在最早学习四则运算的过程中,我们其实就已经掌握了进制算法,这一次我将对二进制运用这个进制算法来实现四则运算。
四则运算
math.c
/**
* 功能:通过位操作实现四则运算
* 算法:完全参照十进制的进制算法
*
* Created with CLion
* User: zzzz76
* Date: 2018-02-10
*/
#include <stdio.h>
#include <assert.h>
#include "math.h"
/**
* 加法:往上递归实现
*
* @param a
* @param b
* @return
*/
int base_add(int a, int b) {
/* 值在函数中的传递只能通过参数或者返回操作,所以递归效果无非是体现在参数和返回操作上 */
if (b == 0) {
return a;
}
int save = a ^b;
int promote = (a & b) << 1;
return base_add(save, promote);
}
/**
* 加法:迭代实现
*
* @param a
* @param b
* @return
*/
int base_add_re(int a, int b) {
while (a && b) {
int promote = (a & b) << 1;
a = a ^ b;
b = promote;
}
return a ^ b;
}
/**
* 减法:往上递归实现
*
* @param a
* @param b
* @return
*/
int base_sub(int a, int b) {
if (b == 0) {
return a;
}
int save = a ^ b;
int reduce = ((~a) & b) << 1;
return base_sub(save, reduce);
}
/**
* 减法:迭代实现
*
* @param a
* @param b
* @return
*/
int base_sub_re(int a, int b) {
while(b) {
int save = a ^ b;
b = ((~a) & b) << 1;
a = save;
}
return a;
}
/**
* 减法:补位实现
*
* @param a
* @param b
* @return
*/
int base_sub_re_re(int a, int b) {
return base_add(a, base_add(~b, 1));
}
/**
* 乘法:递归实现
*
* @param a
* @param b
* @return
*/
int base_mul(int a, int b) {
int count = 0;
if (a == 0) {
return count;
}
if (a & 1) {
count = base_add(count, b);
}
a = (unsigned)a >> 1;
b <<= 1;
count = base_add(count, base_mul(a, b));
return count;
}
/**
* 乘法:迭代实现
*
* @param a
* @param b
* @return
*/
int base_mul_re(int a, int b) {
int count = 0;
while (a) {
if (a & 1) {
count = base_add(count, b);
}
a = (unsigned)a >> 1;
b <<= 1;
}
return count;
}
/**
* 除法:迭代实现
*
* @param a
* @param b
* @return
*/
int base_div(int a, int b) {
assert(b);
int result = 0;
int bit_num = 31;
while (bit_num != -1) {
if (b <= ((unsigned) a >> bit_num)) {
result = base_add(result, 1 << bit_num);
a = base_sub(a, b << bit_num);
}
bit_num = base_sub(bit_num, 1);
}
return result;
}
/**
* 除法:递归实现
*
* @param a
* @param b
* @return
*/
int base_div_re(int a, int b) {
assert(b);
if (a < (unsigned) b) {
return 0;
}
int bit_num = 0;
while (b <= (unsigned) a >> 1 >> bit_num) {
bit_num = base_add(bit_num, 1);
}
int result = 1 << bit_num;
a = base_sub(a, b << bit_num);
result = base_add(result, base_div_re(a, b));
return result;
}
math.h
/**
* Created with CLion
* User: zzzz76
* Date: 2018-02-12
*/
#ifndef MATH_H
#define MATH_H
int base_add(int a, int b);
int base_add_re(int a, int b);
int base_sub(int a, int b);
int base_sub_re(int a, int b);
int base_sub_re_re(int a, int b);
int base_mul(int a, int b);
int base_mul_re(int a, int b);
int base_div(int a, int b);
int base_div_re(int a, int b);
#endif //MATH_H
test.c
/**
* Created with CLion
* User: zzzz76
* Date: 2018-02-12
*/
#include "math.h"
#include <stdio.h>
static int main_ret = 0;
static int test_count = 0;
static int test_pass = 0;
#define EXPECT_EQ_BASE(expect, actual, format) \
do {\
test_count++;\
if ((expect) == (actual)) {\
test_pass++;\
} else {\
fprintf(stderr, "%s:%d: expect: " format " actual: " format "\n", __FILE__, __LINE__, expect, actual);\
main_ret = 1;\
}\
} while(0);
#define EXPECT_EQ_INT(expect, actual) EXPECT_EQ_BASE(expect, actual, "%d");
#define TEST_BASE_ADD(expect, a, b) \
EXPECT_EQ_INT(e