floating point woes
Hi, while I usually cope with the woes of floating point issues, this is one, that I didn't expect: round(2.385, 2) 2.3799 Doesn't the docs say, it's rounded up for this case? quote Values are rounded to the closest multiple of 10 to the power minus n; if two multiples are equally close, rounding is done away from 0 /quote Well, that one is clearly rounding down. What's up, eh, down here? Pete Python 2.6 (r26:66714, Feb 8 2011, 08:50:11) [GCC 4.3.2 [gcc-4_3-branch revision 141291]] on linux2 -- http://mail.python.org/mailman/listinfo/python-list
Re: floating point woes
On Tuesday, February 15, 2011 7:49:34 PM UTC-4, Hans-Peter Jansen wrote: Hi, while I usually cope with the woes of floating point issues, this is one, that I didn't expect: round(2.385, 2) 2.3799 Doesn't the docs say, it's rounded up for this case? The problem is probably that 2.385 can not be represented as 2.3850 a = 2.385 a 2.3848 André quote Values are rounded to the closest multiple of 10 to the power minus n; if two multiples are equally close, rounding is done away from 0 /quote Well, that one is clearly rounding down. What's up, eh, down here? Pete Python 2.6 (r26:66714, Feb 8 2011, 08:50:11) [GCC 4.3.2 [gcc-4_3-branch revision 141291]] on linux2 -- http://mail.python.org/mailman/listinfo/python-list
Re: floating point woes
On Wed, 2011-02-16 at 00:49 +0100, Hans-Peter Jansen wrote: Hi, while I usually cope with the woes of floating point issues, this is one, that I didn't expect: round(2.385, 2) 2.3799 Doesn't the docs say, it's rounded up for this case? quote Values are rounded to the closest multiple of 10 to the power minus n; if two multiples are equally close, rounding is done away from 0 /quote Well, that one is clearly rounding down. What's up, eh, down here? Pete Python 2.6 (r26:66714, Feb 8 2011, 08:50:11) [GCC 4.3.2 [gcc-4_3-branch revision 141291]] on linux2 It's actually rounding up, but 2.38 cannot be represented precisely by floating points. This was fixed in Python 3.1. -- http://mail.python.org/mailman/listinfo/python-list
Re: floating point woes
On Tue, Feb 15, 2011 at 6:49 PM, Hans-Peter Jansen h...@urpla.net wrote: Hi, while I usually cope with the woes of floating point issues, this is one, that I didn't expect: round(2.385, 2) 2.3799 Doesn't the docs say, it's rounded up for this case? quote Values are rounded to the closest multiple of 10 to the power minus n; if two multiples are equally close, rounding is done away from 0 /quote Well, that one is clearly rounding down. What's up, eh, down here? Pete The number you are rounding is not 2.385. It is not possible to represent that number in binary, just like you cannot represent the value 1/3 in decimal. So instead, you're using the nearest approximation that an IEEE 754 Double-Precision Floating Point number can get you, which happens to be about 2.3848. And that rounds down to 2.38. Which also cannot be precisely represented in binary, so you get 2.3799 instead. -- http://mail.python.org/mailman/listinfo/python-list
Re: floating point woes
On Tue, Feb 15, 2011 at 4:49 PM, Hans-Peter Jansen h...@urpla.net wrote: Hi, while I usually cope with the woes of floating point issues, this is one, that I didn't expect: round(2.385, 2) 2.3799 Doesn't the docs say, it's rounded up for this case? quote Values are rounded to the closest multiple of 10 to the power minus n; if two multiples are equally close, rounding is done away from 0 /quote Well, that one is clearly rounding down. What's up, eh, down here? Python 2.5.4 (r254:67916, Dec 23 2008, 15:10:54) [MSC v.1310 32 bit (Intel)] on win32 Type help, copyright, credits or license for more information. 2.385 2.3848 Looks to me like it's working as expected... -- http://mail.python.org/mailman/listinfo/python-list
Re: floating point woes
On Tue, Feb 15, 2011 at 3:49 PM, Hans-Peter Jansen h...@urpla.net wrote:
Hi,
while I usually cope with the woes of floating point issues, this is
one, that I didn't expect:
round(2.385, 2)
2.3799
Doesn't the docs say, it's rounded up for this case?
quote
Values are rounded to the closest multiple of 10 to the power minus n;
if two multiples are equally close, rounding is done away from 0
/quote
Well, that one is clearly rounding down.
What's up, eh, down here?
http://docs.python.org/library/functions.html#round :
Note: The behavior of round() for floats can be surprising: for
example, round(2.675, 2) gives 2.67 instead of the expected 2.68. This
is not a bug: it’s a result of the fact that most decimal fractions
can’t be represented exactly as a float. See Floating Point
Arithmetic: Issues and Limitations[1] for more information.
[1]: http://docs.python.org/tutorial/floatingpoint.html
And indeed:
from decimal import Decimal
Decimal(2.385)
Decimal('2.3847868371792719699442386627197265625')
Which, rounded to 2 decimal places, gives us 2.38, which is in turn
approximated as:
2.37989341858963598497211933135986328125
I encourage reading [1].
Cheers,
Chris
--
http://blog.rebertia.com
--
http://mail.python.org/mailman/listinfo/python-list
Re: floating point woes
On Tue, Feb 15, 2011 at 4:09 PM, Chris Rebert c...@rebertia.com wrote:
On Tue, Feb 15, 2011 at 3:49 PM, Hans-Peter Jansen h...@urpla.net wrote:
Hi,
while I usually cope with the woes of floating point issues, this is
one, that I didn't expect:
round(2.385, 2)
2.3799
Doesn't the docs say, it's rounded up for this case?
quote
Values are rounded to the closest multiple of 10 to the power minus n;
if two multiples are equally close, rounding is done away from 0
/quote
Well, that one is clearly rounding down.
What's up, eh, down here?
http://docs.python.org/library/functions.html#round :
Note: The behavior of round() for floats can be surprising: for
example, round(2.675, 2) gives 2.67 instead of the expected 2.68. This
is not a bug: it’s a result of the fact that most decimal fractions
can’t be represented exactly as a float. See Floating Point
Arithmetic: Issues and Limitations[1] for more information.
[1]: http://docs.python.org/tutorial/floatingpoint.html
And indeed:
from decimal import Decimal
Decimal(2.385)
Decimal('2.3847868371792719699442386627197265625')
Which, rounded to 2 decimal places, gives us 2.38, which is in turn
approximated as:
[*whacks forehead hard*]
Nevermind.
- Chris
--
http://mail.python.org/mailman/listinfo/python-list
Re: floating point woes
On Wednesday 16 February 2011, 01:06:08 Benjamin Kaplan wrote: On Tue, Feb 15, 2011 at 6:49 PM, Hans-Peter Jansen h...@urpla.net wrote: Hi, while I usually cope with the woes of floating point issues, this is one, that I didn't expect: round(2.385, 2) 2.3799 Doesn't the docs say, it's rounded up for this case? quote Values are rounded to the closest multiple of 10 to the power minus n; if two multiples are equally close, rounding is done away from 0 /quote Well, that one is clearly rounding down. What's up, eh, down here? Pete The number you are rounding is not 2.385. It is not possible to represent that number in binary, just like you cannot represent the value 1/3 in decimal. So instead, you're using the nearest approximation that an IEEE 754 Double-Precision Floating Point number can get you, which happens to be about 2.3848. And that rounds down to 2.38. Which also cannot be precisely represented in binary, so you get 2.3799 instead. Thanks for the explanation, Benjamin. Not that I like it, but anyway. If I hadn't quitted smoking a long time ago, I would go and ask, what these engineers smoked during the course of inventing this sh*t. Even more probably, they took way too much of a special form of lysergic acid. OTOH, cdecimals, as in Stefan Krah's package are long overdue to get into the core. Pete -- http://mail.python.org/mailman/listinfo/python-list
Re: floating point woes
On Wednesday 16 February 2011, 01:24:59 Chris Rebert wrote:
On Tue, Feb 15, 2011 at 4:09 PM, Chris Rebert c...@rebertia.com
wrote:
On Tue, Feb 15, 2011 at 3:49 PM, Hans-Peter Jansen h...@urpla.net
wrote:
Hi,
while I usually cope with the woes of floating point issues, this
is
one, that I didn't expect:
round(2.385, 2)
2.3799
Doesn't the docs say, it's rounded up for this case?
quote
Values are rounded to the closest multiple of 10 to the power
minus n; if two multiples are equally close, rounding is done away
from 0 /quote
Well, that one is clearly rounding down.
What's up, eh, down here?
http://docs.python.org/library/functions.html#round :
Note: The behavior of round() for floats can be surprising: for
example, round(2.675, 2) gives 2.67 instead of the expected 2.68.
This is not a bug: it’s a result of the fact that most decimal
fractions can’t be represented exactly as a float. See Floating
Point Arithmetic: Issues and Limitations[1] for more information.
[1]: http://docs.python.org/tutorial/floatingpoint.html
And indeed:
from decimal import Decimal
Decimal(2.385)
Decimal('2.3847868371792719699442386627197265625')
Which, rounded to 2 decimal places, gives us 2.38, which is in turn
approximated as:
If that only wouldn't be so arkward to use:
from cdecimal import Decimal, ROUND_HALF_UP
d = Decimal(2.385)
d
Decimal('2.385')
d.quantize(Decimal('1.00'))
Decimal('2.38')
hrmpf.
d.quantize(Decimal('1.00'), ROUND_HALF_UP)
Decimal('2.39')
Oh, well. This is a bit too Cobolesque. (Yes, sure, I know, I can define
any context, I like.)
[*whacks forehead hard*]
Nevermind.
Too true.
- Chris
Pete
--
http://mail.python.org/mailman/listinfo/python-list
Re: floating point woes
On 2011-02-16, Ian Kelly ian.g.ke...@gmail.com wrote: On Tue, Feb 15, 2011 at 4:49 PM, Hans-Peter Jansen h...@urpla.net wrote: while I usually cope with the woes of floating point issues, this is one, that I didn't expect: round(2.385, 2) 2.3799 Doesn't the docs say, it's rounded up for this case? [...] Python 2.5.4 (r254:67916, Dec 23 2008, 15:10:54) [MSC v.1310 32 bit (Intel)] on win32 Type help, copyright, credits or license for more information. 2.385 2.3848 Looks to me like it's working as expected... Well, it's working as it's supposed to... Whether it's working as expected depends on the user. :) -- Grant -- http://mail.python.org/mailman/listinfo/python-list
Re: floating point woes
On 2011-02-16, Hans-Peter Jansen h...@urpla.net wrote: Thanks for the explanation, Benjamin. Not that I like it, but anyway. If I hadn't quitted smoking a long time ago, I would go and ask, what these engineers smoked during the course of inventing this sh*t. Like most tools, IEEE floating point works brilliantly for what it was intended when used by people who know how to use it. The problem is that it's used for all sorts of things it shouldn't be by people who don't understand how it works (again, like most tools). The problem is that it _appears_ easy to use, but it actually takes some study and effort to use it right. Back in the days before FP hardware was affordable, it used to be fairly common for BCD to be the default FP representation in many non-Fortran languages (BASIC, Pascal, etc.). I think that probably provided a lot fewer surprises to most users. Even more probably, they took way too much of a special form of lysergic acid. OTOH, cdecimals, as in Stefan Krah's package are long overdue to get into the core. There probably needs to be some sort of BCD FP option for the casual user since most people would probably be better off with BCD. Those who need HW FP probably know it (and might even know how to use it). [I may have just barely passed undergrad numerical analysis, but I learned enough to know how ignorant I was.] -- Grant -- http://mail.python.org/mailman/listinfo/python-list
Re: floating point woes
Hans-Peter Jansen wrote: Hi, while I usually cope with the woes of floating point issues, this is one, that I didn't expect: round(2.385, 2) 2.3799 Doesn't the docs say, it's rounded up for this case? quote Values are rounded to the closest multiple of 10 to the power minus n; if two multiples are equally close, rounding is done away from 0 /quote Well, that one is clearly rounding down. What's up, eh, down here? 2.385 isn't really 2.385: Python 2.6.5 (r265:79063, Apr 16 2010, 13:09:56) [GCC 4.4.3] on linux2 Type help, copyright, credits or license for more information. repr (2.385) '2.3848' so it correctly rounded down. You need to use Decimal numbers if you want numbers that behave the way they look. Mel. -- http://mail.python.org/mailman/listinfo/python-list
