Multiplying two variables using bit shift operation

Question

I have two variables(which are actually elements of two different matrices). For example i want to multiply

a[i][k]*b[k][j]  

using bit manipulation, how can i do that.

I saw references to multiply constants, not variables like 3*2, 3*4, 3*8, etc. But how can i apply same techniques to multiplying variables? If a post on this exist, can you point me to that. Thanks!

Answer 1

Given two integral variables

unsigned X, Y;

And given a Commodore 64, Apple ][, or some other architecture that doesn't have its own multiply instruction, this will multiply the numbers.

unsigned answer = 0;
while ( X )
{
  answer <<= 1;
  if ( X & 1 )
    answer += Y;
  X >>= 1;
}

Answer 2

Bit shift multiplication is usable only when multiplying by a power of 2 (2, 4, 8, 16 etc). The multiplication will then be reduced to as single bit shift operation:

  x1 = 2^n;
  result = x2 << n;  // This is the same as x2 * x1

For arbitrary cases, the most efficient way is to use normal multiplication:

a[i][k]*b[k][j]

Answer 3

If you're multiplying huge matrices, what matters is an efficient algorithm that has good cache behavior. For C++, check out the Eigen library . On a modern CPU you can't micro-optimize multiplication of two variables.