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Fractions instantiation revisited #72902
Description
| BPO | 28716 |
|---|---|
| Nosy | @rhettinger, @mdickinson, @scoder, @stevendaprano, @serhiy-storchaka, @jdemeyer, @eric-wieser, @wm75, @MojoVampire |
| Files |
Note: these values reflect the state of the issue at the time it was migrated and might not reflect the current state.
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GitHub fields:
assignee = None
closed_at = None
created_at = <Date 2016-11-16.18:06:27.650>
labels = ['3.8', 'type-bug', 'library']
title = 'Fractions instantiation revisited'
updated_at = <Date 2019-08-05.09:04:19.247>
user = 'https://github.com/wm75'bugs.python.org fields:
activity = <Date 2019-08-05.09:04:19.247>
actor = 'jdemeyer'
assignee = 'none'
closed = False
closed_date = None
closer = None
components = ['Library (Lib)']
creation = <Date 2016-11-16.18:06:27.650>
creator = 'wolma'
dependencies = []
files = ['45507']
hgrepos = []
issue_num = 28716
keywords = ['patch']
message_count = 13.0
messages = ['280977', '280981', '280995', '280997', '280998', '280999', '305611', '310470', '313208', '313741', '313753', '313786', '349037']
nosy_count = 9.0
nosy_names = ['rhettinger', 'mark.dickinson', 'scoder', 'steven.daprano', 'serhiy.storchaka', 'jdemeyer', 'Eric.Wieser', 'wolma', 'josh.r']
pr_nums = []
priority = 'normal'
resolution = None
stage = None
status = 'open'
superseder = None
type = 'behavior'
url = 'https://bugs.python.org/issue28716'
versions = ['Python 3.8']
Activity
wm75 commentedon Nov 16, 2016
I've spent a bit of time lately trying to optimize the instantiation of Fractions. This is related to bpo-22464, but instead of focusing on constructing Fractions from ints, my attempts revolve around improving instantiation from strings, floats and decimals.
I'm attaching a patch with all my changes for discussion, but here's an overview of what's in it:
CHANGES TO INSTANTIATION FROM STRINGS:
isinstance checking for str is performed before the more expensive check for numbers.Rational (which has to go through abc)
instantiation from strings doesn't use a regex pattern anymore for parsing; this is faster in many cases (and never slower) than the current version
while reimplementing string parsing I added PEP-515 support (this is the only behavior change in the patch)
combined this gives me the following performance changes for instantiation of Fractions from different arguments (profiled with 1,000,000 random inputs each):
'x/y'-type of strings:
----------------------
ncalls tottime percall cumtime percall filename:lineno(function)
old:
1000000 12.162 0.000 27.778 0.000 fractions.py:84(new)
new:
1000000 9.619 0.000 12.428 0.000 frc.py:68(new)
scientific notation (e.g., '1.234E-7'):
---------------------------------------
ncalls tottime percall cumtime percall filename:lineno(function)
old:
1000000 18.209 0.000 37.341 0.000 fractions.py:84(new)
new:
1000000 15.509 0.000 21.252 0.000 frc.py:68(new)
integer strings (e.g. '123456'):
--------------------------------
ncalls tottime percall cumtime percall filename:lineno(function)
old:
1000000 11.272 0.000 26.201 0.000 fractions.py:84(new)
new:
1000000 9.347 0.000 12.425 0.000 frc.py:68(new)
from other Fractions (to test effect on instantiation of numbers.Rational):
ncalls tottime percall cumtime percall filename:lineno(function)
old:
1000000 4.708 0.000 10.093 0.000 fractions.py:84(new)
new:
1000000 4.835 0.000 10.572 0.000 frc.py:68(new)
from int subclass (as another numbers.Rational):
ncalls tottime percall cumtime percall filename:lineno(function)
old:
1000000 3.446 0.000 8.044 0.000 fractions.py:84(new)
new:
1000000 3.795 0.000 8.836 0.000 frc.py:68(new)
SUMMARY of this part
====================
+ very significant speedup for instatiation from strings of different forms with (near) negligible effects on instantiation from numbers.Rational.
+ correct parsing of PEP-515-like number strings
CHANGES TO INSTANTIATION FROM FLOAT AND DECIMAL:
no explicit check for float and decimal in standard constructor; instead, simply try to call as_integer_ratio as last resort (even after checking for numbers.Rational)
speed up alternate from_float and from_decimal constructor class methods by rearranging type checks and making use of _normalize flag
import decimal only on demand (when using from_decimal)
Resulting performance changes:
standard constructor with float:
--------------------------------
ncalls tottime percall cumtime percall filename:lineno(function)
old:
1000000 4.362 0.000 12.452 0.000 fractions.py:84(new)
new:
1000000 6.693 0.000 16.020 0.000 frc.py:68(new)
from_float:
-----------
ncalls tottime percall cumtime percall filename:lineno(function)
old:
1000000 3.146 0.000 17.769 0.000 fractions.py:193(from_float)
new:
1000000 2.544 0.000 7.591 0.000 frc.py:205(from_float)
standard constructor with decimal:
--------------------------------
ncalls tottime percall cumtime percall filename:lineno(function)
old:
1000000 4.672 0.000 20.795 0.000 fractions.py:84(new)
new:
1000000 7.097 0.000 24.526 0.000 frc.py:68(new)
from_decimal:
-------------
ncalls tottime percall cumtime percall filename:lineno(function)
old:
1000000 5.054 0.000 34.473 0.000 fractions.py:207(from_decimal)
new:
1000000 2.942 0.000 16.013 0.000 frc.py:220(from_decimal)
SUMMARY of this part:
specialized class methods become a lot faster (for Decimal the benchmarks are based on _pydecimal - with the C implementation the percent differences would be even larger)
I hope at least some of this is interesting.
serhiy-storchaka commentedon Nov 16, 2016
Profiling give you only approximate results. In normal execution the effect of your changes can be opposite. Could you please provide benchmarks without using profiling?
wm75 commentedon Nov 16, 2016
sure, I just happened to have the profiling available since I used it to optimize things. Here's similar microbenchmarks using perf:
STRINGS
=======
FLOATS
======
DECIMALS (using C implementation this time)
===========================================
MojoVampire commentedon Nov 16, 2016
Might it make sense to make instantiation from numbers.Rational duck typing based as well? Just try to get the numerator and denominator attributes, on AttributeError, skip it and move on. Unless there is some concern that a non-Rational type might have both attributes and not intend them to mean it's a Rational?
MojoVampire commentedon Nov 16, 2016
Similarly, type checking for int might be replaced with calling operator.index on the input and handling the TypeError; that way, anything that has declared itself logically int-like is handled without explicit type checking at all.
wm75 commentedon Nov 16, 2016
No, I don't think the numeric tower ABC should be replaced by duck-typing. One of the very reasons the fractions module exists is that it showcases how to use the numeric tower. If you want a class to be picked up as a Rational it should be registered as such. Pretty much the same goes for integer-like things. The direct type check for ints only exists to speed up the most obvious case, but anything integer-like should be registered as a numbers.Integral and it will just work with fractions. Beautiful stuff!
This is not the case for as_integer_ratio because that method is not defined in the numeric tower and this is why I think duck-typing could be of interest here (I'm not sure though whether its worth the somewhat decreased performance). My reasoning is that the standard constructor is anyway slower for floats and ints than the specialized classmethods for the two so people who really care about speed here (probably not too many) can just use the classmethods.
eric-wieser commentedon Nov 5, 2017
This would allow the numpy
np.floatingtypes to take part inFractionconversion as well, which would be great.As far as I can tell,
Decimalalready follows this duck-typing, so it would be a shame for other modules not to.Perhaps an
num, den = operator.rational(x)is needed to unify this code across the places that coerce rational numbers.scoder commentedon Jan 23, 2018
Not sure if it's relevant for this specific change, but here's a benchmark that you could use for Fractions: bpo-22458
scoder commentedon Mar 4, 2018
Just FYI and as further motivation, I reimplemented this dedicated parser for quicktions (in Cython, so the timings and speedups are not comparable).
scoder/quicktions@cc034e0
I was able to get another quite visible improvement by caching the values of "10 ** shift" for 0 <= shift < 58 in a tuple. Higher values are very unlikely in practice, and the memory size of a tuple with 58 values gives a nice multiple of the usual cache line size. (I originally stored 64 values in my commit but then cut it down later.)
scoder/quicktions@c20add5
I suspect that the difference won't be as big for the Python implementation, but it still seems worth a try.
The overall speedup that I got, compared to the initial regex implementation, is 50-70%.
[regex] $ python3.7 -m timeit -s 'from quicktions import Fraction as F' 'F("153456/789344")'
200000 loops, best of 5: 1.19 usec per loop
[native] $ python3.7 -m timeit -s 'from quicktions import Fraction as F' 'F("153456/789344")'
500000 loops, best of 5: 593 nsec per loop
[regex] $ python3.7 -m timeit -s 'from quicktions import Fraction as F' 'F("15.3456789E+4")'
100000 loops, best of 5: 2.3 usec per loop
[native] $ python3.7 -m timeit -s 'from quicktions import Fraction as F' 'F("15.3456789E+4")'
500000 loops, best of 5: 667 nsec per loop
It could be even higher if I additionally moved the int() integer parsing into Cython. Might try that at some point. But that's also not something that concerns the implementation in CPython.
mdickinson commentedon Mar 13, 2018
[Eric Wieser]
I'm confused: as far as I can tell, the NumPy floating-point types don't implement
as_integer_ratio. (Except fornp.float64, which subclassesfloatand so inheritsis_integer_ratiofrom it.) Or are you suggesting that if they were to implementas_integer_ratioat some point in the future, then they'd become compatible withFraction?13 remaining items
pythongh-72902: improve Fraction(str) speed (don't use regexp's)
serhiy-storchaka commentedon May 19, 2025
First, benchmark how it would affect
Fraction->Fractionconversion. While it looks meanless,Fractions()can be applied to a collection of numbers -- integers, floating point, rational... We can also move down theas_integer_ratiocheck, but we need to benchmark Deciaml -> Fraction conversion. Thefloatcheck can be left, and it can be simplified totype(numerator) is floatif there is a benefit. Just for the case, benchmark conversion fromintandfloatsubclasses -- I do not think this is an important use case, but we should know how large the impact.skirpichev commentedon May 20, 2025
@serhiy-storchaka, here are more extended tests on top of #133994 (at e383bdb):
Details
move-abc patch:
serhiy-storchaka commentedon May 20, 2025
Well, it looks that the only slowed down case is for rational numbers without
as_integer_ratio(). I think that from a practical point of view it is worth it.pythongh-72902: improve Fraction constructor speed for typical inputs
skirpichev commentedon May 20, 2025
Ok, I split out this change to #134320
gh-72902: improve Fraction constructor speed for typical inputs (GH-1…
pythongh-72902: improve Fraction constructor speed for typical inputs (…
pythongh-72902: improve Fraction constructor speed for typical inputs (…
gh-72902: Speedup Fraction.from_decimal/float in typical cases (GH-13…
scoder commentedon Jun 26, 2026
The instantiation fast paths make the general assumption that the
.as_integer_ratio()method returns its ratio in lowest terms. This is certainly true for the builtin types, but subtypes and other types (e.g. arbitrary otherRationaltypes) might not follow this constraint. The.as_integer_ratio()method is only 'formally' documented for the builtin types that provide it, not as a general protocol. Thenumbersmodule of ABCs does not mention the method.Therefore, I wonder if we should generally assume that all types obey this constraint, including builtin subtypes and user provided types, or whether we should restrict optimisations to the exact builtin types and otherwise assume (potentially) non-normalised return values, bailing to the regular GCD-normalisation paths.
For performance reasons, assuming a builtin-like implementation that returns lowest terms ratios is obviously attractive, but optimisations should only be applied within safe assumptions, not forfeit correctness. And I would generally expect the large majority of cases (those that merit optimisation) to actually pass the exact builtin types and nothing else, so we shouldn't lose much by playing it safe.
Opinions?
skirpichev commentedon Jun 27, 2026
And this is correct in the merged pr #133251, as it affects only float/Decimal subclasses. Someone can override contract from the parent class method to return None and blow up a nuke instead. I see no way to play nicely with such morons.
That's true, just invalid for builtin subtypes. It was my concern as well:
#120271 (comment)
Notably, that numpy types doesn't document such constraint (despite it seems to be valid):
>>> help(np.float128.as_integer_ratio) Help on method descriptor as_integer_ratio: as_integer_ratio(self, /) unbound numpy.longdouble method longdouble.as_integer_ratio() -> (int, int) Return a pair of integers, whose ratio is exactly equal to the original floating point number, and with a positive denominator. Raise `OverflowError` on infinities and a `ValueError` on NaNs. >>> np.longdouble(10.0).as_integer_ratio() (10, 1) >>> np.longdouble(0.0).as_integer_ratio() (0, 1) >>> np.longdouble(-.25).as_integer_ratio() (-1, 4)(Some canonicalization was mentioned, however.)
This affects following cases:
cpython/Lib/fractions.py
Lines 245 to 250 in 1812162
and:
cpython/Lib/fractions.py
Lines 326 to 329 in 1812162
This assumption was introduced in c8d2630. CC @serhiy-storchaka.
My opinion is that this is API similar to numerator/denominator pairs, it's for interoperation with the Rational type and should be mentioned in the numbers ABC as an optional method for Real types and mandatory for Rational's. It should return a canonicalized fraction.
BTW, there could be a more generic API,
limit_denominator()-like. With infinitemax_denominator- this should provide same value asas_integer_ratio()for Rational types and for some Real types (e.g. floating-point numbers). Though, in certain cases (e.g. for interval arithmetic) - infinitemax_denominatordoesn't make any sense.