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[mathcad] RE: [mathcad]Re: Rounding up/down error

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[mathcad] RE: [mathcad]Re: Rounding up/down error
Author: Sander Lablans    Posted: Tue, 15 Jul 2003 11:01:08 +0200
Well, the problem isn't that actually. I know about hidden digits. The fact is that I DEFINED a variable with: dp := 0.04425 N/mm^2 Therefore, I know that there are NO other digits after the 5. But for my report, I have to use 4 digits instead of 5 (due to conformance throughout the document). It was then that I found out about this strange occurence. I do have to say that I think Chris does have the answer to this strange behavior. I am no MathCad specialist, so I have to take his word for it that MathCad uses a 52-bit normalised mantissa. But it would make sense. In fact: if I change the value of 0.04425 to 0.05425 it is rounded to 0.0542, changing it to 0.06425, it gets rounded to 0.0643. If I change this first non-zero digit from 0 to 9, I get a rather arbitrarily behavior of the last digit, which would point to Chris' explanation. Sander -----Original Message----- From: Markos E. Psarros /> Sent: dinsdag 15 juli 2003 10:28 To: Mathcad Discussion List Subject: [mathcad] [mathcad]Re: Rounding up/down error Dear Sander Have you checked what is the ACTUAL number that underlies 0.04425? If in 6 decimal points accuracy it was 0.044248 it would round in 5 digits as 0.04425 (48 turns to 50) but if it was round to 4 digits it would give 0.0442 (because 248 rounds to 200 since it is NOT more than 250)!! That for, check the result in 6 or even 8 digits accuracy and you'll see! Markos *********** REPLY SEPARATOR *********** On 15/7/2003 at 9:12 pl Sander Lablans wrote: [Edit] and now with attachment... [Edit] Hello list, I have been using a calculation with a number of 0.04425 N/mm^2. However, I noticed a strange behavior when I modified the properties of a result to show me 4 digits. Normally, it would then show me 0.0443 as a 5 always rounds up. However, as you can see in the attached mathcad-sheet, MathCad decides that it does not want to show 0.0443, but 0.0442. I have been playing with a few other numbers, but this is the only one I have found. Can someone tell me, whether this is a bug in MathCad, or that there is an option included in MathCad that makes sure that some results are rounded to a different value? (Or perhaps someone else has encountered the same rounding error somewhere else...) Regards, Sander Lablans --------------------------------- NedTech Engineering B.V. The Netherlands **********END OF INITIAL MESSAGE******* --- The Mathcad List - Discussion, Support & News Contributions: /> Hosted by: Adept Scientific http://www.adeptscience.com List Archive: http://lists.adeptscience.co.uk/ --- Would you like this to come to a different email address? --- Simply leave the mailing list (see below) and re-join by sending a blank email from the new address to: or --- If you do not want to be on the Mathcad list, simply send a blank email (no subject or message needed) to: /> Dr. Markos E. Psarros Ph.D. Civil Engineering General Manager Software Imports and Sales MP & Associates 33 Skoufa Str. ATHENS 106 73 GREECE Tel: +30-210-3633977 Fax: +30-210-3617108 e-mail: /> http://www.mpassociates.gr --- The Mathcad List - Discussion, Support & News Contributions: /> Hosted by: Adept Scientific http://www.adeptscience.com List Archive: http://lists.adeptscience.co.uk/ --- Would you like this to come to a different email address? --- Simply leave the mailing list (see below) and re-join by sending a blank email from the new address to: or --- If you do not want to be on the Mathcad list, simply send a blank email (no subject or message needed) to: />

[mathcad] RE: [mathcad]Re: Rounding up/down error
Author: Dan Khoushy Ph D    Posted: Tue, 15 Jul 2003 10:50:02 +0100
If it were to be true then any instance of 0.04425 will round incorrectly, which is not the case. Just write x:=0.0425 and then x= and format the results to 5 digits and you will get exactly x=0.04425. 52-bit normalised mantissa should be quite enough. If Sandra will let us have her worksheet maybe we can solve the mystery. Best Regards, Dan -----Original Message----- From: Sander Lablans Sent: Tuesday, July 15, 2003 10:01 To: Mathcad Discussion List Subject: [mathcad] RE: [mathcad]Re: Rounding up/down error Well, the problem isn't that actually. I know about hidden digits. The fact is that I DEFINED a variable with: dp := 0.04425 N/mm^2 Therefore, I know that there are NO other digits after the 5. But for my report, I have to use 4 digits instead of 5 (due to conformance throughout the document). It was then that I found out about this strange occurence. I do have to say that I think Chris does have the answer to this strange behavior. I am no MathCad specialist, so I have to take his word for it that MathCad uses a 52-bit normalised mantissa. But it would make sense. In fact: if I change the value of 0.04425 to 0.05425 it is rounded to 0.0542, changing it to 0.06425, it gets rounded to 0.0643. If I change this first non-zero digit from 0 to 9, I get a rather arbitrarily behavior of the last digit, which would point to Chris' explanation. Sander -----Original Message----- From: Markos E. Psarros /> Sent: dinsdag 15 juli 2003 10:28 To: Mathcad Discussion List Subject: [mathcad] [mathcad]Re: Rounding up/down error Dear Sander Have you checked what is the ACTUAL number that underlies 0.04425? If in 6 decimal points accuracy it was 0.044248 it would round in 5 digits as 0.04425 (48 turns to 50) but if it was round to 4 digits it would give 0.0442 (because 248 rounds to 200 since it is NOT more than 250)!! That for, check the result in 6 or even 8 digits accuracy and you'll see! Markos *********** REPLY SEPARATOR *********** On 15/7/2003 at 9:12 pl Sander Lablans wrote: [Edit] and now with attachment... [Edit] Hello list, I have been using a calculation with a number of 0.04425 N/mm^2. However, I noticed a strange behavior when I modified the properties of a result to show me 4 digits. Normally, it would then show me 0.0443 as a 5 always rounds up. However, as you can see in the attached mathcad-sheet, MathCad decides that it does not want to show 0.0443, but 0.0442. I have been playing with a few other numbers, but this is the only one I have found. Can someone tell me, whether this is a bug in MathCad, or that there is an option included in MathCad that makes sure that some results are rounded to a different value? (Or perhaps someone else has encountered the same rounding error somewhere else...) Regards, Sander Lablans --------------------------------- NedTech Engineering B.V. The Netherlands **********END OF INITIAL MESSAGE******* --- The Mathcad List - Discussion, Support & News Contributions: /> Hosted by: Adept Scientific http://www.adeptscience.com List Archive: http://lists.adeptscience.co.uk/ --- Would you like this to come to a different email address? --- Simply leave the mailing list (see below) and re-join by sending a blank email from the new address to: or --- If you do not want to be on the Mathcad list, simply send a blank email (no subject or message needed) to: Dr. Markos E. Psarros Ph.D. Civil Engineering General Manager Software Imports and Sales MP & Associates 33 Skoufa Str. ATHENS 106 73 GREECE Tel: +30-210-3633977 Fax: +30-210-3617108 e-mail: /> http://www.mpassociates.gr --- The Mathcad List - Discussion, Support & News Contributions: /> Hosted by: Adept Scientific http://www.adeptscience.com List Archive: http://lists.adeptscience.co.uk/ --- Would you like this to come to a different email address? --- Simply leave the mailing list (see below) and re-join by sending a blank email from the new address to: or --- If you do not want to be on the Mathcad list, simply send a blank email (no subject or message needed) to: --- The Mathcad List - Discussion, Support & News Contributions: /> Hosted by: Adept Scientific http://www.adeptscience.com List Archive: http://lists.adeptscience.co.uk/ --- Would you like this to come to a different email address? --- Simply leave the mailing list (see below) and re-join by sending a blank email from the new address to: or --- If you do not want to be on the Mathcad list, simply send a blank email (no subject or message needed) to: />

[mathcad] RE: [mathcad]Re: Rounding up/down error
Author: Chris Whitford    Posted: Tue, 15 Jul 2003 11:19:57 +0100
This can lead to unexpected behaviour. Consider if the internal representation is 0.0442499999... Then to 4 places it will become 0.0442 while for 5 or more places it will become 0.0442500... and Mathcad drops the trailing zeroes. Try it! Chris At 10:50 15/07/2003 +0100, you wrote: >If it were to be true then any instance of 0.04425 will round incorrectly, >which is not the case. Just write x:=0.0425 and then x= and format the >results to 5 digits and you will get exactly x=0.04425. > > > >52-bit normalised mantissa should be quite enough. +------------------------------------------------------------------+ + Chris Whitford University of Leicester + + Research Fellow Space Research Centre + + Tel: +44 (0)116 252 3496 Physics and Astronomy Department + + Fax: +44 (0)116 252 2464 University Road + + email: LEICESTER LE1 7RH + + http://www.star.le.ac.uk/ UK + +------------------------------------------------------------------+ --- The Mathcad List - Discussion, Support & News Contributions: /> Hosted by: Adept Scientific http://www.adeptscience.com List Archive: http://lists.adeptscience.co.uk/ --- Would you like this to come to a different email address? --- Simply leave the mailing list (see below) and re-join by sending a blank email from the new address to: or --- If you do not want to be on the Mathcad list, simply send a blank email (no subject or message needed) to: />

[mathcad] RE: [mathcad]Re: Rounding up/down error
Author: Markos E Psarros    Posted: Tue, 15 Jul 2003 13:17:46 +0300
Did you check the units that you are using? What is the Units system that is defined as default in your worksheet? Maybe there is a roundoff error in transforming numbers from one unit system to the other! Markos *********** REPLY SEPARATOR *********** On 15/7/2003 at 11:01 ðì Sander Lablans wrote: Well, the problem isn't that actually. I know about hidden digits. The fact is that I DEFINED a variable with: dp := 0.04425 N/mm^2 Therefore, I know that there are NO other digits after the 5. But for my report, I have to use 4 digits instead of 5 (due to conformance throughout the document). It was then that I found out about this strange occurence. I do have to say that I think Chris does have the answer to this strange behavior. I am no MathCad specialist, so I have to take his word for it that MathCad uses a 52-bit normalised mantissa. But it would make sense. In fact: if I change the value of 0.04425 to 0.05425 it is rounded to 0.0542, changing it to 0.06425, it gets rounded to 0.0643. If I change this first non-zero digit from 0 to 9, I get a rather arbitrarily behavior of the last digit, which would point to Chris' explanation. Sander -----Original Message----- From: Markos E. Psarros /> Sent: dinsdag 15 juli 2003 10:28 To: Mathcad Discussion List Subject: [mathcad] [mathcad]Re: Rounding up/down error Dear Sander Have you checked what is the ACTUAL number that underlies 0.04425? If in 6 decimal points accuracy it was 0.044248 it would round in 5 digits as 0.04425 (48 turns to 50) but if it was round to 4 digits it would give 0.0442 (because 248 rounds to 200 since it is NOT more than 250)!! That for, check the result in 6 or even 8 digits accuracy and you'll see! Markos *********** REPLY SEPARATOR *********** On 15/7/2003 at 9:12 pl Sander Lablans wrote: [Edit] and now with attachment... [Edit] Hello list, I have been using a calculation with a number of 0.04425 N/mm^2. However, I noticed a strange behavior when I modified the properties of a result to show me 4 digits. Normally, it would then show me 0.0443 as a 5 always rounds up. However, as you can see in the attached mathcad-sheet, MathCad decides that it does not want to show 0.0443, but 0.0442. I have been playing with a few other numbers, but this is the only one I have found. Can someone tell me, whether this is a bug in MathCad, or that there is an option included in MathCad that makes sure that some results are rounded to a different value? (Or perhaps someone else has encountered the same rounding error somewhere else...) Regards, Sander Lablans --------------------------------- NedTech Engineering B.V. The Netherlands **********END OF INITIAL MESSAGE******* --- The Mathcad List - Discussion, Support & News Contributions: /> Hosted by: Adept Scientific http://www.adeptscience.com List Archive: http://lists.adeptscience.co.uk/ --- Would you like this to come to a different email address? --- Simply leave the mailing list (see below) and re-join by sending a blank email from the new address to: or --- If you do not want to be on the Mathcad list, simply send a blank email (no subject or message needed) to: /> Dr. Markos E. Psarros Ph.D. Civil Engineering General Manager Software Imports and Sales MP & Associates 33 Skoufa Str. ATHENS 106 73 GREECE Tel: +30-210-3633977 Fax: +30-210-3617108 e-mail: /> http://www.mpassociates.gr --- The Mathcad List - Discussion, Support & News Contributions: /> Hosted by: Adept Scientific http://www.adeptscience.com List Archive: http://lists.adeptscience.co.uk/ --- Would you like this to come to a different email address? --- Simply leave the mailing list (see below) and re-join by sending a blank email from the new address to: or --- If you do not want to be on the Mathcad list, simply send a blank email (no subject or message needed) to: /> **********END OF INITIAL MESSAGE******* --- The Mathcad List - Discussion, Support & News Contributions: /> Hosted by: Adept Scientific http://www.adeptscience.com List Archive: http://lists.adeptscience.co.uk/ --- Would you like this to come to a different email address? --- Simply leave the mailing list (see below) and re-join by sending a blank email from the new address to: or --- If you do not want to be on the Mathcad list, simply send a blank email (no subject or message needed) to: />

[mathcad] RE: [mathcad]Re: Rounding up/down error
Author: Bruff, Stuart    Posted: Tue, 15 Jul 2003 12:58:53 +0100
Sander Does the attached file help any? Both Axum and Matlab round the number down. Excel rounds it up. Stuart Stuart Bruff Senior Systems Engineer Studies Group Alenia Marconi Systems Limited Lyon Way, Frimley, Camberley, Surrey. GU16 7EX United Kingdom GNET : 822-5604 Tel No: +44(0)1276-468604 EMAIL: -----Original Message----- From: Sander Lablans /> Sent: Tuesday, July 15, 2003 10:01 To: Mathcad Discussion List Subject: [mathcad] RE: [mathcad]Re: Rounding up/down error *** WARNING *** This mail has originated outside your organization, either from an external partner or the Global Internet. Keep this in mind if you answer this message. Well, the problem isn't that actually. I know about hidden digits. The fact is that I DEFINED a variable with: dp := 0.04425 N/mm^2 Therefore, I know that there are NO other digits after the 5. But for my report, I have to use 4 digits instead of 5 (due to conformance throughout the document). It was then that I found out about this strange occurence. I do have to say that I think Chris does have the answer to this strange behavior. I am no MathCad specialist, so I have to take his word for it that MathCad uses a 52-bit normalised mantissa. But it would make sense. In fact: if I change the value of 0.04425 to 0.05425 it is rounded to 0.0542, changing it to 0.06425, it gets rounded to 0.0643. If I change this first non-zero digit from 0 to 9, I get a rather arbitrarily behavior of the last digit, which would point to Chris' explanation. Sander ******************************************************************** This email and any attachments are confidential to the intended recipient and may also be privileged. If you are not the intended recipient please delete it from your system and notify the sender. You should not copy it or use it for any purpose nor disclose or distribute its contents to any other person. ********************************************************************
Attachments:  Numeric Roundoff.mcd

[mathcad] RE: [mathcad]Re: Rounding up/down error
Author: Radovan P Omorjan    Posted: Wed, 16 Jul 2003 14:13:56 +0200
Hi Sander and others, I might missing something but consider this (Mcad 2001) If you define a variable x := 0.32245 and format the result (Format=>Result) with 4 decimal places you will get x = 0.3224 but if you take y := round(x,4) you will get y = 0.3225 formating the result with more or equal to 4 decimal places. I consider this as a Mathcad problem. Radovan On 15 Jul 2003 at 11:19, Chris Whitford wrote: > > This can lead to unexpected behaviour. Consider if the internal representation is 0.0442499999... > Then to 4 places it will become 0.0442 while for 5 or more places it will become 0.0442500... > and Mathcad drops the trailing zeroes. Try it! > > Chris --- The Mathcad List - Discussion, Support & News Contributions: /> Hosted by: Adept Scientific http://www.adeptscience.com List Archive: http://lists.adeptscience.co.uk/ --- Would you like this to come to a different email address? --- Simply leave the mailing list (see below) and re-join by sending a blank email from the new address to: or --- If you do not want to be on the Mathcad list, simply send a blank email (no subject or message needed) to: />

[mathcad] RE: [mathcad]Re: Rounding up/down error
Author: Chris Whitford    Posted: Wed, 16 Jul 2003 14:14:11 +0100
It would appear that the algorithm for displaying numbers, and for the "round" function, are different. As another example, write x:=0.32245 y:=x.10000 y=3225 (displayed with no decimal places) y = 3.224 * 10^3 (general format) However, I don't think this is a bug. One must never assume that any real number is exact; there is always the possibility of rounding error. These examples just highlight that in a very direct way. Chris At 14:13 16/07/2003 +0200, you wrote: >I might missing something but consider this (Mcad 2001) >If you define a variable x := 0.32245 and format the result >(Format=>Result) with 4 >decimal places you will get >x = 0.3224 >but if you take y := round(x,4) you will get >y = 0.3225 >formating the result with more or equal to 4 decimal places. >I consider this as a Mathcad problem. +------------------------------------------------------------------+ + Chris Whitford University of Leicester + + Research Fellow Space Research Centre + + Tel: +44 (0)116 252 3496 Physics and Astronomy Department + + Fax: +44 (0)116 252 2464 University Road + + email: LEICESTER LE1 7RH + + http://www.star.le.ac.uk/ UK + +------------------------------------------------------------------+ --- The Mathcad List - Discussion, Support & News Contributions: /> Hosted by: Adept Scientific http://www.adeptscience.com List Archive: http://lists.adeptscience.co.uk/ --- Would you like this to come to a different email address? --- Simply leave the mailing list (see below) and re-join by sending a blank email from the new address to: or --- If you do not want to be on the Mathcad list, simply send a blank email (no subject or message needed) to: />

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