round(x,y) doesn't behave as expected, round error

[shlomoa]

BPO	1565
Nosy	@amauryfa

^{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 2007-12-07.09:46:37.727>
created_at = <Date 2007-12-07.09:30:33.111>
labels = ['interpreter-core', 'invalid']
title = "round(x,y) doesn't behave as expected, round error"
updated_at = <Date 2007-12-07.10:13:48.022>
user = 'https://bugs.python.org/shlomoa'

bugs.python.org fields:

activity = <Date 2007-12-07.10:13:48.022>
actor = 'amaury.forgeotdarc'
assignee = 'none'
closed = True
closed_date = <Date 2007-12-07.09:46:37.727>
closer = 'amaury.forgeotdarc'
components = ['Interpreter Core']
creation = <Date 2007-12-07.09:30:33.111>
creator = 'shlomoa'
dependencies = []
files = []
hgrepos = []
issue_num = 1565
keywords = []
message_count = 4.0
messages = ['58266', '58267', '58268', '58269']
nosy_count = 2.0
nosy_names = ['amaury.forgeotdarc', 'shlomoa']
pr_nums = []
priority = 'normal'
resolution = 'not a bug'
stage = None
status = 'closed'
superseder = None
type = None
url = 'https://bugs.python.org/issue1565'
versions = ['Python 2.5']

[shlomoa]

#Round is unexpectedly wrong
>>> z = complex(1,1)
>>> s=abs(z)
>>> round(s,2)
1.4099999999999999

[amauryfa]

Please see
http://www.python.org/doc/faq/general/#why-are-floating-point-calculations-so-inaccurate

[shlomoa]

>>> def my_round(n,i):
...     t = n * (10**i)
...     s = round(t)
...     r = s / (10**i)
...     return r
... 
>>> print my_round(s,2)
1.41

[amauryfa]

Your function is not better:

>>> print my_round(s,2)
1.41
>>> my_round(s,2)
1.4099999999999999

print uses str(), and restricts itself to 12 significant digits.
the direct call uses repr(), and display the most precise number.

The problem is not in the computation, but is inherent to the 'float'
type which cannot represent 1.41 exactly. Please carefully read the faq
entry above.