Unexpected Fraction.from_float() Behavior

[bsidhom]

BPO	9829
Nosy	@bitdancer

^{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 = <Date 2010-09-11.14:00:03.392>
created_at = <Date 2010-09-11.05:06:24.259>
labels = ['invalid', 'type-bug', 'library']
title = 'Unexpected Fraction.from_float() Behavior'
updated_at = <Date 2010-09-11.14:00:03.368>
user = 'https://bugs.python.org/bsidhom'

bugs.python.org fields:

activity = <Date 2010-09-11.14:00:03.368>
actor = 'r.david.murray'
assignee = 'none'
closed = True
closed_date = <Date 2010-09-11.14:00:03.392>
closer = 'r.david.murray'
components = ['Library (Lib)']
creation = <Date 2010-09-11.05:06:24.259>
creator = 'bsidhom'
dependencies = []
files = []
hgrepos = []
issue_num = 9829
keywords = []
message_count = 2.0
messages = ['116076', '116096']
nosy_count = 2.0
nosy_names = ['r.david.murray', 'bsidhom']
pr_nums = []
priority = 'normal'
resolution = 'not a bug'
stage = None
status = 'closed'
superseder = None
type = 'behavior'
url = 'https://bugs.python.org/issue9829'
versions = ['Python 3.1']

[bsidhom]

The Fractions.from_float() call returns an incorrect value when run on certain numbers. Some test runs have been listed below. Note that this problem does not exist when the same float is converted to a string and then passed to the standard Fraction() constructor; I do not know if this is an inherent problem due to the structure of the float itself or an implementation issue.

>>> for x in [1.23, 1.24, 1.25, 1.26, 1.27]:
	print(Fraction.from_float(x))
	print(Fraction(str(x)))

2769713770832855/2251799813685248
123/100
5584463537939415/4503599627370496
31/25
5/4
5/4
5674535530486825/4503599627370496
63/50
2859785763380265/2251799813685248
127/100

The problem does not exist if a string literal is passed either:

>>> print(Fraction('1.23'))
123/100

[bitdancer]

Please read about floating point arithmetic in the tutorial:

http://docs.python.org/tutorial/floatingpoint.html

Also observe that this works:

    >>> Fraction(Decimal('1.23'))
    Fraction(123, 100)

So yes, it is a limitation in how floating point is represented...in all languages and platforms that use binary floating point.