本来利用一般的思想的是一个数组位存一位数， 需要初始化数组a[1024]，但是可以利用更节省空间的方法。C语言unsigned int 的范围是0-2^32-1,一个数组位就可以存32bit(1个int = 4Bytes = 4*8bit = 32 bit)，1024比特用初始化数组a[1024/32]=a[32]可以储存完。在本程序中，我用a[0]代表实际数组的长度，因此1024比特位的大数需要用数组a[33]存储。
bitmap思想
a[0]------------------------------------数组长度
a[1]------------------------------------0到^32-1
a[2]------------------------------------2^32 -1到2^64-1
举一个例子 :其中0X代表16进制
a[33]={1, 0}代表数字为0的数
a[33]={1, 1}代表数字为1的数
a[33]={2,0xffffffff,1}所代表的数字大小是2^32的数
若要实现 a[33]={1, 0xffffffff}, b[33]={1, 0x1} 的加法 ，
二进制中32比特的加法如下图所示：
需要向前进1，我们可以将a[2]赋值为1，故数组a,b相加可以得到数组c是c[34]={2,0x0,0x1}
数组初始化大小为0的程序是
/****************************************************************************************************大数相加调用方式Add(x,y,z)返回值，z=x+y*****************************************************************************************************/void Add_Big(unsigned int x[], unsigned int y[], unsigned int *z){int i;unsigned int t[34];unsigned int carry = 0;unsigned long long sum = 0;Init(t);Mov_Big(x, t);if (t[0] < y[0]){t[0] = y[0];}for (i = 1; i <= t[0]; i++){sum = y[i];sum = sum + t[i] + carry;t[i] = (unsigned long)sum;carry = (unsigned int)(sum >> 32);}if (carry != 0){t[t[0] + 1] = carry;t[0] = t[0] + 1;}Mov_Big(t, z);}
c语言实现1024bit大数加法的完整程序如下，使用devc++进行编译
#include<stdio.h>#define MAX 32/***************************************************************************************************初始化大数对象，且数组第一位是数组的实际长度****************************************************************************************************/void Init(unsigned int *x){int i;for (i = 1; i < MAX; i++)x[i] = 0;x[0] = 1;}/***************************************************************************************************大数比较调用方式Cmp(x, y)返回值，若x<y返回 - 1；若x>y返回1; 若x = y返回0*****************************************************************************************************/int Cmp(unsigned int x[], unsigned int y[]){int i;if (x[0] > y[0])return 1;if (x[0] < y[0])return -1;for (i = MAX - 1; i >= 1; i--){if (x[i] < y[i])return -1;if (x[i] > y[i])return 1;}return 0;}/****************************************************************************************************大数赋值调用方式Mov(x,y)返回值:y被赋值为x；*****************************************************************************************************/void Mov_Big(unsigned int x[], unsigned int *y){int i;for (i = 0; i <= x[0]; i++){y[i] = x[i];}if (x[0] < MAX)for (i = x[0] + 1; i < MAX; i++){y[i] = 0;}}void Mov_Long(unsigned long long x, unsigned int *y){int i;if (x > 0xffffffff){y[0] = 2;y[1] = (unsigned int)x;y[2] = (unsigned int)(x >> 32);}else{y[0] = 1;y[1] = (unsigned int)x;}for (i = y[0] + 1; i < MAX; i++)y[i] = 0;}/****************************************************************************************************大数相加调用方式Add(x,y,z)返回值，z=x+y*****************************************************************************************************/void Add_Big(unsigned int x[], unsigned int y[], unsigned int *z){int i;unsigned int t[34];unsigned int carry = 0;unsigned long long sum = 0;Init(t);Mov_Big(x, t);if (t[0] < y[0]){t[0] = y[0];}for (i = 1; i <= t[0]; i++){sum = y[i];sum = sum + t[i] + carry;t[i] = (unsigned long)sum;carry = (unsigned int)(sum >> 32);}if (carry != 0){t[t[0] + 1] = carry;t[0] = t[0] + 1;}Mov_Big(t, z);}void Add_Long(unsigned int x[], unsigned long long y, unsigned int *z){unsigned int t[34];unsigned long long sum = 0;Init(t);Mov_Big(x, t);sum = t[1];sum = sum + y;t[1] = (unsigned int)sum;if (sum > 0xffffffff){int i = 2;while (t[i] == 0xffffffff){t[i] = 0;i++;}t[i]++;if (t[0] == i)t[0]++;}Mov_Big(t, z);}int main() {unsigned int a[33]={8, 0x7C66DDDD, 0xE8C4E481, 0x09DC3280, 0xE1E40869, 0x487D01D6, 0xF5ED0704, 0x62BF718F, 0x93DE051D };unsigned int b[33]={8, 0x0A3EA616, 0x0C464CD7, 0xFA602435, 0x1C1C00CB, 0x5C395BBC, 0x63106512, 0x4F21E607, 0x21FE8DDA};unsigned int c[34];Add_Big(a,b,c);int i;printf("a= ");printf("\n ");for(i=a[0];i>=1;i--)printf("%llx",a[i]);printf("\n ");printf("\n ");printf("b= ");printf("\n ");for(i=b[0];i>=1;i--)printf("%llx",b[i]);printf("\n ");printf("\n ");printf("a+b= ");printf("\n ");for(i=c[0];i>=1;i--)printf("%llx",c[i]);return 0;}
大数运算c语言运算结果
