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git subrepo clone --branch=0.30.3 https://github.com/commonmark/cmark.git deps/cmark

Browse Source 
subrepo:
  subdir:   "deps/cmark"
  merged:   "5ba25ff"
upstream:
  origin:   "https://github.com/commonmark/cmark.git"
  branch:   "0.30.3"
  commit:   "5ba25ff"
git-subrepo:
  version:  "0.4.6"
  commit:   "d4444b563"
This commit is contained in:
torque
2023-09-03 20:42:10 -07:00
parent 17a4224cb8
commit 24810cbbbd
120 changed files with 48683 additions and 0 deletions
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16
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> the simple example of a blockquote
> the simple example of a blockquote
> the simple example of a blockquote
> the simple example of a blockquote
... continuation
... continuation
... continuation
... continuation
empty blockquote:
>
>
>
>

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>>>>>> deeply nested blockquote
>>>>> deeply nested blockquote
>>>> deeply nested blockquote
>>> deeply nested blockquote
>> deeply nested blockquote
> deeply nested blockquote
> deeply nested blockquote
>> deeply nested blockquote
>>> deeply nested blockquote
>>>> deeply nested blockquote
>>>>> deeply nested blockquote
>>>>>> deeply nested blockquote

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an
example
of
a code
block

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``````````text
an
example
```
of
a fenced
```
code
block
``````````

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# heading
### heading
##### heading
# heading #
### heading ###
##### heading \#\#\#\#\######
############ not a heading

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* * * * *
- - - - -
________
************************* text

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<div class="this is an html block">
blah blah
</div>
<table>
<tr>
<td>
**test**
</td>
</tr>
</table>
<table>
<tr>
<td>
test
</td>
</tr>
</table>
<![CDATA[
[[[[[[[[[[[... *cdata section - this should not be parsed* ...]]]]]]]]]]]
]]>

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heading
---
heading
===================================
not a heading
----------------------------------- text

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deps/cmark/bench/samples/block-list-flat.md vendored Normal file
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- tidy
- bullet
- list
- loose
- bullet
- list
0. ordered
1. list
2. example
-
-
-
-
1.
2.
3.
- an example
of a list item
with a continuation
this part is inside the list
this part is just a paragraph
1. test
- test
1. test
- test
111111111111111111111111111111111111111111. is this a valid bullet?
- _________________________
- this
- is
a
long
- loose
- list
- with
- some
tidy
- list
- items
- in
- between
- _________________________

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- this
- is
- a
- deeply
- nested
- bullet
- list
1. this
2. is
3. a
4. deeply
5. nested
6. unordered
7. list
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 6
- 5
- 4
- 3
- 2
- 1
- - - - - - - - - deeply-nested one-element item

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[1] [2] [3] [1] [2] [3]
[looooooooooooooooooooooooooooooooooooooooooooooooooong label]
[1]: <http://something.example.com/foo/bar>
[2]: http://something.example.com/foo/bar 'test'
[3]:
http://foo/bar
[ looooooooooooooooooooooooooooooooooooooooooooooooooong label ]:
111
'test'
[[[[[[[[[[[[[[[[[[[[ this should not slow down anything ]]]]]]]]]]]]]]]]]]]]: q
(as long as it is not referenced anywhere)
[[[[[[[[[[[[[[[[[[[[]: this is not a valid reference

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[[[[[[[foo]]]]]]]
[[[[[[[foo]]]]]]]: bar
[[[[[[foo]]]]]]: bar
[[[[[foo]]]]]: bar
[[[[foo]]]]: bar
[[[foo]]]: bar
[[foo]]: bar
[foo]: bar
[*[*[*[*[foo]*]*]*]*]
[*[*[*[*[foo]*]*]*]*]: bar
[*[*[*[foo]*]*]*]: bar
[*[*[foo]*]*]: bar
[*[foo]*]: bar
[foo]: bar

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deps/cmark/bench/samples/inline-autolink.md vendored Normal file
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closed (valid) autolinks:
<ftp://1.2.3.4:21/path/foo>
<http://foo.bar.baz?q=hello&id=22&boolean>
<http://veeeeeeeeeeeeeeeeeeery.loooooooooooooooooooooooooooooooong.autolink/>
<teeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeest@gmail.com>
these are not autolinks:
<ftp://1.2.3.4:21/path/foo
<http://foo.bar.baz?q=hello&id=22&boolean
<http://veeeeeeeeeeeeeeeeeeery.loooooooooooooooooooooooooooooooong.autolink
<teeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeest@gmail.com
< http://foo.bar.baz?q=hello&id=22&boolean >

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`lots`of`backticks`
``i``wonder``how``this``will``be``parsed``

5
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*this* *is* *your* *basic* *boring* *emphasis*
_this_ _is_ _your_ _basic_ _boring_ _emphasis_
**this** **is** **your** **basic** **boring** **emphasis**

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*this *is *a *bunch* of* nested* emphases*
__this __is __a __bunch__ of__ nested__ emphases__
***this ***is ***a ***bunch*** of*** nested*** emphases***

5
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*this *is *a *worst *case *for *em *backtracking
__this __is __a __worst __case __for __em __backtracking
***this ***is ***a ***worst ***case ***for ***em ***backtracking

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entities:
&nbsp; &amp; &copy; &AElig; &Dcaron; &frac34; &HilbertSpace; &DifferentialD; &ClockwiseContourIntegral;
&#35; &#1234; &#992; &#98765432;
non-entities:
&18900987654321234567890; &1234567890098765432123456789009876543212345678987654;
&qwertyuioppoiuytrewqwer; &oiuytrewqwertyuioiuytrewqwertyuioytrewqwertyuiiuytri;

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\t\e\s\t\i\n\g \e\s\c\a\p\e \s\e\q\u\e\n\c\e\s
\!\\\"\#\$\%\&\'\(\)\*\+\,\.\/\:\;\<\=\>\?
\@ \[ \] \^ \_ \` \{ \| \} \~ \- \'
\
\\
\\\
\\\\
\\\\\
\<this\> \<is\> \<not\> \<html\>

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Taking commonmark tests from the spec for benchmarking here:
<a><bab><c2c>
<a/><b2/>
<a /><b2
data="foo" >
<a foo="bar" bam = 'baz <em>"</em>'
_boolean zoop:33=zoop:33 />
<33> <__>
<a h*#ref="hi">
<a href="hi'> <a href=hi'>
< a><
foo><bar/ >
<a href='bar'title=title>
</a>
</foo >
</a href="foo">
foo <!-- this is a
comment - with hyphen -->
foo <!-- not a comment -- two hyphens -->
foo <?php echo $a; ?>
foo <!ELEMENT br EMPTY>
foo <![CDATA[>&<]]>
<a href="&ouml;">
<a href="\*">
<a href="\"">

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deps/cmark/bench/samples/inline-links-flat.md vendored Normal file
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Valid links:
[this is a link]()
[this is a link](<http://something.example.com/foo/bar>)
[this is a link](http://something.example.com/foo/bar 'test')
![this is an image]()
![this is an image](<http://something.example.com/foo/bar>)
![this is an image](http://something.example.com/foo/bar 'test')
[escape test](<\>\>\>\>\>\>\>\>\>\>\>\>\>\>> '\'\'\'\'\'\'\'\'\'\'\'\'\'\'')
[escape test \]\]\]\]\]\]\]\]\]\]\]\]\]\]\]\]](\)\)\)\)\)\)\)\)\)\)\)\)\)\))
Invalid links:
[this is not a link
[this is not a link](
[this is not a link](http://something.example.com/foo/bar 'test'
[this is not a link](((((((((((((((((((((((((((((((((((((((((((((((
[this is not a link]((((((((((()))))))))) (((((((((()))))))))))

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Valid links:
[[[[[[[[](test)](test)](test)](test)](test)](test)](test)]
[ [[[[[[[[[[[[[[[[[[ [](test) ]]]]]]]]]]]]]]]]]] ](test)
Invalid links:
[[[[[[[[[
[ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [
![![![![![![![![![![![![![![![![![![![![![![![![![![![![![![![![![![![![![![

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this\
should\
be\
separated\
by\
newlines
this
should
be
separated
by
newlines
too
this
should
not
be
separated
by
newlines

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deps/cmark/bench/samples/lorem1.md vendored Normal file
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Lorem ipsum dolor sit amet, __consectetur__ adipiscing elit. Cras imperdiet nec erat ac condimentum. Nulla vel rutrum ligula. Sed hendrerit interdum orci a posuere. Vivamus ut velit aliquet, mollis purus eget, iaculis nisl. Proin posuere malesuada ante. Proin auctor orci eros, ac molestie lorem dictum nec. Vestibulum sit amet erat est. Morbi luctus sed elit ac luctus. Proin blandit, enim vitae egestas posuere, neque elit ultricies dui, vel mattis nibh enim ac lorem. Maecenas molestie nisl sit amet velit dictum lobortis. Aliquam erat volutpat.
Vivamus sagittis, diam in [vehicula](https://github.com/markdown-it/markdown-it) lobortis, sapien arcu mattis erat, vel aliquet sem urna et risus. Ut feugiat sapien vitae mi elementum laoreet. Suspendisse potenti. Aliquam erat nisl, aliquam pretium libero aliquet, sagittis eleifend nunc. In hac habitasse platea dictumst. Integer turpis augue, tincidunt dignissim mauris id, rhoncus dapibus purus. Maecenas et enim odio. Nullam massa metus, varius quis vehicula sed, pharetra mollis erat. In quis viverra velit. Vivamus placerat, est nec hendrerit varius, enim dui hendrerit magna, ut pulvinar nibh lorem vel lacus. Mauris a orci iaculis, hendrerit eros sed, gravida leo. In dictum mauris vel augue varius, ac ullamcorper nisl ornare. In eu posuere velit, ac fermentum arcu. Interdum et malesuada fames ac ante ipsum primis in faucibus. Nullam sed malesuada leo, at interdum elit.
Nullam ut tincidunt nunc. [Pellentesque][1] metus lacus, commodo eget justo ut, rutrum varius nunc. Sed non rhoncus risus. Morbi sodales gravida pulvinar. Duis malesuada, odio volutpat elementum vulputate, massa magna scelerisque ante, et accumsan tellus nunc in sem. Donec mattis arcu et velit aliquet, non sagittis justo vestibulum. Suspendisse volutpat felis lectus, nec consequat ipsum mattis id. Donec dapibus vehicula facilisis. In tincidunt mi nisi, nec faucibus tortor euismod nec. Suspendisse ante ligula, aliquet vitae libero eu, vulputate dapibus libero. Sed bibendum, sapien at posuere interdum, libero est sollicitudin magna, ac gravida tellus purus eu ipsum. Proin ut quam arcu.
Suspendisse potenti. Donec ante velit, ornare at augue quis, tristique laoreet sem. Etiam in ipsum elit. Nullam cursus dolor sit amet nulla feugiat tristique. Phasellus ac tellus tincidunt, imperdiet purus eget, ullamcorper ipsum. Cras eu tincidunt sem. Nullam sed dapibus magna. Lorem ipsum dolor sit amet, consectetur adipiscing elit. In id venenatis tortor. In consectetur sollicitudin pharetra. Etiam convallis nisi nunc, et aliquam turpis viverra sit amet. Maecenas faucibus sodales tortor. Suspendisse lobortis mi eu leo viverra volutpat. Pellentesque velit ante, vehicula sodales congue ut, elementum a urna. Cras tempor, ipsum eget luctus rhoncus, arcu ligula fermentum urna, vulputate pharetra enim enim non libero.
Proin diam quam, elementum in eleifend id, elementum et metus. Cras in justo consequat justo semper ultrices. Sed dignissim lectus a ante mollis, nec vulputate ante molestie. Proin in porta nunc. Etiam pulvinar turpis sed velit porttitor, vel adipiscing velit fringilla. Cras ac tellus vitae purus pharetra tincidunt. Sed cursus aliquet aliquet. Cras eleifend commodo malesuada. In turpis turpis, ullamcorper ut tincidunt a, ullamcorper a nunc. Etiam luctus tellus ac dapibus gravida. Ut nec lacus laoreet neque ullamcorper volutpat.
Nunc et leo erat. Aenean mattis ultrices lorem, eget adipiscing dolor ultricies eu. In hac habitasse platea dictumst. Vivamus cursus feugiat sapien quis aliquam. Mauris quam libero, porta vel volutpat ut, blandit a purus. Vivamus vestibulum dui vel tortor molestie, sit amet feugiat sem commodo. Nulla facilisi. Sed molestie arcu eget tellus vestibulum tristique.
[1]: https://github.com/markdown-it

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this is a test for tab expansion, be careful not to replace them with spaces
1 4444
22 333
333 22
4444 1
tab-indented line
space-indented line
tab-indented line
a lot of spaces in between here
a lot of tabs in between here

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## Module statistics.py
##
## Copyright (c) 2013 Steven D'Aprano <steve+python@pearwood.info>.
##
## Licensed under the Apache License, Version 2.0 (the "License");
## you may not use this file except in compliance with the License.
## You may obtain a copy of the License at
##
## http://www.apache.org/licenses/LICENSE-2.0
##
## Unless required by applicable law or agreed to in writing, software
## distributed under the License is distributed on an "AS IS" BASIS,
## WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
## See the License for the specific language governing permissions and
## limitations under the License.
"""
Basic statistics module.
This module provides functions for calculating statistics of data, including
averages, variance, and standard deviation.
Calculating averages
--------------------
================== =============================================
Function Description
================== =============================================
mean Arithmetic mean (average) of data.
median Median (middle value) of data.
median_low Low median of data.
median_high High median of data.
median_grouped Median, or 50th percentile, of grouped data.
mode Mode (most common value) of data.
================== =============================================
Calculate the arithmetic mean ("the average") of data:
>>> mean([-1.0, 2.5, 3.25, 5.75])
2.625
Calculate the standard median of discrete data:
>>> median([2, 3, 4, 5])
3.5
Calculate the median, or 50th percentile, of data grouped into class intervals
centred on the data values provided. E.g. if your data points are rounded to
the nearest whole number:
>>> median_grouped([2, 2, 3, 3, 3, 4]) #doctest: +ELLIPSIS
2.8333333333...
This should be interpreted in this way: you have two data points in the class
interval 1.5-2.5, three data points in the class interval 2.5-3.5, and one in
the class interval 3.5-4.5. The median of these data points is 2.8333...
Calculating variability or spread
---------------------------------
================== =============================================
Function Description
================== =============================================
pvariance Population variance of data.
variance Sample variance of data.
pstdev Population standard deviation of data.
stdev Sample standard deviation of data.
================== =============================================
Calculate the standard deviation of sample data:
>>> stdev([2.5, 3.25, 5.5, 11.25, 11.75]) #doctest: +ELLIPSIS
4.38961843444...
If you have previously calculated the mean, you can pass it as the optional
second argument to the four "spread" functions to avoid recalculating it:
>>> data = [1, 2, 2, 4, 4, 4, 5, 6]
>>> mu = mean(data)
>>> pvariance(data, mu)
2.5
Exceptions
----------
A single exception is defined: StatisticsError is a subclass of ValueError.
"""
__all__ = [ 'StatisticsError',
'pstdev', 'pvariance', 'stdev', 'variance',
'median', 'median_low', 'median_high', 'median_grouped',
'mean', 'mode',
]
import collections
import math
from fractions import Fraction
from decimal import Decimal
# === Exceptions ===
class StatisticsError(ValueError):
pass
# === Private utilities ===
def _sum(data, start=0):
"""_sum(data [, start]) -> value
Return a high-precision sum of the given numeric data. If optional
argument ``start`` is given, it is added to the total. If ``data`` is
empty, ``start`` (defaulting to 0) is returned.
Examples
--------
>>> _sum([3, 2.25, 4.5, -0.5, 1.0], 0.75)
11.0
Some sources of round-off error will be avoided:
>>> _sum([1e50, 1, -1e50] * 1000) # Built-in sum returns zero.
1000.0
Fractions and Decimals are also supported:
>>> from fractions import Fraction as F
>>> _sum([F(2, 3), F(7, 5), F(1, 4), F(5, 6)])
Fraction(63, 20)
>>> from decimal import Decimal as D
>>> data = [D("0.1375"), D("0.2108"), D("0.3061"), D("0.0419")]
>>> _sum(data)
Decimal('0.6963')
Mixed types are currently treated as an error, except that int is
allowed.
"""
# We fail as soon as we reach a value that is not an int or the type of
# the first value which is not an int. E.g. _sum([int, int, float, int])
# is okay, but sum([int, int, float, Fraction]) is not.
allowed_types = set([int, type(start)])
n, d = _exact_ratio(start)
partials = {d: n} # map {denominator: sum of numerators}
# Micro-optimizations.
exact_ratio = _exact_ratio
partials_get = partials.get
# Add numerators for each denominator.
for x in data:
_check_type(type(x), allowed_types)
n, d = exact_ratio(x)
partials[d] = partials_get(d, 0) + n
# Find the expected result type. If allowed_types has only one item, it
# will be int; if it has two, use the one which isn't int.
assert len(allowed_types) in (1, 2)
if len(allowed_types) == 1:
assert allowed_types.pop() is int
T = int
else:
T = (allowed_types - set([int])).pop()
if None in partials:
assert issubclass(T, (float, Decimal))
assert not math.isfinite(partials[None])
return T(partials[None])
total = Fraction()
for d, n in sorted(partials.items()):
total += Fraction(n, d)
if issubclass(T, int):
assert total.denominator == 1
return T(total.numerator)
if issubclass(T, Decimal):
return T(total.numerator)/total.denominator
return T(total)
def _check_type(T, allowed):
if T not in allowed:
if len(allowed) == 1:
allowed.add(T)
else:
types = ', '.join([t.__name__ for t in allowed] + [T.__name__])
raise TypeError("unsupported mixed types: %s" % types)
def _exact_ratio(x):
"""Convert Real number x exactly to (numerator, denominator) pair.
>>> _exact_ratio(0.25)
(1, 4)
x is expected to be an int, Fraction, Decimal or float.
"""
try:
try:
# int, Fraction
return (x.numerator, x.denominator)
except AttributeError:
# float
try:
return x.as_integer_ratio()
except AttributeError:
# Decimal
try:
return _decimal_to_ratio(x)
except AttributeError:
msg = "can't convert type '{}' to numerator/denominator"
raise TypeError(msg.format(type(x).__name__)) from None
except (OverflowError, ValueError):
# INF or NAN
if __debug__:
# Decimal signalling NANs cannot be converted to float :-(
if isinstance(x, Decimal):
assert not x.is_finite()
else:
assert not math.isfinite(x)
return (x, None)
# FIXME This is faster than Fraction.from_decimal, but still too slow.
def _decimal_to_ratio(d):
"""Convert Decimal d to exact integer ratio (numerator, denominator).
>>> from decimal import Decimal
>>> _decimal_to_ratio(Decimal("2.6"))
(26, 10)
"""
sign, digits, exp = d.as_tuple()
if exp in ('F', 'n', 'N'): # INF, NAN, sNAN
assert not d.is_finite()
raise ValueError
num = 0
for digit in digits:
num = num*10 + digit
if exp < 0:
den = 10**-exp
else:
num *= 10**exp
den = 1
if sign:
num = -num
return (num, den)
def _counts(data):
# Generate a table of sorted (value, frequency) pairs.
table = collections.Counter(iter(data)).most_common()
if not table:
return table
# Extract the values with the highest frequency.
maxfreq = table[0][1]
for i in range(1, len(table)):
if table[i][1] != maxfreq:
table = table[:i]
break
return table
# === Measures of central tendency (averages) ===
def mean(data):
"""Return the sample arithmetic mean of data.
>>> mean([1, 2, 3, 4, 4])
2.8
>>> from fractions import Fraction as F
>>> mean([F(3, 7), F(1, 21), F(5, 3), F(1, 3)])
Fraction(13, 21)
>>> from decimal import Decimal as D
>>> mean([D("0.5"), D("0.75"), D("0.625"), D("0.375")])
Decimal('0.5625')
If ``data`` is empty, StatisticsError will be raised.
"""
if iter(data) is data:
data = list(data)
n = len(data)
if n < 1:
raise StatisticsError('mean requires at least one data point')
return _sum(data)/n
# FIXME: investigate ways to calculate medians without sorting? Quickselect?
def median(data):
"""Return the median (middle value) of numeric data.
When the number of data points is odd, return the middle data point.
When the number of data points is even, the median is interpolated by
taking the average of the two middle values:
>>> median([1, 3, 5])
3
>>> median([1, 3, 5, 7])
4.0
"""
data = sorted(data)
n = len(data)
if n == 0:
raise StatisticsError("no median for empty data")
if n%2 == 1:
return data[n//2]
else:
i = n//2
return (data[i - 1] + data[i])/2
def median_low(data):
"""Return the low median of numeric data.
When the number of data points is odd, the middle value is returned.
When it is even, the smaller of the two middle values is returned.
>>> median_low([1, 3, 5])
3
>>> median_low([1, 3, 5, 7])
3
"""
data = sorted(data)
n = len(data)
if n == 0:
raise StatisticsError("no median for empty data")
if n%2 == 1:
return data[n//2]
else:
return data[n//2 - 1]
def median_high(data):
"""Return the high median of data.
When the number of data points is odd, the middle value is returned.
When it is even, the larger of the two middle values is returned.
>>> median_high([1, 3, 5])
3
>>> median_high([1, 3, 5, 7])
5
"""
data = sorted(data)
n = len(data)
if n == 0:
raise StatisticsError("no median for empty data")
return data[n//2]
def median_grouped(data, interval=1):
""""Return the 50th percentile (median) of grouped continuous data.
>>> median_grouped([1, 2, 2, 3, 4, 4, 4, 4, 4, 5])
3.7
>>> median_grouped([52, 52, 53, 54])
52.5
This calculates the median as the 50th percentile, and should be
used when your data is continuous and grouped. In the above example,
the values 1, 2, 3, etc. actually represent the midpoint of classes
0.5-1.5, 1.5-2.5, 2.5-3.5, etc. The middle value falls somewhere in
class 3.5-4.5, and interpolation is used to estimate it.
Optional argument ``interval`` represents the class interval, and
defaults to 1. Changing the class interval naturally will change the
interpolated 50th percentile value:
>>> median_grouped([1, 3, 3, 5, 7], interval=1)
3.25
>>> median_grouped([1, 3, 3, 5, 7], interval=2)
3.5
This function does not check whether the data points are at least
``interval`` apart.
"""
data = sorted(data)
n = len(data)
if n == 0:
raise StatisticsError("no median for empty data")
elif n == 1:
return data[0]
# Find the value at the midpoint. Remember this corresponds to the
# centre of the class interval.
x = data[n//2]
for obj in (x, interval):
if isinstance(obj, (str, bytes)):
raise TypeError('expected number but got %r' % obj)
try:
L = x - interval/2 # The lower limit of the median interval.
except TypeError:
# Mixed type. For now we just coerce to float.
L = float(x) - float(interval)/2
cf = data.index(x) # Number of values below the median interval.
# FIXME The following line could be more efficient for big lists.
f = data.count(x) # Number of data points in the median interval.
return L + interval*(n/2 - cf)/f
def mode(data):
"""Return the most common data point from discrete or nominal data.
``mode`` assumes discrete data, and returns a single value. This is the
standard treatment of the mode as commonly taught in schools:
>>> mode([1, 1, 2, 3, 3, 3, 3, 4])
3
This also works with nominal (non-numeric) data:
>>> mode(["red", "blue", "blue", "red", "green", "red", "red"])
'red'
If there is not exactly one most common value, ``mode`` will raise
StatisticsError.
"""
# Generate a table of sorted (value, frequency) pairs.
table = _counts(data)
if len(table) == 1:
return table[0][0]
elif table:
raise StatisticsError(
'no unique mode; found %d equally common values' % len(table)
)
else:
raise StatisticsError('no mode for empty data')
# === Measures of spread ===
# See http://mathworld.wolfram.com/Variance.html
# http://mathworld.wolfram.com/SampleVariance.html
# http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
#
# Under no circumstances use the so-called "computational formula for
# variance", as that is only suitable for hand calculations with a small
# amount of low-precision data. It has terrible numeric properties.
#
# See a comparison of three computational methods here:
# http://www.johndcook.com/blog/2008/09/26/comparing-three-methods-of-computing-standard-deviation/
def _ss(data, c=None):
"""Return sum of square deviations of sequence data.
If ``c`` is None, the mean is calculated in one pass, and the deviations
from the mean are calculated in a second pass. Otherwise, deviations are
calculated from ``c`` as given. Use the second case with care, as it can
lead to garbage results.
"""
if c is None:
c = mean(data)
ss = _sum((x-c)**2 for x in data)
# The following sum should mathematically equal zero, but due to rounding
# error may not.
ss -= _sum((x-c) for x in data)**2/len(data)
assert not ss < 0, 'negative sum of square deviations: %f' % ss
return ss
def variance(data, xbar=None):
"""Return the sample variance of data.
data should be an iterable of Real-valued numbers, with at least two
values. The optional argument xbar, if given, should be the mean of
the data. If it is missing or None, the mean is automatically calculated.
Use this function when your data is a sample from a population. To
calculate the variance from the entire population, see ``pvariance``.
Examples:
>>> data = [2.75, 1.75, 1.25, 0.25, 0.5, 1.25, 3.5]
>>> variance(data)
1.3720238095238095
If you have already calculated the mean of your data, you can pass it as
the optional second argument ``xbar`` to avoid recalculating it:
>>> m = mean(data)
>>> variance(data, m)
1.3720238095238095
This function does not check that ``xbar`` is actually the mean of
``data``. Giving arbitrary values for ``xbar`` may lead to invalid or
impossible results.
Decimals and Fractions are supported:
>>> from decimal import Decimal as D
>>> variance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])
Decimal('31.01875')
>>> from fractions import Fraction as F
>>> variance([F(1, 6), F(1, 2), F(5, 3)])
Fraction(67, 108)
"""
if iter(data) is data:
data = list(data)
n = len(data)
if n < 2:
raise StatisticsError('variance requires at least two data points')
ss = _ss(data, xbar)
return ss/(n-1)
def pvariance(data, mu=None):
"""Return the population variance of ``data``.
data should be an iterable of Real-valued numbers, with at least one
value. The optional argument mu, if given, should be the mean of
the data. If it is missing or None, the mean is automatically calculated.
Use this function to calculate the variance from the entire population.
To estimate the variance from a sample, the ``variance`` function is
usually a better choice.
Examples:
>>> data = [0.0, 0.25, 0.25, 1.25, 1.5, 1.75, 2.75, 3.25]
>>> pvariance(data)
1.25
If you have already calculated the mean of the data, you can pass it as
the optional second argument to avoid recalculating it:
>>> mu = mean(data)
>>> pvariance(data, mu)
1.25
This function does not check that ``mu`` is actually the mean of ``data``.
Giving arbitrary values for ``mu`` may lead to invalid or impossible
results.
Decimals and Fractions are supported:
>>> from decimal import Decimal as D
>>> pvariance([D("27.5"), D("30.25"), D("30.25"), D("34.5"), D("41.75")])
Decimal('24.815')
>>> from fractions import Fraction as F
>>> pvariance([F(1, 4), F(5, 4), F(1, 2)])
Fraction(13, 72)
"""
if iter(data) is data:
data = list(data)
n = len(data)
if n < 1:
raise StatisticsError('pvariance requires at least one data point')
ss = _ss(data, mu)
return ss/n
def stdev(data, xbar=None):
"""Return the square root of the sample variance.
See ``variance`` for arguments and other details.
>>> stdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
1.0810874155219827
"""
var = variance(data, xbar)
try:
return var.sqrt()
except AttributeError:
return math.sqrt(var)
def pstdev(data, mu=None):
"""Return the square root of the population variance.
See ``pvariance`` for arguments and other details.
>>> pstdev([1.5, 2.5, 2.5, 2.75, 3.25, 4.75])
0.986893273527251
"""
var = pvariance(data, mu)
try:
return var.sqrt()
except AttributeError:
return math.sqrt(var)

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#!/usr/bin/env python3
import sys
import statistics
def pairs(l, n):
return zip(*[l[i::n] for i in range(n)])
# data comes in pairs:
# n - time for running the program with no input
# m - time for running it with the benchmark input
# we measure (m - n)
values = [ float(y) - float(x) for (x,y) in pairs(sys.stdin.readlines(),2)]
print("mean = %.4f, median = %.4f, stdev = %.4f" %
(statistics.mean(values), statistics.median(values),
statistics.stdev(values)))