from __future__ import *
statebox, an eventually consistent data model for Erlang (and Riak)
May 09, 2011 at 09:00 AM | categories: erlang, mochi | View CommentsCross-posted from the Mochi Labs blog: statebox, an eventually consistent data model for Erlang (and Riak).
A few weeks ago when I was on call at work I was chasing down a bug in friendwad [1] and I realized that we had made a big mistake. The data model was broken, it could only work with transactions but we were using Riak. The original prototype was built with Mnesia, which would've been able to satisfy this constraint, but when it was refactored for an eventually consistent data model it just wasn't correct anymore. Given just a little bit of concurrency, such as a popular user, it would produce inconsistent data. Soon after this discovery, I found another service built with the same invalid premise and I also realized that a general solution to this problem would allow us to migrate several applications from Mnesia to Riak.
When you choose an eventually consistent data store you're prioritizing availability and partition tolerance over consistency, but this doesn't mean your application has to be inconsistent. What it does mean is that you have to move your conflict resolution from writes to reads. Riak does almost all of the hard work for you [2], but if it's not acceptable to discard some writes then you will have to set allow_mult to true on your bucket(s) and handle siblings [3] from your application. In some cases, this might be trivial. For example, if you have a set and only support adding to that set, then a merge operation is just the union of those two sets.
statebox is my solution to this problem. It bundles the value with repeatable operations [4] and provides a means to automatically resolve conflicts. Usage of statebox feels much more declarative than imperative. Instead of modifying the values yourself, you provide statebox with a list of operations and it will apply them to create a new statebox. This is necessary because it may apply this operation again at a later time when resolving a conflict between siblings on read.
Design goals (and non-goals):
- The intended use case is for data structures such as dictionaries and sets
- Direct support for counters is not required
- Applications must be able to control the growth of a statebox so that it does not grow indefinitely over time
- The implementation need not support platforms other than Erlang and the data does not need to be portable to nodes that do not share code
- It should be easy to use with Riak, but not be dependent on it (clear separation of concerns)
- Must be comprehensively tested, mistakes at this level are very expensive
- It is ok to require that the servers' clocks are in sync with NTP (but it should be aware that timestamps can be in the future or past)
Here's what typical statebox usage looks like for a trivial application (note: Riak metadata is not merged [5]). In this case we are storing an orddict in our statebox, and this orddict has the keys following and followers.
-module(friends).
-export([add_friend/2, get_friends/1]).
-define(BUCKET, <<"friends">>).
-define(STATEBOX_MAX_QUEUE, 16). %% Cap on max event queue of statebox
-define(STATEBOX_EXPIRE_MS, 300000). %% Expire events older than 5 minutes
-define(RIAK_HOST, "127.0.0.1").
-define(RIAK_PORT, 8087).
-type user_id() :: atom().
-type orddict(T) :: [T].
-type ordsets(T) :: [T].
-type friend_pair() :: {followers, ordsets(user_id())} |
{following, ordsets(user_id())}.
-spec add_friend(user_id(), user_id()) -> ok.
add_friend(FollowerId, FolloweeId) ->
statebox_riak:apply_bucket_ops(
?BUCKET,
[{[friend_id_to_key(FollowerId)],
statebox_orddict:f_union(following, [FolloweeId])},
{[friend_id_to_key(FolloweeId)],
statebox_orddict:f_union(followers, [FollowerId])}],
connect()).
-spec get_friends(user_id()) -> [] | orddict(friend_pair()).
get_friends(Id) ->
statebox_riak:get_value(?BUCKET, friend_id_to_key(Id), connect()).
%% Internal API
connect() ->
{ok, Pid} = riakc_pb_client:start_link(?RIAK_HOST, ?RIAK_PORT),
connect(Pid).
connect(Pid) ->
statebox_riak:new([{riakc_pb_client, Pid},
{max_queue, ?STATEBOX_MAX_QUEUE},
{expire_ms, ?STATEBOX_EXPIRE_MS},
{from_values, fun statebox_orddict:from_values/1}]).
friend_id_to_key(FriendId) when is_atom(FriendId) ->
%% NOTE: You shouldn't use atoms for this purpose, but it makes the
%% example easier to read!
atom_to_binary(FriendId, utf8).
To show how this works a bit more clearly, we'll use the following sequence of operations:
add_friend(alice, bob), %% AB add_friend(bob, alice), %% BA add_friend(alice, charlie). %% AC
Each of these add_friend calls can be broken up into four separate atomic operations, demonstrated in this pseudocode:
%% add_friend(alice, bob) Alice = get(alice), put(update(Alice, following, [bob])), Bob = get(bob), put(update(Bob, followers, [alice])).
Realistically, these operations may happen with some concurrency and cause conflict. For demonstration purposes we will have AB happen concurrently with BA and the conflict will be resolved during AC. For simplicity, I'll only show the operations that modify the key for alice.
AB = get(alice), %% AB (Timestamp: 1) BA = get(alice), %% BA (Timestamp: 2) put(update(AB, following, [bob])), %% AB (Timestamp: 3) put(update(BA, followers, [bob])), %% BA (Timestamp: 4) AC = get(alice), %% AC (Timestamp: 5) put(update(AC, following, [charlie])). %% AC (Timestamp: 6)
- Timestamp 1:
- There is no data for alice in Riak yet, so statebox_riak:from_values([]) is called and we get a statebox with an empty orddict.
Value = [], Queue = [].
- Timestamp 2:
- There is no data for alice in Riak yet, so statebox_riak:from_values([]) is called and we get a statebox with an empty orddict.
Value = [], Queue = [].
- Timestamp 3:
- Put the updated AB statebox to Riak with the updated value.
Value = [{following, [bob]}],
Queue = [{3, {fun op_union/2, following, [bob]}}].
- Timestamp 4:
- Put the updated BA statebox to Riak with the updated value. Note that this will be a sibling of the value stored by AB.
Value = [{followers, [bob]}],
Queue = [{4, {fun op_union/2, followers, [bob]}}].
- Timestamp 5:
- Uh oh, there are two stateboxes in Riak now... so statebox_riak:from_values([AB, BA]) is called. This will apply all of the operations from both of the event queues to one of the current values and we will get a single statebox as a result.
Value = [{followers, [bob]},
{following, [bob]}],
Queue = [{3, {fun op_union/2, following, [bob]}},
{4, {fun op_union/2, followers, [bob]}}].
- Timestamp 6:
- Put the updated AC statebox to Riak. This will resolve siblings created at Timestamp 3 by BA.
Value = [{followers, [bob]},
{following, [bob, charlie]}],
Queue = [{3, {fun op_union/2, following, [bob]}},
{4, {fun op_union/2, followers, [bob]}},
{6, {fun op_union/2, following, [charlie]}}].
Well, that's about it! alice is following both bob and charlie despite the concurrency. No locks were harmed during this experiment, and we've arrived at eventual consistency by using statebox_riak, statebox, and Riak without having to write any conflict resolution code of our own.
| [1] | friendwad manages our social graph for Mochi Social and MochiGames. It is also evidence that naming things is a hard problem in computer science. |
| [2] | See Basho's articles on Why Vector Clocks are Easy and Why Vector Clocks are Hard. |
| [3] | When multiple writes happen to the same place and they have branching history, you'll get multiple values back on read. These are called siblings in Riak. |
| [4] | An operation F is repeatable if and only if F(V) = F(F(V)). You could also call this an idempotent unary operation. |
| [5] | The default conflict resolution algorithm in statebox_riak chooses metadata from one sibling arbitrarily. If you use metadata, you'll need to come up with a clever way to merge it (such as putting it in the statebox and specifying a custom resolve_metadatas in your call to statebox_riak:new/1). |
Playing with PyPy
March 17, 2011 at 02:00 PM | categories: python | View CommentsI've been following the PyPy project since I first heard of it in 2003 or so. The concept behind it is fascinating; it's a Python interpreter written in (a subset of) Python. It's actually a lot more than that because the language front-ends (e.g. Python) are quite separate from the backends (e.g. C, JVM, CLI, Python). This makes it a unique platform for language research because coding Python is typically easier than C, and so much of the work is already done for you.
It's clear that PyPy is very useful for academic research, but it's also quickly becoming a practical target for developing and deploying Python code. At the PyPy Speed Center you can see that it's already several times faster than CPython, and has the potential to fix most of the more fundamental flaws of the CPython VM.
What's awesome right now:
- PyPy has a modern garbage collector, not ref counting
- PyPy's JIT can run string mangling and numerics code very quickly, which removes the need for most C extensions
- PyPy is already fast, and is getting faster all the time
How it can be more awesome (just my opinion, I don't speak for the PyPy team and their implementation goals):
- PyPy has an alpha quality cpyext that will allow you to use CPython extensions (requires a recompile), and when that's polished it will be very easy for CPython users to migrate en masse, even though they may have complicated dependencies such as NumPy, SciPy, PIL, etc.
- PyPy has the potential to eventually remove the GIL, and/or have multiple VMs in the same OS process
- PyPy could add M:N threading and concurrency constructs to the language (some stackless support already exists, but is not currently compatible with the JIT and doesn't take advantage of multiple cores)
- PyPy could simultaneously support Python 2.x and 3.x code in the same process, making it practical to actually make the transition (note: this is a crazy idea that would be terribly difficult)
Playing with PyPy
I've been working on helping the PyPy team with some real world benchmarks for JSON, and helping sort out Mac OS X issues. I've also been tuning a branch of simplejson to run efficiently on PyPy. I'll write more about this in a follow up post, but here's how you can get started.
If you're a library author or an advanced user you should be experimenting with PyPy right now. In these instructions we'll install PyPy in ~/opt and create a virtualenv for it in ~/virtualenv.
Prerequisites
Install Mercurial 1.7 or newer.
Install Xcode 3.2.x (gcc-4.0 is currently required for building PyPy).
Download virtualenv 1.5.2 (or later):
mkdir -p ~/src (cd ~/src; curl -s http://pypi.python.org/packages/source/v/virtualenv/virtualenv-1.5.2.tar.gz | tar zxf -)
Clone jitviewer and pypy:
# Make a ~/src to store all of these clones mkdir -p ~/src # Get the PyPy jitviewer application (install to ~/src/jitviewer) (cd ~/src; hg clone https://bitbucket.org/pypy/jitviewer) # Clone PyPy source, this will take a while (cd ~/src; hg clone https://bitbucket.org/pypy/pypy)
Installing from binary
Follow the link on http://pypy.org/download.html to download one of the Mac OS X binaries (either 32-bit or 64-bit), the current version at this time is 1.4.1.
This will install PyPy to ~/opt and create a virtualenv:
# Unpack PyPy and "install" to ``~/opt``
mkdir -p ~/opt
cd ~/opt
tar jxvf ~/Downloads/pypy-1.4.1-osx64.tar.bz2
# Install virtualenv to this PyPy build, and create a new virtualenv.
# I also like to create a symlink ``~/virtualenv/pypy-env`` to the
# version I am currently working with::
PKG=pypy-1.4.1-osx64
PYPY=~/opt/$PKG/bin/pypy
# install virtualenv
(cd ~/src/virtualenv-1.5.2; $PYPY setup.py install)
# create virtualenv
mkdir -p ~/virtualenv
rm -rf ~/virtualenv/$PKG
~/opt/$PKG/bin/virtualenv --distribute ~/virtualenv/$PKG
# update symlink
(cd ~/virtualenv; rm -f pypy-env; ln -s $PKG pypy-env)
# install jitviewer
(source ~/virtualenv/pypy-env/bin/activate; \
pip install flask pygments simplejson; \
cd ~/src/jitviewer; pypy setup.py develop )
When you want to use PyPy, just activate the virtualenv:
source ~/virtualenv/pypy-env/bin/activate # now you can use PyPy! both "python" and "pypy" will work
Tuning for PyPy 1.4.1
On Mac OS X, PyPy 1.4.1 (and current default) does not choose optimal tuning values for the GC. You will get ~30% better performance by setting this environment variable:
export PYPY_GC_NURSERY=1M
Note that 1M is a machine specific value, so if your Mac isn't the same model as mine there might be a better default for you. The value is very likely to be dependent on the amount of L2/L3 cache and how many physical cores you have, and you can get those values from sysctl:
$ sysctl hw.l3cachesize hw.l2cachesize hw.physicalcpu hw.l3cachesize: 4194304 hw.l2cachesize: 262144 hw.physicalcpu: 2
From the pypy source directory, with a pypy virtualenv activated, you can run this script to see what a good value might be (lowest time is best):
#!/bin/bash
for ((procs=1; procs <= 4 ; procs++)); do
for ram in 128K 256K 512K 768K 1M 2M 3M 4M; do
echo "export PYPY_GC_NURSERY=$ram # procs=$procs"
export PYPY_GC_NURSERY=$ram
for ((p=1; p <= $procs; p++)); do
(cd pypy/translator/goal; pypy gcbench.py | grep 'Completed in') &
done
wait
done
done
The PyPy team is very interested in knowing what the sysctl values are for your machine and the output of the GC benchmark, so if you get this far please send it along to me or the PyPy mailing list! Having output from many different models of Mac will help us come up with a better algorithm for choosing sane defaults.
Building PyPy from source
Make sure to install a binary first. Since translating PyPy is CPU bound, this runs a lot faster if you use PyPy.
These commands will build PyPy, create a release based on the hg revision, update ~/virtualenv/pypy-env, etc.:
# Translate PyPy (expect this a while, at least an hour for me) (cd pypy/translator/goal; pypy translate.py -Ojit) # Build the release BRANCH=$(hg branch) PKG=pypy-$(hg branches|grep "^$BRANCH " | cut -d: -f2)-osx64 mkdir -p ~/opt (cd pypy/tool/release; /usr/bin/python package.py ../../.. $PKG) rm -rf ~/opt/$PKG mv $TMPDIR/usession-$BRANCH-$USER/build/$PKG ~/opt/$PKG # install virtualenv PYPY=~/opt/$PKG/bin/pypy (cd ~/src/virtualenv-1.5.2; $PYPY setup.py install) # create virtualenv mkdir -p ~/virtualenv rm -rf ~/virtualenv/$PKG ~/opt/$PKG/bin/virtualenv --distribute ~/virtualenv/$PKG # make default (cd ~/virtualenv; rm -f pypy-env; ln -s $PKG pypy-env) # install jitviewer (source ~/virtualenv/pypy-env/bin/activate; \ pip install flask pygments simplejson; \ cd ~/src/jitviewer; pypy setup.py develop )
Running jitviewer
jitviewer is an awesome web app for reading PyPy logs, it will help you optimize your code for PyPy (once you have a basic understanding of the output, which is beyond the scope of this post).
Run your code with JIT logging turned on:
# log to pypy-jit.log PYPYLOG=jit-log-opt,jit-backend-counts:pypy-jit.log pypy benchmark.py # start the jitviewer server with pypy-jit.log PYTHONPATH=~/src/pypy jitviewer.py pypy-jit.log
After jitviewer is started, open a web browser to http://127.0.0.1:5000/
Browser Tab Visible Event
April 25, 2010 at 09:15 PM | categories: javascript | View CommentsSadly there's no web standard that I could find to determine when a tab becomes visible. My use case was to delay loading of Flash content until the tab is visible for the first time. Safari seems to do this by default, but none of the other browsers do.
Chrome is the absolute worst offender here, it does not fire window.onmouseover until the mouse has been moved over the page and it does not fire window.onfocus until you switch to that tab... so if the tab was started as a foreground tab, you will not get this event. The only way I managed to detect a tab being active was to poll the window.screenX and window.screenY properties. They are always 0 for a background tab. There is an obvious false positive if the browser happens to be in the screen origin, but in that case a window.onmouseover event will fire once the mouse has moved.
Safari is slightly less bad because it will fire window.onmouseover immediately when the tab is active. This works great but was a less obvious find than window.onfocus.
Firefox and IE8 have the least surprising behavior in that they fire window.onfocus immediately whenever a tab becomes visible, even if it was the foreground tab. I think this was the very first browser compatibility experiment where I've spent less time with IE than any other browser, although to be fair I didn't test anything other than IE8.
For maximum compatibility/longevity I've just provided some raw JavaScript code here. No framework. Feel free to translate this into a snippet or plugin for the framework of your choice. I'd also be interested if someone else does the testing for other browsers such as Opera and older versions of IE.
Tested with:
- Google Chrome 5.0.342.9 (Mac)
- Safari 4.0.5 (Mac)
- Firefox 3.6.3 (Mac)
- Internet Explorer 8.0.6001.18702
var timer = null; function tabVisible() { if (timer) clearInterval(timer); timer = null; window.onfocus = null; window.onmouseover = null; /* your code to dispatch event here */ } // Firefox, IE8 window.onfocus = tabVisible; // Safari window.onmouseover = tabVisible; // dirty hack for Chrome if (navigator.userAgent.indexOf(' Chrome/') != -1) { function dirtyChromePoll() { if (window.screenX || window.screenY) tabVisible(); } timer = setInterval(dirtyChromePoll, 100); }
simplejson 2.1.1
March 31, 2010 at 05:30 PM | categories: python, simplejson | View Commentssimplejson (documentation) is a simple, fast, complete, correct and extensible JSON (RFC 4627) encoder/decoder for Python 2.5+. It is pure Python code with no dependencies, but features an optional C extension for speed-ups.
simplejson 2.1.1 is a minor update with several bug-fixes:
-
Change how setup.py imports ez_setup.py to try and workaround old versions
of setuptools.
http://code.google.com/p/simplejson/issues/detail?id=75 -
Fix compilation on Windows platform (and other platforms with very
picky compilers)
http://code.google.com/p/simplejson/issues/detail?id=74 - Corrected simplejson.__version__ and other minor doc changes.
-
Do not fail speedups tests if speedups could not be built.
http://code.google.com/p/simplejson/issues/detail?id=73
Py3k Unified Numeric Hash Proposal
March 23, 2010 at 08:30 AM | categories: python, hash, math | View CommentsThere has been a recent and interesting set of discussions on python-dev (Decimal <-> float comparisons) for what the best behavior for numeric type interoperability would be. The most prominent "mistake" in the current implementation is that certain float and int/long values compare equal, and certain Decimal and int/long values compare equal, but all float and Decimal comparison operations raise TypeError. Other operations between float and Decimal also raise TypeError. Python 2.x behavior is such that comparison operations between float and Decimal return nonsense results and other operations raise TypeError.
Guido recently pronounced (Mixing float and Decimal) that he'd like to consider changing the behavior to match the principle of least surprise; all operations for all of the numeric types should return correct results. One of the most difficult problems to solve with such a unification is the hash invariant:
for all a and b such that a == b: hash(a) == hash(b).
While this is relatively simple to implement for the integer cases, it's much tricker to do efficiently for Decimal and float (and Fraction!) because Decimals are base 10 and float are base 2.
Note that I started writing this post yesterday after studying version 3 of the patch. I have altered the inline quotes to reflect version 4, which contains vastly improved comments that make most of my post redundant. However, it may still help in some way because it is an independent explanation and it provides some Python code.
Mark Dickinson proposed a very clever algorithm with an efficient implementation in issue8188, which he summarized as follows in the comments of the patch:
For numeric types, the hash of a number x is based on the reduction of x modulo the prime P = 2**_PyHASH_BITS - 1. It's designed so that hash(x) == hash(y) whenever x and y are numerically equal, even if x and y have different types.
A quick summary of the hashing strategy:
(1) First define the 'reduction of x modulo P' for any rational number x; this is a standard extension of the usual notion of reduction modulo P for integers. If x == p/q (written in lowest terms), the reduction is interpreted as the reduction of p times the inverse of the reduction of q, all modulo P; if q is exactly divisible by P then define the reduction to be infinity. So we've got a well-defined map
reduce : { rational numbers } -> { 0, 1, 2, ..., P-1, infinity }.(2) Now for a rational number x, define hash(x) by:
reduce(x) if x >= 0 -reduce(-x) if x < 0If the result of the reduction is infinity (this is impossible for integers, floats and Decimals) then use the predefined hash value
_PyHASH_INF instead.
_PyHASH_INF, _PyHASH_NINF and _PyHASH_NAN are also used for the hashes of float and Decimal infinities and nans.A selling point for the above strategy is that it makes it possible to compute hashes of decimal and binary floating-point numbers efficiently, even if the exponent of the binary or decimal number is large. The key point is that
reduce(x * y) == reduce(x) * reduce(y) (modulo _PyHASH_MASK)provided that {reduce(x), reduce(y)} != {0, infinity}. The reduction of a binary or decimal float is never infinity, since the denominator is a power of 2 (for binary) or a divisor of a power of 10 (for decimal). So we have, for nonnegative x,
reduce(x * 2**e) == reduce(x) * reduce(2**e) % _PyHASH_MASK reduce(x * 10**e) == reduce(x) * reduce(10**e) % _PyHASH_MASKand reduce(10**e) can be computed efficiently by the usual modular exponentiation algorithm. For reduce(2**e) it's even better: since P is of the form 2**n-1, reduce(2**e) is 2**(e mod n), and multiplication by 2**(e mod n) modulo 2**n-1 just amounts to a rotation of bits.
The choices of P for his implementation are (2**31)-1 for 32-bit platforms and (2**61)-1 for 64-bit platforms. These numbers are interesting because they are the eighth and ninth Mersenne prime numbers. I'm not entirely sure yet if these numbers being prime is essential or not, but it's definitely conventional for a hash modulus to be prime. A very important feature of these numbers is that P+1 is a power of two.
One thing that wasn't immediately obvious to me was how to define modulus of a (rational) number f such that 0 < f < 1. We know from the above that in the floating point case we can break f into its mantissa and exponent:
reduce(m * (2**e)) == reduce(reduce(m) * reduce(2**e))
but that leaves the cases where 0 < 2**e < 1. Well, because we are working with a modulus of P, we know that P+1 is the multiplicative identity, so we can find some number n such that ((P+1)**n) * (2**e) is an integer. We also know that ((P+1)**n) * (2**e) mod P must be non-zero because P is prime.
We can demonstrate that reduce(x) where x = 2**e is quite a trivial task for a typical CPU as follows (k is log2(P+1), which is 61 or 31). All of the following expressions mod P are equivalent to x mod P.
(x * (P+1)**n) # multiplicative identity
(x * (2**k)**n) # P+1 == 2**k
(x * (2**(k*n)) # (a**b)**c == a**(b*c)
((2**e) * (2**(k*n))) # x == 2**e
(2**(e + (k * n))) # (a**b)*(a**c) == a**(b+c)
(2**((e + (k * n)) % k)) # 2**k is identity, so exponent is mod k
(2**(e % k)) # (k * n) % k == 0
1 << (e % k) # a * (2**b) == a << b
In Python the naive algorithms would be as follows (ignoring inf and NaN):
from math import frexp
# Doesn't matter whether we use 61 or 31.
HASH_SHIFT = 61
HASH_MODULUS = (2 ** HASH_SHIFT) - 1
def hash_int(n):
if n == 0:
return 0
elif n < 0:
rval = -((-n) % HASH_MODULUS)
return -2 if rval == -1 else rval
else:
return n % HASH_MODULUS
def hash_float(f):
if f == 0.0:
return 0
elif f < 0.0:
rval = -hash_float(-f)
return -2 if rval == -1 else rval
# m = mantissa (float), e = exponent of 2 (integer)
m, e = frexp(f)
# "arbitrarily" process 28 bits at a time. For a normal float,
# this loop will iterate no more than twice since the mantissa
# is 53 bits in a 64-bit IEEE-754 double.
# After the loop, n will be some integer such that n ** e = f
n = 0
BITS = 28
while m:
m *= (2.0 ** BITS)
e -= BITS
m_floor = int(m)
n = (n << BITS) | m_floor
m -= m_floor
# see above "proof" for this definition of reduce(2**e)
return hash_int(hash_int(n) << (e % HASH_SHIFT))
You might notice the strange intentional mapping of -1 to -2, the reason for this is simply that the convention of Python's C API is such that return values of -1 mean that an exception may have occurred (and a global variable must be checked). If -1 is never returned on success then there are no false positives so the general case is faster. Essentially Python is trading this known worst case for a potential hash collision, which is probably the right call.
If you read the actual C implementation there are a few additional math tricks at play, the most important of which is this implementation of long_hash from longobject.c:
static long
long_hash(PyLongObject *v)
{
unsigned long x;
Py_ssize_t i;
int sign;
i = Py_SIZE(v);
switch(i) {
case -1: return v->ob_digit[0]==1 ? -2 : -(sdigit)v->ob_digit[0];
case 0: return 0;
case 1: return v->ob_digit[0];
}
sign = 1;
x = 0;
if (i < 0) {
sign = -1;
i = -(i);
}
while (--i >= 0) {
/* Here x is a quantity in the range [0, _PyHASH_MASK); we
want to compute x * 2**PyLong_SHIFT + v->ob_digit[i] modulo
_PyHASH_MASK.
The computation of x * 2**PyLong_SHIFT % _PyHASH_MASK
amounts to a rotation of the bits of x. To see this, write
x * 2**PyLong_SHIFT = y * 2**_PyHASH_BITS + z
where y = x >> (_PyHASH_BITS - PyLong_SHIFT) gives the top
PyLong_SHIFT bits of x (those that are shifted out of the
original _PyHASH_BITS bits, and z = (x << PyLong_SHIFT) &
_PyHASH_MASK gives the bottom _PyHASH_BITS - PyLong_SHIFT
bits of x, shifted up. Then since 2**_PyHASH_BITS is
congruent to 1 modulo _PyHASH_MASK, y*2**_PyHASH_BITS is
congruent to y modulo _PyHASH_MASK. So
x * 2**PyLong_SHIFT = y + z (mod _PyHASH_MASK).
The right-hand side is just the result of rotating the
_PyHASH_BITS bits of x left by PyLong_SHIFT places; since
not all _PyHASH_BITS bits of x are 1s, the same is true
after rotation, so 0 <= y+z < _PyHASH_MASK and y + z is the
reduction of x*2**PyLong_SHIFT modulo _PyHASH_MASK. */
x = ((x << PyLong_SHIFT) & _PyHASH_MASK) |
(x >> (_PyHASH_BITS - PyLong_SHIFT));
x += v->ob_digit[i];
if (x >= _PyHASH_MASK)
x -= _PyHASH_MASK;
}
x = x * sign;
if (x == (unsigned long)-1)
x = (unsigned long)-2;
return (long)x;
}
In order to understand this better we'll translate this to Python first, but to do that we need to understand the layout of integers in py3k. In py3k integers are represented as a sequence of zero or more digits, where a digit is 2**sys.int_info.bits_per_digit bits wide, and the least significant digit is first in the array. I'm not aware of any Python function to see integers at this level so we'll craft our own way to "disassemble" an integer in the way that the C implementation will see it. Instead of tracking the sign and size as one integer we will track the sign on its own and use the length of the list to track size.
import sys
# Doesn't matter whether we use 61 or 31.
HASH_SHIFT = 61
# The modulus can be used as a bit mask, all bits are set
HASH_MODULUS = (2 ** HASH_SHIFT) - 1
def disassemble_int(i):
bits_per_digit = sys.int_info.bits_per_digit
bit_mask = (1 << bits_per_digit) - 1
if i < 0:
sign = -1
i *= -1
else:
sign = 1
digits = []
# see reassemble_int for inverse of this operation
while i:
digits.append(i & bit_mask)
i >>= bits_per_digit
return sign, digits
def reassemble_int(sign, digits):
# demonstrate similar method for just reassembling the integer
bits_per_digit = sys.int_info.bits_per_digit
if sign == -1:
return -reassemble_int(1, digits)
size = len(digits)
if size == 0:
return 0
elif size == 1:
# just an optimization for small numbers
return digits[0]
x = 0
# traverse digits from most to least significant
# n = bits_per_digit
# d[i] = digit with index of i
# x = d[0] + d[1]*(2**n) + ... + d[i]*(2**(n*i))
# x = d[0] + (2**n)*(d[1] + (2**n)*(d[2] + ...))
# x = d[0] + (d[1] + ((d[2] + (...)) << n) << n
for digit in reversed(digits):
x = x << bits_per_digit
x += digit
return x
def hash_long(sign, digits):
bits_per_digit = sys.int_info.bits_per_digit
if sign == -1:
rval = -hash_long(1, digits)
return -2 if rval == -1 else rval
size = len(digits)
if size == 0:
return 0
elif size == 1:
# just an optimization for small numbers
# since we assume bits_per_digit < HASH_SHIFT
return digits[0]
x = 0
# traverse digits from most to least significant
for digit in reversed(digits):
# rotate the bottom HASH_SHIFT bits left by bits_per_digit,
# in effect this multiplies by 2**bits_per_digit mod HASH_MODULUS
x = (((x << bits_per_digit) & HASH_MODULUS) |
(x >> (HASH_SHIFT - bits_per_digit)))
x += digit
# If the addition overflowed we compensate by decrementing, which
# preserves the value mod HASH_MODULUS.
if x > HASH_MODULUS:
x -= HASH_MODULUS
return x
Now that we have a Python implementation the only trick left to decipher is why the heck are these equivalent for our choices of modulus P (k is log2(P+1), which is 61 or 31):
x * (2**n) % P
((x << n) & P) | (x >> (k - n))
I think that one way to "prove" that multiplying by a power of 2 in mod P is equivalent to bit rotation of a k bit integer would be to decompose x into binary digits as follows (k is log2(P+1)):
for all x such that 0 <= x < P, x == x % P
any x mod P can be decomposed into binary digits (d[0] * 2**0 + d[1] * 2**1 + ... + d[k-1] * 2**(k-1))
# 2**k is a multiplicative identity mod P
2**k mod P == 2**0 == 1
# just decompose x into binary digits
x * (2**0) mod P == (d[0] * 2**(0) + d[1] * 2**(1) + ... + d[k-1] * 2**(k-1))
# show multiply by 2 is a bit rotate left of k bits
x * (2**1) mod P == (d[0] * 2**(1) + d[1] * 2**(2) + ... + d[k-1] * 2**(0))
# generalize into n multiplications of 2
x * (2**n) mod P == (d[0] * 2**((0 + n) % k) + d[1] + 2**((1 + n) % k) + ... + d[k-1] * 2**((k - 1 + n) % k))
x * (2**n) mod P == (d[0] * 2**((0 + n) % k) + d[1] + 2**((1 + n) % k) + ... + d[k-1] * 2**((-1 + n) % k))
I'm definitely not Tim Peters or even a mathematician but I found this problem interesting enough to dive into, especially because Guido didn't find this obvious either (Objects/longobject.c). I think I've covered it in sufficient depth for me to believe that it works and the patch is good, but if I'm missing something please let me know!
PyCon 2010, Analysis: The Other Kind of Testing
March 10, 2010 at 10:45 PM | categories: python, PyCon | View CommentsI gave a talk at PyCon 2010 in Atlanta last month called Analysis: The Other Kind of Testing (video). It's a very simple overview of techniques such as split testing (AB testing) and a call to action to improve django-lean.
Atlanta was a fantastic location for PyCon 2010, and I look forward to returning next year. Hopefully if I give another talk I'll be able to put a little more time into it :)
As per usual, I've been incredibly lazy about updating this blog, so you're much better off following @etrepum on Twitter.
simplejson 2.1.0
March 10, 2010 at 08:24 PM | categories: python, simplejson | View Commentssimplejson (documentation) is a simple, fast, complete, correct and extensible JSON (RFC 4627) encoder/decoder for Python 2.5+. It is pure Python code with no dependencies, but features an optional C extension for speed-ups.
simplejson 2.1.0 is a major update with several new features and bug-fixes:
- Decimal serialization officially supported for encoding with use_decimal=True. For encoding this encodes Decimal objects and for decoding it implies parse_float=Decimal
- Python 2.4 no longer supported (may still work, but no longer tested)
- Decoding performance and memory utilization enhancements http://bugs.python.org/issue7451
- JSONEncoderForHTML class for escaping &, <, > http://code.google.com/p/simplejson/issues/detail?id=66
- Memoization of object keys during encoding (when using speedups)
- Encoder changed to use PyIter_Next for list iteration to avoid potential threading issues
- Encoder changed to use iteritems rather than PyDict_Next in order to support dict subclasses that have a well defined ordering http://bugs.python.org/issue6105
- indent encoding parameter changed to be a string rather than an integer (integer use still supported for backwards compatibility) http://code.google.com/p/simplejson/issues/detail?id=56
- Test suite (python setup.py test) now automatically runs with and without speedups http://code.google.com/p/simplejson/issues/detail?id=55
- Fixed support for older versions of easy_install (e.g. stock Mac OS X config) http://code.google.com/p/simplejson/issues/detail?id=54
- Fixed str/unicode mismatches when using ensure_ascii=False http://code.google.com/p/simplejson/issues/detail?id=48
- Fixed error message when parsing an array with trailing comma with speedups http://code.google.com/p/simplejson/issues/detail?id=46
- Refactor decoder errors to raise JSONDecodeError instead of ValueError http://code.google.com/p/simplejson/issues/detail?id=45
- New ordered_pairs_hook feature in decoder which makes it possible to preserve key order. http://bugs.python.org/issue5381
- Fixed containerless unicode float decoding (same bug as 2.0.4, oops!) http://code.google.com/p/simplejson/issues/detail?id=43
- Share PosInf definition between encoder and decoder
- Minor reformatting to make it easier to backport simplejson changes to Python 2.7/3.1 json module
PyCon 2009, Drop ACID and think about data
April 01, 2009 at 02:11 PM | categories: python, PyCon | View CommentsI'm getting increasingly lazy about updating my blog these days, probably best to follow me on twitter: http://twitter.com/etrepum
Anyway, I gave a talk at PyCon 2009 in Rosemont ("Chicago") last week called Drop ACID and think about data. Basically it is a survey of some of the various kinds of non-traditional database technologies I've been looking at the past few years. Notable technologies NOT talked about are object databases and graph databases. *UPDATE* Video available here: http://blip.tv/file/1949416
Slides are on BitBucket for now: Drop ACID and think about data
I'll be giving a (hopefully updated) version of this talk at OpenSourceBridge, which is in Portland, OR June 17-19.
If you're interested in the content of this talk there is far more insightful information on Jonathan Ellis' Programming Blog, one of the developers working on Cassandra.
simplejson 2.0.9
February 18, 2009 at 04:00 PM | categories: python, simplejson | View Commentssimplejson (documentation) is a simple, fast, complete, correct and extensible JSON (RFC 4627) encoder/decoder for Python 2.4+. It is pure Python code with no dependencies, but features an optional C extension for speed-ups.
simplejson 2.0.9 is a major bug-fix update:
- Adds cyclic GC to the Encoder and Scanner speedups, which could've caused uncollectible cycles in some cases when using custom parser or encoder functions
simplejson 2.0.8
February 15, 2009 at 04:56 PM | categories: python, simplejson | View Commentssimplejson (documentation) is a simple, fast, complete, correct and extensible JSON (RFC 4627) encoder/decoder for Python 2.4+. It is pure Python code with no dependencies, but features an optional C extension for speed-ups.
simplejson 2.0.8 is a minor bug-fix update:
- Documentation fixes
- Fixes encoding True and False as keys
- Fixes checking for True and False by identity for several parameters
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