#!/usr/bin/env python3

import math
import cmath
import numpy

def quad_discriminating_roots(a,b,c, entier = 1e-5):
    """For reference, the naive algorithm which shows complete loss of
    precision on the quadratic in question.  (This function also returns a
    characterization of the roots.)"""
    discriminant = b*b - 4*a*c
    a,b,c,d =complex(a), complex(b), complex(c), complex(discriminant)
    root1 = (-b + cmath.sqrt(d))/2./a
    root2 = (-b - cmath.sqrt(d))/2./a
    if abs(discriminant) < entier:
        return "real and equal", abs(root1), abs(root1)
    if discriminant > 0:
        return "real", root1.real, root2.real
    return "complex", root1, root2

def middlebrook(a, b, c):
    try:
        q = math.sqrt(a*c)/b
        f = .5+ math.sqrt(1-4*q*q)/2
    except ValueError:
        q = cmath.sqrt(a*c)/b
        f = .5+ cmath.sqrt(1-4*q*q)/2
    return (-b/a)*f, -c/(b*f)

def whatevery(a, b, c):
    try:
        d = math.sqrt(b*b-4*a*c)
    except ValueError:
        d = cmath.sqrt(b*b-4*a*c)
    if b > 0:
        return div(2*c, (-b-d)), div((-b-d), 2*a)
    else:
        return div((-b+d), 2*a), div(2*c, (-b+d))

def div(n, d):
    """Divide, with a useful interpretation of division by zero."""
    try:
        return n/d
    except ZeroDivisionError:
        if n:
            return n*float('inf')
        return float('nan')

testcases = [
    (3, 4, 4/3),    # real, equal
    (3, 2, -1),     # real, unequal
    (3, 2, 1),      # complex
    (1, -1e9, 1),   # ill-conditioned "quadratic in question" required by task.
    (1, -1e100, 1),
    (1, -1e200, 1),
    (1, -1e300, 1),
]

print('Naive:')
for c in testcases:
    print("{} {:.5} {:.5}".format(*quad_discriminating_roots(*c)))

print('\nMiddlebrook:')
for c in testcases:
    print(("{:.5} "*2).format(*middlebrook(*c)))

print('\nWhat Every...')
for c in testcases:
    print(("{:.5} "*2).format(*whatevery(*c)))

print('\nNumpy:')
for c in testcases:
    print(("{:.5} "*2).format(*numpy.roots(c)))