?? bigint.cpp
字號(hào):
/*****************************************************************
大數(shù)運(yùn)算源文件：BigInt.cpp
說明：適用于MFC，<=1024位RSA運(yùn)算,運(yùn)用0x100000000進(jìn)制(暫簡(jiǎn)稱32位進(jìn)制）實(shí)現(xiàn)快速運(yùn)算
同時(shí)用拉賓米勒算法來測(cè)試素?cái)?shù)，并能隨即產(chǎn)生需要位數(shù)的素?cái)?shù)，輸入為
十進(jìn)制或十六進(jìn)制的字符串不支持所有字符即需要一次轉(zhuǎn)換才能用此程序
加密，當(dāng)然得到的密文也是十進(jìn)制或十六進(jìn)制的字符串：)
*****************************************************************/
#include "stdafx.h"
#include "BigInt.h"
//小素?cái)?shù)表
const static int PrimeTable[550]=
{ 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, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063,
2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131,
2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221,
2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293,
2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371,
2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437,
2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539,
2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621,
2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689,
2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749,
2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833,
2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909,
2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001,
3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083,
3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187,
3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259,
3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343,
3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433,
3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517,
3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581,
3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659,
3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733,
3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823,
3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911,
3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001
};
//構(gòu)造大數(shù)對(duì)象并初始化為零：構(gòu)造函數(shù)
CBigInt::CBigInt()
{
m_nLength=1;
for(int i=0;i<BI_MAXLEN;i++)m_ulValue[i]=0;
}
//解構(gòu)大數(shù)對(duì)象：析構(gòu)函數(shù)
CBigInt::~CBigInt()
{
}
/****************************************************************************************
大數(shù)比較
調(diào)用方式：N.Cmp(A)
返回值：若N<A返回-1；若N=A返回0；若N>A返回1
思想：比較簡(jiǎn)單，先比較位數(shù)，位數(shù)相等從最高位開始比較
****************************************************************************************/
int CBigInt::Cmp(CBigInt& A)
{
if(m_nLength>A.m_nLength)return 1;
if(m_nLength<A.m_nLength)return -1;
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;
}
/****************************************************************************************
大數(shù)賦值
調(diào)用方式：N.Mov(A)
返回值：無，N被賦值為A
思想：比較簡(jiǎn)單，對(duì)于大數(shù)直接按位賦值，對(duì)于64位普通整數(shù)則需要看此數(shù)是否大與32位(32位進(jìn)制）
****************************************************************************************/
void CBigInt::Mov(CBigInt& A)
{
m_nLength=A.m_nLength;
for(int i=0;i<BI_MAXLEN;i++)m_ulValue[i]=A.m_ulValue[i];
}
void 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;
}
/****************************************************************************************
大數(shù)相加
調(diào)用形式：N.Add(A)
返回值：N+A
思想：與正常加法一樣按位相加，考慮進(jìn)位
****************************************************************************************/
CBigInt CBigInt::Add(CBigInt& A)
{
CBigInt X;
X.Mov(*this);
unsigned carry=0;
unsigned __int64 sum=0;
if(X.m_nLength<A.m_nLength)X.m_nLength=A.m_nLength;
for(unsigned 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;
carry=(unsigned)(sum>>32);
}
X.m_ulValue[X.m_nLength]=carry;
X.m_nLength+=carry;
return X;
}
CBigInt CBigInt::Add(unsigned long A)
{
CBigInt X;
X.Mov(*this);
unsigned __int64 sum;
sum=X.m_ulValue[0];
sum+=A;
X.m_ulValue[0]=(unsigned long)sum;
if(sum>0xffffffff)
{
unsigned i=1;
while(X.m_ulValue[i]==0xffffffff){X.m_ulValue[i]=0;i++;}
X.m_ulValue[i]++;
if(m_nLength==i)m_nLength++;
}
return X;
}
/****************************************************************************************
大數(shù)相減
調(diào)用形式：N.Sub(A)
返回值：N-A
思想：按位相減，考慮借位，當(dāng)結(jié)果<0時(shí)結(jié)果為0；
****************************************************************************************/
CBigInt CBigInt::Sub(CBigInt& A)
{
CBigInt X;
X.Mov(*this);
if(X.Cmp(A)<=0){X.Mov(0);return X;}
unsigned carry=0;
unsigned __int64 num;
unsigned i;
for(i=0;i<m_nLength;i++)
{
if((m_ulValue[i]>A.m_ulValue[i])||((m_ulValue[i]==A.m_ulValue[i])&&(carry==0)))
{
X.m_ulValue[i]=m_ulValue[i]-carry-A.m_ulValue[i];
carry=0;
}
else
{
num=0x100000000+m_ulValue[i];
X.m_ulValue[i]=(unsigned long)(num-carry-A.m_ulValue[i]);
carry=1;
}
}
while(X.m_ulValue[X.m_nLength-1]==0)X.m_nLength--;
return X;
}
CBigInt CBigInt::Sub(unsigned long A)
{
CBigInt X;
X.Mov(*this);
if(X.m_ulValue[0]>=A){X.m_ulValue[0]-=A;return X;}
if(X.m_nLength==1){X.Mov(0);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++;}
X.m_ulValue[i]--;
if(X.m_ulValue[i]==0)X.m_nLength--;
return X;
}
/****************************************************************************************
大數(shù)相乘
調(diào)用形式：N.Mul(A)
返回值：N*A
思想：不是普通的錯(cuò)位相乘，而是依照最終結(jié)果的每一位來進(jìn)行得到這一位所需要的運(yùn)算
****************************************************************************************/
CBigInt CBigInt::Mul(CBigInt& A)
{
if(A.m_nLength==1)return Mul(A.m_ulValue[0]);
CBigInt X;
unsigned __int64 sum,mul=0,carry=0;
unsigned i,j;
X.m_nLength=m_nLength+A.m_nLength-1;
for(i=0;i<X.m_nLength;i++)
{
sum=carry;
carry=0;
for(j=0;j<A.m_nLength;j++)
{
if(((i-j)>=0)&&((i-j)<m_nLength))
{
mul=m_ulValue[i-j];
mul*=A.m_ulValue[j];
carry+=mul>>32;
mul=mul&0xffffffff;
sum+=mul;
}
}
carry+=sum>>32;
X.m_ulValue[i]=(unsigned long)sum;
}
if(carry){X.m_nLength++;X.m_ulValue[X.m_nLength-1]=(unsigned long)carry;}
return X;
}
CBigInt CBigInt::Mul(unsigned long A)
{
CBigInt X;
unsigned __int64 mul;
unsigned long carry=0;
X.Mov(*this);
for(unsigned 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>>32);
}
if(carry){X.m_nLength++;X.m_ulValue[X.m_nLength-1]=carry;}
return X;
}
/****************************************************************************************
大數(shù)相除
調(diào)用形式：N.Div(A)
返回值：N/A
思想：大數(shù)相除是從商的最高位開始找起，然后找到一位就從被除數(shù)(N)中減去這位與除數(shù)(A)的乘積
然后重復(fù)上述操作知道被除數(shù)小與除數(shù)；普通64位整數(shù)除法比較簡(jiǎn)單；
****************************************************************************************/
CBigInt CBigInt::Div(CBigInt& A)
{
if(A.m_nLength==1)
return Div(A.m_ulValue[0]);
CBigInt X,Y,Z;
unsigned i,len;
unsigned __int64 num,div;
Y.Mov(*this);
while(Y.Cmp(A)>=0)
{
div=Y.m_ulValue[Y.m_nLength-1];
num=A.m_ulValue[A.m_nLength-1];
len=Y.m_nLength-A.m_nLength;
if((div==num)&&(len==0))//相等
{
X.Mov(X.Add(1));
break;
}
if((div<=num)&&len)//被除數(shù)(N)最高位比除數(shù)(A)小需要除數(shù)的高2位
{
len--;
div=(div<<32)+Y.m_ulValue[Y.m_nLength-2];
}
div=div/(num+1);
Z.Mov(div);
if(len)
{
Z.m_nLength+=len;
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