"""
Exercise 3.8 from "A primer on...

Use the standard formula for a quadratic
eq, x = -b +- sqrt(b**2 - 4*a*c)/(2*a)
But test the sign of the argument to the
sqrt function and use math if it is
positive (real solution) otherwise cmath 
(complex solution). 
"""

import math
import cmath

def roots(a, b, c):
    disc = b**2 - 4 * a * c
    if disc < 0:
        x1 = (-b + cmath.sqrt(disc))/ (2 * a)
        x2 = (-b - cmath.sqrt(disc))/ (2 * a)
    else:
        x1 = (-b + math.sqrt(disc))/ (2 * a)
        x2 = (-b - math.sqrt(disc))/ (2 * a)
    return x1, x2


def test_roots_float():
    tol = 1e-10
    a, b, c = 2, 3, 1
    expected = -0.5, -1
    computed = roots(a, b, c)
    for e, c in zip(expected, computed):
        assert abs(e-c) < tol



def test_roots_complex():
    tol = 1e-10
    a, b, c = 1, 1, 1
    expected = (-1 + cmath.sqrt(-3)) / 2,  (-1 - cmath.sqrt(-3)) / 2
    computed = roots(a, b, c)
    for e, c in zip(expected, computed):
        assert abs(e - c) < tol

"""
If we want to run the program in the
normal way, for instance with
"python roots_quadratic.py" from the
command line, we need to call the 
test functions here"""
test_roots_float()
test_roots_complex()

"""
An even better alternative is to use pytest, which 
will automatically call all test functions, and we don't
need to call them. See examples below.
"""

"""
Standard run, no output since both tests pass:
Terminal> python roots_quadratic.py 
"""

"""
Run with pytest
Terminal> pytest roots_quadratic.py 
============================= test session starts ==============================
platform darwin -- Python 3.9.7, pytest-6.2.4, py-1.10.0, pluggy-0.13.1
rootdir: /Users/sundnes/Desktop/IN1900_10_sept
plugins: anyio-2.2.0, mock-3.10.0, cov-3.0.0
collected 1 item                                                               

roots_quadratic.py .                                                     [100%]

============================== 1 passed in 0.02s ===============================
"""