Re: python rounding problem.

[Florian Diesch]

"Thomas Bartkus" <[EMAIL PROTECTED]> wrote:

> "Grant Edwards" <[EMAIL PROTECTED]> wrote in message
> news:[EMAIL PROTECTED]
>> On 2006-05-08, Thomas Bartkus <[EMAIL PROTECTED]> wrote:
>>
>> >> does python support true rations, which means that 1/3 is a
>> >> true one-third and not 0.3 rounded off at some
>> >> arbitrary precision?
>> >
>> > At risk of being boring  ;-)
>> >
>> > - Python supports both rational and irrational numbers as
>> >   floating point numbers the way any language on any digital
>> >   computer does - imprecisely.
>> >
>> > A "true" (1/3) can only be expressed as a fraction.
>>
>> At the risk of being both boring and overly pedantic, that's
>> not true.  In base 3, the value in question is precisely
>> representable in floating point: 0.1
>>
>> > As soon as you express it as a floating point - you are in a
>> > bit of trouble because that's impossible.
>>
>> It's not possible in base 2 or base 10.  It's perfectly
>> possible in base 9 (used by the Nenets of Northern Russia) base
>> 12 (popular on planets where everybody has twelve toes) or base
>> 60 (used by th Sumerians).  [I don't know if any of those
>> peoples used floating point in those bases -- I'm just pointing
>> out that your prejudice towards base 10 notation is showing.]
>>
>> > You can not express (1/3) as a floating point in Python any
>> > more than you can do it with pencil and paper.
>>
>> That's true assuming base 2 in Python and base 10 on paper. The
>> base used by Python is pretty much etched in stone (silicon, to
>> be precise).  There used to be articles about people working on
>> base-3 logic gates, but base-3 logic never made it out of the
>> lab. However, you can pick any base you want when using paper
>> and pencil.
>>
>> > You can be precise and write "1/3" or you can surrender to
>> > arithmetic convenience and settle for the imprecise by writing
>> > "0.3", chopping it off at some arbitrary precision.
>>
>> Or you can write  0.1
>>  3
>>
>> :)
>
> Ahhh!
> But if I need to store the value 1/10 (decimal!), what kind of a precision
> pickle will I then find myself while working in base 3 ?  How much better
> for precision if we just learn our fractions and stick to storing integer
> numerators alongside integer denominators in big 128 bit double registers ?
>
> Even the Nenets might become more computationally precise by such means ;-)
> And how does a human culture come to decide on base 9 arithmetic anyway?

Just guessing: 
 * Use one thumb to point at one of the other 9 fingers
 * Every finger (except for the thumb) has 3 segments (and links), each
   of which can easily divided in three part (upper, middle, lower or left
   middle, right for the links) making 9 points for each finger.


> Even base 60 makes more sense if you like it when a lot of divisions come
> out nice and even.

You can count to 60 using two hands: Use the right thumb to point on
one of the 12 segments of the remaining 4 fingers and on the left hand
one finger for each dozen.


Of course this is wasting resources as you can count to 1023 with your
fingers. I never heard of a culture doing so, though.



   Florian
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Re: python rounding problem.

[Tim Roberts]

"chun ping wang" <[EMAIL PROTECTED]> wrote:
>
>Hey i have a stupid question.
>
>How do i get python to print the result in only three decimal place...
>
>Example>>> round (2.9954254, 3)
>2.9951
>
>but i want to get rid of all trailing 0's..how would i do that?

Your "problem" is not a problem in real programs -- it's only a problem
because of the way the interactive interpreter works:

C:\WINDOWS>python
Python 2.4.1 (#65, Mar 30 2005, 09:13:57) [MSC v.1310 32 bit (Intel)] on
win32
Type "help", "copyright", "credits" or "license" for more information.
>>> round(2.99543322,3)
2.9951
>>> print round(2.99543322,3)
2.995
>>>

-- 
- Tim Roberts, [EMAIL PROTECTED]
  Providenza & Boekelheide, Inc.
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Re: python rounding problem.

[Dan Bishop]

Grant Edwards wrote:
> On 2006-05-09, Dan Bishop <[EMAIL PROTECTED]> wrote:
> > Grant Edwards wrote:
> > ...
> >> Did they actually have 60 unique number symbols and use
> >> place-weighting in a manner similar to the arabic/indian system
> >> we use?
> >
> > The Bablyonians did use a place-value system, but they only had two
> > basic numerals: a Y-like symbol for 1 and a <-like symbol for ten.
> > These were combined to make base-60 digits.  For example, 59 was
> > represented by
> >
> >  <   YYY
> > < <  YYY
> >< <   YYY
> >
> > Zero (used as a placeholder, but not as a number in itself) was
> > represented by a space.
>
> And they also (acording to the web pages I found) used base-60
> floating point notation, but without an actual symbol to
> represent the sexagesimal point.  Which seems really ambiguous --
> even to somebody who does know how to use a slide rule.

Yes, it was.  ("Our spy's message says that Cyrus the Great has '6 '
troops.  Does that mean 360 or 21,600?")

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Re: python rounding problem.

[Grant Edwards]

On 2006-05-09, Dan Bishop <[EMAIL PROTECTED]> wrote:
> Grant Edwards wrote:
> ...
>> Did they actually have 60 unique number symbols and use
>> place-weighting in a manner similar to the arabic/indian system
>> we use?
>
> The Bablyonians did use a place-value system, but they only had two
> basic numerals: a Y-like symbol for 1 and a <-like symbol for ten.
> These were combined to make base-60 digits.  For example, 59 was
> represented by
>
>  <   YYY
> < <  YYY
>< <   YYY
>
> Zero (used as a placeholder, but not as a number in itself) was
> represented by a space.

And they also (acording to the web pages I found) used base-60
floating point notation, but without an actual symbol to
represent the sexagesimal point.  Which seems really ambiguous --
even to somebody who does know how to use a slide rule.

-- 
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  at   DESPONDENT over the LIBYAN
   visi.comsituation and the price
   of CHICKEN...
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Re: python rounding problem.

[Dan Bishop]

Grant Edwards wrote:
...
> Did they actually have 60 unique number symbols and use
> place-weighting in a manner similar to the arabic/indian system
> we use?

The Bablyonians did use a place-value system, but they only had two
basic numerals: a Y-like symbol for 1 and a <-like symbol for ten.
These were combined to make base-60 digits.  For example, 59 was
represented by

  <   YYY
 < <  YYY
< <   YYY

Zero (used as a placeholder, but not as a number in itself) was
represented by a space.

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Re: python rounding problem.

[Grant Edwards]

On 2006-05-09, Thomas Bartkus <[EMAIL PROTECTED]> wrote:

>>> Even base 60 makes more sense if you like it when a lot of
>>> divisions come out nice and even.
>>
>> Did they actually have 60 unique number symbols and use
>> place-weighting in a manner similar to the arabic/indian
>> system we use?
>
> I don't know.

I googled around a while last night, and they ahd sort of a
hybrid notation.  The Sumerians started withindividual "tic
marks" up to 9, and symbols for 10, 60, 600, 3600 and so on.
That evolved into the Babylonian base-60 position-weighted
system (without a zero symbol) that used only the 1 symbol and
the 10 symbol.

http://it.stlawu.edu/%7Edmelvill/mesomath/sumerian.html
http://www.ancientscripts.com/sumerian.html
http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_numerals.html

> I do know that we have 360 degrees in a circle

And 60 seconds in a minute, 60 minutes in a hour (for both time
and angles), and 60 minutes in a degree.

-- 
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  at   speaking ENGLISH?
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Re: python rounding problem.

[Thomas Bartkus]

"Grant Edwards" <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]
> On 2006-05-08, Thomas Bartkus <[EMAIL PROTECTED]> wrote:
>
> >> Or you can write  0.1
> >>  3
> >>
> >> :)
> >
> > Ahhh!
> >
> > But if I need to store the value 1/10 (decimal!), what kind of
> > a precision pickle will I then find myself while working in
> > base 3?
>
> Then we're right back where we started.  No matter what base
> you choose, any fixed length floating-point representation can
> only represent 0% of all rational numbers.
>
> So, clearly what we need are floating point objects with
> configurable bases -- bases that automatically adjust to
> maintain exact representation of calculation results.  Which
> probably exactly the same as just storing rational numbers as
> numerator,denominator tuples as you suggest.
>
> > How much better for precision if we just learn our fractions
> > and stick to storing integer numerators alongside integer
> > denominators in big 128 bit double registers ?

I completely overlooked the infinite (presumably!) length integer handling
in Python.  You can do integer arithmetic on integers of large and arbitrary
lengths and if ultimate precision were indeed so important (and I can't
imagine why!) then working with numerators and denominators stored as tuples
is quite practical.

Anyone old enough to remember Forth might remember the arguments about how
unnecessary floating point is.  True enough!  Floating point is merely a
convenience for which we sacrifice some (insignificant!) arithmetic
precision to enjoy.

> > Even the Nenets might become more computationally precise by
> > such means ;-) And how does a human culture come to decide on
> > base 9 arithmetic anyway?
>
> I've no clue, whatsoever.  I just stumbled across that factoid
> when I used Wikipedia to look up which civilizations used
> base-60.  For some reason I can never remember whether it was
> one of the mesoamerican ones or one of the mesopotamian ones.

I suspect a hoax or an urban legend here.  A brief and casual googling
brings up the Nenets but no mention of base 9 arithmetic which I would find
rather astonishing.
Look up the Tasaday tribe together with the word "hoax".  A great joke on
academic anthropologists really.

On the other hand, the name "Nenet" is full of "N"s and so evocative of the
number nine ;-)

> > Even base 60 makes more sense if you like it when a lot of
> > divisions come out nice and even.
>
> Did they actually have 60 unique number symbols and use
> place-weighting in a manner similar to the arabic/indian system
> we use?

I don't know.
I do know that we have 360 degrees in a circle for the simple reason that
this is evenly divisible by so damned many integers.  A significant and
logical convenience if you have to do all your calculations on a wooden
board using the chunk of charcoal you hold in your fist.

Thomas Bartkus

> > Do the Nenets amputate the left pinky as a rite of adulthood
> > ;-)
>
> Nah, winters up there are so friggin' cold that nobody ever has
> more than nine digits by the time they reach adulthood.
>
> -- 
> Grant Edwards   grante Yow!  Hello. Just walk
>   at   along and try NOT to
think
>visi.comabout your INTESTINES
being
>almost FORTY YARDS
LONG!!


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Re: python rounding problem.

[Grant Edwards]

On 2006-05-08, Thomas Bartkus <[EMAIL PROTECTED]> wrote:

>> Or you can write  0.1
>>  3
>>
>> :)
>
> Ahhh!
>
> But if I need to store the value 1/10 (decimal!), what kind of
> a precision pickle will I then find myself while working in
> base 3?

Then we're right back where we started.  No matter what base
you choose, any fixed length floating-point representation can
only represent 0% of all rational numbers.

So, clearly what we need are floating point objects with
configurable bases -- bases that automatically adjust to
maintain exact representation of calculation results.  Which
probably exactly the same as just storing rational numbers as
numerator,denominator tuples as you suggest.

> How much better for precision if we just learn our fractions
> and stick to storing integer numerators alongside integer
> denominators in big 128 bit double registers ?
>
> Even the Nenets might become more computationally precise by
> such means ;-) And how does a human culture come to decide on
> base 9 arithmetic anyway?

I've no clue, whatsoever.  I just stumbled across that factoid
when I used Wikipedia to look up which civilizations used
base-60.  For some reason I can never remember whether it was
one of the mesoamerican ones or one of the mesopotamian ones.

> Even base 60 makes more sense if you like it when a lot of
> divisions come out nice and even.

Did they actually have 60 unique number symbols and use
place-weighting in a manner similar to the arabic/indian system
we use?

> Do the Nenets amputate the left pinky as a rite of adulthood
> ;-)

Nah, winters up there are so friggin' cold that nobody ever has
more than nine digits by the time they reach adulthood.

-- 
Grant Edwards   grante Yow!  Hello. Just walk
  at   along and try NOT to think
   visi.comabout your INTESTINES being
   almost FORTY YARDS LONG!!
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Re: python rounding problem.

[Thomas Bartkus]

"Grant Edwards" <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]
> On 2006-05-08, Thomas Bartkus <[EMAIL PROTECTED]> wrote:
>
> >> does python support true rations, which means that 1/3 is a
> >> true one-third and not 0.3 rounded off at some
> >> arbitrary precision?
> >
> > At risk of being boring  ;-)
> >
> > - Python supports both rational and irrational numbers as
> >   floating point numbers the way any language on any digital
> >   computer does - imprecisely.
> >
> > A "true" (1/3) can only be expressed as a fraction.
>
> At the risk of being both boring and overly pedantic, that's
> not true.  In base 3, the value in question is precisely
> representable in floating point: 0.1
>
> > As soon as you express it as a floating point - you are in a
> > bit of trouble because that's impossible.
>
> It's not possible in base 2 or base 10.  It's perfectly
> possible in base 9 (used by the Nenets of Northern Russia) base
> 12 (popular on planets where everybody has twelve toes) or base
> 60 (used by th Sumerians).  [I don't know if any of those
> peoples used floating point in those bases -- I'm just pointing
> out that your prejudice towards base 10 notation is showing.]
>
> > You can not express (1/3) as a floating point in Python any
> > more than you can do it with pencil and paper.
>
> That's true assuming base 2 in Python and base 10 on paper. The
> base used by Python is pretty much etched in stone (silicon, to
> be precise).  There used to be articles about people working on
> base-3 logic gates, but base-3 logic never made it out of the
> lab. However, you can pick any base you want when using paper
> and pencil.
>
> > You can be precise and write "1/3" or you can surrender to
> > arithmetic convenience and settle for the imprecise by writing
> > "0.3", chopping it off at some arbitrary precision.
>
> Or you can write  0.1
>  3
>
> :)

Ahhh!
But if I need to store the value 1/10 (decimal!), what kind of a precision
pickle will I then find myself while working in base 3 ?  How much better
for precision if we just learn our fractions and stick to storing integer
numerators alongside integer denominators in big 128 bit double registers ?

Even the Nenets might become more computationally precise by such means ;-)
And how does a human culture come to decide on base 9 arithmetic anyway?
Even base 60 makes more sense if you like it when a lot of divisions come
out nice and even.

Do the Nenets amputate the left pinky as a rite of adulthood ;-)
Thomas Bartkus




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Re: python rounding problem.

[Grant Edwards]

On 2006-05-08, Thomas Bartkus <[EMAIL PROTECTED]> wrote:

>> does python support true rations, which means that 1/3 is a
>> true one-third and not 0.3 rounded off at some
>> arbitrary precision?
>
> At risk of being boring  ;-)
>
> - Python supports both rational and irrational numbers as
>   floating point numbers the way any language on any digital
>   computer does - imprecisely.
>
> A "true" (1/3) can only be expressed as a fraction.

At the risk of being both boring and overly pedantic, that's
not true.  In base 3, the value in question is precisely
representable in floating point: 0.1

> As soon as you express it as a floating point - you are in a
> bit of trouble because that's impossible.

It's not possible in base 2 or base 10.  It's perfectly
possible in base 9 (used by the Nenets of Northern Russia) base
12 (popular on planets where everybody has twelve toes) or base
60 (used by th Sumerians).  [I don't know if any of those
peoples used floating point in those bases -- I'm just pointing
out that your prejudice towards base 10 notation is showing.]

> You can not express (1/3) as a floating point in Python any
> more than you can do it with pencil and paper.

That's true assuming base 2 in Python and base 10 on paper. The
base used by Python is pretty much etched in stone (silicon, to
be precise).  There used to be articles about people working on
base-3 logic gates, but base-3 logic never made it out of the
lab. However, you can pick any base you want when using paper
and pencil. 

> You can be precise and write "1/3" or you can surrender to
> arithmetic convenience and settle for the imprecise by writing
> "0.3", chopping it off at some arbitrary precision.

Or you can write  0.1
 3

:)

-- 
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  at   DOBERMAN!!
   visi.com
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Re: python rounding problem.

[Thomas Bartkus]

"Gary Wessle" <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]
> Erik Max Francis <[EMAIL PROTECTED]> writes:
>
> > chun ping wang wrote:
> >
> > > Hey i have a stupid question.
> > > How do i get python to print the result in only three decimal
> > > place...
> > > Example>>> round (2.9954254, 3)
> > > 2.9951
> > > but i want to get rid of all trailing 0's..how would i do that?
> >
> > Floating point arithmetic is inherently imprecise.  This is not a
> > Python problem.
>
> does python support true rations, which means that 1/3 is a true
> one-third and not 0.3 rounded off at some arbitrary precision?

At risk of being boring  ;-)

- Python supports both rational and irrational numbers as floating point
numbers the way any language on any digital computer does - imprecisely.

A "true" (1/3) can only be expressed as a fraction. As soon as you express
it as a floating point - you are in a bit of trouble because that's
impossible.  You can not express (1/3) as a floating point in Python any
more than you can do it with pencil and paper.  You can be precise and write
"1/3" or you can surrender to arithmetic convenience and settle for the
imprecise by writing "0.3", chopping it off at some arbitrary
precision.

Which is exactly what you did in your post ;-)
Thomas Bartkus


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Re: python rounding problem.

[Raymond L. Buvel]

Gary Wessle wrote:
> Erik Max Francis <[EMAIL PROTECTED]> writes:
> 
> 
>>chun ping wang wrote:
>>
>>
>>>Hey i have a stupid question.
>>>How do i get python to print the result in only three decimal
>>>place...
>>>Example>>> round (2.9954254, 3)
>>>2.9951
>>>but i want to get rid of all trailing 0's..how would i do that?
>>
>>Floating point arithmetic is inherently imprecise.  This is not a
>>Python problem.
> 
> 
> does python support true rations, which means that 1/3 is a true
> one-third and not 0.3 rounded off at some arbitrary precision?
> 

Python doesn't directly support rationals but there are at least two
third party modules that add this capability to Python.

http://calcrpnpy.sourceforge.net/clnumManual.html

http://gmpy.sourceforge.net/
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Re: python rounding problem.

[Gary Wessle]

Erik Max Francis <[EMAIL PROTECTED]> writes:

> chun ping wang wrote:
> 
> > Hey i have a stupid question.
> > How do i get python to print the result in only three decimal
> > place...
> > Example>>> round (2.9954254, 3)
> > 2.9951
> > but i want to get rid of all trailing 0's..how would i do that?
> 
> Floating point arithmetic is inherently imprecise.  This is not a
> Python problem.

does python support true rations, which means that 1/3 is a true
one-third and not 0.3 rounded off at some arbitrary precision?

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Re: python rounding problem.

[gene tani]

Erik Max Francis wrote:
> chun ping wang wrote:
>
> > Hey i have a stupid question.
> >
> > How do i get python to print the result in only three decimal place...
> >
> > Example>>> round (2.9954254, 3)
> > 2.9951
> >
> > but i want to get rid of all trailing 0's..how would i do that?
>
> Floating point arithmetic is inherently imprecise.  This is not a Python
> problem.
> 

http://www2.hursley.ibm.com/decimal/
(read about IEEE754 here)

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Re: python rounding problem.

[Erik Max Francis]

chun ping wang wrote:

> Hey i have a stupid question.
> 
> How do i get python to print the result in only three decimal place...
> 
> Example>>> round (2.9954254, 3)
> 2.9951
> 
> but i want to get rid of all trailing 0's..how would i do that?

Floating point arithmetic is inherently imprecise.  This is not a Python 
problem.

If you want to print it to only three digits, then use something like::

 >>> '%.3f' % 2.9954254
'2.995'

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python rounding problem.

[chun ping wang]

Hey i have a stupid question.

How do i get python to print the result in only three decimal place...

Example>>> round (2.9954254, 3)
2.9951

but i want to get rid of all trailing 0's..how would i do that?

_
Express yourself instantly with MSN Messenger! Download today - it's FREE! 
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