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test.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""Unit tests of contfrac.py"""
import fractions
import math
import typing
import unittest
import contfrac
class TestEvaluateContfrac(unittest.TestCase):
def test_evaluate_continued_fraction(self):
test_values = {
(): 0,
(0,): 0,
(1,): 1,
(20,): 20,
(0, 20): 1 / 20,
(-20,): -20,
(1, 2): 1 + 1 / 2,
(-1, 2): -1 + 1 / 2,
(0, 1): 0 + 1 / 1,
(0, 0, 0, 1): 0 + 1 / (0 + (1 / (0 + (1 / 1)))),
(0, 0, 0, 17): 0 + 1 / (0 + (1 / (0 + (1 / 17)))),
(1, 2, 3): 1 + 1 / (2 + 1 / 3),
(1, 2, 3, 4): 1 + 1 / (2 + (1 / (3 + (1 / 4)))),
(1, 2, -3, 4): 1 + 1 / (2 + (1 / (-3 + (1 / 4)))),
(1.1, 2, -3.34, 4): 1.1 + 1 / (2 + (1 / (-3.34 + (1 / 4)))),
(3, 4, 12, 4): 649 / 200,
(4, 2, 6, 7): 415 / 93,
range(1, 5): 1 + 1 / (2 + (1 / (3 + (1 / 4)))),
b'CD': 67 + 1 / 68,
}
for input_value, expected_output in test_values.items():
with self.subTest(contfrac_of=input_value):
result = contfrac.evaluate(input_value)
self.assertAlmostEqual(expected_output, result, places=6)
def test_evaluate_continued_fraction_with_zero_end(self):
values = [
[1, 0],
[1, 2, 3, 0],
[1, 2, 3, 0.0],
[1, 2, 3, 0, 0, 0, 0],
]
for value in values:
with self.subTest(input_value=value):
with self.assertRaises(ZeroDivisionError):
contfrac.evaluate(value)
def test_evaluate_continued_fraction_unsupported_type_raises(self):
self.assertRaises(TypeError, contfrac.evaluate, None)
self.assertRaises(TypeError, contfrac.evaluate, 1)
self.assertRaises(TypeError, contfrac.evaluate, 1.1)
self.assertRaises(TypeError, contfrac.evaluate, 'hello')
class TestArithmeticExpression(unittest.TestCase):
def test_expression_continued_fraction(self):
test_values = {
(): '',
(0,): '0',
(1,): '1',
(20,): '20',
(0, 20): '0 + 1/(20)',
(-20,): '-20',
(1, 2): '1 + 1/(2)',
(-1, 2): '-1 + 1/(2)',
(1, -2): '1 + 1/(-2)',
(0, 1): '0 + 1/(1)',
(0, 0, 0, 1): '0 + 1/(0 + 1/(0 + 1/(1)))',
(0, 0, 0, 17): '0 + 1/(0 + 1/(0 + 1/(17)))',
(1, 2, 3): '1 + 1/(2 + 1/(3))',
(1, 2, 3, 4): '1 + 1/(2 + 1/(3 + 1/(4)))',
(1, 2, -3, 4): '1 + 1/(2 + 1/(-3 + 1/(4)))',
(1.1, 2, -3.34, 4): '1.1 + 1/(2 + 1/(-3.34 + 1/(4)))',
range(1, 5): '1 + 1/(2 + 1/(3 + 1/(4)))',
}
for input_value, expected_default in test_values.items():
with self.subTest(contfrac_of=input_value):
result = contfrac.arithmetical_expr(input_value)
expected_output = expected_default
self.assertEqual(expected_output, result)
with self.subTest(contfrac_of=input_value, spaces=False):
result = contfrac.arithmetical_expr(input_value,
with_spaces=False)
expected_output = expected_default.replace(' ', '')
self.assertEqual(expected_output, result)
with self.subTest(contfrac_of=input_value, floats=True):
result = contfrac.arithmetical_expr(input_value,
force_floats=True)
expected_output = expected_default.replace('1/', '1.0/')
self.assertEqual(expected_output, result)
with self.subTest(contfrac_of=input_value,
spaces=False, floats=True):
result = contfrac.arithmetical_expr(input_value,
with_spaces=False,
force_floats=True)
expected_output = expected_default.replace(' ', '')
expected_output = expected_output.replace('1/', '1.0/')
self.assertEqual(expected_output, result)
class TestContfracComputation(unittest.TestCase):
def test_continued_fraction_is_generators(self):
result = contfrac.continued_fraction(1)
self.assertIsInstance(result, typing.Generator)
def test_continued_fraction_legal_values(self):
test_values = {
# Integers
0: [0],
1: [1],
123: [123],
-1: [-1],
-123: [-123],
# Tuples: (nominator, denominator)
(649, 200): [3, 4, 12, 4],
(415, 93): [4, 2, 6, 7],
(-649, 200): [-4, 1, 3, 12, 4],
(415, -93): [-5, 1, 1, 6, 7],
# Fractions
fractions.Fraction(649, 200): [3, 4, 12, 4],
fractions.Fraction(415, 93): [4, 2, 6, 7],
fractions.Fraction(-649, 200): [-4, 1, 3, 12, 4],
fractions.Fraction(415, -93): [-5, 1, 1, 6, 7],
# Floats
649 / 200: [3, 4, 12, 4],
-649 / 200: [-3, -4, -12, -4],
415 / 93: [4, 2, 6, 7],
0.84375: [0, 1, 5, 2, 2],
}
for input_value, expected_output in test_values.items():
with self.subTest(contfrac_of=input_value):
result = list(contfrac.continued_fraction(input_value))
self.assertListEqual(expected_output, result)
with self.subTest(evaluating_contfrac_of=input_value):
if isinstance(input_value, tuple):
input_value = input_value[0] / input_value[1]
elif isinstance(input_value, fractions.Fraction):
input_value = float(input_value)
evaluated = contfrac.evaluate(result)
self.assertAlmostEqual(input_value, evaluated, delta=1e-8)
def test_continued_fraction_illegal_maxlen(self):
self.assertRaises(ValueError, contfrac.continued_fraction, 2.2,
maxlen=-1)
self.assertRaises(ValueError, contfrac.continued_fraction, 2.2,
maxlen=0)
list(contfrac.continued_fraction(2.2, maxlen=1))
def test_continued_fraction_unsupported_type_raises(self):
self.assertRaises(TypeError, contfrac.continued_fraction, None)
self.assertRaises(TypeError, contfrac.continued_fraction, 'hello')
self.assertRaises(TypeError, contfrac.continued_fraction, b'hello')
self.assertRaises(TypeError, contfrac.continued_fraction, dict())
def test_continued_fraction_golden_ratio(self):
golden_ratio = (1 + math.sqrt(5)) / 2
expected = [1] * 40
result = list(contfrac.continued_fraction(golden_ratio, maxlen=2))
self.assertListEqual(expected[:2], result)
result = list(contfrac.continued_fraction(golden_ratio, maxlen=20))
self.assertListEqual(expected[:20], result)
result = list(contfrac.continued_fraction(golden_ratio, maxlen=31))
self.assertListEqual(expected[:31], result)
def test_rounding_errors(self):
golden_ratio = (1 + math.sqrt(5)) / 2
as_ratio = golden_ratio.as_integer_ratio()
result = list(contfrac.continued_fraction(golden_ratio, maxlen=50))
self.assertNotEqual([1] * 50, result)
evaluated_value = contfrac.evaluate(result)
self.assertEqual(golden_ratio, evaluated_value)
result = list(contfrac.continued_fraction(as_ratio, maxlen=50))
self.assertNotEqual([1] * 50, result)
evaluated_value = contfrac.evaluate(result)
self.assertEqual(as_ratio, evaluated_value.as_integer_ratio())
class TestConvergents(unittest.TestCase):
def test_convergents(self):
x = 0.84375
expected = [(0, 1), (1, 1), (5, 6), (11, 13), (27, 32)]
result = list(contfrac.convergents(x))
self.assertListEqual(expected, result)
x = math.sqrt(9073)
expected = [(95, 1), (286, 3), (381, 4), (10192, 107), (20765, 218)]
result = list(contfrac.convergents(x, max_grade=4))
self.assertListEqual(expected, result)
x = (6792605526025, 9449868410449)
expected = [(0, 1), (1, 1), (2, 3), (3, 4), (5, 7), (18, 25), (23, 32),
(409, 569), (1659, 2308)]
result = list(contfrac.convergents(x, max_grade=8))
self.assertListEqual(expected, result)
def test_convergent(self):
x = 0.84375
expected = (11, 13)
result = contfrac.convergent(x, 3)
self.assertTupleEqual(expected, result)
x = math.sqrt(9073)
expected = (381, 4)
result = contfrac.convergent(x, 2)
self.assertTupleEqual(expected, result)
x = (6792605526025, 9449868410449)
expected = (1, 1)
result = contfrac.convergent(x, 1)
self.assertTupleEqual(expected, result)
class TestExampleUsage(unittest.TestCase):
def test_example_usage_as_in_readme(self):
import contfrac
value = 415/93
coefficients = list(contfrac.continued_fraction(value))
print(coefficients)
expression = contfrac.arithmetical_expr(coefficients)
print('Value: {:f} = {:s}'.format(value, expression))
eval_value = contfrac.evaluate(coefficients)
print(eval_value, value)
convergents = list(contfrac.convergents(value))
print(convergents)
def test_example_high_accuracy(self):
import contfrac
value = (415, 93)
coefficients = list(contfrac.continued_fraction(value))
print(coefficients)
expression = contfrac.arithmetical_expr(coefficients)
print('Value: {:} = {:s}'.format(value, expression))
eval_value = contfrac.evaluate(coefficients)
print(eval_value, value[0]/value[1])
convergents = list(contfrac.convergents(value))
print(convergents)
def test_example_irrational(self):
import contfrac
import math
coefficients = list(contfrac.continued_fraction(math.e, maxlen=10))
print(coefficients)
convergent = contfrac.convergent(math.e, 3)
print(convergent, convergent[0]/convergent[1], math.e)
convergent = contfrac.convergent(math.e, 7)
print(convergent, convergent[0]/convergent[1], math.e)