C语言实现大数加减乘除

/*
* file name : calculatorv4.c
* desp : calculator version 4
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define BASE (10)
#define MAX(x,y) ((x)>(y)?(x):(y))

// 大数数据结构
typedef struct bignumber_s {
    char sign; // 代表大数的符号，1为负数，0为正数
    int len;   // 代表大数的位数
    char data[]; // 大数的数据内容，data[0]代表个位，data[1]代表十位，data[2]代表百位....
} bignumber_s;

bignumber_s* calc_add (bignumber_s* a, bignumber_s* b);
bignumber_s* calc_sub (bignumber_s* a, bignumber_s* b);

// 构造大数模板，len指向大数的数据位数，sign表示该大数的符号
bignumber_s* make_bignumber_temp (int len, int sign) {
    // 分配bignumber_s及其所代表数据 所需的内存
    bignumber_s* temp = malloc (sizeof (bignumber_s) + len);
    if (NULL == temp) {
        perror ("Malloc");
        exit (-1);
    }
    temp->sign = sign;
    temp->len = len;
    memset (temp->data, 0, len);
    return temp;
}

// 处理数字字符串冗余的0，即"00123" -> "123"
const char* strip_str (const char* str) {
    int i = 0;
    int len = strlen (str);
    for (i = 0; i < len - 1 && str[i] == '0'; i++);
    return str + i;
}
// 将字符串数据填充进模板中
void fill_data_fromstr (bignumber_s* n, const char* str) {
    int i = 0;
    int len = n->len;
    for (i = 0; i < len; i++) {
        int d = str[len - 1 - i] - '0';
        if (d >= 0 && d <= 9)
            n->data[i] = d;
        else {
            fprintf (stderr, "Invalid Number:%s\n", str);
            exit (-1);
        }
    }
}
// 从字符串构造一个大数
bignumber_s* make_bignumber_fromstr (const char* str) {
    // 处理负数字符串，即"-123"
    int sign = 0;
    if (str[0] == '-') {
        sign = 1;
        str++;
    }
    // 处理数字字符串冗余的0，即"00123" -> "123"
    const char* striped_str = strip_str (str);

    int len = strlen (striped_str);
    // 指定数据位长度即符号，创建一个大数模板
    bignumber_s* temp = make_bignumber_temp (len, sign);
    // 将字符串数据填充进模板中，完成大数创建
    fill_data_fromstr (temp, striped_str);
    return temp;
}

// 以字符串的形式打印输出一个大数
void print_bignumber (bignumber_s* b) {
    int len = b->len;
    char* str = malloc (len + 1);
    int i = 0;

    for (i = 0; i < len; i++) {
        str[i] = b->data[len - i - 1] + '0';
    }
    str[len] = '\0';

    fprintf (stdout, "%s%s\n", b->sign == 1 ? "-" : "", strip_str (str));
    free (str);
}

void usage (const char* s) {
    fprintf (stderr, "Usage:%s number1 +-x/ number2.\n", s);
    exit (-1);
}

// 实现无符号加法，a和b为加数，r为和
void add_impl (bignumber_s* a, bignumber_s* b, bignumber_s* r) {
    int i = 0;
    char carry = 0;
    int len = r->len;
    for (i = 0; i < len; i++) {
        if (i < a->len)carry += a->data[i];
        if (i < b->len)carry += b->data[i];
        r->data[i] = carry % BASE;
        carry /= BASE;
    }
}

bignumber_s* calc_add (bignumber_s* a, bignumber_s* b) {
    // 情况一和情况四
    if (a->sign == b->sign) {
        // n位数+m位数，其和最大为max(n,m)+1位数
        int len = MAX (a->len, b->len) + 1;
        bignumber_s* result = make_bignumber_temp (len, a->sign);

        add_impl (a, b, result);
        return result;
    } else if (a->sign == 0 && b->sign == 1) {//情况二
        b->sign = 0; //b数去绝对值
        return calc_sub (a, b);
    } else if (a->sign == 1 && b->sign == 0) {//情况三
        a->sign = 0; //a数去绝对值
        return calc_sub (b, a);
    }
}

// 实现无符号减法，a-b , r为差
void sub_impl (bignumber_s* a, bignumber_s* b, bignumber_s* r) {
    int i = 0;
    int borrow = 0;
    int len = r->len;
    int temp = 0;
    for (i = 0; i < len; i++) {
        temp = a->data[i] + BASE - borrow - ((i < b->len) ? b->data[i] : 0);
        r->data[i] = temp % BASE;
        borrow = temp / BASE ? 0 : 1;
    }
}

int valid_len (bignumber_s* a) {
    int len = a->len;
    int i = len - 1;
    for (i = len - 1; i >= 0; i--) {
        if (a->data[i] == 0) len--;
        else break;
    }
    return len;
}
// 判断两个大数的大小
// a > b 返回1 ，a<b 返回 -1 , a==b 返回0
int cmp (bignumber_s* a, bignumber_s* b) {

    if (a->sign == 0 && b->sign == 1) return 1;
    if (a->sign == 1 && b->sign == 0) return -1;

    int sign = a->sign;
    int alen = valid_len (a);
    int blen = valid_len (b);
    if (alen > blen) return (sign == 1 ? -1 : 1);
    else if (alen < blen) return (sign == 1 ? 1 : -1);
    else {
        int i = 0;
        int len = alen;
        for (i = len - 1; i >= 0; i--) {
            if (a->data[i] > b->data[i])return (sign == 1 ? -1 : 1);
            else if (a->data[i] < b->data[i]) return (sign == 1 ? 1 : -1);
        }
        return 0;
    }
}

bignumber_s* calc_sub (bignumber_s* a, bignumber_s* b) {
    // 情况一
    if (a->sign == 0 && b->sign == 0) {
        if (cmp (a, b) >= 0) { // 被减数大于等于减数，即差大于等于0时
            int len = a->len;
            bignumber_s* result = make_bignumber_temp (len, 0);
            sub_impl (a, b, result);
            return result;
        } else { // 被减数小于减数，即差小于0时
            int len = b->len;
            bignumber_s* result = make_bignumber_temp (len, 1);
            sub_impl (b, a, result);
            return result;
        }
    } else if (a->sign == 1 && b->sign == 1) { //情况四
        b->sign = 0;
        a->sign = 0;
        return calc_sub (b, a); //调换减数和被减数，变成情况一
    } else if (a->sign == 0 && b->sign == 1) { // 情况二
        b->sign = 0;
        bignumber_s* result = calc_add (a, b);
        result->sign = 0;
        return result;
    } else if (a->sign == 1 && b->sign == 0) { // 情况三
        a->sign = 0;
        bignumber_s* result = calc_add (a, b);
        result->sign = 1;
        return result;
    }
}

// 实现无符号乘法，x * y , z为积
void mul_impl (bignumber_s* x, bignumber_s* y, bignumber_s* z) {
    int n = x->len;
    int m = y->len;
    int i = 0;
    int j = 0;
    int carry = 0;
    for (i = 0; i < m; i++) {
        // y的每一位乘以x，即计算y[i] * x[0...n] 并累加到z[i...i+n]中
        for (j = 0; j < n; j++) {
            carry += y->data[i] * x->data[j] + z->data[i + j];
            z->data[i + j] = carry % BASE;
            carry /= BASE;
        }

        // 将剩余的进位,继续在z[i+n...n+m]中累加，从而完成y[i]乘以x[0...n]其积累加到z[i...m+n]中
        for (; j + i < n + m; j++) {
            carry += z->data[i + j];
            z->data[i + j] = carry % BASE;
            carry /= BASE;
        }
    }
}

bignumber_s* calc_mul (bignumber_s* a, bignumber_s* b) {
    bignumber_s* zero = make_bignumber_temp (1, 0);
    //乘数当中有0，直接返回0
    if (cmp (a, zero) == 0 || cmp (b, zero) == 0) return zero;
    int len = a->len + b->len;
    bignumber_s* result = make_bignumber_temp (len, a->sign == b->sign ? 0 : 1); //a->sign==b->sign为情况一，否则为情况二。
    mul_impl (a, b, result);
    return result;
}

// 大数加一操作
void plusone (bignumber_s* a) {
    int len = a->len;
    int i;
    int carry = 1;
    for (i = 0; i < len; i++) {
        carry += a->data[i];
        a->data[i] = carry % BASE;
        carry /= BASE;
    }
}
// 大数除法实现
bignumber_s* calc_div (bignumber_s* a, bignumber_s* b) {
    bignumber_s* zero = make_bignumber_temp (1, 0);
    if (cmp (b, zero) == 0) {// 除数为0 报错
        fprintf (stderr, "Integer division by zero\n");
        exit (-1);
    } else if (cmp (a, zero) == 0) { // 被除数为0 ，结果为0
        return zero;
    }

    int len = a->len;
    bignumber_s* result = make_bignumber_temp (len, a->sign == b->sign ? 0 : 1);
    a->sign = 0;
    b->sign = 0;
    bignumber_s* temp = make_bignumber_temp (len, 0);
    bignumber_s* aa = a;
    while (1) {
        if (cmp (aa, b) >= 0) {
            sub_impl (aa, b, temp);
            plusone (result);
            aa = temp;
        } else {
            free (temp);
            return result;
        }
    }
}

int main (int argc, char* argv[]) {
    bignumber_s* a = make_bignumber_fromstr (argv[1]);
    bignumber_s* b = make_bignumber_fromstr (argv[3]);
    if (argc != 4) usage (argv[0]);

    if (0 == strcmp (argv[2], "+"))
        print_bignumber (calc_add (a, b));
    else if (0 == strcmp (argv[2], "-"))
        print_bignumber (calc_sub (a, b));
    else if (0 == strcmp (argv[2], "x"))
        print_bignumber (calc_mul (a, b));
    else if (0 == strcmp (argv[2], "/"))
        print_bignumber (calc_div (a, b));
    else usage (argv[0]);
    return 0;
}