?? bigint.h
字號:
#ifndef BIGINT_H
#define BIGINT_H
#include <iostream.h>
#include <stdlib.h>
static const unsigned int PrimeTable[302]=
{ 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
37, 41, 43, 47, 53, 59, 61, 67, 71, 73,
79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
131, 137, 139, 149, 151, 157, 163, 167, 173, 179,
181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
239, 241, 251, 257, 263, 269, 271, 277, 281, 283,
293, 307, 311, 313, 317, 331, 337, 347, 349, 353,
359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
421, 431, 433, 439, 443, 449, 457, 461, 463, 467,
479, 487, 491, 499, 503, 509, 521, 523, 541, 547,
557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
613, 617, 619, 631, 641, 643, 647, 653, 659, 661,
673, 677, 683, 691, 701, 709, 719, 727, 733, 739,
743, 751, 757, 761, 769, 773, 787, 797, 809, 811,
821, 823, 827, 829, 839, 853, 857, 859, 863, 877,
881, 883, 887, 907, 911, 919, 929, 937, 941, 947,
953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019,
1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,
1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153,
1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229,
1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297,
1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381,
1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453,
1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523,
1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597,
1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663,
1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741,
1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823,
1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901,
1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993,
1997, 1999};
class BigInt
{
unsigned int a[64];
int length;
friend ostream& operator << (ostream&,const BigInt&);
public:
BigInt();
BigInt(const unsigned int&);
BigInt(const BigInt&);
BigInt(unsigned char *,int);
int Length() {return length;}
unsigned int operator [](int i) {return a[i];}
BigInt& operator = (const BigInt&);
BigInt& operator = (const unsigned int&);
bool operator < (const BigInt&);
bool operator == (const unsigned int&);
BigInt operator - (const BigInt&);
BigInt operator - (const unsigned int&);
BigInt& operator += (const BigInt&);
BigInt& operator += (const unsigned int&);
BigInt operator * (const BigInt&);
BigInt operator * (const unsigned int&);
BigInt& operator <<= (const unsigned int&);
BigInt operator >> (const unsigned int&);
BigInt operator % (BigInt&);
unsigned int operator % (const unsigned int&);
BigInt DIV(BigInt&,BigInt&);
BigInt PowerMod(const BigInt&,BigInt&);
void GetRand(const unsigned int&);
bool IsPrime();
void GetPrime(const unsigned int&);
BigInt Euc(BigInt&,BigInt&);
};
inline BigInt::BigInt()
{
length=0;
}
inline BigInt::BigInt(const unsigned int& X)
{
if(X)
{
length=1;
a[0]=X;
}
else length=0;
}
inline BigInt::BigInt(const BigInt& X)
{
length=X.length;
for(int i=0;i<length;i++)
a[i]=X.a[i];
}
inline BigInt::BigInt(unsigned char *c,int len)
{
length=len>>2;
int pad=len&0x3,i=0,j=length-1;
if(pad)
{
length++;
a[length-1]=0;
while(pad)
{
a[length-1]<<=8;
a[length-1]|=c[i];
i++;
pad--;
}
}
for(;j>=0;j--,i+=4)
a[j]=((unsigned int)c[i]<<24)|((unsigned int)c[i+1]<<16)|((unsigned int)c[i+2]<<8)|(unsigned int)c[i+3];
}
inline BigInt& BigInt::operator = (const BigInt& X)
{
length=X.length;
for(int i=0;i<length;i++)
a[i]=X.a[i];
return *this;
}
inline BigInt& BigInt::operator = (const unsigned int& X)
{
if(X)
{
length=1;
a[0]=X;
}
else length=0;
return *this;
}
inline bool BigInt::operator < (const BigInt& X)
{
if(length<X.length) return true;
if(length>X.length) return false;
for(int i=length-1;i>=0;i--)
if(a[i]<X.a[i]) return true;
else if(a[i]>X.a[i]) return false;
return false;
}
inline bool BigInt::operator == (const unsigned int& X)
{
return (length==1 && X==a[0]) || (length==0 && X==0);
}
inline BigInt BigInt::operator - (const BigInt& X)
{
int borrow=0,i;
BigInt M=*this;
for(i=0;i<X.length;i++)
if(a[i]<X.a[i]+borrow)
{
M.a[i]+=((unsigned _int64)1<<32)-X.a[i]-borrow;
borrow=1;
}
else
{
M.a[i]-=X.a[i]+borrow;
borrow=0;
}
while(borrow)
{
if(M.a[i]==0)
M.a[i]=0xffffffff;
else
{
M.a[i]--;
borrow=0;
}
i++;
}
while(M.length && M.a[M.length-1]==0) M.length--;
return M;
}
inline BigInt BigInt::operator - (const unsigned int& X)
{
BigInt M=*this;
if(M.a[0]<X)
{
M.a[0]+=((unsigned int)1<<32)-X;
int i=1;
while(M.a[i]==0)
{
M.a[i]=0xffffffff;
i++;
}
M.a[i]--;
}
else M.a[0]-=X;
if(M.a[length-1]==0) M.length--;
return M;
}
inline BigInt& BigInt::operator += (const BigInt& X)
{
BigInt M;
unsigned _int64 temp;
int carry=0,i;
if(length<X.length)
{
M=*this;
*this=X;
}
else M=X;
for(i=0;i<M.length;i++)
{
temp=(unsigned _int64)a[i]+M.a[i]+carry;
a[i]=temp;
carry=temp>>32;
}
while(carry && i<length)
{
temp=(unsigned _int64)a[i]+carry;
a[i]=temp;
carry=temp>>32;
i++;
}
if(carry)
{
a[length]=1;
length++;
}
return *this;
}
inline BigInt& BigInt::operator += (const unsigned int& X)
{
if(length)
{
unsigned _int64 temp=a[0];
temp+=X;
a[0]=temp;
if(temp>0xffffffff)
{
int carry=1,i=1;
while(i<length && a[i]==0xffffffff)
{
a[i]=0;
i++;
}
if(i==length)
{
a[i]=1;
length++;
}
else a[i]++;
}
}
else *this=X;
return *this;
}
inline BigInt BigInt::operator * (const BigInt& X)
{
BigInt temp;
if(X.length && length)
{
temp.length=length+X.length-1;
unsigned _int64 carry=0,tt;
for(int i=0;i<temp.length;i++)
{
tt=carry;
carry=0;
for(int j=(i<X.length?0:i-X.length+1);j<=i && j<length;j++)
{
tt+=(unsigned _int64)this->a[j]*X.a[i-j];
carry+=tt>>32;
tt&=0xffffffff;
}
temp.a[i]=tt;
}
if(carry)
{
temp.a[temp.length]=carry;
temp.length++;
}
}
return temp;
}
inline BigInt BigInt::operator * (const unsigned int& X)
{
BigInt M;
if(length && X)
{
unsigned _int64 temp,carry=0;
int i;
M.length=length;
for(i=0;i<length;i++)
{
temp=(unsigned _int64)a[i]*X+carry;
M.a[i]=temp;
carry=temp>>32;
}
if(carry)
{
M.a[i]=carry;
M.length++;
}
}
return M;
}
inline BigInt& BigInt::operator <<= (const unsigned int& X)
{
if(length)
{
int i;
length+=X;
for(i=length-1;i>=X;i--)
a[i]=a[i-X];
for(i=0;i<X;i++)
a[i]=0;
}
return *this;
}
inline BigInt BigInt::operator >> (const unsigned int& X)
{
BigInt M;
if(length>X)
{
M=*this;
M.length-=X;
for(int i=0;i<M.length;i++)
M.a[i]=M.a[i+X];
}
return M;
}
inline BigInt BigInt::operator % (BigInt& X)
{
BigInt Y;
if(!(*this<X))
{
int i;
unsigned int yy;
Y=*this>>(length-X.length);
unsigned _int64 tt;
for(i=length-X.length;i>=0;i--)
{
if(!(Y<X))
{
do {
tt=Y.a[Y.length-1];
if(Y.length!=X.length) tt=(tt<<32)+Y.a[Y.length-2];
yy=tt/((unsigned _int64)X.a[X.length-1]+1);
if(!yy) yy=1;
Y=Y-X*yy;
}while(!(Y<X));
}
if(i!=0)
{
Y<<=1;
Y+=a[i-1];
}
}
}
else Y=*this;
return Y;
}
inline BigInt BigInt::DIV(BigInt& X,BigInt& Y)
{
BigInt M;
if(!(*this<X))
{
int i;
unsigned int yy;
Y=*this>>(length-X.length);
M.length=length-X.length+1;
unsigned _int64 tt,quoa;
for(i=M.length-1;i>=0;i--)
{
quoa=0;
if(!(Y<X))
{
do {
tt=Y.a[Y.length-1];
if(Y.length!=X.length) tt=(tt<<32)+Y.a[Y.length-2];
yy=tt/((unsigned _int64)X.a[X.length-1]+1);
if(!yy) yy=1;
quoa+=yy;
Y=Y-X*yy;
}while(!(Y<X));
}
M.a[i]=quoa;
if(i!=0)
{
Y<<=1;
Y+=a[i-1];
}
}
if(M.a[M.length-1]==0) M.length--;
}
return M;
}
inline BigInt BigInt::PowerMod(const BigInt& M,BigInt& N)
{
BigInt result=1;
for(int i=M.length-1;i>=0;i--)
for(int j=31;j>=0;j--)
{
result=result*result;
result=result%N;
if(M.a[i]&(1<<j))
{
result=result*(*this);
result=result%N;
}
}
return result;
}
inline void BigInt::GetRand(const unsigned int& len)
{
length=len;
for(int i=0;i<len;i++)
a[i]=(rand()<<16)+rand();
a[0]|=1;
a[len-1]|=0x80000000;
}
bool BigInt::IsPrime()
{
int i;
BigInt M;
for(i=0;i<302;i++)
if(*this%PrimeTable[i]==0) return false;
for(i=0;i<5;i++)
{
M.GetRand(1);
if(!(M.PowerMod(*this-1,*this)==1)) return false;
}
return true;
}
inline ostream& operator << (ostream& os,const BigInt& X)
{
if(X.length)
{
os.setf(ios::hex|ios::uppercase);
for(int i=X.length-1;i>=0;i--)
{
os.width(8);
os.fill('0');
os<<X.a[i];
}
}
else os<<0;
return os;
}
inline unsigned int BigInt::operator % (const unsigned int& X)
{
unsigned _int64 tt=0;
for(int i=length-1;i>=0;i--)
{
tt=(tt<<32)+a[i];
tt%=X;
}
return (unsigned int)tt;
}
inline void BigInt::GetPrime(const unsigned int& X)
{
GetRand(X);
while(!IsPrime()) *this+=2;
}
inline BigInt BigInt::Euc(BigInt& X,BigInt& Y)
{
BigInt A=X,B=*this,Q,R,X1=0,X2=1;
int sign_1=1,sign_2=1;
while(!(B==0))
{
Q=A.DIV(B,R);
A=B;
B=R;
R=X2;
X2=X2*Q;
if(sign_1==sign_2)
if(X2<X1) X2=X1-X2;
else
{
X2=X2-X1;
sign_2=1-sign_2;
}
else
{
X2+=X1;
sign_1=sign_2;
sign_2=1-sign_2;
}
X1=R;
}
if(!sign_1) X1=X-X1;
Y=A;
return X1;
}
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