如何将一个数除3而不使用*、/、+、-、%等运算符?

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当前回答

使用cblas,作为OS X加速框架的一部分。

[02:31:59] [william@relativity ~]$ cat div3.c
#import <stdio.h>
#import <Accelerate/Accelerate.h>

int main() {
    float multiplicand = 123456.0;
    float multiplier = 0.333333;
    printf("%f * %f == ", multiplicand, multiplier);
    cblas_sscal(1, multiplier, &multiplicand, 1);
    printf("%f\n", multiplicand);
}

[02:32:07] [william@relativity ~]$ clang div3.c -framework Accelerate -o div3 && ./div3
123456.000000 * 0.333333 == 41151.957031

其他回答

为什么我们不直接用在大学里学过的定义呢?结果可能效率低,但很清楚,因为乘法只是递归的减法,减法是加法,那么加法可以通过递归的异或/和逻辑端口组合来执行。

#include <stdio.h>

int add(int a, int b){
   int rc;
   int carry;
   rc = a ^ b; 
   carry = (a & b) << 1;
   if (rc & carry) 
      return add(rc, carry);
   else
      return rc ^ carry; 
}

int sub(int a, int b){
   return add(a, add(~b, 1)); 
}

int div( int D, int Q )
{
/* lets do only positive and then
 * add the sign at the end
 * inversion needs to be performed only for +Q/-D or -Q/+D
 */
   int result=0;
   int sign=0;
   if( D < 0 ) {
      D=sub(0,D);
      if( Q<0 )
         Q=sub(0,Q);
      else
         sign=1;
   } else {
      if( Q<0 ) {
         Q=sub(0,Q);
         sign=1;
      } 
   }
   while(D>=Q) {
      D = sub( D, Q );
      result++;
   }
/*
* Apply sign
*/
   if( sign )
      result = sub(0,result);
   return result;
}

int main( int argc, char ** argv ) 
{
    printf( "2 plus 3=%d\n", add(2,3) );
    printf( "22 div 3=%d\n", div(22,3) );
    printf( "-22 div 3=%d\n", div(-22,3) );
    printf( "-22 div -3=%d\n", div(-22,-3) );
    printf( "22 div 03=%d\n", div(22,-3) );
    return 0;
}

有人说……首先让它工作。注意,该算法应该适用于负Q…

使用fma()库函数的解决方案,适用于任何正数:

#include <stdio.h>
#include <math.h>

int main()
{
    int number = 8;//Any +ve no.
    int temp = 3, result = 0;
    while(temp <= number){
        temp = fma(temp, 1, 3); //fma(a, b, c) is a library function and returns (a*b) + c.
        result = fma(result, 1, 1);
    } 
    printf("\n\n%d divided by 3 = %d\n", number, result);
}

请看我的另一个答案。

Yet another solution. This should handle all ints (including negative ints) except the min value of an int, which would need to be handled as a hard coded exception. This basically does division by subtraction but only using bit operators (shifts, xor, & and complement). For faster speed, it subtracts 3 * (decreasing powers of 2). In c#, it executes around 444 of these DivideBy3 calls per millisecond (2.2 seconds for 1,000,000 divides), so not horrendously slow, but no where near as fast as a simple x/3. By comparison, Coodey's nice solution is about 5 times faster than this one.

public static int DivideBy3(int a) {
    bool negative = a < 0;
    if (negative) a = Negate(a);
    int result;
    int sub = 3 << 29;
    int threes = 1 << 29;
    result = 0;
    while (threes > 0) {
        if (a >= sub) {
            a = Add(a, Negate(sub));
            result = Add(result, threes);
        }
        sub >>= 1;
        threes >>= 1;
    }
    if (negative) result = Negate(result);
    return result;
}
public static int Negate(int a) {
    return Add(~a, 1);
}
public static int Add(int a, int b) {
    int x = 0;
    x = a ^ b;
    while ((a & b) != 0) {
        b = (a & b) << 1;
        a = x;
        x = a ^ b;
    }
    return x;
}

这是c#,因为这是我手边的东西,但与c的区别应该很小。

我会用这段代码除所有正数,非浮点数。基本上你要把除数位向左对齐以匹配被除数位。对于被除数的每一段(除数的大小),你想要检查是否被除数的每一段大于除数,然后你想要左Shift,然后在第一个注册器中OR。这个概念最初是在2004年创建的(我相信是斯坦福大学),这里是一个C版本,它使用了这个概念。注:(我做了一点修改)

int divide(int a, int b)
{
    int c = 0, r = 32, i = 32, p = a + 1;
    unsigned long int d = 0x80000000;

    while ((b & d) == 0)
    {
        d >>= 1;
        r--;
    }

    while (p > a)
    {
        c <<= 1;
        p = (b >> i--) & ((1 << r) - 1);
        if (p >= a)
            c |= 1;
    }
    return c; //p is remainder (for modulus)
}

使用示例:

int n = divide( 3, 6); //outputs 2

没有反复检查这个答案是否已经发表。如果程序需要扩展到浮点数,可以将这些数字乘以所需精度的10*数,然后可以再次应用下面的代码。

#include <stdio.h>

int main()
{
    int aNumber = 500;
    int gResult = 0;

    int aLoop = 0;

    int i = 0;
    for(i = 0; i < aNumber; i++)
    {
        if(aLoop == 3)
        {
           gResult++;
           aLoop = 0;
        }  
        aLoop++;
    }

    printf("Reulst of %d / 3 = %d", aNumber, gResult);

    return 0;
}