isqrtn

The isqrtn function, often found in programming libraries or mathematical contexts, calculates the integer square root of a non-negative integer. The integer square root of a number n is the largest integer s such that s squared is less than or equal to n. For example, the integer square root of 10 is 3, because 3*3 = 9, and 4*4 = 16, which is greater than 10. Similarly, the integer square root of 9 is 3.

This function is distinct from the standard mathematical square root function, which typically returns a floating-point number. The isqrtn function guarantees an integer result, making it suitable for applications where only whole number precision is required or beneficial. These applications can include algorithms involving discrete mathematics, array indexing, or computational geometry where floating-point inaccuracies could lead to errors.

Various algorithms can be employed to compute the integer square root efficiently. Common methods include binary search, Newton's method adapted for integers, or digit-by-digit algorithms. The choice of algorithm often depends on factors like the expected range of input numbers and performance requirements. The isqrtn function is typically defined for unsigned integer types, ensuring that the input is non-negative.