Python hypothesis example.

hypothesis_sqrt.py

"""
Simple hypothesis example.
Test that sqrt computed using Newton-Raphson is correct.

Run with:
    $ py.test --hypothesis-show-statistics sqrt.py
"""
import hypothesis.strategies as st
from hypothesis import given, settings

EPS = 1e-3


def nr_sqrt(a: float, eps: float) -> float:
    """
    f(x)  = x**2 - a
    f'(x) = 2x
    x_new = x_old - f(x) / f'(x)
    """
    if a == 0:
        return 0
    x_old = float("inf")
    x_new = a / 2
    while abs(x_new - x_old) > eps:
        x_old = x_new
        x_new = 0.5 * (x_old + a / x_old)
    return x_new


@settings(max_examples=5000)
@given(
    st.floats(
        min_value=0,
        max_value=1e6,
        allow_nan=None,
        allow_infinity=None,
        width=32,
    )
)
def test(a):
    s = nr_sqrt(a, eps=EPS)
    assert abs(s ** 2 - a) < EPS