?? bigint.cpp
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#include "stdafx.h"
#include "BigInt.h"
CBigInt::CBigInt()
{
m_nSign=1;
m_nLength=1;
for(int i=0;i<BI_MAXLEN;i++)
m_ulValue[i]=0;
}
CBigInt::~CBigInt()
{
}
//大數比較，如果大數A位數比大數B多，當然A>B
//如果位數相同，則從高位開始比較，直到分出大小
int CBigInt::Cmp(CBigInt& A)
{
if(m_nLength>A.m_nLength)return 1; //this > A
if(m_nLength<A.m_nLength)return -1; //this < A
for(int i=m_nLength-1;i>=0;i--)
{
if(m_ulValue[i]>A.m_ulValue[i])return 1;
if(m_ulValue[i]<A.m_ulValue[i])return -1;
}
return 0;
}
CBigInt& CBigInt::Mov(CBigInt& A)
{
m_nLength=A.m_nLength;
for(int i=0;i<BI_MAXLEN;i++)
m_ulValue[i]=A.m_ulValue[i];
return *this;
}
CBigInt& CBigInt::Mov(unsigned __int64 A)
{
if(A>0xffffffff)
{
m_nLength=2;
m_ulValue[1]=(unsigned long)(A>>32);
m_ulValue[0]=(unsigned long)A;
}
else
{
m_nLength=1;
m_ulValue[0]=(unsigned long)A;
}
for(int i=m_nLength;i<BI_MAXLEN;i++)m_ulValue[i]=0;
return *this;
}
//大數相加
//調用形式：N.Add(A)，返回值：N+A
//若兩大數符號相同，其值相加，否則改變參數符號再調用大數相減函數
/******************************************************************
例如：
A B C
+ D E
--------------
= S F G H
其中,若C+E<=0xffffffff，則H=C+E，carry(進位標志)=0
若C+E> 0xffffffff，則H=C+E-0x100000000，carry=1
若B+D+carry<=0xfffffff，則G=B+D，carry=0
若B+D+carry> 0xfffffff，則G=B+D+carry-0x10000000，carry=1
若carry=0，則F=A，S=0
若carry=1，A<0xfffffff，則F=A+1，S=0
若carry=1，A=0xfffffff，則F=0，S=1
*****************************************************************/
CBigInt CBigInt::Add(CBigInt& A)
{
CBigInt X;
if(X.m_nSign==A.m_nSign)
{
X.Mov(*this);
int carry=0;
unsigned __int64 sum=0;
if(X.m_nLength<A.m_nLength)X.m_nLength=A.m_nLength;
for(int i=0;i<X.m_nLength;i++)
{
sum=A.m_ulValue[i];
sum=sum+X.m_ulValue[i]+carry;
X.m_ulValue[i]=(unsigned long)sum;
if(sum>0xffffffff)carry=1;
else carry=0;
}
if(X.m_nLength<BI_MAXLEN)
{
X.m_ulValue[X.m_nLength]=carry;
X.m_nLength+=carry;
}
return X;
}
else{X.Mov(A);X.m_nSign=1-X.m_nSign;return Sub(X);}
}
CBigInt CBigInt::Add(long A)
{
CBigInt X;
if((m_nSign*A)>=0)
{
X.Mov(*this);
unsigned __int64 sum;
sum=A+X.m_ulValue[0];
X.m_ulValue[0]=(unsigned long)sum;
if(sum>0xffffffff)
{
int i=1;
while(X.m_ulValue[i]==0xffffffff){X.m_ulValue[i]=0;i++;}
X.m_ulValue[i]++;
if(i<BI_MAXLEN)X.m_nLength=i+1;
}
return X;
}
else return Sub(-A);
}
//大數相減
//調用形式：N.Sub(A)，返回值：N-A
//若兩大數符號相同，其值相減，否則改變參數符號再調用大數相加函數
/******************************************************************
例如：
A B C
- D E
--------------
= F G H
其中,若C>=E，則H=C-E，carry(借位標志)=0
若C<E， 則H=C-E+0x100000000，carry=1
若B-carry>=D，則G=B-carry-D，carry=0
若B-carry<D， 則G=B-carry-D+0x10000000，carry=1
若carry=0，則F=A
若carry=1，A>1，則F=A-1
若carry=1，A=1，則F=0
*****************************************************************/
CBigInt CBigInt::Sub(CBigInt& A)
{
CBigInt X;
if(m_nSign==A.m_nSign)
{
X.Mov(*this);
int cmp=X.Cmp(A);
if(cmp==0){X.Mov(0);return X;}
int len,carry=0;
unsigned __int64 num;
unsigned long *s,*d;
if(cmp>0){s=X.m_ulValue;d=A.m_ulValue;len=X.m_nLength;}
if(cmp<0){s=A.m_ulValue;d=X.m_ulValue;len=A.m_nLength;X.m_nSign=1-X.m_nSign;}
for(int i=0;i<len;i++)
{
if((s[i]-carry)>=d[i])
{
X.m_ulValue[i]=s[i]-carry-d[i];
carry=0;
}
else
{
num=0x100000000+s[i];
X.m_ulValue[i]=(unsigned long)(num-carry-d[i]);
carry=1;
}
}
while(X.m_ulValue[len-1]==0)len--;
X.m_nLength=len;
return X;
}
else{X.Mov(A);X.m_nSign=1-X.m_nSign;return Add(X);}
}
CBigInt CBigInt::Sub(long A)
{
CBigInt X;
if((m_nSign*A)>=0)
{
X.Mov(*this);
if(X.m_ulValue[0]>=(unsigned long)A){X.m_ulValue[0]-=A;return X;}
if(X.m_nLength==1){X.m_ulValue[0]=A-X.m_ulValue[0];X.m_nSign=1-X.m_nSign;return X;}
unsigned __int64 num=0x100000000+X.m_ulValue[0];
X.m_ulValue[0]=(unsigned long)(num-A);
int i=1;
while(X.m_ulValue[i]==0){X.m_ulValue[i]=0xffffffff;i++;}
if(X.m_ulValue[i]==1)X.m_nLength--;
X.m_ulValue[i]--;
return X;
}
else return Add(-A);
}
//大數相乘
//調用形式：N.Mul(A)，返回值：N*A
/******************************************************************
例如：
A B C
* D E
----------------
= S F G H
+ T I J K
----------------
= U V L M N
其中，SFGH=ABC*E，TIJK=ABC*D
而對于：
A B C
* E
-------------
= S F G H
其中,若C*E<=0xffffffff，則H=C*E，carry(進位標志)=0
若C*E> 0xffffffff，則H=(C*E)&0xffffffff, carry=(C*E)/0xffffffff
若B*E+carry<=0xffffffff，則G=B*E+carry，carry=0
若B*E+carry> 0xffffffff，則G=(B*E+carry)&0xffffffff, carry=(B*E+carry)/0xffffffff
若A*E+carry<=0xffffffff，則F=A*E+carry，carry=0
若A*E+carry> 0xffffffff，則F=(A*E+carry)&0xffffffff, carry=(A*E+carry)/0xffffffff, S=carry
*****************************************************************/
CBigInt CBigInt::Mul(CBigInt& A)
{
CBigInt X,Y;
unsigned __int64 mul;
unsigned long carry;
for(int i=0;i<A.m_nLength;i++)
{
Y.m_nLength=m_nLength;
carry=0;
for(int j=0;j<m_nLength;j++)
{
mul=m_ulValue[j];
mul=mul*A.m_ulValue[i]+carry;
Y.m_ulValue[j]=(unsigned long)mul;
carry=(unsigned long)(mul>>32);
}
if(carry&&(Y.m_nLength<BI_MAXLEN))
{
Y.m_nLength++;
Y.m_ulValue[Y.m_nLength-1]=carry;
}
if(Y.m_nLength<BI_MAXLEN-i)
{
Y.m_nLength+=i;
for(int k=Y.m_nLength-1;k>=i;k--)Y.m_ulValue[k]=Y.m_ulValue[k-i];
for(k=0;k<i;k++)Y.m_ulValue[k]=0;
}
X.Mov(X.Add(Y));
}
if(m_nSign+A.m_nSign==1)X.m_nSign=0;
else X.m_nSign=1;
return X;
}
CBigInt CBigInt::Mul(long A)
{
CBigInt X;
unsigned __int64 mul;
unsigned long carry=0;
X.Mov(*this);
for(int i=0;i<m_nLength;i++)
{
mul=m_ulValue[i];
mul=mul*A+carry;
X.m_ulValue[i]=(unsigned long)mul;
carry=(unsigned long)((mul-X.m_ulValue[i])>>32);
}
if(carry&&(X.m_nLength<BI_MAXLEN)){X.m_nLength++;X.m_ulValue[X.m_nLength-1]=carry;}
if(A<0)
X.m_nSign=1-X.m_nSign;
return X;
}
//大數相除
//調用形式：N.Div(A)，返回值：N/A
//除法的關鍵在于“試商”，然后就變成了乘法和減法
//這里將被除數與除數的試商轉化成了被除數最高位與除數最高位的試商
CBigInt CBigInt::Div(CBigInt& A)
{
CBigInt X,Y,Z;
int len;
unsigned __int64 num,div;
unsigned long carry=0;
Y.Mov(*this);
while(Y.Cmp(A)>0)
{
if(Y.m_ulValue[Y.m_nLength-1]>A.m_ulValue[A.m_nLength-1])
{
len=Y.m_nLength-A.m_nLength;
div=Y.m_ulValue[Y.m_nLength-1]/(A.m_ulValue[A.m_nLength-1]+1);
}
else if(Y.m_nLength>A.m_nLength)
{
len=Y.m_nLength-A.m_nLength-1;
num=Y.m_ulValue[Y.m_nLength-1];
num=(num<<32)+Y.m_ulValue[Y.m_nLength-2];
if(A.m_ulValue[A.m_nLength-1]==0xffffffff)div=(num>>32);
else div=num/(A.m_ulValue[A.m_nLength-1]+1);
}
else
{
X.Mov(X.Add(1));
break;
}
Z.Mov(div);
Z.m_nLength+=len;
for(int i=Z.m_nLength-1;i>=len;i--)Z.m_ulValue[i]=Z.m_ulValue[i-len];
for(i=0;i<len;i++)Z.m_ulValue[i]=0;
X.Mov(X.Add(Z));
Z.Mov(Z.Mul(A));
Y.Mov(Y.Sub(Z));
}
if(Y.Cmp(A)==0)X.Mov(X.Add(1));
if(m_nSign+A.m_nSign==1)X.m_nSign=0;
else X.m_nSign=1;
return X;
}
//大數求模
//調用形式：N.Mod(A)，返回值：N%A
//求模與求商原理相同
CBigInt CBigInt::Div(long A)
{
CBigInt X;
X.Mov(*this);
if(X.m_nLength==1){X.m_ulValue[0]=X.m_ulValue[0]/A;return X;}
unsigned __int64 div,mul;
unsigned long carry=0;
for(int i=X.m_nLength-1;i>=0;i--)
{
div=carry;
div=(div<<32)+X.m_ulValue[i];
X.m_ulValue[i]=(unsigned long)(div/A);
mul=(div/A)*A;
carry=(unsigned long)(div-mul);
}
if(X.m_ulValue[X.m_nLength-1]==0)X.m_nLength--;
if(A<0)X.m_nSign=1-X.m_nSign;
return X;
}
CBigInt CBigInt::Mod(CBigInt& A)
{
CBigInt X,Y;
int len;
unsigned __int64 num,div;
unsigned long carry=0;
X.Mov(*this);
while(X.Cmp(A)>0)
{
if(X.m_ulValue[X.m_nLength-1]>A.m_ulValue[A.m_nLength-1])
{
len=X.m_nLength-A.m_nLength;
div=X.m_ulValue[X.m_nLength-1]/(A.m_ulValue[A.m_nLength-1]+1);
}
else if(X.m_nLength>A.m_nLength)
{
len=X.m_nLength-A.m_nLength-1;
num=X.m_ulValue[X.m_nLength-1];
num=(num<<32)+X.m_ulValue[X.m_nLength-2];
if(A.m_ulValue[A.m_nLength-1]==0xffffffff)div=(num>>32);
else div=num/(A.m_ulValue[A.m_nLength-1]+1);
}
else
{
X.Mov(X.Sub(A));
break;
}
Y.Mov(div);
Y.Mov(Y.Mul(A));
Y.m_nLength+=len;
for(int i=Y.m_nLength-1;i>=len;i--)Y.m_ulValue[i]=Y.m_ulValue[i-len];
for(i=0;i<len;i++)Y.m_ulValue[i]=0;
X.Mov(X.Sub(Y));
}
if(X.Cmp(A)==0)X.Mov(0);
return X;
}
long CBigInt::Mod(long A)
{
if(m_nLength==1)return(m_ulValue[0]%A);
unsigned __int64 div;
unsigned long carry=0;
for(int i=m_nLength-1;i>=0;i--)
{
div=carry*0x100000000+m_ulValue[i];
carry=(unsigned long)(div-((div/A)*A));
}
return carry;
}
int CBigInt::InPutFromStr(CString& str, const unsigned int system=DEC)
{
int len=str.GetLength();
Mov(0);
for(int i=0;i<len;i++)
{
Mov(Mul(system));
int k=str[i]-48;
Mov(Add(k));
}
return 0;
}
int CBigInt::OutPutToStr(CString& str, const unsigned int system=DEC)
{
str="";
char ch;
CBigInt X;
X.Mov(*this);
while(X.m_ulValue[X.m_nLength-1]>0)
{
ch=X.Mod(system)+48;
str.Insert(0,ch);
X.Mov(X.Div(system));
}
return 0;
}
//歐幾里德算法:
//定理基礎: gcd(a,b) = gcd(b,a mod b)
//*********************************************//
//歐幾里德算法求：Y=X.Euc(A)，使滿足：YX mod A=1
//相當于對不定方程ax-by=1求最小整數解
//實際上就是廣義輾轉相除法
/********************************************************************
例如：11x-49y=1，求x(求11關于模49的逆元，結果是58)
11 x - 49 y = 1 a)
49%11=5 -> 11 x - 5 y = 1 b)
11%5 =1 -> x - 5 y = 1 c)
令y=1 代入c)式 得x=6
令x=6 代入b)式 得y=13
令y=13 代入a)式 得x=58
********************************************************************/
CBigInt CBigInt::Euc(CBigInt& A)
{
CBigInt X,Y;
X.Mov(*this);
Y.Mov(A);
if((X.m_nLength==1)&&(X.m_ulValue[0]==1))
return X;
if((Y.m_nLength==1)&&(Y.m_ulValue[0]==1))
{
X.Mov(X.Sub(1));
return X;
}
//輾轉相除
if(X.Cmp(Y)==1) // X > Y
X.Mov(X.Mod(Y)); // X = X % Y
else // X <= Y
Y.Mov(Y.Mod(X)); // Y = Y % X
X.Mov(X.Euc(Y)); // 遞歸
Y.Mov(*this);
if(Y.Cmp(A)==1)
{
X.Mov(X.Mul(Y));
X.Mov(X.Sub(1));
X.Mov(X.Div(A));
}
else
{
X.Mov(X.Mul(A));
X.Mov(X.Add(1));
X.Mov(X.Div(Y));
}
return X;
}
//蒙哥馬利算法求：Y=X.Mon(A,B)，使滿足：X^A mod B=Y
//就是反復平方法
CBigInt CBigInt::Mon(CBigInt& A, CBigInt& B)
{
CBigInt X,Y,Z;
X.Mov(1);
Y.Mov(*this);
Z.Mov(A);
while((Z.m_nLength!=1)||Z.m_ulValue[0])
{
if(Z.m_ulValue[0]&1)
{
Z.Mov(Z.Sub(1));
X.Mov(X.Mul(Y));
X.Mov(X.Mod(B));
}
else
{
Z.Mov(Z.Div(2));
Y.Mov(Y.Mul(Y));
Y.Mov(Y.Mod(B));
}
}
return X;
}
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