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Algorithms in Python: Binary Operations

Xavier — Sat, 17 Jul 2010 19:08:22 +0000

Today I’d like to demonstrate a simple implementation of Kenneth Rosen‘s binary addition and multiplication algorithms as outlined in "Discrete Mathematics and its Applications". Both algorithms are very simple and work the same way we’ve all learned to do decimal additions and multiplications by hand in grade-school.

As usual, I’ve also provided a unit-test suite for each algorithm.

Please note: This is only intended to demonstrate the algorithms. If you are actually trying to do some real work with binary numbers in Python, note that the language itself provides a highly optimized implementation of binary numbers and related operations. Here are a few examples:

# Decimal to binary conversion:
>>> bin(15)
'0b1111'
 
# Binary to decimal conversion:
>>> str(0b1111)
'15'
 
# Binary addition:
>>> bin(0b1111 + 0b10011)
'0b100010'
 
# Binary multiplication:
>>> bin(0b1111 * 0b10011)
'0b100011101'

Binary Addition

We will use strings in this example to represent sequences of bits. The algorithm operates right-to-left, maintaining a carry each time it adds two 1-valued bits.

Code:

"""Simple binary operation algorithm."""
 
import math
 
# a and b should be string representation of the binary components
# You could easily extend this to overload the + operator for binaries,
# but this is already built into python.
def binary_addition(bin_a, bin_b):
    """Performs a binary addition against two provided binary numbers"""
 
    # Pad the components so they are of equal length
    max_length = max(len(bin_a), len(bin_b))
    bin_a, bin_b = bin_a.zfill(max_length), bin_b.zfill(max_length)
 
 
    carry = 0
    result = ''
 
    # Note that we work from right to left
    for i in range(0, max_length)[::-1]:
        tmp = int(math.floor((int(bin_a[i]) + int(bin_b[i]) + carry)/2))
        res = str(int(bin_a[i]) + int(bin_b[i]) + carry - 2*tmp)
        result += res
        carry = tmp
 
    result = (result + str(carry))[::-1]
    try:
        return result[result.index('1'):]
    except ValueError, ex:
        return '0'

Unit Test:

"""Unit test for binary_addition.py"""
 
import unittest
from binary_addition import binary_addition
 
class TestBinaryAddition(unittest.TestCase):
 
    """Comparing python binary addition against our own"""
 
    def test_add_same_length(self):
 
        """Adding 2 binary numbers of the same length"""
 
        bin_a = '001001101'
        bin_b = '011011010'
 
        self._compare_additions(bin_a, bin_b)
 
    def test_add_b_larger(self):
 
        """ B has more digits than A """
 
        bin_a = '01000101'
        bin_b = '1110010110101011101101011101000101'
 
        self._compare_additions(bin_a, bin_b)
 
    def test_add_b_smaller(self):
 
        """B has less digits than A"""
 
 
        bin_a = '1110001001001001001101101011000101'
        bin_b = '0110010'
 
        self._compare_additions(bin_a, bin_b)
 
    def _compare_additions(self, bin_a, bin_b):
 
        """Compares the python implementation against ours"""
 
        bin_add = binary_addition(bin_a, bin_b)
        py_add = bin(eval("0b%s" % bin_a) + eval("0b%s" % bin_b))
 
        algo_res = bin_add[bin_add.index('1'):]
        py_res = py_add[py_add.index('1'):]
 
        self.assertEqual(py_res, algo_res)
 
 
 
if '__main__' == __name__:
    unittest.main()

Binary Multiplication

We are still using strings to represent bit sequences. We are still working from right to left, shifting to the left every number from the first number that needs to be multiplied by 1 in the second number. We then append the result to a list that we sum at the end, using the previous algorithm.

Code:

"""Simple Binary multiplication algorithm"""
 
 
import sys
import os.path
 
from binary_addition import binary_addition
 
 
def binary_multiplication(bin_a, bin_b):
    """Multiplies two binary numbers by using python lists to
    easily shift digits around"""
 
    temp_result = []
    result = "0"
 
    # Remove any unnecessary padding
    bin_a = bin_a[bin_a.index('1'):]
    bin_b = bin_b[bin_b.index('1'):]
 
    for i in range(0, len(bin_b))[::-1]:
        if bin_b[i] == '1':
            temp_result.append("%s%s" % (bin_a, "0" * (len(bin_b)-i-1)))
        else:
            temp_result.append("0")
 
 
    for val in temp_result:
        result = binary_addition(str(result), str(val))
 
    return result

Unit Test:

"""Unit test for binary_addition.py"""
 
import unittest
from binary_multiplication import binary_multiplication
 
class TestBinaryAddition(unittest.TestCase):
 
    """Comparing python binary multiplication against our own"""
 
    def test_add_same_length(self):
 
        """Multiplying 2 binary numbers of the same length"""
 
        bin_a = '001001101'
        bin_b = '011011010'
 
        self._compare_multiplications(bin_a, bin_b)
 
    def test_simple(self):
 
        """Multiplying 2 simple binary numbers"""
        bin_a = '110'
        bin_b = '101'
 
        self._compare_multiplications(bin_a, bin_b)
 
    def test_add_b_larger(self):
 
        """B has more digits than A"""
 
        bin_a = '010'
        bin_b = '111001011000101'
 
        self._compare_multiplications(bin_a, bin_b)
 
    def test_add_b_smaller(self):
 
        """ B has less digits than A """
 
        bin_a = '111001011000101'
        bin_b = '010'
 
        self._compare_multiplications(bin_a, bin_b)
 
    def _compare_multiplications(self, bin_a, bin_b):
 
        """Compares the python implementation against ours"""
 
        bin_mult = binary_multiplication(bin_a, bin_b)
        py_mult = bin(eval("0b%s" % bin_a) * eval("0b%s" % bin_b))
 
        algo_res = bin_mult[bin_mult.index('1'):]
        py_res = py_mult[py_mult.index('1'):]
 
        self.assertEqual(py_res, algo_res)
 
 
 
if '__main__' == __name__:
    unittest.main()

Algorithms in Python: Base Expansion

Xavier — Sun, 11 Jul 2010 00:53:49 +0000

I felt it would be helpful to folks interested in Python and studying algorithms, to review some commonly studied algorithms in Computer Science by providing a small description and a Python implementation of each algorithm.

This week, we’ll cover an introductory algorithm for converting from one numeral base to another. Here is the python code:

"""Simple implementation of a base expansion algorithm"""
 
import math
 
def base_expand(base, val):
    """This simple function performs a base-expansion from decimal
    using moduli and a translation table. The translation table is
    a clear limitation here, in that it implies the maximum base
    is 36."""
 
    if (base < 2) or (base > 36):
        raise BaseOutOfBoundsError(base)
 
    trans_table = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'
    res = ''
 
    while val != 0:
        res += trans_table[(int(val % base))]
        val = math.floor(val / base)
    return res[::-1]
 
class BaseOutOfBoundsError(Exception):
    """Base must be between 2 and 36"""
    def __init__(self, val):
        self.val = val
    def __str__(self):
        print "\nInvalid base: %s. Base must be (x | x > 1; x < 37)" % \
            self.val

Here is a unit-test for base_expand.py:

"""Unit tests for base_expansion.py"""
 
import unittest
from base_expansion import base_expand, BaseOutOfBoundsError
 
# Unit tests for base_expansion.py
class TestVals(unittest.TestCase):
    """Test suite"""
 
    def test_known_values(self):
        """Testing against known values"""
 
        vals = [{'val': 8, 'base': 2, 'expect': '1000'},
            {'val': 915652, 'base': 16, 'expect': 'DF8C4'},
            {'val': 256, 'base': 10, 'expect': '256'},
            {'val': 88189, 'base': 8, 'expect': '254175'}]
 
        for val in vals:
            self.assertEqual(val['expect'], \
                base_expand(val['base'], val['val']))
 
    def test_invalid_base(self):
        """ Testing invalid bases """
 
        bases = [1, 37, 50, 100]
        for base in bases:
            self.assertRaises(BaseOutOfBoundsError, base_expand, \
                base, 1)
 
 
 
if '__main__' == __name__:
    unittest.main()

Algorithms in Python: Binary Operations

Django Context Processors Best Practice

Xavier — Thu, 08 Apr 2010 00:59:39 +0000

In this post, i’ll show you a simple trick to ensure your Django context-processors don’t break when Django 1.2 (and possibly future releases as well) is released.

If you’re not familiar with the concept of context-processors, I’ll also explain what those are and how they work, so don’t panic. Finally, i’ll also spend a minute explaining why I consider this to be best-practice.

What are template context processors?

Django’s context processors are a facility that allows you to provide data and callbacks to your templates.

You can do so in one of two ways:

On an individual request basis: by passing a custom Context value to your render_to_response() call
Globally: by creating a context processor method that accepts a HttpRequest object as input, and returns a payload or callback, then registering the context processor in your settings.py, then providing your render_to_response() call with the built-in RequestContext attribute instead of your own (you can always extend RequestContext to add more data on an individual request basis of course).

If that approach for passing data to templates sounded absurd and obfuscated to you, you’re not alone. The complexity involved in such a simple operation is unwarranted and counter-productive, but every system has its shortcomings.

The Issue

If you follow the Django documentation or The Django Book‘s approach to configuring your own custom context-processors, you’ll notice that you are encouraged to add to your settings.py a hardcoded list of built-in context processors. If you follow that approach, your context-processors declaration will look like this:

TEMPLATE_CONTEXT_PROCESSORS = ("django.contrib.auth.context_processors.auth",
"django.core.context_processors.debug",
"django.core.context_processors.i18n",
"django.core.context_processors.media",
"django.contrib.messages.context_processors.messages")

But if you pay close attention to the development version’s documentation, you’ll notice a couple of interesting notes:

Changed in Django Development version: “django.contrib.messages.context_processors.messages” was added to the default. For more information, see the messages documentation.
Changed in Django Development version: The auth context processor was moved in this release from its old location django.core.context_processors.auth to django.contrib.auth.context_processors.auth.

This is a red flag! The Django dev team would like you to use hardcoded values that reference to classes that will no longer exist once the next version is released, and that omit new processors that you are likely to require.

The Solution

Obviously Django has access to its own default settings, so there must be a way to simply extend the defaults instead of overriding them with hardcoded values. You just need to dig around a bit in the Django source code to find exactly how. I’ll save you some digging:

Add this at the top of your settings.py file:

import django.conf.global_settings as DEFAULT_SETTINGS

Then extend the default context processors:

TEMPLATE_CONTEXT_PROCESSORS = DEFAULT_SETTINGS.TEMPLATE_CONTEXT_PROCESSORS + (
"myapp.context_processors.example",
"myapp.context_processors.other_example",
# etc...
)

Why is this a best-practice approach?

In software-engineering, you want to ensure maximum (reasonable) future interoperability of all your components, and there is really no component as important as your actual development framework, Django or otherwise.

Using hardcoded values that are already defined somewhere not only breaks DRY, but it also introduces possible breakage on framework upgrades. I know you are diligent and always read the release notes before upgrading critical components, and I know you use a staging environment to test those changes, but by actively looking out for this kind of traps, you have just saved yourself some debugging time and some head-scratching.

Happy coding!

Extending PostgreSQL with Python

Extending PostgreSQL with Python

Xavier — Sat, 07 Mar 2009 22:56:31 +0000

One of the features I enjoy the most about PostgreSQL is the ability to write stored procedures in C, Perl, TCL, PgSQL, and yes… obviously also in Python. I’ve been using this feature since 7.4, so any recent version of PostgreSQL is pretty much guaranteed to support it, but you’ll need to have the pl/python procedural language contrib module installed. Once it’s installed, you can activate it for your current database using the following query:

CREATE PROCEDURAL LANGUAGE plpythonu;

Once the language bindings have been activated, you can start writing your stored procedures in python, however you should really read up on the following subjects first:

As an example, I’ve written a little SP in PL/Python to provide support for PCRE since the stock distribution of PostgreSQL only supports LIKE/SIMILAR, and POSIX Style Regular Expressions.

Let’s create our Python language binding, and create a standard text storage table:

-- Activate PL/Python
CREATE PROCEDURAL LANGUAGE plpythonu;
 
-- Create a plain text-storage table
CREATE TABLE text_storage
(
  id serial NOT NULL,
  payload character varying(128),
  CONSTRAINT text_storage_pkey PRIMARY KEY (id)
)
WITH (OIDS=FALSE);
ALTER TABLE text_storage OWNER TO xavier;
 
-- Let's throw in an index on the payload field for good measure
CREATE INDEX txt_payload_idx
  ON text_storage
  USING btree
  (payload);

Let’s now populate our table with some junk data:

INSERT INTO text_storage (payload) VALUES ('hello, world');
INSERT INTO text_storage (payload) VALUES ('the quick brown fox, blah blah blah');
INSERT INTO text_storage (payload) VALUES ('PCREs in Postgres');
INSERT INTO text_storage (payload) VALUES ('All hail Python!');
INSERT INTO text_storage (payload) VALUES ('Hello, test data!');
INSERT INTO text_storage (payload) VALUES ('Python would like to say Hello!');

And now we can go ahead and create our Python SP itself:

CREATE OR REPLACE FUNCTION pcre(text, text)
  RETURNS INTEGER AS
$BODY$import re
 
regex  = args[0]
in_str = args[1]
 
compiled = re.compile(regex)
 
IF compiled.search(in_str):
	RETURN 1
ELSE:
	RETURN 0$BODY$
  LANGUAGE 'plpythonu' VOLATILE
  COST 100;

As you can see, our PCRE matching system is extremely simple, yet pretty powerful. We import Python’s built-in re module, compile the specified regex argument, then attempt to match it against the other argument. Here’s a usage example on our test table:

SELECT id, payload FROM text_storage WHERE pcre('[H|h]ello', payload) = 1;
 id |             payload
----+---------------------------------
  1 | hello, world
  5 | Hello, test DATA!
  6 | Python would LIKE TO say Hello!
(3 rows)

As always, feel free to suggest any improvements.

Fixing custom sequences in PostgreSQL

Xavier — Sat, 07 Mar 2009 00:52:47 +0000

PostgreSQL provides a mechanism called sequences, which I believe is extracted from ANSI-SQL92, though I’m too lazy to check, which are basically stateful counters that provide some helper functions. The primary use of sequences in PostgreSQL and Oracle, is to implement auto-incrementing counters as a table field.

PostgreSQL will automatically create a sequence when you use the “SERIAL” datatype for your field, and will take care of assigning the default value of your field as the result of the nextval() call on the sequence, so most of the time you don’t need to interact directly with sequences.

Where things can get hairy however, is when you back up your data using pg_dump or any other mechanism, and restore that data in a table that is already populated. A common scenario for example, is populating a table that already has some recent data, with some older data you’ve been storing in archival. The opposite is true if you are trying to archive data from a table to a backup database for example.

Whenever you manually have to provide a value for the field assigned to a sequence, you are pretty much guaranteed to break the sequence unless you take the time to nextval() your sequence until it is in sync. This is a real problem, as pg_dump does not include sequence synchronization in its output.

The quickest way to synchronize a sequence, based on my observations, is to run the following query, taking care to replace the name of the sequence [SEQ] and the name of the associated table [TABLE] and field [FIELD]:

SELECT SETVAL([SEQ], COALESCE((SELECT [FIELD] FROM [TABLE] ORDER BY [FIELD] DESC LIMIT 1), 0)+1)

This will fetch the highest value of [FIELD] in [TABLE], increment it by 1, and synchronize the sequence [SEQ] to the new value.

I’ve also written the following little Python script that will look for any non-system sequence in the specified database, and use this method to repair it. Let me know if it works out for you, or if you’d like to suggest some improvements.

Requirements: Python 2.5+, PsycoPG2 Python module (python-psycopg2)

#!/usr/bin/env python
# -*- coding: utf-8 -*-
 
 
# Standard imports
import sys
import os
import time
from optparse import OptionParser
 
# psycopg2 import
try:
    import psycopg2
except ImportError, e:
    print 'You must install the python module named "psycopg2" in order to use this module.'
    sys.exit(os.EX_SOFTWARE)
 
 
 
class PgRepairman:
    def __init__(self, options, parser):
        self.options = options
        try:
            dsn = "dbname=%s host=%s user=%s" % (options.db, options.host, options.user)
            dsn += ("" != options.passwd) and ("password=%s" % options.password) or ""
            self.conn = psycopg2.connect(dsn)
            self.curs = self.conn.cursor()
        except Exception, e:
            print "ERROR - %s" % e
            sys.exit(1)
 
 
    # Returns a dict for a psycopg2 row object
    def _to_dict(self, desc, res):
        return dict(zip([x[0] for x in desc], res))
 
 
    # Attempt to locate all custom sequences
    def findSequences(self):
        seq_query = """
        SELECT pc1.relname AS seq, pc2.relname AS table, c.attname AS field
        FROM pg_depend, pg_class pc1, pg_class pc2, pg_attribute c
        WHERE pc1.oid = pg_depend.objid
            AND pc2.oid = pg_depend.refobjid
            AND c.attnum = pg_depend.refobjsubid
            AND c.attrelid = pc2.oid
            AND pc1.relkind = 'S'
            AND pc1.relname NOT LIKE 'pg_toast%%'
        """
 
        try:
            self.print_verbose(seq_query)
            self.curs.execute(seq_query)
        except Exception, e:
            print "[ERROR] - %s" % e
            sys.exit(1)
 
        desc = self.curs.description
        for row in self.curs.fetchall():
            yield self._to_dict(desc, row)
 
 
    # Increment the key value to the value of the sequence + 1
    def fixSequences(self):
        for seq in self.findSequences():
            print "Fixing sequence %s in table %s" % (seq['seq'], seq['table'])
            fix_query = "SELECT setval('%s', COALESCE((SELECT %s FROM %s ORDER BY %s DESC LIMIT 1), 0)+1)" % (seq['seq'], seq['field'], seq['table'], seq['field'])
            try:
                self.print_verbose(fix_query)
                self.curs.execute(fix_query)
            except Exception, e:
                print "[WARNING] - %s" % e
                pass
 
    def print_verbose(self, msg):
        if (True == self.options.verbose):
            print "[DEBUG] - %s" % msg
 
if __name__=='__main__':
    usage       = "Usage: %prog  [-v --verbose] [-u --username | -p --password \ -o --host | -d --database]"
    version     = "%prog v1.0\nDistributed under the LGPL2 License"
    description = "Increments all sequences in a PostgreSQL database"
    parser = OptionParser(usage=usage, version=version, description=description)
    parser.add_option("-v", "--verbose", action="store_true", dest="verbose", default=False, help="Enable extra output")
    parser.add_option("-o", "--host", action="store", dest="host", default="127.0.0.1", help="Database hostname/IP")
    parser.add_option("-u", "--username", action="store", dest="user", default="postgres", help="Database Username")
    parser.add_option("-p", "--password", action="store", dest="passwd", default="", help="Database Password")
    parser.add_option("-d", "--database", action="store", dest="db", default="template1", help="Database Name")
 
 
    try:
        (options, args) = parser.parse_args()
        obj = PgRepairman(options, parser)
        obj.fixSequences()
    except KeyboardInterrupt, e:
        sys.exit(1)

You can also download the script here.