def test_set_digits_from_int_decimal_too_large(self):
"""
Setting excessively large value from int (simulated decimal)
Verify that any attempt to set a value beyond the maximum
range of the number, from an integer, raises an OverflowError
"""
func = lambda x: 10 # Simulated decimal number
for length in range(1, self.DIGITS_MAX + 1, self.DIGITS_STEP):
radxs = (10, ) * length # Simulated decimal number
test_int = 10**length
# Value of test_int should be always one ahead of its max
cbn = CustomBaseNumberP(radxs)
with self.subTest(length=length):
with self.assertRaises(OverflowError):
cbn.set_digits_from_int(test_int)
def test_set_digits_from_int_decimal(self):
"""
Setting value from int (using simulated decimal number)
Verify that the value of a number can be converted from
an integer, by informal proof.
"""
func = lambda x: 10 # Simulate decimal number
for length in range(1, self.DIGITS_MAX + 1, self.DIGITS_STEP):
radxs = (10, ) * length # Simulated decimal number
test_int = 9
for iii in range(length - 1):
# Extend test_int with more 9's until it has
# as many digits as defined in length
test_int *= 10
test_int += 9
cbn = CustomBaseNumberP(radxs)
cbn.set_digits_from_int(test_int)
digits = cbn._digits
for iii in range(len(digits)):
with self.subTest(length=length, iii=iii):
self.assertEqual(digits[iii], 9)
def test_incr_zero_decimal(self):
"""
Increment from zero
Verify that incrementing a zero-value number by one produces
a value of exactly one, by informal proof.
"""
for length in range(1, self.DIGITS_MAX + 1, self.DIGITS_STEP):
radxs = (10, ) * length # Simulated decimal number
test_int = 0
cbn = CustomBaseNumberP(radxs)
cbn.incr() # Increment the number from 0 to 1
digits = cbn.digits()
for iii in range(len(digits) - 2):
# Verify that all digits except the least significant
# are zeroes
with self.subTest(length=length, iii=iii):
self.assertEqual(
digits[iii], 0,
'Digits before least significant must be zero')
self.assertEqual(digits[len(digits) - 1], 1,
'First digit must be one')
def test_get_digits(self):
"""
Retrieval of digits
Verify that the method to return the digits of the number,
get_digits(), does this correctly, by informal proof.
"""
func = lambda x: 2 # Simulated binary number
for length in range(1, self.DIGITS_MAX + 1, self.DIGITS_STEP):
radxs = (2, ) * length # Simulated binary number
test_int = 1
for iii in range(length - 1):
# create an integer which is all 1's expressed in
# binary
test_int <<= 1
test_int += 1
cbn = CustomBaseNumberP(radxs)
cbn.set_digits_from_int(test_int)
digits = cbn.digits()
ref = (1, ) * length
with self.subTest(length=length):
self.assertEqual(digits, ref)
def test_len(self):
"""
Output of len()
Verify that len() returns the number of digits in the
Custom-Base Number correctly, by informal proof.
"""
func = lambda x: 1 # Dummy zero-value number
for length in range(1, self.DIGITS_MAX + 1, self.DIGITS_STEP):
radxs = (1, ) * length # Dummy always-zero number
cbn = CustomBaseNumberP(radxs)
with self.subTest(length=length):
self.assertEqual(len(cbn), length)
def test_set_digits_binary_digit_exceed_max(self):
"""
Setting of digits to exceed radix
Verify that any attempt to set any digit past the maximum
value defined by its radix raises a ValueError
"""
func = lambda x: 2 # Simulated binary number
for length in range(1, self.DIGITS_MAX + 1, self.DIGITS_STEP):
radxs = (2, ) * length # Simulated binary number
digits_test = (2, ) * length
for iii in range(len(digits_test)):
with self.subTest(length=length, iii=iii):
with self.assertRaises(ValueError):
cbn = CustomBaseNumberP(radxs, digits_test)
def test_set_digits_binary_digit_negative(self):
"""
Setting of digits to negative values
Verify that any attempt to set a negative value on any
digit of a number raises a ValueError
"""
func = lambda x: 2 # Simulated binary number
for length in range(1, self.DIGITS_MAX + 1, self.DIGITS_STEP):
radxs = (2, ) * length # Simulated binary number
digits_test = (-1, ) * length
for iii in range(len(digits_test)):
with self.subTest(length=length, iii=iii):
with self.assertRaises(ValueError):
cbn = CustomBaseNumberP(radxs, digits_test)
def test_new_number_default_value(self):
"""
Creation of a new number with default values
Verify that a Custom-Base Number created with no initial
digits has exactly zero value, by informal proof
"""
func = lambda x: 1 # Dummy number always has zero value
for length in range(1, self.DIGITS_MAX + 1, self.DIGITS_STEP):
radxs = (1, ) * length # Dummy always-zero number
cbn = CustomBaseNumberP(radxs)
digits = cbn._digits
for iii in range(len(digits)):
with self.subTest(length=length, iii=iii):
self.assertEqual(digits[iii], 0)
def test_set_digits_binary_zero_length(self):
"""
Specifying empty sequence as digits during number creation
Verify that any attempt to create a number by specifying
an empty sequence in place of actual digits raises a
ValueError
"""
func = lambda x: 2 # Simulated binary number
for length in range(1, self.DIGITS_MAX + 1, self.DIGITS_STEP):
radxs = (2, ) * length # Simulated binary number
digits_test = ()
for iii in range(len(digits_test)):
with self.subTest(length=length, iii=iii):
with self.assertRaises(ValueError):
cbn = CustomBaseNumberP(radxs, digits_test)
def test_set_digits_binary_too_few(self):
"""
Specifying too few digits during number creation
Verify that any attempt to create a number with less
digits than the declared digit length of the number
raises a ValueError
"""
func = lambda x: 2 # Simulated binary number
for length in range(2, self.DIGITS_MAX + 1, self.DIGITS_STEP):
radxs = (2, ) * length # Simulated binary number
digits_test = (-1, ) * (length - 1)
for iii in range(len(digits_test)):
with self.subTest(length=length, iii=iii):
with self.assertRaises(ValueError):
cbn = CustomBaseNumberP(radxs, digits_test)
def test_set_digits_binary(self):
"""
Setting of digits (using simulated binary number)
Verify that method to set the digits of a number directly
works correctly by informal proof
"""
func = lambda x: 2 # Simulated binary number
for length in range(1, self.DIGITS_MAX + 1, self.DIGITS_STEP):
radxs = (2, ) * length # Simulated binary number
digits_test = (1, ) * length
cbn = CustomBaseNumberP(radxs, digits_test)
digits = cbn._digits
for iii in range(len(digits_test)):
with self.subTest(length=length, iii=iii):
self.assertEqual(digits[iii], digits_test[iii])
def test_set_digits_binary_too_many(self):
"""
Specifying too many digits during number creation
Verify that any attempt to create a number with more
digits than the declared digit length of the number
raises a ValueError
"""
func = lambda x: 2 # Simulated binary number
for length in range(1, self.DIGITS_MAX + 1, self.DIGITS_STEP):
radxs = (2, ) * length # Simulated binary number
digits_test = (0, ) * (length + 1)
# PROTIP: You need the parentheses around length+1,
# because OPERATOR PRECEDENCE
for iii in range(len(digits_test)):
with self.subTest(length=length, iii=iii):
with self.assertRaises(ValueError):
cbn = CustomBaseNumberP(radxs, digits_test)
def test_incr_overflow_decimal(self):
"""
Increment overflow
Verify that incrementing a number at its maximum value by one
wraps it back to zero, by informal proof.
"""
func = lambda x: 10 # Simulated decimal number
for length in range(1, self.DIGITS_MAX + 1, self.DIGITS_STEP):
radxs = (10, ) * length # Simulated decimal number
test_int = 9
for iii in range(length - 1):
# Create an integer of all 9's
test_int *= 10
test_int += 9
cbn = CustomBaseNumberP(radxs)
cbn.set_digits_from_int(test_int)
cbn.incr() # Increment the number past max value
digits = cbn._digits
for jjj in range(len(digits) - 1):
# Verify that every digit is zero
with self.subTest(length=length):
self.assertEqual(digits[jjj], 0, 'All digits must be zero')