def test_inverse(self):
"""Test inverse function."""
self.assertEqual(common.inverse(5), 1 / 5)
self.assertEqual(common.inverse(-5), -1 / 5)
self.assertEqual(common.inverse(-1 / 5), -5)
# Test divisor of 0.
with self.assertRaises(the_exception.InputError):
common.inverse(0)
def tanh(argument: float) -> float:
"""Returns an approximation of the value of tanh('argument').
Args:
argument (float): Input to hyperbolic tan function
Returns:
float: Approximation of the value of tanh('argument')
"""
e = exp.pow_e(argument)
return (e - common.inverse(e)) / (e + common.inverse(e))
def pow_int(base: float, exponent: int) -> float:
"""Returns value of 'base' to the power of 'exponent' using exponentiation by squaring where the latter is an integer.
Args:
base (float): Base of power to be returned
exponent (int): Exponent of power to be returned
Returns:
float: Value of 'base' to the power of 'exponent'
Raises:
InputError: If 'exponent' is not an integer
"""
# Ensure that exponent is an integer.
if not isinstance(exponent, int):
raise exceptions.InputError(
exponent,
"Exponentiation by squaring does not work with non-integer exponents."
)
# If exponent is negative, use the property x^y = (1/x)^-y.
if common.is_negative(exponent):
base = common.inverse(base)
exponent *= -1
# Iterate over bits in exponent
result = 1
while common.is_positive(exponent):
# If exponent is odd, we can use the fact that x^y = x(x^2)^((n-1)/2)
if common.is_odd(exponent):
result *= base
# Normally, we'd subtract 1 from y here but we don't actually need to since it will be lost in the coming bit-shift.
# Now that y is even, we can use the fact that x^y = (x^2)^(n/2) when y is even
base *= base
exponent >>= 1
return result