How to multiply an int with a fraction

I need to multiply an int by a fraction using bitwise operators without loops and such.

For example, I need to multiply by x by 3/8.

I thought you would:

int value = (x << 1) + x;  // Multiply by 3
value = (value >> 3); 开发者_如何学Python         // Divide by 8

But that doesnt work. I tried googling binary times fraction but that give floating point examples. I dont know exactly if this homework is for floating point but my hunch is no but getting me prepared for it. So any suggestions?

I need to round toward zero so any suggestions? This doesnt work for the number -268435457.

You probably want

int value = (x << 1) + x;
value = (value >> 3);

note that:

(x << 1) + 1 = 2*x + 1; // ignoring issues about overflow

To adjust for negative values, you can explicitly check for sign:

int value = (x << 1) + x;
value = value >> 3;
value = value + ((x >> 31) & 1); // for 32 bit; for 64 bit you have to use x >> 63

Did you try:

int value = (x << 1) + x;  // Multiply by 3
value = (value >> 3);      // Divide by 8

i.e. in your second statement replace 'x' with 'value'. Also, value will loose the decimal points.

To avoid an overflow you can cast to (long long) and back to (int) for the final result. To cause the >> 3 to round toward zero you need to add 7 (8-1) for a negative number. There are a few ways of doing this. Using these approaches gives you -100663296.