一个测试

在OJ上进行了测试，选取的题目是 \(\text{FFT}\)多项式乘法

• 读入优化(只测试了普通cin/解绑cin/fastio)

  • 不开O2

    \(cin/cout\) \(5400ms\)

    洛谷上抄的\(cin/cout\) \(5026ms\)

    解绑的\(cin/cout\) \(4980ms\)

    \(wkh2008\)的\(qcin/qcout\) \(4962ms\)

    \(joke3579\)的\(cin/cout\) \(4835ms\)

  • 开\(O2\)

    \(cin/cout\) \(2231ms\)

    洛谷上抄的\(cin/cout\) \(1520ms\)

    解绑的\(cin/cout\) \(1813ms\)

    \(whk2008\)的\(qcin/qcout\) \(1455ms\)

    \(joke3579\)的\(cin/cout\) \(1431ms\)

• FFT在\(O2\)和非\(O2\)环境下的差距(均使用\(FastIO\))

  • 不开O2

    \(4835ms\)

  • 开O2

    \(1431ms\)

• \(register\)(均使用O2环境与fastio)

  • 不加\(register\)

    \(1431ms\)

  • 加\(register\)

    \(1403ms\)

• 手写复数和\(STL\)复数(均使用\(O2\)环境与\(FastIO\),\(register\))

  • 手写

    1403ms

  • STL自带

    1515ms

本文使用的代码Fastio如下

• 洛谷上抄来的

  namespace Fast_I {char *_Buf, *_Start_ptr, *_End_ptr;std::streambuf* inbuf;unsigned int Size;bool _Ok;struct Fast_Istream {operator bool(){return _Ok; }Fast_Istream(std::streambuf*, unsigned int);Fast_Istream(unsigned int);Fast_Istream(const char*, unsigned int);Fast_Istream& operator>>(char&);Fast_Istream& operator>>(char*);Fast_Istream& operator>>(bool&);Fast_Istream& operator>>(short&);Fast_Istream& operator>>(int&);Fast_Istream& operator>>(long&);Fast_Istream& operator>>(long long&);Fast_Istream& operator>>(unsigned short&);Fast_Istream& operator>>(unsigned int&);Fast_Istream& operator>>(unsigned long&);Fast_Istream& operator>>(unsigned long long&);Fast_Istream& operator>>(float&);Fast_Istream& operator>>(double&);Fast_Istream& operator>>(long double&);Fast_Istream& operator>>(std::string&);template <typename Typex>void operator()(Typex& _Val) { *this >> _Val; }template <typename Typex, typename... More>void operator()(Typex&, More&...);std::streambuf* rdbuf() { return inbuf; }void rdbuf(std::streambuf* _inbuf) { inbuf = _inbuf; }void rdbuf(const char*);void pop();char peek();};}
  namespace Fast_O {std::string buf;std::streambuf* outbuf;struct Fast_Ostream {Fast_Ostream(std::streambuf*, unsigned int);Fast_Ostream(std::streambuf* out) { outbuf = out; }Fast_Ostream(const char*, unsigned int);Fast_Ostream(unsigned int);void flush();~Fast_Ostream();void endl() { buf.push_back('\n'); }template <typename Typex>void endl(const Typex& _Val);template <typename Typex, typename... More>void endl(const Typex&, const More&...);template <typename Typex>void operator()(const Typex& _Val);template <typename Typex, typename... More>void operator()(const Typex&, const More&...);Fast_Ostream& operator<<(char);Fast_Ostream& operator<<(const char*);Fast_Ostream& operator<<(const std::string&);Fast_Ostream& operator<<(bool);Fast_Ostream& operator<<(short);Fast_Ostream& operator<<(int);Fast_Ostream& operator<<(long);Fast_Ostream& operator<<(long long);Fast_Ostream& operator<<(unsigned short);Fast_Ostream& operator<<(unsigned int);Fast_Ostream& operator<<(unsigned long);Fast_Ostream& operator<<(unsigned long long);std::streambuf* rdbuf() { return outbuf; }void rdbuf(std::streambuf* _outbuf) { outbuf = _outbuf; }void rdbuf(const char*);};}
  namespace Fast_IO {Fast_I::Fast_Istream fin(std::cin.rdbuf(), 1048576);Fast_O::Fast_Ostream fout(std::cout.rdbuf()); }
  #define cin Fast_IO::fin
  #define cout Fast_IO::fout
  namespace Fast_I {Fast_Istream::Fast_Istream(std::streambuf* in, unsigned int Sz) {_Ok = 1;Fast_I::Size = Sz;inbuf = in;_Start_ptr = _End_ptr = _Buf = new char[Sz];}Fast_Istream::Fast_Istream(const char* in, unsigned int Sz) {_Ok = 1;Fast_I::Size = Sz;rdbuf(in);_Start_ptr = _End_ptr = _Buf = new char[Sz];}Fast_Istream::Fast_Istream(unsigned int Sz) {_Ok = 1;Fast_I::Size = Sz;_Start_ptr = _End_ptr = _Buf = new char[Sz];}void Fast_Istream::rdbuf(const char* File) {static std::ifstream __In__(File);rdbuf(__In__.rdbuf());}void Get_Char(char& _Val) {if (_Start_ptr == _End_ptr) {_Start_ptr = _Buf;_End_ptr = _Buf + inbuf->sgetn(_Buf, Size);}if (_Start_ptr == _End_ptr) {_Val = -1;_Ok = 0;} else {_Val = *_Start_ptr++;}}Fast_Istream& Fast_Istream::operator>>(char& _Val) {if(_Ok){Get_Char(_Val);while (_Val == 32 || _Val == 10 || _Val == 13 || _Val == 8 || _Val == 9 || _Val == 7 || _Val == 12 || _Val == 11) {Get_Char(_Val);}}return *this;}Fast_Istream& Fast_Istream::operator>>(char* _Val) {if (_Ok) {Get_Char(*_Val);while (*_Val == 32 || *_Val == 10 || *_Val == 13 || *_Val == 8 ||*_Val == 9 || *_Val == 7 || *_Val == 12 || *_Val == 11) {Get_Char(*_Val);}while (*_Val != 32 && *_Val != 10 && *_Val && *_Val != -1 && *_Val != 9 &&*_Val != 11 && *_Val != 12) {Get_Char(*++_Val);}*_Val = 0;--_Start_ptr;}return *this;}Fast_Istream& Fast_Istream::operator>>(std::string& _Val) {if (_Ok) {char c;Get_Char(c);while (c == 32 || c == 10 || c == 13 || c == 8 || c == 9 || c == 7 ||c == 12 || c == 11) {Get_Char(c);}for (_Val.clear();c != 32 && c != 10 && c && c != -1 && c != 9 && c != 11 && c != 12;Get_Char(c)) {_Val.push_back(c);}--_Start_ptr;}return *this;}template <typename Typex>void Get_Int(Typex& _Val) {if (_Ok) {char ch;bool _F = 0;for (Get_Char(ch); (ch < 48 || ch > 57) && ch != -1; Get_Char(ch)) {_F = ch == 45;}for (_Val = 0; ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val = _Val * 10 + (ch ^ 48);}if (_F) {_Val = ~_Val + 1;}--_Start_ptr;}}template <typename Typex>void Get_Unsigned(Typex& _Val) {if (_Ok) {char ch;Get_Char(ch);while ((ch < 48 || ch > 57) && ch != -1) {Get_Char(ch);}for (_Val = 0; ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val = _Val * 10 + (ch ^ 48);}--_Start_ptr;}}template <typename Typex>void Get_Double(Typex& _Val) {if(_Ok){char ch;bool _F = 0;for (Get_Char(ch); (ch < 48 || ch > 57) && ch != -1; Get_Char(ch)) {_F = ch == 45;}for (_Val = 0; ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val = _Val * 10 + (ch ^ 48);}if (ch == 46) {unsigned long long _Pow = 1;for (Get_Char(ch); ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val += Typex((ch ^ 48) * 1.0 / (_Pow *= 10));}}if (_F) {_Val = -_Val;}--_Start_ptr;}}Fast_Istream& Fast_Istream::operator>>(bool& _Val) {if(_Ok){char ch;Get_Char(ch);while (ch == 32 || ch == 10 || ch == 13 || ch == 8 || ch == 9 || ch == 7 ||ch == 12 || ch == 11) {Get_Char(ch);}while (ch != 32 && ch != 10 && ch && ch != -1 && ch != 9 && ch != 11 &&ch != 12) {_Val |= ch != 48;Get_Char(ch);}--_Start_ptr;}return *this;}Fast_Istream& Fast_Istream::operator>>(short& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(int& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(long& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(long long& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned short& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned int& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned long& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned long long& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(float& _Val) {Get_Double(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(double& _Val) {Get_Double(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(long double& _Val) {Get_Double(_Val);return *this;}template <typename Typex, typename... More>void Fast_Istream::operator()(Typex& _Val, More&... _More) {*this >> _Val;operator()(_More...);}void Fast_Istream::pop() {char ch;Get_Char(ch);}char Fast_Istream::peek() {if (_Start_ptr == _End_ptr) {_Start_ptr = _Buf;_End_ptr = _Buf + inbuf->sgetn(_Buf, Size);}if (_Start_ptr == _End_ptr) {_Ok = 0;return -1;} else {return *_Start_ptr;}}}
  namespace Fast_O {Fast_Ostream::Fast_Ostream(std::streambuf* out, unsigned int Size) {buf.reserve(Size);outbuf = out;}Fast_Ostream::Fast_Ostream(const char* File, unsigned int Size) {buf.reserve(Size);rdbuf(File);}void Fast_Ostream::rdbuf(const char* File) {static std::ofstream __Out__(File);rdbuf(__Out__.rdbuf());}Fast_Ostream::Fast_Ostream(unsigned int Size) {buf.reserve(Size);}void Fast_Ostream::flush() {outbuf->sputn(buf.data(), buf.size());buf.clear();}Fast_Ostream::~Fast_Ostream() {flush();}Fast_Ostream& Fast_Ostream::operator<<(char _Val) {buf.push_back(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(const char* _Val) {while (*_Val) {buf.push_back(*_Val++);}return *this;}Fast_Ostream& Fast_Ostream::operator<<(const std::string& _Val) {for (auto&& i : _Val) {buf.push_back(i);}return *this;}template <typename Typex>void Put_Unsigned(Typex _Val) {char* _Stack = (char*)malloc(sizeof(Typex) * 3);unsigned S_top = 0;while (_Val) {_Stack[++S_top] = (_Val % 10) ^ 48;_Val /= 10;}if (!S_top) {buf.push_back('0');}while (S_top) {buf.push_back(_Stack[S_top--]);}free(_Stack);}void Put_Int(long long _Val) {if (_Val < 0) {buf.push_back('-');Put_Unsigned(~_Val + 1);} else {Put_Unsigned(_Val);}}Fast_Ostream& Fast_Ostream::operator<<(bool _Val) {buf.push_back(_Val ? '1' : '0');return *this;}Fast_Ostream& Fast_Ostream::operator<<(short _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(int _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(long _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(long long _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned short _Val) {Put_Unsigned(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned int _Val) {Put_Unsigned(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned long _Val) {Put_Unsigned(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned long long _Val) {Put_Unsigned(_Val);return *this;}template <typename Typex>void Fast_Ostream::endl(const Typex& _Val) {*this << _Val << '\n';}template <typename Typex, typename... More>void Fast_Ostream::endl(const Typex& _Val, const More&... _More) {*this << _Val;endl(_More...);}template <typename Typex>void Fast_Ostream::operator()(const Typex& _Val) {*this << _Val;}template <typename Typex, typename... More>void Fast_Ostream::operator()(const Typex& _Val, const More&... _More) {*this << _Val;operator()(_More...);}}
  

• wkh2008的fastio

  #define LOCAL
  namespace IO {
  #ifdef LOCAL
  FILE *Fin(fopen("d.in", "r")), *Fout(fopen("d.out", "w"));
  #else
  FILE *Fin(stdin), *Fout(stdout);
  #endif
  class qistream {static const size_t SIZE=1<<16,BLOCK=32;FILE*fp;char buf[SIZE];int p;public:qistream(FILE *_fp=stdin ):fp(_fp),p(0){fread(buf+p,1,SIZE-p,fp);}void flush(){memmove(buf, buf +p,SIZE-p),fread(buf+SIZE-p,1,p,fp),p=0;} qistream &operator>>(char &str){str = getch();while(isspace(str))str = getch();return*this;} template<class T>qistream &operator>>(T &x){x=0;p+BLOCK>=SIZE?flush():void();bool flag=false;for(;!isdigit(buf[p]);++p)flag=buf[p]=='-';for(;isdigit(buf[p]);++p)x=(x<<3)+(x<<1)+buf[p]-'0';x=flag?-x:x;return*this;}char getch(){return buf[p++];}qistream &operator>>(char*str){char ch=getch();while(ch<=' ')ch=getch();int i;for(i=0;ch>' '; ++i,ch=getch())str[i] = ch;str[i] = '\0';return*this;}}qcin(Fin);
  class qostream {static const size_t SIZE=1<<16,BLOCK=32;FILE*fp;char buf[SIZE];int p;public:qostream(FILE *_fp=stdout):fp(_fp),p(0){}~qostream(){fwrite(buf,1,p,fp);}void flush(){fwrite(buf, 1,p,fp),p=0;}template<class T>qostream &operator<<(T x){int len=0;p+BLOCK>=SIZE?flush():void();x<0?(x=-x,buf[p++]='-'):0;do buf[p+len]=x%10+'0',x/=10,++len;while (x);for(int i=0,j=len-1;i<j;++i,--j)swap(buf[p+i],buf[p+j]);p+=len;return*this;}qostream&operator<<(char x){putch(x);return*this;}void putch(char ch){p+BLOCK>=SIZE?flush():void();buf[p++]=ch;}qostream &operator<<(char*str){for(int i=0;str[i];++i)putch(str[i]);return*this;}} qcout(Fout);}using namespace IO;
  #define cin qcin
  #define cout qcout
  

• joke3579的fastio

  namespace Fread{const int SIZE = (1 << 18);char buf[SIZE],*S,*T;inline char getchar() {if(S==T){T = (S = buf) + fread(buf,1,SIZE,stdin); if(S==T) return '\n';} return *S++;}}
  namespace Fwrite {const int SIZE = (1 << 18);char buf[SIZE],*S=buf,*T=buf+SIZE;inline void flush(){fwrite(buf,1,S-buf,stdout), S=buf;}inline void putchar(char c){*S++=c;if(S==T)flush();}struct NTR{ ~NTR() { flush(); }}ztr;}
  
  #ifdef ONLINE_JUDGE
  #define getchar Fread::getchar
  #define putchar Fwrite::putchar
  #endif
  namespace Fastio{
  	struct Reader{
  		template <typename T>
  		Reader&operator>>(T&x){char c=getchar();bool f=false;while (c<'0'||c>'9') { if(c == '-')f = true;c=getchar();}x=0;while(c>='0'&&c<='9'){x=(x<<1)+(x<<3)+(c^48);c=getchar();}if(f)x=-x;return *this;}
  		Reader&operator>>(double & x) {char c=getchar();short f=1,s=0;x=0;double t=0;while((c<'0'||c>'9')&&c!='.'){if(c=='-')f*=-1;c=getchar();}while(c>='0'&&c<='9'&&c!='.')x=x*10+(c^48),c=getchar();if(c=='.')c=getchar();else return x*=f,*this;while(c>='0'&&c<='9')t=t*10+(c^48),s++,c=getchar();while(s--)t/=10.0;x=(x+t)*f;return*this;}
  		Reader&operator>>(long double&x){char c=getchar();short f=1,s=0;x=0;long double t=0;while((c<'0'||c>'9')&&c!='.'){if(c=='-')f*=-1;c=getchar();}while(c>='0'&&c<='9'&&c!='.')x=x*10+(c^48),c=getchar();if(c=='.')c=getchar();else return x*=f,*this;while(c>='0'&&c<='9')t=t*10+(c^48),s++,c=getchar();while(s--)t/=10.0;x=(x+t)*f;return*this;}
  		Reader&operator>>(__float128&x){char c=getchar();short f=1,s=0;x=0;__float128 t=0;while((c<'0'||c>'9')&&c!='.'){if(c=='-')f*=-1;c=getchar();}while(c>='0'&&c<='9'&&c!='.')x=x*10+(c^48),c=getchar();if(c=='.') c = getchar();else return x*=f, *this;while(c>='0'&&c<='9')t=t*10+(c^48),s++,c=getchar();while(s--)t/=10.0;x=(x+t)*f;return *this;}
  		Reader&operator>>(char&c){c=getchar();while(c=='\n'||c==' '||c=='\r')c=getchar();return *this;}
  		Reader&operator>>(char*str){int len=0;char c=getchar();while(c=='\n'||c==' '||c=='\r')c=getchar();while(c!='\n'&&c!=' '&&c!='\r')str[len++]=c,c=getchar();str[len]='\0';return *this;}
  		Reader&operator>>(string&str){char c=getchar();str.clear();while(c=='\n'||c==' '||c=='\r')c=getchar();while(c!='\n'&&c!=' '&&c!='\r')str.push_back(c),c=getchar();return *this;}
  		template<class _Tp>
  		Reader&operator>>(vector<_Tp>&vec){for(unsigned i=0;i<vec.size();i++)cin>>vec[i];return *this;}
  		template<class _Tp,class _tp>
  		Reader&operator>>(pair<_Tp,_tp>&a){cin>>a.first>>a.second;return *this;}
  		Reader(){}
  	}cin;
  	struct Writer{
  	static const int set_precision = 6;
  	typedef int mxdouble;
  		template<typename T>
  		Writer&operator<<(T x){if(x==0)return putchar('0'),*this;if(x<0)putchar('-'),x=-x;static int sta[45];int top=0;while(x)sta[++top]=x%10,x/=10;while(top)putchar(sta[top]+'0'),--top;return*this;}
  		Writer&operator<<(double x){if(x<0)putchar('-'),x=-x;mxdouble _=x;x-=(double)_;static int sta[45];int top=0;while(_)sta[++top]=_%10,_/=10;if(!top)putchar('0');while(top)putchar(sta[top]+'0'),--top;putchar('.');for(int i=0;i<set_precision;i++)x*=10;_=x;while(_)sta[++top]=_%10,_/=10;for(int i=0;i<set_precision-top;i++)putchar('0');while(top)putchar(sta[top]+'0'),--top;return*this;}
  		Writer&operator<<(long double x){if(x<0)putchar('-'),x=-x;mxdouble _=x;x-=(long double)_;static int sta[45];int top=0;while(_)sta[++top]=_%10,_/=10;if(!top)putchar('0');while(top)putchar(sta[top]+'0'),--top;putchar('.');for(int i=0;i<set_precision;i++)x*=10;_=x;while(_)sta[++top]=_%10,_/=10;for(int i=0;i<set_precision-top;i++)putchar('0');while(top)putchar(sta[top]+'0'),--top;return*this;}
  		Writer&operator<<(__float128 x){if(x<0)putchar('-'),x=-x;mxdouble _=x;x-=(__float128)_;static int sta[45];int top=0;while(_)sta[++top]=_%10,_/=10;if(!top)putchar('0');while(top)putchar(sta[top]+'0'),--top;putchar('.');for(int i=0;i<set_precision;i++)x*=10;_=x;while(_)sta[++top]=_%10,_/=10;for(int i=0;i<set_precision-top;i++)putchar('0');while(top)putchar(sta[top]+'0'),--top;return*this;}
  		Writer&operator<<(char c){putchar(c);return*this;}
  		Writer& operator<<(char*str){int cur=0;while(str[cur])putchar(str[cur++]);return *this;}
  		Writer&operator<<(const char*str){int cur=0;while(str[cur])putchar(str[cur++]);return *this;}
  		Writer&operator<<(string str){int st=0,ed=str.size();while(st<ed) putchar(str[st++]);return *this;}
  		template<class _Tp>
  		Writer&operator<<(vector<_Tp>vec){for(unsigned i=0;i<vec.size()-1;i++)cout<<vec[i]<<" ";cout<<vec[vec.size()-1];return *this;}
  		template<class _Tp,class _tp>
  		Writer&operator<<(pair<_Tp,_tp>a){cout<<a.first<<" "<<a.second;return *this;}
  		Writer(){}
  	}cout;
  }
  #define cin Fastio :: cin
  #define cout Fastio :: cout
  

本文使用的FFT

void fft(Complex a[],int inv){
    for(int i=0;i<tot;i++)
        if(i<rev[i])
            swap(a[i],a[rev[i]]);
    for(int mid=1;mid<tot;mid<<=1){
        auto w1=Complex({cos(PI/mid),inv*sin(PI/mid)});
        for(int i=0;i<tot;i+=mid*2){
            auto wk=Complex({1,0});
            for(int j=0;j<mid;j++,wk=wk*w1){
                auto x=a[i+j],y=wk*a[i+j+mid];
                a[i+j]=x+y,a[i+j+mid]=x-y;
            }
        }
    }
}

本文使用的复数

struct Complex{
    double x,y;
    Complex operator+(const Complex&t)const{
        return {x+t.x , y+t.y};
    } 
    Complex operator-(const Complex&t)const{
        return {x-t.x,y-t.y};
    }
    Complex operator*(const Complex&t)const{
        return {x*t.x-y*t.y,x*t.y+y*t.x};
    }
}a[N],b[N];