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 <div class="section" id="brief-tour-of-the-standard-library-part-ii">
<h1>11. Brief Tour of the Standard Library — Part II<a class="headerlink" href="#brief-tour-of-the-standard-library-part-ii" title="Permalink to this headline">¶</a></h1>
This second tour covers more advanced modules that support professional
programming needs. These modules rarely occur in small scripts.
<div class="section" id="output-formatting">
<h2>11.1. Output Formatting<a class="headerlink" href="#output-formatting" title="Permalink to this headline">¶</a></h2>
The <a class="reference internal" href="../library/reprlib.html#module-reprlib" title="reprlib: Alternate repr() implementation with size limits."><code class="xref py py-mod docutils literal notranslate">reprlib</code></a> module provides a version of <a class="reference internal" href="../library/functions.html#repr" title="repr"><code class="xref py py-func docutils literal notranslate">repr()</code></a> customized for
abbreviated displays of large or deeply nested containers:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; import reprlib
&gt;&gt;&gt; reprlib.repr(set(&#39;supercalifragilisticexpialidocious&#39;))
&quot;{&#39;a&#39;, &#39;c&#39;, &#39;d&#39;, &#39;e&#39;, &#39;f&#39;, &#39;g&#39;, ...}&quot;
</pre></div>
</div>
The <a class="reference internal" href="../library/pprint.html#module-pprint" title="pprint: Data pretty printer."><code class="xref py py-mod docutils literal notranslate">pprint</code></a> module offers more sophisticated control over printing both
built-in and user defined objects in a way that is readable by the interpreter.
When the result is longer than one line, the “pretty printer” adds line breaks
and indentation to more clearly reveal data structure:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; import pprint
&gt;&gt;&gt; t = [[[[&#39;black&#39;, &#39;cyan&#39;], &#39;white&#39;, [&#39;green&#39;, &#39;red&#39;]], [[&#39;magenta&#39;,
... &#39;yellow&#39;], &#39;blue&#39;]]]
...
&gt;&gt;&gt; pprint.pprint(t, width=30)
[[[[&#39;black&#39;, &#39;cyan&#39;],
 &#39;white&#39;,
 [&#39;green&#39;, &#39;red&#39;]],
 [[&#39;magenta&#39;, &#39;yellow&#39;],
 &#39;blue&#39;]]]
</pre></div>
</div>
The <a class="reference internal" href="../library/textwrap.html#module-textwrap" title="textwrap: Text wrapping and filling"><code class="xref py py-mod docutils literal notranslate">textwrap</code></a> module formats paragraphs of text to fit a given screen
width:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; import textwrap
&gt;&gt;&gt; doc = &quot;&quot;&quot;The wrap() method is just like fill() except that it returns
... a list of strings instead of one big string with newlines to separate
... the wrapped lines.&quot;&quot;&quot;
...
&gt;&gt;&gt; print(textwrap.fill(doc, width=40))
The wrap() method is just like fill()
except that it returns a list of strings
instead of one big string with newlines
to separate the wrapped lines.
</pre></div>
</div>
The <a class="reference internal" href="../library/locale.html#module-locale" title="locale: Internationalization services."><code class="xref py py-mod docutils literal notranslate">locale</code></a> module accesses a database of culture specific data formats.
The grouping attribute of locale’s format function provides a direct way of
formatting numbers with group separators:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; import locale
&gt;&gt;&gt; locale.setlocale(locale.LC_ALL, &#39;English_United States.1252&#39;)
&#39;English_United States.1252&#39;
&gt;&gt;&gt; conv = locale.localeconv() # get a mapping of conventions
&gt;&gt;&gt; x = 1234567.8
&gt;&gt;&gt; locale.format(&quot;%d&quot;, x, grouping=True)
&#39;1,234,567&#39;
&gt;&gt;&gt; locale.format_string(&quot;%s%.*f&quot;, (conv[&#39;currency_symbol&#39;],
... conv[&#39;frac_digits&#39;], x), grouping=True)
&#39;$1,234,567.80&#39;
</pre></div>
</div>
</div>
<div class="section" id="templating">
<h2>11.2. Templating<a class="headerlink" href="#templating" title="Permalink to this headline">¶</a></h2>
The <a class="reference internal" href="../library/string.html#module-string" title="string: Common string operations."><code class="xref py py-mod docutils literal notranslate">string</code></a> module includes a versatile <a class="reference internal" href="../library/string.html#string.Template" title="string.Template"><code class="xref py py-class docutils literal notranslate">Template</code></a> class
with a simplified syntax suitable for editing by end-users. This allows users
to customize their applications without having to alter the application.
The format uses placeholder names formed by <code class="docutils literal notranslate">$</code> with valid Python identifiers
(alphanumeric characters and underscores). Surrounding the placeholder with
braces allows it to be followed by more alphanumeric letters with no intervening
spaces. Writing <code class="docutils literal notranslate">$$</code> creates a single escaped <code class="docutils literal notranslate">$</code>:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; from string import Template
&gt;&gt;&gt; t = Template(&#39;${village}folk send $$10 to $cause.&#39;)
&gt;&gt;&gt; t.substitute(village=&#39;Nottingham&#39;, cause=&#39;the ditch fund&#39;)
&#39;Nottinghamfolk send $10 to the ditch fund.&#39;
</pre></div>
</div>
The <a class="reference internal" href="../library/string.html#string.Template.substitute" title="string.Template.substitute"><code class="xref py py-meth docutils literal notranslate">substitute()</code></a> method raises a <a class="reference internal" href="../library/exceptions.html#KeyError" title="KeyError"><code class="xref py py-exc docutils literal notranslate">KeyError</code></a> when a
placeholder is not supplied in a dictionary or a keyword argument. For
mail-merge style applications, user supplied data may be incomplete and the
<a class="reference internal" href="../library/string.html#string.Template.safe_substitute" title="string.Template.safe_substitute"><code class="xref py py-meth docutils literal notranslate">safe_substitute()</code></a> method may be more appropriate —
it will leave placeholders unchanged if data is missing:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; t = Template(&#39;Return the $item to $owner.&#39;)
&gt;&gt;&gt; d = dict(item=&#39;unladen swallow&#39;)
&gt;&gt;&gt; t.substitute(d)
Traceback (most recent call last):
 ...
KeyError: &#39;owner&#39;
&gt;&gt;&gt; t.safe_substitute(d)
&#39;Return the unladen swallow to $owner.&#39;
</pre></div>
</div>
Template subclasses can specify a custom delimiter. For example, a batch
renaming utility for a photo browser may elect to use percent signs for
placeholders such as the current date, image sequence number, or file format:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; import time, os.path
&gt;&gt;&gt; photofiles = [&#39;img_1074.jpg&#39;, &#39;img_1076.jpg&#39;, &#39;img_1077.jpg&#39;]
&gt;&gt;&gt; class BatchRename(Template):
... delimiter = &#39;%&#39;
&gt;&gt;&gt; fmt = input(&#39;Enter rename style (%d-date %n-seqnum %f-format): &#39;)
Enter rename style (%d-date %n-seqnum %f-format): Ashley_%n%f

&gt;&gt;&gt; t = BatchRename(fmt)
&gt;&gt;&gt; date = time.strftime(&#39;%d%b%y&#39;)
&gt;&gt;&gt; for i, filename in enumerate(photofiles):
... base, ext = os.path.splitext(filename)
... newname = t.substitute(d=date, n=i, f=ext)
... print(&#39;{0} --&gt; {1}&#39;.format(filename, newname))

img_1074.jpg --&gt; Ashley_0.jpg
img_1076.jpg --&gt; Ashley_1.jpg
img_1077.jpg --&gt; Ashley_2.jpg
</pre></div>
</div>
Another application for templating is separating program logic from the details
of multiple output formats. This makes it possible to substitute custom
templates for XML files, plain text reports, and HTML web reports.
</div>
<div class="section" id="working-with-binary-data-record-layouts">
<h2>11.3. Working with Binary Data Record Layouts<a class="headerlink" href="#working-with-binary-data-record-layouts" title="Permalink to this headline">¶</a></h2>
The <a class="reference internal" href="../library/struct.html#module-struct" title="struct: Interpret bytes as packed binary data."><code class="xref py py-mod docutils literal notranslate">struct</code></a> module provides <a class="reference internal" href="../library/struct.html#struct.pack" title="struct.pack"><code class="xref py py-func docutils literal notranslate">pack()</code></a> and
<a class="reference internal" href="../library/struct.html#struct.unpack" title="struct.unpack"><code class="xref py py-func docutils literal notranslate">unpack()</code></a> functions for working with variable length binary
record formats. The following example shows
how to loop through header information in a ZIP file without using the
<a class="reference internal" href="../library/zipfile.html#module-zipfile" title="zipfile: Read and write ZIP-format archive files."><code class="xref py py-mod docutils literal notranslate">zipfile</code></a> module. Pack codes <code class="docutils literal notranslate">&quot;H&quot;</code> and <code class="docutils literal notranslate">&quot;I&quot;</code> represent two and four
byte unsigned numbers respectively. The <code class="docutils literal notranslate">&quot;&lt;&quot;</code> indicates that they are
standard size and in little-endian byte order:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>import struct

with open(&#39;myfile.zip&#39;, &#39;rb&#39;) as f:
 data = f.read()

start = 0
for i in range(3): # show the first 3 file headers
 start += 14
 fields = struct.unpack(&#39;&lt;IIIHH&#39;, data[start:start+16])
 crc32, comp_size, uncomp_size, filenamesize, extra_size = fields

start += 16
 filename = data[start:start+filenamesize]
 start += filenamesize
 extra = data[start:start+extra_size]
 print(filename, hex(crc32), comp_size, uncomp_size)

start += extra_size + comp_size # skip to the next header
</pre></div>
</div>
</div>
<div class="section" id="multi-threading">
<h2>11.4. Multi-threading<a class="headerlink" href="#multi-threading" title="Permalink to this headline">¶</a></h2>
Threading is a technique for decoupling tasks which are not sequentially
dependent. Threads can be used to improve the responsiveness of applications
that accept user input while other tasks run in the background. A related use
case is running I/O in parallel with computations in another thread.
The following code shows how the high level <a class="reference internal" href="../library/threading.html#module-threading" title="threading: Thread-based parallelism."><code class="xref py py-mod docutils literal notranslate">threading</code></a> module can run
tasks in background while the main program continues to run:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>import threading, zipfile

class AsyncZip(threading.Thread):
 def __init__(self, infile, outfile):
 threading.Thread.__init__(self)
 self.infile = infile
 self.outfile = outfile

def run(self):
 f = zipfile.ZipFile(self.outfile, &#39;w&#39;, zipfile.ZIP_DEFLATED)
 f.write(self.infile)
 f.close()
 print(&#39;Finished background zip of:&#39;, self.infile)

background = AsyncZip(&#39;mydata.txt&#39;, &#39;myarchive.zip&#39;)
background.start()
print(&#39;The main program continues to run in foreground.&#39;)

background.join() # Wait for the background task to finish
print(&#39;Main program waited until background was done.&#39;)
</pre></div>
</div>
The principal challenge of multi-threaded applications is coordinating threads
that share data or other resources. To that end, the threading module provides
a number of synchronization primitives including locks, events, condition
variables, and semaphores.
While those tools are powerful, minor design errors can result in problems that
are difficult to reproduce. So, the preferred approach to task coordination is
to concentrate all access to a resource in a single thread and then use the
<a class="reference internal" href="../library/queue.html#module-queue" title="queue: A synchronized queue class."><code class="xref py py-mod docutils literal notranslate">queue</code></a> module to feed that thread with requests from other threads.
Applications using <a class="reference internal" href="../library/queue.html#queue.Queue" title="queue.Queue"><code class="xref py py-class docutils literal notranslate">Queue</code></a> objects for inter-thread communication and
coordination are easier to design, more readable, and more reliable.
</div>
<div class="section" id="logging">
<h2>11.5. Logging<a class="headerlink" href="#logging" title="Permalink to this headline">¶</a></h2>
The <a class="reference internal" href="../library/logging.html#module-logging" title="logging: Flexible event logging system for applications."><code class="xref py py-mod docutils literal notranslate">logging</code></a> module offers a full featured and flexible logging system.
At its simplest, log messages are sent to a file or to <code class="docutils literal notranslate">sys.stderr</code>:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>import logging
logging.debug(&#39;Debugging information&#39;)
logging.info(&#39;Informational message&#39;)
logging.warning(&#39;Warning:config file %s not found&#39;, &#39;server.conf&#39;)
logging.error(&#39;Error occurred&#39;)
logging.critical(&#39;Critical error -- shutting down&#39;)
</pre></div>
</div>
This produces the following output:
<div class="highlight-none notranslate"><div class="highlight"><pre>WARNING:root:Warning:config file server.conf not found
ERROR:root:Error occurred
CRITICAL:root:Critical error -- shutting down
</pre></div>
</div>
By default, informational and debugging messages are suppressed and the output
is sent to standard error. Other output options include routing messages
through email, datagrams, sockets, or to an HTTP Server. New filters can select
different routing based on message priority: <code class="xref py py-const docutils literal notranslate">DEBUG</code>,
<code class="xref py py-const docutils literal notranslate">INFO</code>, <code class="xref py py-const docutils literal notranslate">WARNING</code>, <code class="xref py py-const docutils literal notranslate">ERROR</code>,
and <code class="xref py py-const docutils literal notranslate">CRITICAL</code>.
The logging system can be configured directly from Python or can be loaded from
a user editable configuration file for customized logging without altering the
application.
</div>
<div class="section" id="weak-references">
<h2>11.6. Weak References<a class="headerlink" href="#weak-references" title="Permalink to this headline">¶</a></h2>
Python does automatic memory management (reference counting for most objects and
<a class="reference internal" href="../glossary.html#term-garbage-collection">garbage collection</a> to eliminate cycles). The memory is freed shortly
after the last reference to it has been eliminated.
This approach works fine for most applications but occasionally there is a need
to track objects only as long as they are being used by something else.
Unfortunately, just tracking them creates a reference that makes them permanent.
The <a class="reference internal" href="../library/weakref.html#module-weakref" title="weakref: Support for weak references and weak dictionaries."><code class="xref py py-mod docutils literal notranslate">weakref</code></a> module provides tools for tracking objects without creating a
reference. When the object is no longer needed, it is automatically removed
from a weakref table and a callback is triggered for weakref objects. Typical
applications include caching objects that are expensive to create:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; import weakref, gc
&gt;&gt;&gt; class A:
... def __init__(self, value):
... self.value = value
... def __repr__(self):
... return str(self.value)
...
&gt;&gt;&gt; a = A(10) # create a reference
&gt;&gt;&gt; d = weakref.WeakValueDictionary()
&gt;&gt;&gt; d[&#39;primary&#39;] = a # does not create a reference
&gt;&gt;&gt; d[&#39;primary&#39;] # fetch the object if it is still alive
10
&gt;&gt;&gt; del a # remove the one reference
&gt;&gt;&gt; gc.collect() # run garbage collection right away
0
&gt;&gt;&gt; d[&#39;primary&#39;] # entry was automatically removed
Traceback (most recent call last):
 File &quot;&lt;stdin&gt;&quot;, line 1, in &lt;module&gt;
 d[&#39;primary&#39;] # entry was automatically removed
 File &quot;C:/python36/lib/weakref.py&quot;, line 46, in __getitem__
 o = self.data[key]()
KeyError: &#39;primary&#39;
</pre></div>
</div>
</div>
<div class="section" id="tools-for-working-with-lists">
<h2>11.7. Tools for Working with Lists<a class="headerlink" href="#tools-for-working-with-lists" title="Permalink to this headline">¶</a></h2>
Many data structure needs can be met with the built-in list type. However,
sometimes there is a need for alternative implementations with different
performance trade-offs.
The <a class="reference internal" href="../library/array.html#module-array" title="array: Space efficient arrays of uniformly typed numeric values."><code class="xref py py-mod docutils literal notranslate">array</code></a> module provides an <a class="reference internal" href="../library/array.html#array.array" title="array.array"><code class="xref py py-class docutils literal notranslate">array()</code></a> object that is like
a list that stores only homogeneous data and stores it more compactly. The
following example shows an array of numbers stored as two byte unsigned binary
numbers (typecode <code class="docutils literal notranslate">&quot;H&quot;</code>) rather than the usual 16 bytes per entry for regular
lists of Python int objects:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; from array import array
&gt;&gt;&gt; a = array(&#39;H&#39;, [4000, 10, 700, 22222])
&gt;&gt;&gt; sum(a)
26932
&gt;&gt;&gt; a[1:3]
array(&#39;H&#39;, [10, 700])
</pre></div>
</div>
The <a class="reference internal" href="../library/collections.html#module-collections" title="collections: Container datatypes"><code class="xref py py-mod docutils literal notranslate">collections</code></a> module provides a <a class="reference internal" href="../library/collections.html#collections.deque" title="collections.deque"><code class="xref py py-class docutils literal notranslate">deque()</code></a> object
that is like a list with faster appends and pops from the left side but slower
lookups in the middle. These objects are well suited for implementing queues
and breadth first tree searches:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; from collections import deque
&gt;&gt;&gt; d = deque([&quot;task1&quot;, &quot;task2&quot;, &quot;task3&quot;])
&gt;&gt;&gt; d.append(&quot;task4&quot;)
&gt;&gt;&gt; print(&quot;Handling&quot;, d.popleft())
Handling task1
</pre></div>
</div>
<div class="highlight-python3 notranslate"><div class="highlight"><pre>unsearched = deque([starting_node])
def breadth_first_search(unsearched):
 node = unsearched.popleft()
 for m in gen_moves(node):
 if is_goal(m):
 return m
 unsearched.append(m)
</pre></div>
</div>
In addition to alternative list implementations, the library also offers other
tools such as the <a class="reference internal" href="../library/bisect.html#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-mod docutils literal notranslate">bisect</code></a> module with functions for manipulating sorted
lists:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; import bisect
&gt;&gt;&gt; scores = [(100, &#39;perl&#39;), (200, &#39;tcl&#39;), (400, &#39;lua&#39;), (500, &#39;python&#39;)]
&gt;&gt;&gt; bisect.insort(scores, (300, &#39;ruby&#39;))
&gt;&gt;&gt; scores
[(100, &#39;perl&#39;), (200, &#39;tcl&#39;), (300, &#39;ruby&#39;), (400, &#39;lua&#39;), (500, &#39;python&#39;)]
</pre></div>
</div>
The <a class="reference internal" href="../library/heapq.html#module-heapq" title="heapq: Heap queue algorithm (a.k.a. priority queue)."><code class="xref py py-mod docutils literal notranslate">heapq</code></a> module provides functions for implementing heaps based on
regular lists. The lowest valued entry is always kept at position zero. This
is useful for applications which repeatedly access the smallest element but do
not want to run a full list sort:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; from heapq import heapify, heappop, heappush
&gt;&gt;&gt; data = [1, 3, 5, 7, 9, 2, 4, 6, 8, 0]
&gt;&gt;&gt; heapify(data) # rearrange the list into heap order
&gt;&gt;&gt; heappush(data, -5) # add a new entry
&gt;&gt;&gt; [heappop(data) for i in range(3)] # fetch the three smallest entries
[-5, 0, 1]
</pre></div>
</div>
</div>
<div class="section" id="decimal-floating-point-arithmetic">
<h2>11.8. Decimal Floating Point Arithmetic<a class="headerlink" href="#decimal-floating-point-arithmetic" title="Permalink to this headline">¶</a></h2>
The <a class="reference internal" href="../library/decimal.html#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic Specification."><code class="xref py py-mod docutils literal notranslate">decimal</code></a> module offers a <a class="reference internal" href="../library/decimal.html#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate">Decimal</code></a> datatype for
decimal floating point arithmetic. Compared to the built-in <a class="reference internal" href="../library/functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate">float</code></a>
implementation of binary floating point, the class is especially helpful for
<ul class="simple">
<li>financial applications and other uses which require exact decimal
representation,</li>
<li>control over precision,</li>
<li>control over rounding to meet legal or regulatory requirements,</li>
<li>tracking of significant decimal places, or</li>
<li>applications where the user expects the results to match calculations done by
hand.</li>
</ul>
For example, calculating a 5% tax on a 70 cent phone charge gives different
results in decimal floating point and binary floating point. The difference
becomes significant if the results are rounded to the nearest cent:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; from decimal import *
&gt;&gt;&gt; round(Decimal(&#39;0.70&#39;) * Decimal(&#39;1.05&#39;), 2)
Decimal(&#39;0.74&#39;)
&gt;&gt;&gt; round(.70 * 1.05, 2)
0.73
</pre></div>
</div>
The <a class="reference internal" href="../library/decimal.html#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate">Decimal</code></a> result keeps a trailing zero, automatically
inferring four place significance from multiplicands with two place
significance. Decimal reproduces mathematics as done by hand and avoids
issues that can arise when binary floating point cannot exactly represent
decimal quantities.
Exact representation enables the <a class="reference internal" href="../library/decimal.html#decimal.Decimal" title="decimal.Decimal"><code class="xref py py-class docutils literal notranslate">Decimal</code></a> class to perform
modulo calculations and equality tests that are unsuitable for binary floating
point:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; Decimal(&#39;1.00&#39;) % Decimal(&#39;.10&#39;)
Decimal(&#39;0.00&#39;)
&gt;&gt;&gt; 1.00 % 0.10
0.09999999999999995

&gt;&gt;&gt; sum([Decimal(&#39;0.1&#39;)]*10) == Decimal(&#39;1.0&#39;)
True
&gt;&gt;&gt; sum([0.1]*10) == 1.0
False
</pre></div>
</div>
The <a class="reference internal" href="../library/decimal.html#module-decimal" title="decimal: Implementation of the General Decimal Arithmetic Specification."><code class="xref py py-mod docutils literal notranslate">decimal</code></a> module provides arithmetic with as much precision as needed:
<div class="highlight-python3 notranslate"><div class="highlight"><pre>&gt;&gt;&gt; getcontext().prec = 36
&gt;&gt;&gt; Decimal(1) / Decimal(7)
Decimal(&#39;0.142857142857142857142857142857142857&#39;)
</pre></div>
</div>
</div>
</div>

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 <ul>
<li><a class="reference internal" href="#">11. Brief Tour of the Standard Library — Part II</a><ul>
<li><a class="reference internal" href="#output-formatting">11.1. Output Formatting</a></li>
<li><a class="reference internal" href="#templating">11.2. Templating</a></li>
<li><a class="reference internal" href="#working-with-binary-data-record-layouts">11.3. Working with Binary Data Record Layouts</a></li>
<li><a class="reference internal" href="#multi-threading">11.4. Multi-threading</a></li>
<li><a class="reference internal" href="#logging">11.5. Logging</a></li>
<li><a class="reference internal" href="#weak-references">11.6. Weak References</a></li>
<li><a class="reference internal" href="#tools-for-working-with-lists">11.7. Tools for Working with Lists</a></li>
<li><a class="reference internal" href="#decimal-floating-point-arithmetic">11.8. Decimal Floating Point Arithmetic</a></li>
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