Python's Fraction data type is an excellent way to do exact calculations with unlimited rational numbers and largely beats Decimal in terms of simplicity, accuracy and safety. Clearly not in terms of speed, though, given the cdecimal accelerator in Python 3.3+.

quicktions is an adaptation of the original fractions module (as included in CPython 3.13a3) that is compiled and optimised with Cython into a fast, native extension module.

Compared to the standard library fractions module of CPython, computations in quicktions are about

• 10x faster in Python 2.7 and 3.4
• 6x faster in Python 3.5
• 3-4x faster in Python 3.10

Compared to the fractions module in CPython 3.10, instantiation of a Fraction in quicktions is also

• 5-15x faster from a floating point string value (e.g. Fraction("123.456789"))
• 3-5x faster from a floating point value (e.g. Fraction(123.456789))
• 2-4x faster from an integer numerator-denominator pair (e.g. Fraction(123, 456))

We provide a set of micro-benchmarks here:

As of quicktions 1.12, the different number types and implementations compare as follows in CPython 3.10:

Average times for all 'create' benchmarks:
float               :    36.17 us (1.0x)
Decimal             :   111.71 us (3.1x)
Fraction            :   111.98 us (3.1x)
PyFraction          :   398.80 us (11.0x)

Average times for all 'compute' benchmarks:
float               :     4.53 us (1.0x)
Decimal             :    16.62 us (3.7x)
Fraction            :    72.91 us (16.1x)
PyFraction          :   251.93 us (55.6x)

While not as fast as the C implemented decimal module in Python 3, quicktions is about 15x faster than the Python implemented decimal module in Python 2.7.

For documentation, see the Python standard library's fractions module:

ChangeLog

1.19 (2024-11-29)

• Support for Python 2.7 as well as 3.7 and earlier has been removed.

• Generally use .as_integer_ratio() in the constructor if available.

• Add a classmethod .from_number() that requires a number argument, not a string.

• Mixed calculations with other Rational classes could return the wrong type.

• In mixed calculations with complex, the Fraction is now converted to float instead of complex to avoid certain corner cases in complex calculation.

• Using complex numbers in division shows better tracebacks.

• Subclass instantiations and calculations could fail in some cases.

1.18 (2024-04-03)

• New binary wheels were added built with gcc 12 (manylinux_2_28).
• x86_64 wheels now require SSE4.2.
• Built using Cython 3.0.10.

1.17 (2024-03-24)

• Math operations were sped up by inlined binary GCD calculation.

1.16 (2024-01-10)

• Formatting support was improved, following CPython 3.13a3 as of

• Add support for Python 3.13 by using Cython 3.0.8 and calling math.gcd().

1.15 (2023-08-27)

• Add support for Python 3.12 by using Cython 3.0.2.

1.14 (2023-03-19)

• Implement __format__ for Fraction, following

• Implement Fraction.is_integer(), following

• Fraction.limit_denominator() is faster, following

• Internal creation of result Fractions is about 10% faster if the calculated numerator/denominator pair is already normalised, following

• Built using Cython 3.0.0b1.

1.13 (2022-01-11)

• Parsing very long numbers from a fraction string was very slow, even slower than fractions.Fraction. The parser is now faster in all cases (and still much faster for shorter numbers).
• Fraction did not implement __int__.

1.12 (2022-01-07)

• Faster and more space friendly pickling and unpickling.

• Algorithmically faster arithmetic for large denominators, although slower for small fraction components. Original patch for CPython by Sergey B. Kirpichev and Raymond Hettinger.

• Make sure bool(Fraction) always returns a bool.

• Built using Cython 3.0.0a10.

1.11 (2019-12-19)

• Fix OverflowError when parsing string values with long decimal parts.

1.10 (2019-08-23)

• hash(fraction) is substantially faster in Py3.8+, following an optimisation in CPython 3.9 ().
• New method fraction.as_integer_ratio().

1.9 (2018-12-26)

• Substantially faster normalisation (and therefore instantiation) in Py3.5+.
• // (floordiv) now follows the expected rounding behaviour when used with floats (by converting to float first), and is much faster for integer operations.
• Fix return type of divmod(), where the first item should be an integer.
• Further speed up mod and divmod operations.

1.8 (2018-12-26)

• Faster mod and divmod calculation.

1.7 (2018-10-16)

• Faster normalisation and fraction string parsing.
• Add support for Python 3.7.
• Built using Cython 0.29.

1.6 (2018-03-23)

• Speed up Fraction creation from a string value by 3-5x.
• Built using Cython 0.28.1.

1.5 (2017-10-22)

• Result of power operator (**) was not normalised for negative values.
• Built using Cython 0.27.2.

1.4 (2017-09-16)

• Rebuilt using Cython 0.26.1 to improve support of Python 3.7.

1.3 (2016-07-24)

• repair the faster instantiation from Decimal values in Python 3.6
• avoid potential glitch for certain large numbers in normalisation under Python 2.x

1.2 (2016-04-08)

• change hash function in Python 2.x to match that of fractions.Fraction

1.1 (2016-03-29)

• faster instantiation from float values
• faster instantiation from Decimal values in Python 3.6

1.0 (2015-09-10)

• Fraction.imag property could return non-zero
• parsing strings with long fraction parts could use an incorrect scale

0.7 (2014-10-09)

• faster instantiation from float and string values
• fix test in Python 2.x

0.6 (2014-10-09)

• faster normalisation (and thus instantiation)

0.5 (2014-10-06)

• faster math operations

0.4 (2014-10-06)

• enable legacy division support in Python 2.x

0.3 (2014-10-05)

• minor behavioural fixes in corner cases under Python 2.x (now passes all test in Py2.7 as well)

0.2 (2014-10-03)

• cache hash value of Fractions

0.1 (2014-09-24)

• initial public release