Algorithms: Number Theory Tutorials and Code Examples - Page 14

Exponentiation by Squaring in C++

Binary exponentiation evaluates an integer power using the bits of the exponent.

cpp

int power(int base, int exponent) {
    alg_require((exponent >= 0));
    int result = 1;
    while ((exponent > 0)) {
        if (((exponent % 2) == 1)) {
            result = alg_mul(result, base);
        }
        exponent = (exponent / 2);
        if ((exponent > 0)) {
            base = alg_mul(base, base);
        }
    }

Nov 15, 2026 C++

Algorithms: Number Theory

Exponentiation by Squaring in C

Binary exponentiation evaluates an integer power using the bits of the exponent.

c

int power(int base, int exponent) {
    int alg_error = 0;
    int alg_result = INT_MIN;
    errno = 0;
    if (!((exponent >= 0))) { errno = EINVAL; alg_result = INT_MIN; goto alg_cleanup; }
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    int result = 1;
    if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
    while (1) {
        int alg_condition = (exponent > 0);
        if (alg_error) { errno = ERANGE; alg_result = INT_MIN; goto alg_cleanup; }
        if (!alg_condition) break;

Nov 15, 2026 C

Algorithms: Number Theory

Exponentiation by Squaring in Python

Binary exponentiation evaluates an integer power using the bits of the exponent.

python

def power(base: int, exponent: int) -> int:
    alg_require(type(base) is int and -2147483648 <= base <= 2147483647)
    alg_require(type(exponent) is int and -2147483648 <= exponent <= 2147483647)
    alg_require(exponent >= 0)
    result: int = 1
    while exponent > 0:
        if exponent % 2 == 1:
            result *= base
        exponent = exponent // 2
        if exponent > 0:
            base *= base
    return result

Nov 15, 2026 python

Algorithms: Number Theory

Exponentiation by Squaring in JavaScript

Binary exponentiation evaluates an integer power using the bits of the exponent.

javascript

function power(base, exponent) {
    alg_require(Number.isInteger(base) && base >= -2147483648 && base <= 2147483647);
    alg_require(Number.isInteger(exponent) && exponent >= -2147483648 && exponent <= 2147483647);
    alg_require((exponent >= 0));
    let result = 1;
    while ((exponent > 0)) {
        if (((exponent % 2) == 1)) {
            result = alg_mul(result, base);
        }
        exponent = Math.floor(exponent / 2);
        if ((exponent > 0)) {
            base = alg_mul(base, base);

Nov 15, 2026 javascript

Algorithms: Number Theory

Exponentiation by Squaring in Java

Binary exponentiation evaluates an integer power using the bits of the exponent.

java

    static int power(int base, int exponent) {
        alg_require((exponent >= 0));
        int result = 1;
        while ((exponent > 0)) {
            if (((exponent % 2) == 1)) {
                result = Math.multiplyExact(result, base);
            }
            exponent = (exponent / 2);
            if ((exponent > 0)) {
                base = Math.multiplyExact(base, base);
            }
        }

Nov 15, 2026 Java