Excel 2003 calculation bug - subtraction of 1 decimal place

Hi,

I think I have found a bug on Excel 2003, but I am not sure if it is fixed.
I have written a very simple "program" in a new clean workbook:

A1 : 30.2
B1 : 32.3
C1 : 1.1
D1 : 1
E1 : =A1-B1+C1+D1

The result is 2.22045E-15..........I suppose it should be zero.
The numbers are so simple, and the formula is straight forward enough that I 
don't think it is ignorable. I understand that using ROUND function or check 
the option "precision as display" can solve the problem, but is it a little 
bit too much to do for such simple work?

Could anyone provide me the bug fix number (if any), or any reference on 
this? 

Thank you very much.

Amazing Bug.

Jensan
0
Jensan (3)
8/1/2007 10:26:03 AM
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It is not a bug, it is floating point arithmetic, 
http://en.wikipedia.org/wiki/IEEE_754

-- 
---
HTH

Bob

(there's no email, no snail mail, but somewhere should be gmail in my addy)



"Jensan" <Jensan@discussions.microsoft.com> wrote in message 
news:5F8BBECB-C030-4076-98F1-83BCBBFC5AB3@microsoft.com...
> Hi,
>
> I think I have found a bug on Excel 2003, but I am not sure if it is 
> fixed.
> I have written a very simple "program" in a new clean workbook:
>
> A1 : 30.2
> B1 : 32.3
> C1 : 1.1
> D1 : 1
> E1 : =A1-B1+C1+D1
>
> The result is 2.22045E-15..........I suppose it should be zero.
> The numbers are so simple, and the formula is straight forward enough that 
> I
> don't think it is ignorable. I understand that using ROUND function or 
> check
> the option "precision as display" can solve the problem, but is it a 
> little
> bit too much to do for such simple work?
>
> Could anyone provide me the bug fix number (if any), or any reference on
> this?
>
> Thank you very much.
>
> Amazing Bug.
>
> Jensan 


0
bob.NGs1 (1661)
8/1/2007 11:14:13 AM
=A1-B1+(C1+D1)  returns 0


Gord Dibben  MS Excel MVP


On Wed, 1 Aug 2007 03:26:03 -0700, Jensan <Jensan@discussions.microsoft.com>
wrote:

>Hi,
>
>I think I have found a bug on Excel 2003, but I am not sure if it is fixed.
>I have written a very simple "program" in a new clean workbook:
>
>A1 : 30.2
>B1 : 32.3
>C1 : 1.1
>D1 : 1
>E1 : =A1-B1+C1+D1
>
>The result is 2.22045E-15..........I suppose it should be zero.
>The numbers are so simple, and the formula is straight forward enough that I 
>don't think it is ignorable. I understand that using ROUND function or check 
>the option "precision as display" can solve the problem, but is it a little 
>bit too much to do for such simple work?
>
>Could anyone provide me the bug fix number (if any), or any reference on 
>this? 
>
>Thank you very much.
>
>Amazing Bug.
>
>Jensan

0
Gord
8/1/2007 2:17:33 PM
Excel (and almost all other software) does binary math (as described in Bob's 
link).  In binary, most terminating decimal fractions are non-terminating 
binary fractions that can only be approximated (just as 1/3 can only be 
approximated as a decimal fraction).  When your inputs are only approximately 
what you intended, it should be no surprise when the output is also only an 
approximation.

IEEE double precision gives at least 15 figure accuracy in its approximation 
to floating point numbers.  That means that your problem is effectively
  30.2000000000000???
 -32.3000000000000???
  +1.10000000000000??
  +1
 --------------------------
  00.0000000000000???
which is what you got, since 2.22045E-15 is beyond the 15-figure precision 
of your input numbers.

Specifically, the binary approximations have decimal values of
  30.199999999999999289457264239899814128875732421875
 -32.2999999999999971578290569595992565155029296875
  +1.100000000000000088817841970012523233890533447265625
  +1
  ---------------------------------------------------------------------------
  00.000000000000002220446049250313080847263336181640625
which is arithmetically correct if you care to check the math.

Jerry

"Jensan" wrote:

> Hi,
> 
> I think I have found a bug on Excel 2003, but I am not sure if it is fixed.
> I have written a very simple "program" in a new clean workbook:
> 
> A1 : 30.2
> B1 : 32.3
> C1 : 1.1
> D1 : 1
> E1 : =A1-B1+C1+D1
> 
> The result is 2.22045E-15..........I suppose it should be zero.
> The numbers are so simple, and the formula is straight forward enough that I 
> don't think it is ignorable. I understand that using ROUND function or check 
> the option "precision as display" can solve the problem, but is it a little 
> bit too much to do for such simple work?
> 
> Could anyone provide me the bug fix number (if any), or any reference on 
> this? 
> 
> Thank you very much.
> 
> Amazing Bug.
> 
> Jensan
0
post_a_reply (1395)
8/1/2007 9:04:00 PM
Thanks a lot for all your replies.

So, do you mean that there is no way to ensure the calculation is exactly 
correct except using the ROUND function?

This formula is one of the most basic ones, and it could happens anytime but 
you may not have noticed this.
Perhaps using different displaying formats can help in some cases, but it 
does not help any more if there is any checking included. For example in my 
case, I add a checking at the end like this:
F1: IF(E1=0)
I will get a FALSE value then.

Any suggestion on this?

Thank you for your attention.
0
Jensan (3)
8/2/2007 10:22:03 AM
With finite precision arithmetic (even if binary conversions were not 
involved), you cannot prevent cancellation of accuracy due to subtraction or 
division.  If the only subtraction/division is the last operation, then you 
can easily predict how much accuracy will be lost.  Other operation orders 
may lose less accuracy, but predicting the amount of accuracy left is not 
trivial in general.  

As a result, you should avoid tests like A=B, and instead use 
ABS(A-B)<epsilon, where epsilon is an appropriate tolerance for the 
particular calculation.  It is not possible to define a general epsilon that 
will work for every situation.  However, if you are only adding and 
subtractin numbers with no data beyond the nth decimal place, then you could 
use epsilon = 0.5*10^(-n), or equivalently ask whether ROUND(A-B,n)=0.

Jerry

"Jensan" wrote:

> Thanks a lot for all your replies.
> 
> So, do you mean that there is no way to ensure the calculation is exactly 
> correct except using the ROUND function?
> 
> This formula is one of the most basic ones, and it could happens anytime but 
> you may not have noticed this.
> Perhaps using different displaying formats can help in some cases, but it 
> does not help any more if there is any checking included. For example in my 
> case, I add a checking at the end like this:
> F1: IF(E1=0)
> I will get a FALSE value then.
> 
> Any suggestion on this?
> 
> Thank you for your attention.
0
post_a_reply (1395)
8/2/2007 12:12:03 PM
Thank you.

"Jerry W. Lewis" wrote:

> With finite precision arithmetic (even if binary conversions were not 
> involved), you cannot prevent cancellation of accuracy due to subtraction or 
> division.  If the only subtraction/division is the last operation, then you 
> can easily predict how much accuracy will be lost.  Other operation orders 
> may lose less accuracy, but predicting the amount of accuracy left is not 
> trivial in general.  
> 
> As a result, you should avoid tests like A=B, and instead use 
> ABS(A-B)<epsilon, where epsilon is an appropriate tolerance for the 
> particular calculation.  It is not possible to define a general epsilon that 
> will work for every situation.  However, if you are only adding and 
> subtractin numbers with no data beyond the nth decimal place, then you could 
> use epsilon = 0.5*10^(-n), or equivalently ask whether ROUND(A-B,n)=0.
> 
> Jerry
> 
> "Jensan" wrote:
> 
> > Thanks a lot for all your replies.
> > 
> > So, do you mean that there is no way to ensure the calculation is exactly 
> > correct except using the ROUND function?
> > 
> > This formula is one of the most basic ones, and it could happens anytime but 
> > you may not have noticed this.
> > Perhaps using different displaying formats can help in some cases, but it 
> > does not help any more if there is any checking included. For example in my 
> > case, I add a checking at the end like this:
> > F1: IF(E1=0)
> > I will get a FALSE value then.
> > 
> > Any suggestion on this?
> > 
> > Thank you for your attention.
0
Jensan (3)
8/3/2007 1:08:01 AM
Hi Jensan,
I'm not a .NET Developer. But i noticed it is there in excel 2007 also. One another thing that might help debugging it might be the fact that because there is a switching of signs, it is showing the error

A1-B1 is negative then you are adding two positive values to make it zero. if you just pull "-B1" to the end it will be fixed for now. 

I think microsoft should look into this. this is too silly a mistake which will be overlooked. Though it wont matter unless used in precision calculations that multiplies the value by several millions, it is quite unprofessional from microsoft part.

Regards,

Daniel



Jensa wrote:

Excel 2003 calculation bug - subtraction of 1 decimal place
01-Aug-07

Hi,

I think I have found a bug on Excel 2003, but I am not sure if it is fixed.
I have written a very simple "program" in a new clean workbook:

A1 : 30.2
B1 : 32.3
C1 : 1.1
D1 : 1
E1 : =A1-B1+C1+D1

The result is 2.22045E-15..........I suppose it should be zero.
The numbers are so simple, and the formula is straight forward enough that I 
don't think it is ignorable. I understand that using ROUND function or check 
the option "precision as display" can solve the problem, but is it a little 
bit too much to do for such simple work?

Could anyone provide me the bug fix number (if any), or any reference on 
this? 

Thank you very much.

Amazing Bug.

Jensan

EggHeadCafe - Software Developer Portal of Choice 
Sum of Numbers Captcha: Keeping it Simple
http://www.eggheadcafe.com/tutorials/aspnet/8eacfaca-3629-4d40-9d83-8eb1c526ca7f/sum-of-numbers-captcha-k.aspx
0
Daniel
10/6/2009 4:56:50 AM
Also playing with brackets you can get all sorts of answers try:
=A1-(B1+C1+D1)  or =A1-(B1+C1)+D1 or 
the answer your looking for =A1-B1+(C1+D1)

"Daniel Paul" wrote:

> Hi Jensan,
> I'm not a .NET Developer. But i noticed it is there in excel 2007 also. One another thing that might help debugging it might be the fact that because there is a switching of signs, it is showing the error
> 
> A1-B1 is negative then you are adding two positive values to make it zero. if you just pull "-B1" to the end it will be fixed for now. 
> 
> I think microsoft should look into this. this is too silly a mistake which will be overlooked. Though it wont matter unless used in precision calculations that multiplies the value by several millions, it is quite unprofessional from microsoft part.
> 
> Regards,
> 
> Daniel
> 
> 
> 
> Jensa wrote:
> 
> Excel 2003 calculation bug - subtraction of 1 decimal place
> 01-Aug-07
> 
> Hi,
> 
> I think I have found a bug on Excel 2003, but I am not sure if it is fixed.
> I have written a very simple "program" in a new clean workbook:
> 
> A1 : 30.2
> B1 : 32.3
> C1 : 1.1
> D1 : 1
> E1 : =A1-B1+C1+D1
> 
> The result is 2.22045E-15..........I suppose it should be zero.
> The numbers are so simple, and the formula is straight forward enough that I 
> don't think it is ignorable. I understand that using ROUND function or check 
> the option "precision as display" can solve the problem, but is it a little 
> bit too much to do for such simple work?
> 
> Could anyone provide me the bug fix number (if any), or any reference on 
> this? 
> 
> Thank you very much.
> 
> Amazing Bug.
> 
> Jensan
> 
> EggHeadCafe - Software Developer Portal of Choice 
> Sum of Numbers Captcha: Keeping it Simple
> http://www.eggheadcafe.com/tutorials/aspnet/8eacfaca-3629-4d40-9d83-8eb1c526ca7f/sum-of-numbers-captcha-k.aspx
> 
0
RonBuy (107)
10/6/2009 6:00:03 AM
Read this:

http://support.microsoft.com/kb/78113

-- 
Kind regards,

Niek Otten
Microsoft MVP - Excel

"Daniel Paul" wrote in message news:200910605650danielpaul007@gmail.com...
> Hi Jensan,
> I'm not a .NET Developer. But i noticed it is there in excel 2007 also. 
> One another thing that might help debugging it might be the fact that 
> because there is a switching of signs, it is showing the error
>
> A1-B1 is negative then you are adding two positive values to make it zero. 
> if you just pull "-B1" to the end it will be fixed for now.
>
> I think microsoft should look into this. this is too silly a mistake which 
> will be overlooked. Though it wont matter unless used in precision 
> calculations that multiplies the value by several millions, it is quite 
> unprofessional from microsoft part.
>
> Regards,
>
> Daniel
>
>
>
> Jensa wrote:
>
> Excel 2003 calculation bug - subtraction of 1 decimal place
> 01-Aug-07
>
> Hi,
>
> I think I have found a bug on Excel 2003, but I am not sure if it is 
> fixed.
> I have written a very simple "program" in a new clean workbook:
>
> A1 : 30.2
> B1 : 32.3
> C1 : 1.1
> D1 : 1
> E1 : =A1-B1+C1+D1
>
> The result is 2.22045E-15..........I suppose it should be zero.
> The numbers are so simple, and the formula is straight forward enough that 
> I
> don't think it is ignorable. I understand that using ROUND function or 
> check
> the option "precision as display" can solve the problem, but is it a 
> little
> bit too much to do for such simple work?
>
> Could anyone provide me the bug fix number (if any), or any reference on
> this?
>
> Thank you very much.
>
> Amazing Bug.
>
> Jensan
>
> EggHeadCafe - Software Developer Portal of Choice
> Sum of Numbers Captcha: Keeping it Simple
> http://www.eggheadcafe.com/tutorials/aspnet/8eacfaca-3629-4d40-9d83-8eb1c526ca7f/sum-of-numbers-captcha-k.aspx 

0
nicolaus (2022)
10/6/2009 7:37:01 AM
Reply:

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