# Bitwise multiplication with correction for overflow

-1

I am trying to use Bitwise operators ( ! ~ & ^ | + << >> ) in C to achieve a multiplication of 4 while also correcting for Positive and Negative overflow by returning the Max value and Minimum value, respectively. For example,

``````Function(0x10000000) = 0x40000000
Function(0x20000000) = 0x7FFFFFFF
Function(0x80000000) = 0x80000000
``````

My primary method is checking the sign of the product to find if it changed expectedly.

``````    int funcMultBy4(int x){
int signedBit=(x>>31);
int minValue= 1<<31;
int xtimes4= x<<2;
int maxValue= (x ^ xtimes4) >> 31;
int saturate= maxValue & (signedBit ^ ~minValue);
return saturate | (xtimes4 ^ ~maxValue) ;
}
``````

Currently, when multiplying 0x7fffffff, I am getting -1 rather than an expected 0x7FFFFFFF. I understand there is probably a necessary shift by 1 somewhere, but am having trouble finding my error.

c
bit-manipulation

2

It is the `^` in the last line that needs to be `&` and overflow must be detected in both the first and second bit-shift.

This slight reorganisation of the function seems more intuitive to me:

``````     int funcMultBy4(int x)
{
int signedBit = (x>>31);
int minValue = 1<<31;
int xtimes4 = x<<2;
int overflow = (x ^ (x<<1) | (x ^ (x<<2))) >> 31;
int saturate = (signedBit ^ ~minValue);
return (overflow & saturate) | (~overflow & xtimes4) ;
}
``````

Of course, the code depends on the int size to be 32 bits. You may either use the fixed-width type `int32_t` or replace `31` by `((int)((sizeof(int)<<3)-1))` (could be defined in a macro).

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