need help on generator...

[Craig Ringer]

Re: need help on need help on generator...

On Sat, 2005-01-22 at 10:10 +0100, Alex Martelli wrote:
[color=blue]
> The answer for the current implementation, BTW, is "in between" -- some
> buffering, but bounded consumption of memory -- but whether that tidbit
> of pragmatics is part of the file specs, heh, that's anything but clear
> (just as for other important tidbits of Python pragmatics, such as the
> facts that list.sort is wickedly fast, 'x in alist' isn't, 'x in adict'
> IS...).[/color]

A particularly great example when it comes to unexpected buffering
effects is the file iterator. Take code that reads a header from a file
using an (implicit) iterator, then tries to read() the rest of the file.
Taking the example of reading an RFC822-like message into a list of
headers and a body blob:

..>>> inpath = '/tmp/msg.eml'
..>>> infile = open(inpath)
..>>> for line in infile:
..... if not line.strip():
..... break
..... headers.append( tuple(line.spli t(':',1)))
..>>> body = infile.read()


(By the way, if you ever implement this yourself for real, you should
probably be hurt - use the 'email' or 'rfc822' modules instead. For one
thing, reinventing the wheel is rarely a good idea. For another, the
above code is horrid - in particular it doesn't handle malformed headers
at all, isn't big on readability/comments, etc.)

If you run the above code on a saved email message, you'd expect 'body'
to contain the body of the message, right? Nope. The iterator created
from the file when you use it in that for loop does internal read-ahead
for efficiency, and has already read in the entire file or at least a
chunk more of it than you've read out of the iterator. It doesn't
attempt to hide this from the programmer, so the file position marker is
further into the file (possibly at the end on a smaller file) than you'd
expect given the data you've actually read in your program.

I'd be interested to know if there's a better solution to this than:

..>>> inpath = '/tmp/msg.eml'
..>>> infile = open(inpath)
..>>> initer = iter(infile)
..>>> headers = []
..>>> for line in initer:
..... if not line.strip():
..... break
..... headers.append( tuple(line.spli t(':',1)))
..>>> data = ''.join(x for x in initer)

because that seems like a pretty ugly hack (and please ignore the
variable names). Perhaps a way to get the file to seek back to the point
last read from the iterator when the iterator is destroyed?

--
Craig Ringer

[Francis Girard]

Re: need help on need help on generator...

Le samedi 22 Janvier 2005 10:10, Alex Martelli a écrit :[color=blue]
> Francis Girard <francis.girard @free.fr> wrote:
> ...
>[color=green]
> > But besides the fact that generators are either produced with the new
> > "yield" reserved word or by defining the __new__ method in a class
> > definition, I don't know much about them.[/color]
>
> Having __new__ in a class definition has nothing much to do with
> generators; it has to do with how the class is instantiated when you
> call it. Perhaps you mean 'next' (and __iter__)? That makes instances
> of the class iterators, just like iterators are what you get when you
> call a generator.
>[/color]

Yes, I meant "next".

[color=blue][color=green]
> > In particular, I don't know what Python constructs does generate a
> > generator.[/color]
>
> A 'def' of a function whose body uses 'yield', and in 2.4 the new genexp
> construct.
>[/color]

Ok. I guess I'll have to update to version 2.4 (from 2.3) to follow the
discussion.
[color=blue][color=green]
> > I know this is now the case for reading lines in a file or with the new
> > "iterator" package.[/color]
>
> Nope, besides the fact that the module you're thinking of is named
> 'itertools': itertools uses a lot of C-coded special types, which are
> iterators but not generators. Similarly, a file object is an iterator
> but not a generator.
>[color=green]
> > But what else ?[/color]
>
> Since you appear to conflate generators and iterators, I guess the iter
> built-in function is the main one you missed. iter(x), for any x,
> either raises an exception (if x's type is not iterable) or else returns
> an iterator.
>[/color]

You're absolutly right, I take the one for the other and vice-versa. If I
understand correctly, a "generator" produce something over which you can
iterate with the help of an "iterator". Can you iterate (in the strict sense
of an "iterator") over something not generated by a "generator" ?

[color=blue][color=green]
> > Does Craig Ringer answer mean that list
> > comprehensions are lazy ?[/color]
>
> Nope, those were generator expressions.
>[color=green]
> > Where can I find a comprehensive list of all the
> > lazy constructions built in Python ?[/color]
>
> That's yet a different question -- at least one needs to add the
> built-in xrange, which is neither an iterator nor a generator but IS
> lazy (a historical artefact, admittedly).
>
> But fortunately Python's built-ins are not all THAT many, so that's
> about it.
>[color=green]
> > (I think that to easily distinguish lazy
> > from strict constructs is an absolute programmer need -- otherwise you
> > always end up wondering when is it that code is actually executed like in
> > Haskell).[/color]
>
> Encapsulation doesn't let you "easily distinguish" issues of
> implementation. For example, the fact that a file is an iterator (its
> items being its lines) doesn't tell you if that's internally implemented
> in a lazy or eager way -- it tells you that you can code afile.next() to
> get the next line, or "for line in afile:" to loop over them, but does
> not tell you whether the code for the file object is reading each line
> just when you ask for it, or whether it reads all lines before and just
> keeps some state about the next one, or somewhere in between.
>[/color]

You're right. I was much more talking (mistakenly) about lazy evaluation of
the arguments to a function (i.e. the function begins execution before its
arguments get evaluated) -- in such a case I think it should be specified
which arguments are "strict" and which are "lazy" -- but I don't think
there's such a thing in Python (... well not yet as Python get more and more
akin to FP).
[color=blue]
> The answer for the current implementation, BTW, is "in between" -- some
> buffering, but bounded consumption of memory -- but whether that tidbit
> of pragmatics is part of the file specs, heh, that's anything but clear
> (just as for other important tidbits of Python pragmatics, such as the
> facts that list.sort is wickedly fast, 'x in alist' isn't, 'x in adict'
> IS...).
>
>
> Alex[/color]

Thank you

Francis Girard
FRANCE

[Craig Ringer]

Re: need help on need help on generator...

On Sat, 2005-01-22 at 17:46 +0800, I wrote:
[color=blue]
> I'd be interested to know if there's a better solution to this than:
>
> .>>> inpath = '/tmp/msg.eml'
> .>>> infile = open(inpath)
> .>>> initer = iter(infile)
> .>>> headers = []
> .>>> for line in initer:
> .... if not line.strip():
> .... break
> .... headers.append( tuple(line.spli t(':',1)))
> .>>> data = ''.join(x for x in initer)
>
> because that seems like a pretty ugly hack (and please ignore the
> variable names). Perhaps a way to get the file to seek back to the point
> last read from the iterator when the iterator is destroyed?[/color]

And now, answering my own question (sorry):

Answer: http://tinyurl.com/6avdt

so we can slightly simplify the above to:

..>>> inpath = '/tmp/msg.eml'
..>>> infile = open(inpath)
..>>> headers = []
..>>> for line in infile:
..... if not line.strip():
..... break
..... headers.append( tuple(line.spli t(':',1)))
..>>> data = ''.join(x for x in infile)

at the cost of making it less clear what's going on and having someone
later go "duh, why isn't he using read() here instead" but can't seem to
do much more than that.

Might it be worth providing a way to have file objects seek back to the
current position of the iterator when read() etc are called? If not, I
favour the suggestion in the referenced post - file should probably fail
noisily, or at least emit a warning.

What are others thoughts on this?

--
Craig Ringer

[Alex Martelli]

Re: need help on need help on generator...

Francis Girard <francis.girard @free.fr> wrote:
...[color=blue][color=green]
> > A 'def' of a function whose body uses 'yield', and in 2.4 the new genexp
> > construct.[/color]
>
> Ok. I guess I'll have to update to version 2.4 (from 2.3) to follow the
> discussion.[/color]

It's worth upgrading even just for the extra speed;-).

[color=blue][color=green]
> > Since you appear to conflate generators and iterators, I guess the iter
> > built-in function is the main one you missed. iter(x), for any x,
> > either raises an exception (if x's type is not iterable) or else returns
> > an iterator.[/color]
>
> You're absolutly right, I take the one for the other and vice-versa. If I
> understand correctly, a "generator" produce something over which you can
> iterate with the help of an "iterator". Can you iterate (in the strict sense
> of an "iterator") over something not generated by a "generator" ?[/color]

A generator function (commonly known as a generator), each time you call
it, produces a generator object AKA a generator-iterator. To wit:
[color=blue][color=green][color=darkred]
>>> def f(): yield 23[/color][/color][/color]
....[color=blue][color=green][color=darkred]
>>> f[/color][/color][/color]
<function f at 0x75fe70>[color=blue][color=green][color=darkred]
>>> x = f()
>>> x[/color][/color][/color]
<generator object at 0x75aa58>[color=blue][color=green][color=darkred]
>>> type(x)[/color][/color][/color]
<type 'generator'>

A generator expression (genexp) also has a result which is a generator
object:
[color=blue][color=green][color=darkred]
>>> x = (23 for __ in [0])
>>> type(x)[/color][/color][/color]
<type 'generator'>


Iterators need not be generator-iterators, by any means. Generally, the
way to make sure you have an iterator is to call iter(...) on something;
if the something was already an iterator, NP, then iter's idempotent:
[color=blue][color=green][color=darkred]
>>> iter(x) is x[/color][/color][/color]
True


That's what "an iterator" means: some object x such that x.next is
callable without arguments and iter(x) is x.

Since iter(x) tries calling type(x).__iter_ _(x) [[slight simplification
here by ignoring custom metaclasses, see recent discussion on python-dev
as to why this is only 99% accurate, not 100% accurate]], one way to
code an iterator is as a class. For example:

class Repeater(object ):
def __iter__(self): return self
def next(self): return 23

Any instance of Repeater is an iterator which, as it happens, has just
the same behavior as itertools.repea t(23), which is also the same
behavior you get from iterators obtained by calling:

def generepeat():
while True: yield 23

In other words, after:

a = Repeater()
b = itertools.repea t(23)
c = generepeat()

the behavior of a, b and c is indistinguishab le, though you can easily
tell them apart by introspection -- type(a) != type(b) != type(c).


Python's penchant for duck typing -- behavior matters more, WAY more
than implementation details such as type() -- means we tend to consider
a, b and c fully equivalent. Focusing on ``generator'' is at this level
an implementation detail.


Most often, iterators (including generator-iterators) are used in a for
statement (or equivalently a for clause of a listcomp or genexp), which
is why one normally doesn't think about built-in ``iter'': it's called
automatically by these ``for'' syntax-forms. In other words,

for x in <<<whatever>> >:
...body...

is just like:

__tempiter = iter(<<<whateve r>>>)
while True:
try: x = __tempiter.next ()
except StopIteration: break
...body...

((Simplificatio n alert: the ``for'' statement has an optional ``else''
which this allegedly "just like" form doesn't mimic exactly...))

[color=blue]
> You're right. I was much more talking (mistakenly) about lazy evaluation of
> the arguments to a function (i.e. the function begins execution before its
> arguments get evaluated) -- in such a case I think it should be specified
> which arguments are "strict" and which are "lazy" -- but I don't think
> there's such a thing in Python (... well not yet as Python get more and more
> akin to FP).[/color]

Python's strict that way. To explicitly make some one argument "lazy",
sorta, you can put a "lambda:" in front of it at call time, but then you
have to "call the argument" to get it evaluated; a bit of a kludge.
There's a PEP out to allow a ``prefix :'' to mean just the same as this
"lambda:", but even though I co-authored it I don't think it lowers the
kludge quotient by all that much.

Guido, our beloved BDFL, is currently musing about optional typing of
arguments, which might perhaps open a tiny little crack towards letting
some arguments be lazy. I don't think Guido wants to go there, though.

My prediction is that even Python 3000 will be strict. At least this
makes some things obvious at each call-site without having to study the
way a function is defined, e.g., upon seeing
f(a+b, c*d)
you don't have to wonder, or study the ``def f'', to find out when the
addition and the multiplication happen -- they happen before f's body
gets a chance to run, and thus, in particular, if either operation
raises an exception, there's nothing f can do about it.

And that's a misunderstandin g I _have_ seen repeatedly even in people
with a pretty good overall grasp of Python, evidenced in code such as:
self.assertRais es(SomeError, f(23))
with astonishment that -- if f(23) does indeed raise SomeError -- this
exception propagates, NOT caught by assertRaises; and if mistakenly
f(23) does NOT raise, you typically get a TypeError about None not being
callable. The way to do the above call, _since Python is strict_, is:
self.assertRais es(SomeError, f, 23)
i.e. give assertRaises the function (or other callable) and arguments to
pass to it -- THIS way, assertRaises performs the call under its own
control (inside the try clause of a try/except statement) and can and
does catch and report things appropriately.

The frequency of this misunderstandin g is high enough to prove to me
that strictness is not FULLY understood by some "intermedia te level"
Pythonistas. However, I doubt the right solution is to complicate
Python with the ability to have some arguments be strict, and other
lazy, much as sometimes one might yearn for it. _Maybe_ one could have
some form that makes ALL arguments lazy, presenting them as an iterator
to the function itself. But even then the form _should_, I suspect, be
obvious at the call site, rather than visible only in the "def"...



Alex

[Alex Martelli]

Re: need help on need help on generator...

Craig Ringer <craig@postnews papers.com.au> wrote:
[color=blue]
> .>>> data = ''.join(x for x in infile)[/color]

Maybe ''.join(infile) is a better way to express this functionality?
Avoids 2.4 dependency and should be faster as well as more concise.

[color=blue]
> Might it be worth providing a way to have file objects seek back to the
> current position of the iterator when read() etc are called? If not, I[/color]

It's certainly worth doing a patch and see what the python-dev crowd
thinks of it, I think; it might make it into 2.5.
[color=blue]
> favour the suggestion in the referenced post - file should probably fail
> noisily, or at least emit a warning.[/color]

Under what conditions, exactly, would you want such an exception?


Alex

[Craig Ringer]

Re: need help on need help on generator...

On Sat, 2005-01-22 at 12:20 +0100, Alex Martelli wrote:[color=blue]
> Craig Ringer <craig@postnews papers.com.au> wrote:
>[color=green]
> > .>>> data = ''.join(x for x in infile)[/color]
>
> Maybe ''.join(infile) is a better way to express this functionality?
> Avoids 2.4 dependency and should be faster as well as more concise.[/color]

Thanks - for some reason I hadn't clicked to that. Obvious in hindsight,
but I just completely missed it.
[color=blue][color=green]
> > Might it be worth providing a way to have file objects seek back to the
> > current position of the iterator when read() etc are called? If not, I[/color]
>
> It's certainly worth doing a patch and see what the python-dev crowd
> thinks of it, I think; it might make it into 2.5.[/color]

I'll certainly look into doing so. I'm not dumb enough to say "Sure,
I'll do that" before looking into the code involved and thinking more
about what issues could pop up. Still, it's been added to my
increasingly frightening TODO list.
[color=blue][color=green]
> > favour the suggestion in the referenced post - file should probably fail
> > noisily, or at least emit a warning.[/color]
>
> Under what conditions, exactly, would you want such an exception?[/color]

When read() or other methods suffering from the same issue are called
after next() without an intervening seek(). It'd mean another state flag
for the file to keep track of - but I doubt it'd make any detectable
difference in performance given that there's disk I/O involved.

I'd be happier to change the behaviour so that a warning isn't
necessary, though, and I suspect it can be done without introducing
backward compatibility issues. Well, so long as nobody is relying on the
undefined file position after using an iterator - and I'm not dumb
enough to say nobody would ever do that.

I've really got myself into hot water now though - I'm going to have to
read over the `file' source code before impulsively saying anything
REALLY stupid.

--
Craig Ringer

[Francis Girard]

Classical FP problem in python : Hamming problem

Hi,

First,

My deepest thanks to Craig Ringer, Alex Martelli, Nick Coghlan and Terry Reedy
for having generously answered on the "Need help on need help on generator"
thread. I'm compiling the answers to sketch myself a global pictures about
iterators, generators, iterator-generators and laziness in python.

In the meantime, I couldn't resist to test the new Python features about
laziness on a classical FP problem, i.e. the "Hamming" problem.

The name of the game is to produce the sequence of integers satisfying the
following rules :

(i) The list is in ascending order, without duplicates
(ii) The list begins with the number 1
(iii) If the list contains the number x, then it also contains the numbers
2*x, 3*x, and 5*x
(iv) The list contains no other numbers.

The algorithm in FP is quite elegant. Simply suppose that the infinite
sequence is produced, then simply merge the three sequences (2*x,3*x,5*x) for
each x in the infinite sequence we supposed as already produced ; this is
O(n) complexity for n numbers.

I simply love those algorithms that run after their tails.

In haskell, the algorithm is translated as such :

-- BEGIN SNAP
-- hamming.hs

-- Merges two infinite lists
merge :: (Ord a) => [a] -> [a] -> [a]
merge (x:xs)(y:ys)
| x == y = x : merge xs ys
| x < y = x : merge xs (y:ys)
| otherwise = y : merge (x:xs) ys

-- Lazily produce the hamming sequence
hamming :: [Integer]
hamming
= 1 : merge (map (2*) hamming) (merge (map (3*) hamming) (map (5*) hamming))
-- END SNAP


In Python, I figured out this implementation :

-- BEGIN SNAP
import sys
from itertools import imap

## Merges two infinite lists
def imerge(xs, ys):
x = xs.next()
y = ys.next()
while True:
if x == y:
yield x
x = xs.next()
y = ys.next()
elif x < y:
yield x
x = xs.next()
else: # if y < x:
yield y
y = ys.next()

## Lazily produce the hamming sequence
def hamming():
yield 1 ## Initialize the machine
for n in imerge(imap(lam bda h: 2*h, hamming()),
imerge(imap(lam bda h: 3*h, hamming()),
imap(lambda h: 5*h, hamming()))):
yield n
print "Falling out -- We should never get here !!"

for n in hamming():
sys.stderr.writ e("%s " % str(n)) ## stderr for unbuffered output
-- END SNAP


My goal is not to compare Haskell with Python on a classical FP problem, which
would be genuine stupidity.

Nevertheless, while the Haskell version prints Hamming sequence for as longas
I can stand it, and with very little memory consumation, the Python version
only prints :
[color=blue][color=green][color=darkred]
>>>>>> hamming.py[/color][/color][/color]
1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54 60 64 7275
80 81 90 96 100 108 120 125 128 135 144 150 160 162 180 192 200 216 225 240
243 250 256 270 288 300 320 324 360 375 384 400 405 432 450 480 486 500 512
540 576 600 625 640 648 675 720 729 750 768 800 810 864 900 960 972 1000 1024
1080 1125 1152 1200 1215 1250 1280 1296 1350 1440 1458 1500 1536 1600 1620
1728 1800 1875 1920 1944 2000 2025 2048 2160 2187 2250 2304 2400 2430 2500
2560 2592 2700 2880 2916 3000 3072 3125 3200 3240 3375 3456 3600 3645 3750
3840 3888 4000 4050 4096 4320 4374 4500 4608 4800 4860 5000 5120 5184 5400
5625 5760 5832 6000 6075 6144 6250 6400 6480 6561 6750 6912 7200 7290 7500
7680 7776 8000 8100 8192 8640 8748 9000 9216 9375 9600 9720 10000 10125 10240
10368 10800 10935 11250 11520 11664 12000 12150 12288 12500 12800 12960 13122
13500 13824 14400 14580 15000 15360 15552 15625 16000 16200 16384 16875 17280
17496 18000 18225 18432 18750 19200 19440 19683 20000 20250 20480 20736 21600
21870 22500 23040 23328 24000 24300 24576 25000 25600 25920 26244 27000 27648
28125 28800 29160 30000 30375 30720 31104 31250 32000 32400 32768 32805 33750
34560 34992 36000 36450 36864 37500 38400 38880 39366 40000 40500 40960 41472
43200 43740 45000 46080 46656 46875 48000 48600 49152 50000 50625 51200 51840
52488 54000 54675 55296 56250 57600
Processus arrêté

After 57600, my machine begins swapping like crazy and I do have to kill the
python processus.

I think I should not have this kind of behaviour, even using recursion, since
I'm only using lazy constructs all the time. At least, I would expect the
program to produce much more results before surrending.

What's going on ?

Thank you

Francis Girard
FRANCE

[Jeff Epler]

Re: Classical FP problem in python : Hamming problem

Your formulation in Python is recursive (hamming calls hamming()) and I
think that's why your program gives up fairly early.

Instead, use itertools.tee() [new in Python 2.4, or search the internet
for an implementation that works in 2.3] to give a copy of the output
sequence to each "multiply by N" function as well as one to be the
return value.

Here's my implementation, which matched your list early on but
effortlessly reached larger values. One large value it printed was
641235181318963 2 (a Python long) which indeed has only the distinct
prime factors 2 and 3. (2**43 * 3**6)

Jeff

from itertools import tee
import sys

def imerge(xs, ys):
x = xs.next()
y = ys.next()
while True:
if x == y:
yield x
x = xs.next()
y = ys.next()
elif x < y:
yield x
x = xs.next()
else:
yield y
y = ys.next()

def hamming():
def _hamming(j, k):
yield 1
hamming = generators[j]
for i in hamming:
yield i * k
generators = []
generator = imerge(imerge(_ hamming(0, 2), _hamming(1, 3)), _hamming(2, 5))
generators[:] = tee(generator, 4)
return generators[3]

for i in hamming():
print i,
sys.stdout.flus h()

-----BEGIN PGP SIGNATURE-----
Version: GnuPG v1.2.6 (GNU/Linux)

iD8DBQFB9CTeJd0 1MZaTXX0RAlHPAJ 4gJwuPxCzBdnWiM 1/Rs3eUPk1HMwCeJU Xh
selUGrwJc9T8wE6 aCQOjq+Q=
=AW5F
-----END PGP SIGNATURE-----

[Tim Peters]

Re: Classical FP problem in python : Hamming problem

[Francis Girard][color=blue]
> ...
> In the meantime, I couldn't resist to test the new Python features about
> laziness on a classical FP problem, i.e. the "Hamming" problem.[/color]
....[color=blue]
> Nevertheless, while the Haskell version prints Hamming sequence for as long as
> I can stand it, and with very little memory consumation, the Python version
> only prints :[/color]
....[color=blue]
> I think I should not have this kind of behaviour, even using recursion, since
> I'm only using lazy constructs all the time. At least, I would expect the
> program to produce much more results before surrending.
>
> What's going on ?[/color]

You can find an explanation in Lib/test/test_generators .py, which uses
this problem as an example; you can also find one efficient way to
write it there.

[Francis Girard]

Re: Classical FP problem in python : Hamming problem

Ok, I think that the bottom line is this :

For all the algorithms that run after their tail in an FP way, like the
Hamming problem, or the Fibonacci sequence, (but unlike Sieve of Eratosthene
-- there's a subtle difference), i.e. all those algorithms that typically
rely upon recursion to get the beginning of the generated elements in order
to generate the next one ...

... so for this family of algorithms, we have, somehow, to abandon recursion,
and to explicitely maintain one or many lists of what had been generated.

One solution for this is suggested in "test_generator s.py". But I think that
this solution is evil as it looks like recursion is used but it is not and it
depends heavily on how the m235 function (for example) is invoked.
Furthermore, it is _NOT_ memory efficient as pretended : it leaks ! It
internally maintains a lists of generated results that grows forever while it
is useless to maintain results that had been "consumed". Just for a gross
estimate, on my system, percentage of memory usage for this program grows
rapidly, reaching 21.6 % after 5 minutes. CPU usage varies between 31%-36%.
Ugly and inefficient.

The solution of Jeff Epler is far more elegant. The "itertools. tee" function
does just what we want. It internally maintain a list of what had been
generated and deletes the "consumed" elements as the algo unrolls. To follow
with my gross estimate, memory usage grows from 1.2% to 1.9% after 5 minutes
(probably only affected by the growing size of Huge Integer). CPU usage
varies between 27%-29%.
Beautiful and effecient.

You might think that we shouldn't be that fussy about memory usage on
generating 100 digits numbers but we're talking about a whole family of
useful FP algorithms ; and the best way to implement them should be
established.

For this family of algorithms, itertools.tee is the way to go.

I think that the semi-tutorial in "test_generator s.py" should be updated to
use "tee". Or, at least, a severe warning comment should be written.

Thank you,

Francis Girard
FRANCE

Le dimanche 23 Janvier 2005 23:27, Jeff Epler a écrit :[color=blue]
> Your formulation in Python is recursive (hamming calls hamming()) and I
> think that's why your program gives up fairly early.
>
> Instead, use itertools.tee() [new in Python 2.4, or search the internet
> for an implementation that works in 2.3] to give a copy of the output
> sequence to each "multiply by N" function as well as one to be the
> return value.
>
> Here's my implementation, which matched your list early on but
> effortlessly reached larger values. One large value it printed was
> 641235181318963 2 (a Python long) which indeed has only the distinct
> prime factors 2 and 3. (2**43 * 3**6)
>
> Jeff
>
> from itertools import tee
> import sys
>
> def imerge(xs, ys):
> x = xs.next()
> y = ys.next()
> while True:
> if x == y:
> yield x
> x = xs.next()
> y = ys.next()
> elif x < y:
> yield x
> x = xs.next()
> else:
> yield y
> y = ys.next()
>
> def hamming():
> def _hamming(j, k):
> yield 1
> hamming = generators[j]
> for i in hamming:
> yield i * k
> generators = []
> generator = imerge(imerge(_ hamming(0, 2), _hamming(1, 3)), _hamming(2,
> 5)) generators[:] = tee(generator, 4)
> return generators[3]
>
> for i in hamming():
> print i,
> sys.stdout.flus h()[/color]

[Francis Girard]

Re: Classical FP problem in python : Hamming problem

The following implementation is even more speaking as it makes self-evident
and almost mechanical how to translate algorithms that run after their tail
from recursion to "tee" usage :

*** BEGIN SNAP
from itertools import tee, imap
import sys

def imerge(xs, ys):
x = xs.next()
y = ys.next()
while True:
if x == y:
yield x
x = xs.next()
y = ys.next()
elif x < y:
yield x
x = xs.next()
else:
yield y
y = ys.next()


def hamming():
def _hamming():
yield 1
hamming2 = hammingGenerato rs[0]
hamming3 = hammingGenerato rs[1]
hamming5 = hammingGenerato rs[2]
for n in imerge(imap(lam bda h: 2*h, iter(hamming2)) ,
imerge(imap(lam bda h: 3*h, iter(hamming3)) ,
imap(lambda h: 5*h, iter(hamming5)) )):
yield n
hammingGenerato rs = tee(_hamming(), 4)
return hammingGenerato rs[3]

for i in hamming():
print i,
sys.stdout.flus h()
*** END SNAP

Here's an implementation of the fibonacci sequence that uses "tee" :

*** BEGIN SNAP
from itertools import tee
import sys

def fib():
def _fib():
yield 1
yield 1
curGen = fibGenerators[0]
curAheadGen = fibGenerators[1]
curAheadGen.nex t()
while True:
yield curGen.next() + curAheadGen.nex t()
fibGenerators = tee(_fib(), 3)
return fibGenerators[2]

for n in fib():
print n,
sys.stdout.flus h()
*** END SNAP

Francis Girard
FRANCE


Le lundi 24 Janvier 2005 14:09, Francis Girard a écrit :[color=blue]
> Ok, I think that the bottom line is this :
>
> For all the algorithms that run after their tail in an FP way, like the
> Hamming problem, or the Fibonacci sequence, (but unlike Sieve of
> Eratosthene -- there's a subtle difference), i.e. all those algorithms that
> typically rely upon recursion to get the beginning of the generated
> elements in order to generate the next one ...
>
> ... so for this family of algorithms, we have, somehow, to abandon
> recursion, and to explicitely maintain one or many lists of what had been
> generated.
>
> One solution for this is suggested in "test_generator s.py". But I think
> that this solution is evil as it looks like recursion is used but it is not
> and it depends heavily on how the m235 function (for example) is invoked.
> Furthermore, it is _NOT_ memory efficient as pretended : it leaks ! It
> internally maintains a lists of generated results that grows forever while
> it is useless to maintain results that had been "consumed". Just for a
> gross estimate, on my system, percentage of memory usage for this program
> grows rapidly, reaching 21.6 % after 5 minutes. CPU usage varies between
> 31%-36%. Ugly and inefficient.
>
> The solution of Jeff Epler is far more elegant. The "itertools. tee"
> function does just what we want. It internally maintain a list of what had
> been generated and deletes the "consumed" elements as the algo unrolls. To
> follow with my gross estimate, memory usage grows from 1.2% to 1.9% after5
> minutes (probably only affected by the growing size of Huge Integer). CPU
> usage varies between 27%-29%.
> Beautiful and effecient.
>
> You might think that we shouldn't be that fussy about memory usage on
> generating 100 digits numbers but we're talking about a whole family of
> useful FP algorithms ; and the best way to implement them should be
> established.
>
> For this family of algorithms, itertools.tee is the way to go.
>
> I think that the semi-tutorial in "test_generator s.py" should be updated to
> use "tee". Or, at least, a severe warning comment should be written.
>
> Thank you,
>
> Francis Girard
> FRANCE
>
> Le dimanche 23 Janvier 2005 23:27, Jeff Epler a écrit :[color=green]
> > Your formulation in Python is recursive (hamming calls hamming()) and I
> > think that's why your program gives up fairly early.
> >
> > Instead, use itertools.tee() [new in Python 2.4, or search the internet
> > for an implementation that works in 2.3] to give a copy of the output
> > sequence to each "multiply by N" function as well as one to be the
> > return value.
> >
> > Here's my implementation, which matched your list early on but
> > effortlessly reached larger values. One large value it printed was
> > 641235181318963 2 (a Python long) which indeed has only the distinct
> > prime factors 2 and 3. (2**43 * 3**6)
> >
> > Jeff
> >
> > from itertools import tee
> > import sys
> >
> > def imerge(xs, ys):
> > x = xs.next()
> > y = ys.next()
> > while True:
> > if x == y:
> > yield x
> > x = xs.next()
> > y = ys.next()
> > elif x < y:
> > yield x
> > x = xs.next()
> > else:
> > yield y
> > y = ys.next()
> >
> > def hamming():
> > def _hamming(j, k):
> > yield 1
> > hamming = generators[j]
> > for i in hamming:
> > yield i * k
> > generators = []
> > generator = imerge(imerge(_ hamming(0, 2), _hamming(1, 3)),
> > _hamming(2, 5)) generators[:] = tee(generator, 4)
> > return generators[3]
> >
> > for i in hamming():
> > print i,
> > sys.stdout.flus h()[/color][/color]

[Tim Peters]

Re: Classical FP problem in python : Hamming problem

[Francis Girard][color=blue]
> For all the algorithms that run after their tail in an FP way, like the
> Hamming problem, or the Fibonacci sequence, (but unlike Sieve of Eratosthene
> -- there's a subtle difference), i.e. all those algorithms that typically
> rely upon recursion to get the beginning of the generated elements in order
> to generate the next one ...
>
> ... so for this family of algorithms, we have, somehow, to abandon recursion,
> and to explicitely maintain one or many lists of what had been generated.
>
> One solution for this is suggested in "test_generator s.py". But I think that
> this solution is evil as it looks like recursion is used but it is not and it
> depends heavily on how the m235 function (for example) is invoked.[/color]

Well, yes -- "Heh. Here's one way to get a shared list, complete with
an excruciating namespace renaming trick" was intended to warn you in
advance that it wasn't pretty <wink>.
[color=blue]
> Furthermore, it is _NOT_ memory efficient as pretended : it leaks ![/color]

Yes. But there are two solutions to the problem in that file, and the
second one is in fact extremely memory-efficient compared to the first
one. "Efficiency " here was intended in a relative sense.
[color=blue]
> It internally maintains a lists of generated results that grows forever while it
> is useless to maintain results that had been "consumed". Just for a gross
> estimate, on my system, percentage of memory usage for this program grows
> rapidly, reaching 21.6 % after 5 minutes. CPU usage varies between 31%-36%.
> Ugly and inefficient.[/color]

Try the first solution in the file for a better understanding of what
"inefficien t" means <wink>.
[color=blue]
> The solution of Jeff Epler is far more elegant. The "itertools. tee" function
> does just what we want. It internally maintain a list of what had been
> generated and deletes the "consumed" elements as the algo unrolls. To follow
> with my gross estimate, memory usage grows from 1.2% to 1.9% after 5 minutes
> (probably only affected by the growing size of Huge Integer). CPU usage
> varies between 27%-29%.
> Beautiful and effecient.[/color]

Yes, it is better. tee() didn't exist when generators (and
test_generators .py) were written, so of course nothing in the test
file uses them.
[color=blue]
> You might think that we shouldn't be that fussy about memory usage on
> generating 100 digits numbers but we're talking about a whole family of
> useful FP algorithms ; and the best way to implement them should be
> established.[/color]

Possibly -- there really aren't many Pythonistas who care about this.
[color=blue]
> For this family of algorithms, itertools.tee is the way to go.
>
> I think that the semi-tutorial in "test_generator s.py" should be updated to
> use "tee". Or, at least, a severe warning comment should be written.[/color]

Please submit a patch. The purpose of that file is to test
generators, so you should add a third way of doing it, not replace the
two ways already there. It should also contain prose explaining why
the third way is better (just as there's prose now explaining why the
second way is better than the first).

[Francis Girard]

Re: Classical FP problem in python : Hamming problem

Ok I'll submit the patch with the prose pretty soon.
Thank you
Francis Girard
FRANCE

Le mardi 25 Janvier 2005 04:29, Tim Peters a écrit :[color=blue]
> [Francis Girard]
>[color=green]
> > For all the algorithms that run after their tail in an FP way, like the
> > Hamming problem, or the Fibonacci sequence, (but unlike Sieve of
> > Eratosthene -- there's a subtle difference), i.e. all those algorithms
> > that typically rely upon recursion to get the beginning of the generated
> > elements in order to generate the next one ...
> >
> > ... so for this family of algorithms, we have, somehow, to abandon
> > recursion, and to explicitely maintain one or many lists of what had been
> > generated.
> >
> > One solution for this is suggested in "test_generator s.py". But I think
> > that this solution is evil as it looks like recursion is used but it is
> > not and it depends heavily on how the m235 function (for example) is
> > invoked.[/color]
>
> Well, yes -- "Heh. Here's one way to get a shared list, complete with
> an excruciating namespace renaming trick" was intended to warn you in
> advance that it wasn't pretty <wink>.
>[color=green]
> > Furthermore, it is _NOT_ memory efficient as pretended : it leaks ![/color]
>
> Yes. But there are two solutions to the problem in that file, and the
> second one is in fact extremely memory-efficient compared to the first
> one. "Efficiency " here was intended in a relative sense.
>[color=green]
> > It internally maintains a lists of generated results that grows forever
> > while it is useless to maintain results that had been "consumed". Just
> > for a gross estimate, on my system, percentage of memory usage for this
> > program grows rapidly, reaching 21.6 % after 5 minutes. CPU usage varies
> > between 31%-36%. Ugly and inefficient.[/color]
>
> Try the first solution in the file for a better understanding of what
> "inefficien t" means <wink>.
>[color=green]
> > The solution of Jeff Epler is far more elegant. The "itertools. tee"
> > function does just what we want. It internally maintain a list of what
> > had been generated and deletes the "consumed" elements as the algo
> > unrolls. To follow with my gross estimate, memory usage grows from 1.2%
> > to 1.9% after 5 minutes (probably only affected by the growing size of
> > Huge Integer). CPU usage varies between 27%-29%.
> > Beautiful and effecient.[/color]
>
> Yes, it is better. tee() didn't exist when generators (and
> test_generators .py) were written, so of course nothing in the test
> file uses them.
>[color=green]
> > You might think that we shouldn't be that fussy about memory usage on
> > generating 100 digits numbers but we're talking about a whole family of
> > useful FP algorithms ; and the best way to implement them should be
> > established.[/color]
>
> Possibly -- there really aren't many Pythonistas who care about this.
>[color=green]
> > For this family of algorithms, itertools.tee is the way to go.
> >
> > I think that the semi-tutorial in "test_generator s.py" should be updated
> > to use "tee". Or, at least, a severe warning comment should be written.[/color]
>
> Please submit a patch. The purpose of that file is to test
> generators, so you should add a third way of doing it, not replace the
> two ways already there. It should also contain prose explaining why
> the third way is better (just as there's prose now explaining why the
> second way is better than the first).[/color]

[Michael Spencer]

Re: Classical FP problem in python : Hamming problem

Francis Girard wrote:[color=blue]
> The following implementation is even more speaking as it makes self-evident
> and almost mechanical how to translate algorithms that run after their tail
> from recursion to "tee" usage :
>[/color]

Thanks, Francis and Jeff for raising a fascinating topic. I've enjoyed trying
to get my head around both the algorithm and your non-recursive implementation.

Here's a version of your implementation that uses a helper class to make the
algorithm itself prettier.

from itertools import tee, imap

def hamming():
def _hamming():
yield 1
for n in imerge(2 * hamming, imerge(3 * hamming, 5 * hamming)):
yield n

hamming = Tee(_hamming())
return iter(hamming)


class Tee(object):
"""Provides an indepent iterator (using tee) on every iteration request
Also implements lazy iterator arithmetic"""
def __init__(self, iterator):
self.iter = tee(iterator,1)[0]
def __iter__(self):
return self.iter.__cop y__()
def __mul__(self, number):
return imap(lambda x: x * number,self.__i ter__())

def imerge(xs, ys):
x = xs.next()
y = ys.next()
while True:
if x == y:
yield x
x = xs.next()
y = ys.next()
elif x < y:
yield x
x = xs.next()
else: # if y < x:
yield y
y = ys.next()
[color=blue][color=green][color=darkred]
>>> hg = hamming()
>>> for i in range(10000):[/color][/color][/color]
.... n = hg.next()
.... if i % 1000 == 0: print i, n
....
0 1
1000 51840000
2000 8100000000
3000 279936000000
4000 4707158941350
5000 50960793600000
6000 409600000000000
7000 263882790666240 0
8000 143327232000000 00
9000 680244480000000 00


Regards

Michael

[Nick Craig-Wood]

Re: Classical FP problem in python : Hamming problem

Francis Girard <francis.girard @free.fr> wrote:[color=blue]
> def hamming():
> def _hamming():
> yield 1
> hamming2 = hammingGenerato rs[0]
> hamming3 = hammingGenerato rs[1]
> hamming5 = hammingGenerato rs[2]
> for n in imerge(imap(lam bda h: 2*h, iter(hamming2)) ,
> imerge(imap(lam bda h: 3*h, iter(hamming3)) ,
> imap(lambda h: 5*h, iter(hamming5)) )):
> yield n
> hammingGenerato rs = tee(_hamming(), 4)
> return hammingGenerato rs[3][/color]

If you are after readability, you might prefer this...

def hamming():
def _hamming():
yield 1
for n in imerge(imap(lam bda h: 2*h, iter(hamming2)) ,
imerge(imap(lam bda h: 3*h, iter(hamming3)) ,
imap(lambda h: 5*h, iter(hamming5)) )):
yield n
hamming2, hamming3, hamming5, result = tee(_hamming(), 4)
return result

PS interesting thread - never heard of Hamming sequences before!
--
Nick Craig-Wood <nick@craig-wood.com> -- http://www.craig-wood.com/nick