It is an alternative constructor which only accepts a single numeric argument.
Unlike to Fraction.from_float() and Fraction.from_decimal() it accepts any
real numbers supported by the standard constructor (int, float, Decimal,
Rational numbers, objects with as_integer_ratio()).
Unlike to the standard constructor, it does not accept strings.
When using the ** operator or pow() with Fraction as the base
and an exponent that is not rational, a float, or a complex, the
fraction is no longer converted to a float.
If one calls pow(fractions.Fraction, x, module) with modulo not None, the error message now says that the types are incompatible rather than saying pow only takes 2 arguments. Implemented by having fractions.Fraction __pow__ accept optional modulo argument and return NotImplemented if not None. pow() then raises with appropriate message.
---------
Co-authored-by: Mark Dickinson <dickinsm@gmail.com>
Fix a bug in the regex used for parsing a string input to the `fractions.Fraction` constructor. That bug led to an inconsistent exception message being given for some inputs.
---------
Co-authored-by: blurb-it[bot] <43283697+blurb-it[bot]@users.noreply.github.com>
Co-authored-by: Mark Dickinson <dickinsm@gmail.com>
PR #100161 added fancy float-style formatting for the Fraction type,
but left us in a state where basic formatting for fractions (alignment,
fill, minimum width, thousands separators) still wasn't supported.
This PR adds that support.
---------
Co-authored-by: Serhiy Storchaka <storchaka@gmail.com>
Make docstrings for `as_integer_ratio` consistent across types, and document that
the returned pair is always normalized (coprime integers, with positive denominator).
---------
Co-authored-by: Owain Davies <116417456+OTheDev@users.noreply.github.com>
Co-authored-by: Mark Dickinson <dickinsm@gmail.com>
This PR adds a private `Fraction._from_coprime_ints` classmethod for internal creations of `Fraction` objects, replacing the use of `_normalize=False` in the existing constructor. This speeds up creation of `Fraction` objects arising from calculations. The `_normalize` argument to the `Fraction` constructor has been removed.
Co-authored-by: Pieter Eendebak <pieter.eendebak@gmail.com>
Co-authored-by: Mark Dickinson <dickinsm@gmail.com>
This PR adds support for float-style formatting for `Fraction` objects: it supports the `"e"`, `"E"`, `"f"`, `"F"`, `"g"`, `"G"` and `"%"` presentation types, and all the various bells and whistles of the formatting mini-language for those presentation types. The behaviour almost exactly matches that of `float`, but the implementation works with the exact `Fraction` value and does not do an intermediate conversion to `float`, and so avoids loss of precision or issues with numbers that are outside the dynamic range of the `float` type.
Note that the `"n"` presentation type is _not_ supported. That support could be added later if people have a need for it.
There's one corner-case where the behaviour differs from that of float: for the `float` type, if explicit alignment is specified with a fill character of `'0'` and alignment type `'='`, then thousands separators (if specified) are inserted into the padding string:
```python
>>> format(3.14, '0=11,.2f')
'0,000,003.14'
```
The exact same effect can be achieved by using the `'0'` flag:
```python
>>> format(3.14, '011,.2f')
'0,000,003.14'
```
For `Fraction`, only the `'0'` flag has the above behaviour with respect to thousands separators: there's no special-casing of the particular `'0='` fill-character/alignment combination. Instead, we treat the fill character `'0'` just like any other:
```python
>>> format(Fraction('3.14'), '0=11,.2f')
'00000003.14'
>>> format(Fraction('3.14'), '011,.2f')
'0,000,003.14'
```
The `Fraction` formatter is also stricter about combining these two things: it's not permitted to use both the `'0'` flag _and_ explicit alignment, on the basis that we should refuse the temptation to guess in the face of ambiguity. `float` is less picky:
```python
>>> format(3.14, '0<011,.2f')
'3.140000000'
>>> format(Fraction('3.14'), '0<011,.2f')
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/Users/mdickinson/Repositories/python/cpython/Lib/fractions.py", line 414, in __format__
raise ValueError(
ValueError: Invalid format specifier '0<011,.2f' for object of type 'Fraction'; can't use explicit alignment when zero-padding
```
Make some trivial performance optimizations in Fraction
Uses private class attributes `_numerator` and `_denominator` in place of the `numerator` and `denominator` property accesses.
Co-authored-by: hauntsaninja <hauntsaninja@gmail.com>
When we construct the upper and lower candidates in limit_denominator,
the numerator and denominator are already relatively prime (and the
denominator positive) by construction, so there's no need to go through
the usual normalisation in the constructor. This saves a couple of
potentially expensive gcd calls.
Suggested by Michael Scott Asato Cuthbert in GH-93477.
* bpo-44258: support PEP 515 for Fraction's initialization from string
* regexps's version
* A different regexps version, which doesn't suffer from catastrophic backtracking
* revert denom -> den
* strip "_" from the decimal str, add few tests
* drop redundant tests
* Add versionchanged & whatsnew entry
* Amend Fraction constructor docs
* Change .. versionchanged:...
Obviously, the former was a little misleading: not only rationals
may be considered as "infinite-precision, real numbers" - but, for
example, any real finite extension of the rationals.
bpo-43420: Implement standard transformations in + - * / that can often reduce the size of intermediate integers needed. For rationals with large components, this can yield dramatic speed improvements, but for small rationals can run 10-20% slower, due to increased fixed overheads in the longer-winded code. If those slowdowns turn out to be a problem, see the PR discussion for low-level implementation tricks that could cut other fixed overheads.
Co-authored-by: Tim Peters <tim.peters@gmail.com>
Co-authored-by: Mark Dickinson <dickinsm@gmail.com>
Fix regression in fractions.Fraction if the numerator and/or the
denominator is an int subclass. The math.gcd() function is now
used to normalize the numerator and denominator. math.gcd() always
return a int type. Previously, the GCD type depended on numerator
and denominator.
Some numerator types used (specifically NumPy) decides to not
return a Python boolean for the "a != b" operation. Using the equivalent
call to bool() guarantees a bool return also for such types.
* bpo-35588: Implement mod and divmod operations for Fraction type by spelling out the numerator/denominator calculation, instead of instantiating and normalising Fractions along the way. This speeds up '%' and divmod() by 2-3x.
* bpo-35588: Also reimplement Fraction.__floordiv__() using integer operations to make it ~4x faster.
* Improve code formatting.
Co-Authored-By: scoder <stefan_ml@behnel.de>
* bpo-35588: Fix return type of divmod(): the result of the integer division should be an integer.
* bpo-35588: Further specialise __mod__() and inline the original helper function _flat_divmod() since it's no longer reused.
* bpo-35588: Add some tests with large numerators and/or denominators.
* bpo-35588: Use builtin "divmod()" function for implementing __divmod__() in order to simplify the implementation, even though performance results are mixed.
* Rremove accidentally added empty line.
* bpo-35588: Try to provide more informative output on test failures.
* bpo-35588: Improve wording in News entry.
Co-Authored-By: scoder <stefan_ml@behnel.de>
* Remove stray space.
Make mixed-type `%` and `//` operations involving `Fraction` and `float` objects behave like all other mixed-type arithmetic operations: first the `Fraction` object is converted to a `float`, then the `float` operation is performed as normal. This fixes some surprising corner cases, like `Fraction('1/3') % inf` giving a NaN.
Thanks Elias Zamaria for the patch.
(instances of int, float, complex, decimal.Decimal and
fractions.Fraction) that makes it easy to maintain the invariant that
hash(x) == hash(y) whenever x and y have equal value.
the Fraction type doesn't know how to handle the comparison without
loss of accuracy. Also, make sure that comparisons between Fractions
and float infinities or nans do the right thing.
