C语言编写大整数

C语言编写大整数
本人写的大整数是256进制的，每一个字节里面的每一位都是有用的，因此比较节省空间。

前面我用宏定义定义了大整数最大为128字节，也就是1024位，当然你可以改变SIZE的大小来改变大整数的位数。

大整数结构如下：
typedef struct BigNum//大整数结构
{
UCHAR data[SIZE]; //空间为(SIZE * sizeof(UCHAR))，就是SIZE个字节}BigNum;
以下是头文件BigNum.h
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// #ifndef_BIGNUM_H_
#define_BIGNUM_H_
#define SIZE128 //一个大整数用个字节保存，最多表示位大整数#define SIZE_10 2 * SIZE
typedef unsigned char UCHAR;
typedef unsigned short USHORT;
UCHAR atox(char ch); //将一个十六进制的字符(4位)转位数字，转换失败返回xff
typedef struct BigNum//大整数结构
{
UCHAR data[SIZE]; //空间为(SIZE * sizeof(UCHAR))，就是SIZE个字节}BigNum;
BigNum Init(char* str); //初始化大整数，str为十六进制字符串
int GetByte(BigNum bignum); //判断有多少个字节不为
BigNum MovByteLetf(BigNum bignum, int n); //左移n个字节
BigNum MovByteRight(BigNum bignum, int n); //右移n个字节
int Cmp(BigNum bignum_a, BigNum bignum_b); //大整数比较大小，>返回，<返回-1，==返回
BigNum Add(BigNum bignum_a, BigNum bignum_b); //大整数加法
BigNum Sub(BigNum bignum_a, BigNum bignum_b); //大整数减法
//BigNum Mul(BigNum bignum_a, UCHAR uchar); //大整数乘法UCHAR BigNum Mul(BigNum bignum_a, BigNum bignum_b); //大整数乘法
BigNum Div(BigNum bignum_a, BigNum bignum_b); //大整数除法
BigNum Mod(BigNum bignum_a, BigNum bignum_b); //大整数模运算BigNum Pow(BigNum bignum, int n); //大整数乘方运算
void Print_16(BigNum bignum); //打印十六进制大整数
void Print_10(BigNum bignum); //打印十进制大整数
#endif
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////以下是C文件BigNum.c
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// // BigNum.c : 定义控制台应用程序的入口点。

//
#include<stdio.h>
#include<string.h>
#include"BigNum.h"
UCHAR atox(char ch) //将一个十六进制的字符(4位)转位数字，转换失败返回xff
{
UCHAR res;
if (ch >= '0' && ch <= '9')
{
res = ch - '0';
}
else if (ch >= 'a' && ch <= 'f')
{
res = ch - 'a' + 10;
}
else if (ch >= 'A' && ch <= 'F')
{
res = ch - 'A' + 10;
}
else
{
printf("change error!\n");
return 0xff;
}
return res;
}
int GetByte(BigNum bignum) //判断有多少个字节不为
{
int ByteOfBigNum = SIZE;
while ((bignum.data[ByteOfBigNum - 1] == 0) && (ByteOfBigNum > 0)) {
ByteOfBigNum--;
}
return ByteOfBigNum;
}
BigNum MovByteLetf(BigNum bignum, int n) //左移n个字节
{
int i;
int bignum_len = GetByte(bignum);
for (i = bignum_len - 1; i >= 0; i--)
{
if (i + n >= SIZE)
{
continue;
}
bignum.data[i + n] = bignum.data[i];
}
for (i = n - 1; i >= 0; i--)
{
bignum.data[i] = 0;
}
return bignum;
}
BigNum MovByteRight(BigNum bignum, int n) //右移n个字节
{
int i;
int bignum_len = GetByte(bignum);
for (i = 0; i < bignum_len; i++)
{
if (i + n >= SIZE)
{
bignum.data[i] = 0;
continue;
}
bignum.data[i] = bignum.data[i + n];
}
return bignum;
}
BigNum Init(char* str) //初始化大整数，str为十六进制字符串
{
BigNum bignum;
int len = (int)strlen(str);
int i;
int j = 0;
if (len > 2 * SIZE)
{
len = 2 * SIZE;
}
for (i = len - 1; i > 0; i -= 2)
{
bignum.data[j] = atox(str[i]) + atox(str[i - 1]) * 16;
j++;
}
if (i == 0)
{
bignum.data[j] = atox(str[i]);
j++;
}
while (j < SIZE)
{
bignum.data[j] = 0;
j++;
}
return bignum;
}
int Cmp(BigNum bignum_a, BigNum bignum_b) //大整数比较大小，>返回，<返回-1，==返回
{
int bignum_a_len = GetByte(bignum_a);
int bignum_b_len = GetByte(bignum_b);
int max = bignum_a_len > bignum_b_len ? bignum_a_len : bignum_b_len;
int i;
for (i = max - 1; i >= 0; i--)
{
if (bignum_a.data[i] > bignum_b.data[i])
{
return 1;
}
if (bignum_a.data[i] < bignum_b.data[i])
{
return -1;
}
}
return 0;
}
BigNum Add(BigNum bignum_a, BigNum bignum_b) //大整数加法{
BigNum bignum_c;
USHORT temp;
UCHAR carry = 0;
int i;
for (i = 0; i < SIZE; i++)
{
temp = bignum_a.data[i] + bignum_b.data[i] + carry;
bignum_c.data[i] = temp & 0x00ff;
carry = (temp >> 8) & 0xff;
}
return bignum_c;
}
BigNum Sub(BigNum bignum_a, BigNum bignum_b) //大整数减法{
BigNum bignum_c;
USHORT temp;
UCHAR carry = 0;
int i;
for (i = 0; i < SIZE; i++)
{
temp = bignum_a.data[i] - bignum_b.data[i] - carry;
bignum_c.data[i] = temp & 0x00ff;
carry = (temp >> 15) & 0x01;
}
return bignum_c;
}
BigNum Mul(BigNum bignum_a, BigNum bignum_b) //大整数乘法{
BigNum bignum_c = Init("0");
USHORT temp;
UCHAR carry;
int i, j;
for (i = 0; i < SIZE; i++)
{
carry = 0;
for (j = 0; j < SIZE; j++)
{
temp = bignum_a.data[i] * bignum_b.data[j] + bignum_c.data[j + i] + carry;
bignum_c.data[j + i] = temp & 0x00ff;
carry = (temp >> 8) & 0xff;
}
}
return bignum_c;
}
BigNum Div(BigNum bignum_a, BigNum bignum_b) //大整数除法{
BigNum bignum_c = Init("0");
BigNum B;
int bignum_a_len;
int bignum_b_len;
int bignum_c_len;
if (Cmp(bignum_b, bignum_c) == 0)
{
printf("错误！除数为\n");
return bignum_c;
}
bignum_a_len = GetByte(bignum_a);
bignum_b_len = GetByte(bignum_b);
bignum_c_len = bignum_a_len - bignum_b_len;
while (bignum_c_len >= 0)
{
B = MovByteLetf(bignum_b, bignum_c_len);
while (Cmp(bignum_a, B) != -1)
{
bignum_a = Sub(bignum_a, B);
bignum_c.data[bignum_c_len]++;
}
bignum_c_len--;
}
return bignum_c;
}
BigNum Mod(BigNum bignum_a, BigNum bignum_b) //大整数模运算{
BigNum bignum_c = Init("0");
BigNum B;
int bignum_a_len;
int bignum_b_len;
int bignum_c_len;
if (Cmp(bignum_b, bignum_c) == 0)
{
printf("错误！除数为\n");
return bignum_c;
}
bignum_a_len = GetByte(bignum_a);
bignum_b_len = GetByte(bignum_b);
bignum_c_len = bignum_a_len - bignum_b_len;
while (bignum_c_len >= 0)
{
B = MovByteLetf(bignum_b, bignum_c_len);
while (Cmp(bignum_a, B) != -1)
{
bignum_a = Sub(bignum_a, B);
}
bignum_c_len--;
}
return bignum_a;
}
BigNum Pow(BigNum bignum, int n) //大整数乘方运算
{
int i;
BigNum bignum_res = Init("1");
for (i = 0; i < n; i++)
{
bignum_res = Mul(bignum_res, bignum);
}
return bignum_res;
}
void Print_16(BigNum bignum) //打印十六进制大整数
{
int i;
int nFlag = 0;
for (i = SIZE - 1; i >= 0; i--)
{
if (nFlag == 0 && bignum.data[i] == 0) //前面是的不打印
{
continue;
}
else
{
nFlag++;
if (nFlag == 1) //首位的不打印，如x01，只打印
{
printf("%x", bignum.data[i]);
}
else//后面的要打印
{
printf("%02x", bignum.data[i]);
}
}
}
if (nFlag == 0)
{
printf("0");
}
printf("\n");
}
void Print_10(BigNum bignum) //打印十进制大整数
{
int data_10[SIZE_10];
int i = 0;
int j;
while (Cmp(bignum, Init("0")) == 1)
{
data_10[i] = (Mod(bignum, Init("a"))).data[0];
bignum = (Div(bignum, Init("a")));
i++;
}
for (j = i - 1; j >= 0; j--)
{
printf("%d", data_10[j]);
}
printf("\n");
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////虽然本人的方法不是最好的，但能够基本实现1024位甚至更大的数的运算，只需要改变SIZE的大小就可以了。