def _exact_ratio(x):
"""Convert Real number x exactly to (numerator, denominator) pair.
>>> _exact_ratio(0.25)
(1, 4)
x is expected to be an int, Fraction, Decimal or float.
"""
try:
try:
# int, Fraction
return (x.numerator, x.denominator)
except AttributeError:
# float
try:
return x.as_integer_ratio()
except AttributeError:
# Decimal
try:
return _decimal_to_ratio(x)
except AttributeError:
msg = "can't convert type '{}' to numerator/denominator"
raise TypeError(msg.format(type(x).__name__)) from None
except (OverflowError, ValueError):
# INF or NAN
if __debug__:
# Decimal signalling NANs cannot be converted to float :-(
if isinstance(x, Decimal):
assert not x.is_finite()
else:
assert not math.isfinite(x)
return (x, None)
# FIXME This is faster than Fraction.from_decimal, but still too slow.
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