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Old 02-05-2009, 08:58 AM   #1
indienick
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Question Strange floating-point behaviour in Python


At work, I - sadly - am limited to Windows for my 3D mechanical design work.

Every now and then, I have to do some basic math with a calculator but sometimes it is much easier to do things in one, long mathematical expression and have it evaluated (with proper bracketing).

I installed Python on my Window XP workstation, and I noticed something VERY strange when I did a simple calculation (let's just say this boils down to laziness):
Code:
>>> (11.175 - 3) / 2
4.0875000000000004
WTF?! Why so many zeros and that trailing "4"?

I got somewhat upset and installed "Lisp in a Box" (oh darn, eh?) and did the exact same calculation:
Code:
CL-USER> (/ (- 11.175 3) 2)
4.0875
Beautiful! Why the difference; why does Python give me a messed up value, and CLISP not?
 
Old 02-05-2009, 09:08 AM   #2
colucix
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What about this?
Code:
>>> 0.1
0.10000000000000001
Reason explained here: http://docs.python.org/tutorial/floatingpoint.html.
 
Old 02-05-2009, 09:12 AM   #3
indienick
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Thanks for the reply, and the link, colucix!

However, I am still left with a feeling of, "Why isn't this fixable? Why is it CLISP doesn't do that, and Python does?"
 
Old 02-05-2009, 09:16 AM   #4
colucix
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Maybe because of the different method to convert numbers to string upon displaying on the terminal. The following should give the expected number, since the str function consider only 12 significant digits
Code:
>>> print str((11.175 - 3) / 2)
4.0875
 
Old 02-05-2009, 10:15 AM   #5
Randux
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If you think that was cool try running a program to calculate factorials. I couldn't believe how fast common lisp could get the result in 100s of digits!

Note to self: learn Lisp!
 
Old 02-05-2009, 10:21 AM   #6
indienick
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It's a beautiful language.

Again, thank you for your responses colucix.
 
Old 02-05-2009, 07:04 PM   #7
jlinkels
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Interesting. It is well known that certain rational figures (are they called like this in English as well) cannot be represented in binary as they are represented in decimal, with a finite number of bits.

However, can someone explain this?

Code:
donald_pc:/tmp$ echo "64 k 11.175 3 - 2 / p" | dc
4.0875000000000000000000000000000000000000000000000000000000000000
DC is an aribitrary precision RPN calculator.

It is really not cheating!

Code:
donald_pc:/tmp$ echo "64 k 11.175000000000000000000000000000000000000000000000001 3 - 2 / p" | dc
4.0875000000000000000000000000000000000000000000000005000000000000
I expected some less accurate results, that is normal floating point errors.

The most amazing is, I can invert the operation with the result I got, and then the outcome is exactly the number I started with. Is there something really smart going on?

jlinkels

Last edited by jlinkels; 02-05-2009 at 07:06 PM.
 
  


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