Square Root Without Built-ins | Dataford Interview Questions

Freddie Mac analytics services may need a predictable square-root calculation without relying on language-provided math functions. Implement an algorithm that computes the square root of a nonnegative number using binary search.

Formal Specification

Write sqrt_approx(x, epsilon):

x is a nonnegative integer or floating-point number.
epsilon is a positive floating-point tolerance.
Return a floating-point value r such that abs(r * r - x) <= epsilon.
Do not use built-in square-root, exponentiation, logarithm, or power functions. Basic arithmetic and comparisons are allowed.
For x = 0, return 0.0.

The evaluator accepts answers within the required squared-error tolerance. Aim for logarithmic convergence rather than scanning candidate values incrementally.

Constraints

0 <= x <= 10^12
10^-12 <= epsilon <= 1
x is an integer or floating-point number
epsilon is positive
Do not use square-root, exponentiation, logarithm, or power functions

Function Signature

def sqrt_approx(x, epsilon):

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