize();?


}
?


void?Foo()?{?
????Widget?giantWidget;?
????Midgetize(giantWidget);??
//?fine?


}
?


?

Claim #6: "auto"-modified pointers cannot be initialized or assigned
from heap-allocated deterministic objects.

If "auto"-modified pointers manipulated the reference count, their
efficiency advantage would be lost. If they didn't, a type-unsafe
situation can easily occur.

Does operator delete still exist?
=================================

For collected objects, delete is inoperant, as is for static or
automatic objects. On a heap-allocated deterministic object, delete can
simply check if the reference count is 1, and if so, reassign zero to
the pointer. If the reference count is greater than one, issue a hard ?
error.

Note that this makes delete entirely secure. There is no way to have a
working program that issues a dangling access after delete has been ?
invoked.

Regime of Static Storage
========================

Static storage has the peculiarity that it can easily engender
post-destruction access. This is because the order of module
initialization is not defined, and therefore cross-module dependencies
among objects of static duration are problematic.

This article delays discussion of the regime of static storage.
Hopefully with help from the community, a workable solution to the
cross-module initialization would ensue.

Templates
=========

Claim #7: The collection regime of any type must be accessible during
compilation to templated code.

Here's a simple question: is vector<T> deterministic or collected?

If it were collected, it couldn't hold deterministic types (because at
the end of the day vector<T> must embed a T*). If it were deterministic,
collected types couldn't hold vectors of pointers to collected types,
which would be a major and gratuitous restriction.

So the right answer is: vector<T> has the same regime as T.

?

template?<class?T,?class?A>?
class?[T::collection_regime]?vector?{?//?or?some?other?syntax?
???...?

}
;?


?

The New World: How Does it Look Like?
=====================================

After this design almost happening as a natural consequence of an
initial set of constraints, the natural question arises: how would
programs look like in a C++ with these amenities?

Below are some considerations:

* Pointer arithmetic, unions, and casts must be reconsidered (a source
of unsafety not thoroughly discussed)

* Most types would be [collected]. Only a minority of types, those that
manage non-memory resources, would live in the deterministic realm.

* Efficiency of the system will not degrade compared to today's C++. The
reduced need for reference-counted resources would allow free and fast
pointer copying for many objects; the minority that need care in
lifetime management will stay tracked by the compiler, the way they
likely were manipulated (by hand) anyway.

* Given that the compiler can apply advanced analysis to eliminate
reference count manipulation in many cases, it is likely that the
quality of built-in reference counting would be superior to
manually-implemented reference counting, and on a par with advanced
manual careful manipulation of a mix of raw and smart pointers.

----------------------

Whew! Please send any comments you have to this group. Thanks!

Andrei

? ? ? [ See http://www.gotw.ca/resources/clcm.htm for info about ]
? ? ? [ comp.lang.c++.moderated. ? ?First time posters: Do this! ]

posted @ 2006-03-21 10:01 Windreamer Is Not DREAMER 閱讀(634) | 評論 (1)編輯 收藏

2005年12月16日

Is it a mistake in TAOCP  
Maggie McLoughlin <mam@theory.stanford.edu> to Windreamer

Sequences with n=0 are empty. It's important in mathematics
to deal with empty sets and strings etc in a meaningful way.
If n = 0 and you're supposed to do something for 1 <= j <= n,
you don't have to do anything.

Thanks for your interest in my book! -- Don Knuth

呵呵,原來是我年少無知了,再次贊一下Knuth爺爺寫書的精致
posted @ 2005-12-16 10:05 Windreamer Is Not DREAMER 閱讀(595) | 評論 (1)編輯 收藏

2005年12月12日

要說的話好多,列個提綱先


TAOCP初讀感受

        《The Art of Computer Programming》的第一卷,大理石花紋的封皮,拿在手里沉甸甸的,這部書給我的第一印象就是這樣--"厚重"--帶有著神秘感和歷史感。

        其實這部書的中文版前言,我早就有幸拜讀過,不過和英文原文相比較,在中文翻譯的味道真的是差了很多,我覺得只有讀原文才能感到Knuth略帶詼諧的而又同是不是嚴謹?shù)娘L格,他寫文章的風格其實真的挺天馬行空的,從寫程序扯到做飯,從算法這個詞聊起,追著這個詞的來歷,竟然還帶出了萊布尼茨?真暈,開句玩笑,Knuth絕對是那種老頑童型的人物,他這本書達到如此厚度估計此類"廢話"功不可沒。

        從Algorithm到Euclid's Algorithm也就是我們熟悉的輾轉相除求最大公約數(shù)法,我這個算法小白開始進入了他打開的算法世界......

        Knuth行文很喜歡比較、比喻、對比,這讓讀者看起來很輕松愉悅,不過當他真的玩起數(shù)學來,我就有點吃不消了,最后面對算法的一個形式化描述,消耗了我不少精力,不過目前看來還是大致明白了

         總之,這本盛名之下的書,也的確有很多獨到的地方,作為計算機科學領域的史詩,它給我的第一印象的確很棒。希望我能堅持著看下去,從中吸收營養(yǎng)。




今天的收獲

           雖然只看了一節(jié),不過也消耗了我不少的時間和精力(看來別的一些事情也不能太耽誤,也要抓緊了)

            今天的收獲很多,首先對算法這個名詞有了更多一些的感性認識,Knuth提出的“有限、明確定義、有輸入、有輸出、有效率”這幾個原則總結得真是不錯,尤其最前面的兩點和效率問題,往往構成了很多復雜的問題,著名的圖靈機停機問題大概就是在說這個問題吧……

            另外對于輾轉相除法的一些數(shù)學上的推導也給了我不錯的感覺,雖然書上沒有明確的給一個嚴格的證明,但是根據(jù)他的敘述我馬上就體會到了用比較嚴格的方法如何寫這個證明,以及這個證明的關鍵點(我覺得證明中其實用到了通過雙包含來爭相等的手法,這個是關鍵)

            算法的形式化描述應起了我大的興趣,回來的路上想,貌似這個好像形成了某種數(shù)學結構,而其上的f映射,構成了某種代數(shù)結構,沒有仔細想過,不過好像是這樣子的哦,我覺得貌似算法的本質就是某種自動狀態(tài)機,只不過不一定是有限狀態(tài)的吧,至少從他的意思上看是這樣的

            開始沒有理解第二個,加上了效率約束的的形式化表達方法的意思,后來花了點時間看了下Ex1.1.8,我覺得我似乎明白了點

我認為Ex1.1.8是這樣的一個狀態(tài)表

            

j Theta_j Phi_j a_j b_j
0 a a 5 1
1 ab c 3 2
2 bc cb 1 2
3 b a 4 3
4 c b 0 4
5 c c 5 5

        為了驗證,我寫了個簡單的程序來試驗我的狀態(tài)表(真是不行了,好多東西要翻看手冊,寫程序的速度總是上不來)

 1#include    <iostream>
 2#include    <string>
 3
 4using namespace std;
 5int main ( int argc, char *argv[] )
 6{
 7    //                   0,     1,     2,     3,     4,     5
 8    string theta[]={   "a",  "ab",  "cb",      "b",   "c",   "c"};
 9    string phi  []={   "a",   "c",  "bc",    "a",   "b",   "c"};
10    int    a    []={     5,     3,     1,     4,     0,     5};
11    int    b    []={     1,     2,     2,     3,     4,     5};
12
13    int j=0;
14    int i=0;
15    string stat;
16    getline (cin,stat);
17    while(true)
18    {
19        unsigned int loc=stat.find(theta[j],0);
20        if (loc==string::npos)
21        {
22            j=a[j];
23        }

24        else
25        {
26            string temp=stat.substr(0,loc)+phi[j]+stat.substr(loc+theta[j].length());
27            stat=temp;
28            j=b[j];
29        }

30        cout<<i++<<":\tj("<<j<<")\tloc("<<loc<<")\t"<<stat<<endl;
31        cin.get();
32    }

33    return EXIT_SUCCESS;
34}
                /* ----------  end of function main  ---------- */
35


         最后一定要提的是,我好像發(fā)現(xiàn)了書里的一處小Bug,而且好像官方網站里的Errata里面沒有這個(中文版同樣有這個問題),我已經寫信給Knuth了,希望我是真的找到了一個沒人發(fā)現(xiàn)的Bug啊(其實我知道這個不可能)




關于Galgo庫的"瞎想"

         念叨做一個泛型的算法庫已經有好長時間了,我覺得這個事情與其一直這么YY,還不如高興了就寫一點,不高興,就扔著,

         其實,這個世界是不缺泛型算法庫的,STL,Boost,Blitz++中的泛型算法很全面了,我的計劃是把他們中間缺少的部分補起來,不能互操作的地方粘合起來,再有就是增加對MetaProgramming的支持
         呵呵,應該還算是一個比較雄偉的計劃吧
         我希望這套庫能盡可能的高效率、容易使用、同事保證安全,理想的境地是能夠代替ACM集訓隊使用的模塊

         目前我的設想是整個庫放在Galgo這個namespace里,這個namespace分為兩個子namespace,分別是泛型算法Generic和元編程算法Meta

          我覺得這樣一個庫的建立與維護,任重而道遠不說,沒準前人已經作過360遍了,不過沒關系,權當娛樂了。



First Step——Euclid GCD的一個實現(xiàn)


           不說什么廢話了,先貼代碼:
 1//-------------------------------BEGIN:GAlgo_Euclid_GCD.hpp--------------------------//
 2#ifndef _GAlgo_Euclid_GCD_H_
 3#define _GAlgo_Euclid_GCD_H_
 4namespace GAlgo
 5{
 6    namespace Generic
 7    {
 8        template <typename T>
 9        T Euclid_GCD(const T& a,const T& b)
10        {
11            return ((a%b)==0)?b:Euclid_GCD(b,a%b);
12        }

13    }

14    namespace Meta
15    {
16        template <int A,int B>
17        struct Euclid_GCD
18        {
19            static const int value=Euclid_GCD<B,A%B>::value;
20        }
;
21
22        template <int A>
23        struct Euclid_GCD<A,0>
24        {
25            static const int value=A;
26        }
;
27    }

28}

29#endif
30
31//-------------------------------END:GAlgo_Euclid_GCD.hpp--------------------------//

         應該沒什么好說的,比較中規(guī)中矩,常規(guī)手法,不過根據(jù)TAOCP上的說法,可能在某些m,n的取值上需要很多重的遞歸這時候Meta的方法可能會遇到困難(其實第一種也有運行時堆棧溢出的危險),所以說……說什么好呢,就這樣了

下面是個簡單的測試
 1#include "GAlgo_Euclid_GCD.hpp" 
 2#include <iostream>
 3using namespace std;
 4int main()
 5{
 6    cout<<GAlgo::Generic::Euclid_GCD(6,9)<<endl;
 7    cout<<GAlgo::Meta::Euclid_GCD<6,9>::value<<endl;
 8    return 0;
 9}

10



個人覺得今后有研究價值的方向

         我覺得對于算法描述和圖靈機、有限狀態(tài)機、以及隱隱約約我看到的馬爾科夫的某些工作(馬爾科夫鏈)之間的關系深入挖掘一下應該會有不少收獲,那個我對這個問題可能會有一個數(shù)學結構的猜想估計也可能可以在這個方向上證實或證偽……
         突然想去向偶像黃兆鎮(zhèn)請教一下……還是等我把膽子先練大再去吧……
posted @ 2005-12-12 21:48 Windreamer Is Not DREAMER 閱讀(1467) | 評論 (4)編輯 收藏

2005年12月10日

終于無聊到來寫書評,最近的項目一直都沒和C++有什么關系,不過看的書卻都是C++方面的,而最近看到的幾本書中感覺最好的莫過于這本《C++ Templates》

Nicolai M. Josuttis的書我很喜歡,從他的那本《The C++ Standard Template Library》就看出了他很多獨特的風格,令我愛不釋手,所以這本《C++ Template》   也進入了我的必看書單。粗讀之后,感覺整本書絕對將成為C++泛型領域的圣經級著作

  1. 這本書角度選得很好,全書分三個部分,分別介紹模板基礎、模版的編譯器實現(xiàn)、模板的高級技巧,三個部分相輔相成、相互照應,由淺入深而又自然而然,還方便分開閱讀(比如我就重點看了第一第三部分,模版實現(xiàn)被我略過了)卻又全面覆蓋了這一領域
  2. 這本書英文很淺顯(比《Modern C++ Design》淺顯了不知多少倍),語言嚴謹而又不晦澀,尤其要贊的就是廢話尤其地少!
  3. 章節(jié)安排很合理,很方別作為工具書應急查閱(《C++STL》就有這個優(yōu)點,與這本書科學家+工程師的組合不無關系)
  4. 書中好多技術,我是聞所未聞,驚為天人,尤其第三部分,可以算得上眼花繚亂,而且給出的實現(xiàn)感覺既符合標準、實用、而且沒有炫技的成分

同類書籍據(jù)我所知沒有可以達到這個高度的,大部分C++泛型方面的專著只局限于怎么用STL,將模板基礎的書,也僅限于最表面的語法,像模版參數(shù)推導這種問題鮮有涉及,更不用提關于Metaprogramming,這本書圣經的地位估計后人也是難以企及了。

下面是我看書時畫下來的一些覺得自己平時應該注意的地方,放在這里做備忘好了

  1. (P12) [Argument Deducion] If we pass two ints to the parameter type T const&  the C++ compiler must conclude that T must be int. Note that no automatic type conversion is allowed here,Each T must match exactly.

    template <typename T>
    inline T 
    const& max (T const& a,T const& b);

    max(
    4,7)//OK:T is int for both arguments
    max(4,4.2)//ERROR:first T is int,second T is double

  2. (P13)[Template Parameters] In function templates(unlike class template) no default template arguments can be specified
  3. (P14)[Template Parameters]Deducation can be seen as part of  overlaod resolution-a process tha is not based on selection of return type either.The sole exception is the return type of conversion operator members.
  4. (P18)[Overloading Function Template] The fact that not all overloaded functions are visible when a corresponding function call is made may or may not matter.
  5. (P39)[Nontype Function Template Parameters] Function templates are considered to name a set of overloaded function.However,according to the current standard,sets of overload functions cannot be used for template parameter deducation.Thus you have to cast to the exactly type of the function template arguments

    template <typename T,int VAL>
    T addValue (T 
    const& x)
    {
        
    return x+VAL
    }


    std::transform(source.begin(),source.end(),
    //start and end of source
    dest.begin(),//start of destination
    (int(*)(int  const&))addValue<int,5>);//operation

  6. (P40)[Restrictions for Nontype Template Parameters] 太長了,略過
  7. (P44)[The .template Construct]

    template <int N>
    void printBitset (std::bitset<N> const& bs)
    {
        std::cout
    <<bs.to_string<char,char_traits<char>,allacator<char> >();//ERROR:can't recogonize the template
    }


    template 
    <int N>
    void printBitset (std::bitset<N> const& bs)
    {
        std::cout
    <<bs.template to_string<char,char_traits<char>,allacator<char> >();//OK
    }

  8. (P45)[Using this->]

    template <typename T>
    class Base
    {
    public:
        
    void bar();
    }
    ;

    template 
    <typename T>
    class Derived : Base<T>
    {
    public:
        
    void foo()
        
    {
            bar();
    //call external bar() or error
        }

    }


    template 
    <typename T>
    class Derived : Base<T>
    {
    public:
        
    void foo()
        
    {
            
    this->bar();//OK
        }

    }

  9. 同樣精彩的還有(P57)[Using String Literals as Arguments for Function Templates]
  10. 令我驚異的SFINE技術(substitution-failure-is-not-an-error)

    template <typename T>
    class IsClassT
    {
    private:
        typedef 
    char One;
        typedef 
    struct {char a[2];} Two;
        template 
    <typename C> static One test (int::C*);
        template 
    <typename C> static Two test();
    public:
        
    enum {Yes=sizeof(IsClassT<T>::test<T>(0))==1};
        
    enum {No=!Yes};
    }
    ;

總而言之,此書帶給了我前所未有的閱讀享受......我今年震撼大獎一定會投它一票
posted @ 2005-12-10 12:36 Windreamer Is Not DREAMER 閱讀(652) | 評論 (3)編輯 收藏

2005年12月5日

主要喜歡他的語法著色功能,真的很方便,RSS等方面的功能也很全面......

測試一下:

//////////////////////////////
//Prime.cpp
//////////////////////////////

template
<int Val>
struct IntType
{
 
const static int value = Val ;
}
;
template
<bool flag, typename T, typename U>
struct Select
{
 typedef T Result;
}
;

template
<typename T, typename U>
struct Select<false, T, U>
{
 typedef U Result;
}
;
template 
<unsigned int N,unsigned int x>
struct FindRoot
{
 
const static int value=Select<(N/x)==x||((N/x+x)/2==x),IntType<x>,FindRoot<N,(N/x+x)/2> >::Result::value;
}
;

template 
<unsigned int N>
struct Sqrt
{
 
const static int value=FindRoot<N,N/2>::value;
}
;

template 
<>
struct Sqrt<0> ;

template 
<int N,int divider>
struct TestPrime
{
 
const static int value=Select<(N%divider)==0,IntType<0>,TestPrime<N,divider-1> >::Result::value;
}
;

template 
<int N>
struct TestPrime<N,1>
{
 
const static int value=1;
}
;

template 
<unsigned int N>
struct IsPrime
{
 
const static int value=TestPrime<N,Sqrt<N>::value+1>::value;
}
;

template 
<>
struct IsPrime<2>
{
 
const static int value=1;
}
;

template 
<>
struct IsPrime<1>;

int printf(const char*,);

int main()
{
 
const int yes=IsPrime<123127>::value;
 printf(
"%d\n",yes);
}

posted @ 2005-12-05 09:45 Windreamer Is Not DREAMER 閱讀(391) | 評論 (1)編輯 收藏
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