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Russian Peasent Math: Multiplication and Exponentiation

if b is even, a*b is (a*2)*(b/2). If b is odd, a*b is ((a*2)*(b/2) + a) where b/2 is an integer divide, e.g. the result is rounded down. If we apply this fact recursivly, we have the following method:

To put a number a times a number b into a number c:
Set a number c to zero.
While b is more than zero
	if b is odd, add a to c.
	Double a. Halve b.

In C, this might be:

unsigned int mult_rp(unsigned int a, unsigned int b){
	int c = 0; // initialize result
	while (b > 0) {
		if (b & 1) //odd?
			c += a; //accumulate
		a <<= 1; //shift left 1 bit, doubling
        	b >>= 1; //shift right 1 bit, halving
	return c;


This is also useful for raising a number to an exponent with the minimum number of multiplications, but instead of starting with 0, we start with 1, and instead of adding and doubling, we multiply and square.

int exp_rp(int a, int b) {
	c = 1; //initialize to 1 instead of 0
	while (b > 0) {
		if (b & 1) //odd?
			c *= a; //multiply the result by a
		b >>= 1; //shift right 1 bit, halving
		a *= a; //square
	return c;

See also:

file: /Techref/method/math/russianpeasent.htm, 2KB, , updated: 2021/6/13 10:05, local time: 2024/7/18 04:21,

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