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Home » Tip Bank » C++
Language: C++
Expertise: Beginner
Jul 26, 2002

A Fast Multiplication Method for Integer Numbers


The multiplication operation for integer numbers is implemented in the processor as repeated additions. The number of additions can be reduced by considering the representation in base 2 of the multiplier, as in this example:
 
int i = 111;
//We need to compute int j = i * 15; but 15 = 1 + 2 + 4 + 8 
= 2^0 + 2^1 +
2^2 + 2^3,
//so we can reduce the multiplication to some shift operations 
and just 3 additions

int j = i + (I<<1) + (I<<2) + (I<<3);

If you have multiplications in some lengthy iterative loops, using this trick can substantially increase CPU saving.
George Anescu
 
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