C语言【微项目19】—大整数字符串乘法器[纯字符串乘法][乘法表与加法表]【2022-11-27】

• 1.函数功能
• 2 简要测试结果
• 3.BigInterNoLimitMutiString.c
• 3.大整数字符串乘法器实现思路
• 4. 大整数字符串乘法器典型使用流程main.c

【TDTX】
【C99】
【编译与运行环境】64位Windows操作系统，TDM-gcc 4.9.2 64bit（-std=c99）编译。

【项目Gitee仓库】C语言-微项目。

【简介】C语言大整数乘法器，纯字符串处理，根据人手算乘法的方式，精确相乘，字符串乘法，最后可以数字格式化输出。

1.函数功能

2 简要测试结果

1.测试数据如下：
  其中，第一个数字表示测试的是n位乘n位的运算，第二个数字是C语言采用clock_t方式计算出的时间，如“120,0.016”表示一个120位整数乘以一个120位整数，乘法完成得到积的运行时间为0.016。

30,0.0
40,0.0
60,0.0
80,0.015
100,0.015
120,0.016
140,0.031
160,0.047
180,0.063
200,0.098
220,0.125
240,0.157
280,0.266
320,0.390
360,0.562
400,0.766
440,1.015
480,1.333
560,2.065
640,3.106
960,10.527
1920,86.268

2.乘法测试结果

3.BigInterNoLimitMutiString.c

#include 
#include 
#include 
#include char addResults[2] = {'0','0'}; 
char mutiResults[2] = {'0','0'}; char* add(char a,char b)
{//清空结果 addResults[0] = '0';addResults[1] = '0';if(a == '0'){addResults[0] = '0';addResults[1] = b;return addResults;}else if(b == '0'){addResults[0] = '0';addResults[1] = a;return addResults;}switch(a){case '1':switch(b){case '1':addResults[0] = '0';addResults[1] = '2';return addResults;case '2':addResults[0] = '0';addResults[1] = '3';return addResults;case '3':addResults[0] = '0';addResults[1] = '4';return addResults;case '4':addResults[0] = '0';addResults[1] = '5';return addResults;case '5':addResults[0] = '0';addResults[1] = '6';return addResults;	case '6':addResults[0] = '0';addResults[1] = '7';return addResults;	case '7':addResults[0] = '0';addResults[1] = '8';return addResults;	case '8':addResults[0] = '0';addResults[1] = '9';return addResults;	case '9':addResults[0] = '1';addResults[1] = '0';return addResults;	}break;case '2':switch(b){case '1':addResults[0] = '0';addResults[1] = '3';return addResults;case '2':addResults[0] = '0';addResults[1] = '4';return addResults;case '3':addResults[0] = '0';addResults[1] = '5';return addResults;case '4':addResults[0] = '0';addResults[1] = '6';return addResults;case '5':addResults[0] = '0';addResults[1] = '7';return addResults;	case '6':addResults[0] = '0';addResults[1] = '8';return addResults;	case '7':addResults[0] = '0';addResults[1] = '9';return addResults;	case '8':addResults[0] = '1';addResults[1] = '0';return addResults;	case '9':addResults[0] = '1';addResults[1] = '1';return addResults;	}break;case '3':switch(b){case '1':addResults[0] = '0';addResults[1] = '4';return addResults;case '2':addResults[0] = '0';addResults[1] = '5';return addResults;case '3':addResults[0] = '0';addResults[1] = '6';return addResults;case '4':addResults[0] = '0';addResults[1] = '7';return addResults;case '5':addResults[0] = '0';addResults[1] = '8';return addResults;	case '6':addResults[0] = '0';addResults[1] = '9';return addResults;	case '7':addResults[0] = '1';addResults[1] = '0';return addResults;	case '8':addResults[0] = '1';addResults[1] = '1';return addResults;	case '9':addResults[0] = '1';addResults[1] = '2';return addResults;	}break;case '4':switch(b){case '1':addResults[0] = '0';addResults[1] = '5';return addResults;case '2':addResults[0] = '0';addResults[1] = '6';return addResults;case '3':addResults[0] = '0';addResults[1] = '7';return addResults;case '4':addResults[0] = '0';addResults[1] = '8';return addResults;case '5':addResults[0] = '0';addResults[1] = '9';return addResults;	case '6':addResults[0] = '1';addResults[1] = '0';return addResults;	case '7':addResults[0] = '1';addResults[1] = '1';return addResults;	case '8':addResults[0] = '1';addResults[1] = '2';return addResults;	case '9':addResults[0] = '1';addResults[1] = '3';return addResults;	}break;case '5':switch(b){case '1':addResults[0] = '0';addResults[1] = '6';return addResults;case '2':addResults[0] = '0';addResults[1] = '7';return addResults;case '3':addResults[0] = '0';addResults[1] = '8';return addResults;case '4':addResults[0] = '0';addResults[1] = '9';return addResults;case '5':addResults[0] = '1';addResults[1] = '0';return addResults;	case '6':addResults[0] = '1';addResults[1] = '1';return addResults;	case '7':addResults[0] = '1';addResults[1] = '2';return addResults;	case '8':addResults[0] = '1';addResults[1] = '3';return addResults;	case '9':addResults[0] = '1';addResults[1] = '4';return addResults;	}break;case '6':switch(b){case '1':addResults[0] = '0';addResults[1] = '7';return addResults;case '2':addResults[0] = '0';addResults[1] = '8';return addResults;case '3':addResults[0] = '0';addResults[1] = '9';return addResults;case '4':addResults[0] = '1';addResults[1] = '0';return addResults;case '5':addResults[0] = '1';addResults[1] = '1';return addResults;	case '6':addResults[0] = '1';addResults[1] = '2';return addResults;	case '7':addResults[0] = '1';addResults[1] = '3';return addResults;	case '8':addResults[0] = '1';addResults[1] = '4';return addResults;	case '9':addResults[0] = '1';addResults[1] = '5';return addResults;	}break;case '7':switch(b){case '1':addResults[0] = '0';addResults[1] = '8';return addResults;case '2':addResults[0] = '0';addResults[1] = '9';return addResults;case '3':addResults[0] = '1';addResults[1] = '0';return addResults;case '4':addResults[0] = '1';addResults[1] = '1';return addResults;case '5':addResults[0] = '1';addResults[1] = '2';return addResults;	case '6':addResults[0] = '1';addResults[1] = '3';return addResults;	case '7':addResults[0] = '1';addResults[1] = '4';return addResults;	case '8':addResults[0] = '1';addResults[1] = '5';return addResults;	case '9':addResults[0] = '1';addResults[1] = '6';return addResults;	}break;case '8':switch(b){case '1':addResults[0] = '0';addResults[1] = '9';return addResults;case '2':addResults[0] = '1';addResults[1] = '0';return addResults;case '3':addResults[0] = '1';addResults[1] = '1';return addResults;case '4':addResults[0] = '1';addResults[1] = '2';return addResults;case '5':addResults[0] = '1';addResults[1] = '3';return addResults;	case '6':addResults[0] = '1';addResults[1] = '4';return addResults;	case '7':addResults[0] = '1';addResults[1] = '5';return addResults;	case '8':addResults[0] = '1';addResults[1] = '6';return addResults;	case '9':addResults[0] = '1';addResults[1] = '7';return addResults;	}break;case '9':switch(b){case '1':addResults[0] = '1';addResults[1] = '0';return addResults;case '2':addResults[0] = '1';addResults[1] = '1';return addResults;case '3':addResults[0] = '1';addResults[1] = '2';return addResults;case '4':addResults[0] = '1';addResults[1] = '3';return addResults;case '5':addResults[0] = '1';addResults[1] = '4';return addResults;	case '6':addResults[0] = '1';addResults[1] = '5';return addResults;	case '7':addResults[0] = '1';addResults[1] = '6';return addResults;	case '8':addResults[0] = '1';addResults[1] = '7';return addResults;	case '9':addResults[0] = '1';addResults[1] = '8';return addResults;	}break;default:break;}return addResults;
}char* mutip(char a,char b)
{//清空结果 mutiResults[0] = '0';mutiResults[1] = '0';if(a == '0' || b == '0'){mutiResults[0] = '0';mutiResults[1] = '0';return mutiResults;}if(a == '1'){mutiResults[0] = '0';mutiResults[1] = b;return mutiResults;}else if(b == '1'){mutiResults[0] = '0';mutiResults[1] = a;return mutiResults;}switch(a){case '2':switch(b){case '2':mutiResults[0] = '0';mutiResults[1] = '4';return mutiResults;case '3':mutiResults[0] = '0';mutiResults[1] = '6';return mutiResults;case '4':mutiResults[0] = '0';mutiResults[1] = '8';return mutiResults;case '5':mutiResults[0] = '1';mutiResults[1] = '0';return mutiResults;	case '6':mutiResults[0] = '1';mutiResults[1] = '2';return mutiResults;	case '7':mutiResults[0] = '1';mutiResults[1] = '4';return mutiResults;	case '8':mutiResults[0] = '1';mutiResults[1] = '6';return mutiResults;	case '9':mutiResults[0] = '1';mutiResults[1] = '8';return mutiResults;	}break;case '3':switch(b){case '2':mutiResults[0] = '0';mutiResults[1] = '6';return mutiResults;case '3':mutiResults[0] = '0';mutiResults[1] = '9';return mutiResults;case '4':mutiResults[0] = '1';mutiResults[1] = '2';return mutiResults;case '5':mutiResults[0] = '1';mutiResults[1] = '5';return mutiResults;	case '6':mutiResults[0] = '1';mutiResults[1] = '8';return mutiResults;	case '7':mutiResults[0] = '2';mutiResults[1] = '1';return mutiResults;	case '8':mutiResults[0] = '2';mutiResults[1] = '4';return mutiResults;	case '9':mutiResults[0] = '2';mutiResults[1] = '7';return mutiResults;	}break;case '4':switch(b){case '2':mutiResults[0] = '0';mutiResults[1] = '8';return mutiResults;case '3':mutiResults[0] = '1';mutiResults[1] = '2';return mutiResults;case '4':mutiResults[0] = '1';mutiResults[1] = '6';return mutiResults;case '5':mutiResults[0] = '2';mutiResults[1] = '0';return mutiResults;	case '6':mutiResults[0] = '2';mutiResults[1] = '4';return mutiResults;	case '7':mutiResults[0] = '2';mutiResults[1] = '8';return mutiResults;	case '8':mutiResults[0] = '3';mutiResults[1] = '2';return mutiResults;	case '9':mutiResults[0] = '3';mutiResults[1] = '6';return mutiResults;	}break;case '5':switch(b){case '2':mutiResults[0] = '1';mutiResults[1] = '0';return mutiResults;case '3':mutiResults[0] = '1';mutiResults[1] = '5';return mutiResults;case '4':mutiResults[0] = '2';mutiResults[1] = '0';return mutiResults;case '5':mutiResults[0] = '2';mutiResults[1] = '5';return mutiResults;	case '6':mutiResults[0] = '3';mutiResults[1] = '0';return mutiResults;	case '7':mutiResults[0] = '3';mutiResults[1] = '5';return mutiResults;	case '8':mutiResults[0] = '4';mutiResults[1] = '0';return mutiResults;	case '9':mutiResults[0] = '4';mutiResults[1] = '5';return mutiResults;	}break;case '6':switch(b){case '2':mutiResults[0] = '1';mutiResults[1] = '2';return mutiResults;case '3':mutiResults[0] = '1';mutiResults[1] = '8';return mutiResults;case '4':mutiResults[0] = '2';mutiResults[1] = '4';return mutiResults;case '5':mutiResults[0] = '3';mutiResults[1] = '0';return mutiResults;	case '6':mutiResults[0] = '3';mutiResults[1] = '6';return mutiResults;	case '7':mutiResults[0] = '4';mutiResults[1] = '2';return mutiResults;	case '8':mutiResults[0] = '4';mutiResults[1] = '8';return mutiResults;	case '9':mutiResults[0] = '5';mutiResults[1] = '4';return mutiResults;	}break;case '7':switch(b){case '2':mutiResults[0] = '1';mutiResults[1] = '4';return mutiResults;case '3':mutiResults[0] = '2';mutiResults[1] = '1';return mutiResults;case '4':mutiResults[0] = '2';mutiResults[1] = '8';return mutiResults;case '5':mutiResults[0] = '3';mutiResults[1] = '5';return mutiResults;	case '6':mutiResults[0] = '4';mutiResults[1] = '2';return mutiResults;	case '7':mutiResults[0] = '4';mutiResults[1] = '9';return mutiResults;	case '8':mutiResults[0] = '5';mutiResults[1] = '6';return mutiResults;	case '9':mutiResults[0] = '6';mutiResults[1] = '3';return mutiResults;	}break;case '8':switch(b){case '2':mutiResults[0] = '1';mutiResults[1] = '6';return mutiResults;case '3':mutiResults[0] = '2';mutiResults[1] = '4';return mutiResults;case '4':mutiResults[0] = '3';mutiResults[1] = '2';return mutiResults;case '5':mutiResults[0] = '4';mutiResults[1] = '0';return mutiResults;	case '6':mutiResults[0] = '4';mutiResults[1] = '8';return mutiResults;	case '7':mutiResults[0] = '5';mutiResults[1] = '6';return mutiResults;	case '8':mutiResults[0] = '6';mutiResults[1] = '4';return mutiResults;	case '9':mutiResults[0] = '7';mutiResults[1] = '2';return mutiResults;	}break;case '9':switch(b){case '2':mutiResults[0] = '1';mutiResults[1] = '8';return mutiResults;case '3':mutiResults[0] = '2';mutiResults[1] = '7';return mutiResults;case '4':mutiResults[0] = '3';mutiResults[1] = '6';return mutiResults;case '5':mutiResults[0] = '4';mutiResults[1] = '5';return mutiResults;	case '6':mutiResults[0] = '5';mutiResults[1] = '4';return mutiResults;	case '7':mutiResults[0] = '6';mutiResults[1] = '3';return mutiResults;	case '8':mutiResults[0] = '7';mutiResults[1] = '2';return mutiResults;	case '9':mutiResults[0] = '8';mutiResults[1] = '1';return mutiResults;	}break;default:break;}return mutiResults;
}void addToResultForMutip(char* result,char* toAdd)
{//乘法：按位乘再求和的模式下，做加法绝对不会溢出 result[strlen(result)] = '\0';toAdd[strlen(result)] = '\0';//puts(result);char w = '0'; for(int i = strlen(result) - 1;i >= 0;i--){char* t = add(result[i],toAdd[i]);char tw = t[0];char* tt = add(t[1],w);result[i] = tt[1];char* ttt = add(tt[0],tw);w = ttt[1]; }//puts(result);
}void printAddTables(void)
{char num[10] = {'0','1','2','3','4','5','6','7','8','9'};for(int i = 0;i < 10;i ++){for(int j = 0;j < 10;j ++){char* s = add(num[i],num[j]);printf("%c + %c = %c%c ",num[i],num[j],s[0],s[1]);}puts("");}
}
void printMutiTables(void)
{char num[10] = {'0','1','2','3','4','5','6','7','8','9'};for(int i = 0;i < 10;i ++){for(int j = 0;j < 10;j ++){char* s = mutip(num[i],num[j]);printf("%c x %c = %c%c ",num[i],num[j],s[0],s[1]);}puts("");}
}void printNumber(char* number)
{puts(number);
} 
void printFormatNumber(char* number)
{int len = strlen(number);for(int i = 0;i < len;i++){if(len % 3 == 0){if(i % 3 == 0 && i != 0){printf(",%c",number[i]);}else{printf("%c",number[i]);}}else{if(i < (len % 3)){printf("%c",number[i]);}else{if((i - len % 3) % 3 == 0 && i != 0){printf(",%c",number[i]);}else{printf("%c",number[i]);}}}}
} char* makeNoLimitMutip(char* ta,char* tb)
{int aWeight = strlen(ta) - 1;int bWeight = strlen(tb) - 1;int length = aWeight + bWeight + 3;char* result = (char*) malloc(sizeof(char) * length);char* toAdd = (char*) malloc(sizeof(char) * length);for(int i = 0;i < length;i++){if(i != length - 1){result[i] = '0';toAdd[i] = '0';}else{result[i] = '\0';toAdd[i] = '\0';}}for(int i = 0;i < strlen(ta);i++){//puts("\n------------------------");for(int j = 0;j < strlen(tb);j++){char* s = mutip(ta[i],tb[j]);toAdd[length - 1] = '\0';for(int k = length - 2;k >= 0;k--){if(k > (length - 2 - (bWeight + aWeight))){toAdd[k] = '0';}else if(k == (length - 2 - (bWeight + aWeight))){toAdd[k--] = s[1];toAdd[k] = s[0];}else{toAdd[k] = '0';}}addToResultForMutip(result,toAdd);bWeight--;}bWeight = strlen(tb) - 1;aWeight--;}free(toAdd); return result;
}

3.大整数字符串乘法器实现思路

两数相乘a×b，例如：1234×987654，ta:1234，tb:987654：

由于ta是4位整数、tb是6位整数，所以乘法积位数最多是10位，无非就是可能有0前缀数字，所以就直接当结果是10位。
所以，定义积字符串和临时乘法结果字符串：

int aWeight = strlen(ta) - 1;
int bWeight = strlen(tb) - 1;
int length = aWeight + bWeight + 3;
char* result = (char*) malloc(sizeof(char) * length);
char* toAdd = (char*) malloc(sizeof(char) * length);

result初始化为：0000000000

1. 拿出tb的最高位9，去和ta的每一位一次相乘，每乘一次就会得到一个临时结果：
   9乘1得09，且9后面还有5位、1后面还有3位，所以相乘结果字符串toAdd：0900000000，然后将toAdd加到result中。
   9乘2得18，且9后面还有5位、2后面还有2位，所以相乘结果字符串toAdd：0180000000，然后将toAdd加到result中。
   9乘3得27，且9后面还有5位、3后面还有1位，所以相乘结果字符串toAdd：0027000000，然后将toAdd加到result中。
   9乘4得36，且9后面还有5位、4后面还有0位，所以相乘结果字符串toAdd：0003600000，然后将toAdd加到result中。
2. 拿出tb的8，去和去和ta的每一位一次相乘，每乘一次就会得到一个临时结果：
   8乘1得08，且8后面还有4位、1后面还有3位，所以相乘结果字符串toAdd：0080000000，然后将toAdd加到result中。
   8乘2得16，且8后面还有4位、2后面还有2位，所以相乘结果字符串toAdd：0016000000，然后将toAdd加到result中。
   8乘3得24，且8后面还有4位、3后面还有1位，所以相乘结果字符串toAdd：0002400000，然后将toAdd加到result中。
   8乘4得32，且8后面还有4位、4后面还有0位，所以相乘结果字符串toAdd：0000320000，然后将toAdd加到result中。
3. 拿出tb的7，去和去和ta的每一位一次相乘，每乘一次就会得到一个临时结果：
   …………
4. 拿出tb的6，去和去和ta的每一位一次相乘，每乘一次就会得到一个临时结果：
   …………
5. 拿出tb的7，去和去和ta的每一位一次相乘，每乘一次就会得到一个临时结果：
   …………
6. 拿出tb的4，去和去和ta的每一位一次相乘，每乘一次就会得到一个临时结果：
   …………

4. 大整数字符串乘法器典型使用流程main.c

#include "BigInterNoLimitMutiString.c"int main(void)
{char num[10] = {'0','1','2','3','4','5','6','7','8','9'};char ta[10000] = {'\0'};char tb[10000] = {'\0'};gets(ta);gets(tb);printf("\ntalen-tblen:%d-%d",strlen(ta),strlen(tb));clock_t start = clock();char* result = makeNoLimitMutip(ta,tb);clock_t end = clock();printf("\nrun time is :%f\n",(double)(end - start) / CLOCKS_PER_SEC);puts("\n乘法积：");for(int i = 0;i < strlen(result);i++){if(result[i] != '0'){printFormatNumber(&result[i]);//puts("");//printNumber(result);break;}}free(result);//	puts("");
//	printAddTables();
//	puts("");
//	printMutiTables();return 0;
}