Re: [Haskell-cafe] Why 'round' does not just round numbers ?
On Mon, 27 Oct 2008, L.Guo wrote: I think this is unresonable. then try it in GHC 6.8.3. Prelude round 3.5 4 Prelude round 2.5 2 Is there any explanation about that ? It's the definition we learnt in school ... I think one reason is that repeated rounding should not be worse than rounding in one go. Consider the rule 'use ceiling when the first removed digit is 5'. Then 0.45 - (round to one place) - 0.5 - (round to integer) - 1 but 0.45 - (round to integer) - 0 This is avoided by the school definition. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
RE: [Haskell-cafe] Why 'round' does not just round numbers ?
Hi, That is a fairly standard implementation of rounding for financial institutions. Consider sum . map round Over the list [3.5,2.5] With rounding to the nearest even integer for 0.5's you get 6, otherwise if you always round up you get 7. If you bias towards rounding up you get a general upwards trend as numbers are rounded, which is bad, while the even condition ensures that statistically it averages to the same thing. For more details see: http://en.wikipedia.org/wiki/Rounding#Round-to-even_method Thanks Neil -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of L.Guo Sent: 27 October 2008 9:49 am To: MailList Haskell-Cafe Subject: [Haskell-cafe] Why 'round' does not just round numbers ? Hi all: I just read about definitions of Prelude [1], and noticing that. In 6.4.6 Coercions and Component Extraction, it discribes like this: round x returns the nearest integer to x, the even integer if x is equidistant between two integers. I think this is unresonable. then try it in GHC 6.8.3. Prelude round 3.5 4 Prelude round 2.5 2 Is there any explanation about that ? [1] The Haskell 98 Report: Predefined Types and Classes http://haskell.org/onlinereport/basic.html Regards -- L.Guo 2008-10-27 ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe == Please access the attached hyperlink for an important electronic communications disclaimer: http://www.credit-suisse.com/legal/en/disclaimer_email_ib.html == ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
Henning Thielemann wrote: On Mon, 27 Oct 2008, L.Guo wrote: I think this is unresonable. then try it in GHC 6.8.3. Prelude round 3.5 4 Prelude round 2.5 2 Is there any explanation about that ? It's the definition we learnt in school ... Hmm, Henning, this is strange. The two of us went to the very same school, but I know for a fact that I learnt 2.5 to round to 3, not 2 as above. ;-) I think one reason is that repeated rounding should not be worse than rounding in one go. Consider the rule 'use ceiling when the first removed digit is 5'. Then 0.45 - (round to one place) - 0.5 - (round to integer) - 1 but 0.45 - (round to integer) - 0 That is of course true (and was the topic of heated discussion with my fourth grade math teacher), but does not explain 2.5 - 2. Ciao, Janis. -- Dr. Janis Voigtlaender http://wwwtcs.inf.tu-dresden.de/~voigt/ mailto:[EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
On Mon, 27 Oct 2008, Janis Voigtlaender wrote: Henning Thielemann wrote: On Mon, 27 Oct 2008, L.Guo wrote: I think this is unresonable. then try it in GHC 6.8.3. Prelude round 3.5 4 Prelude round 2.5 2 Is there any explanation about that ? It's the definition we learnt in school ... Hmm, Henning, this is strange. The two of us went to the very same school, but I know for a fact that I learnt 2.5 to round to 3, not 2 as above. ;-) I meant the school before GCG! :-] So it seems to differ between schools and even teachers. (Much like the question whether zero should be counted as natural number or not.) I think one reason is that repeated rounding should not be worse than rounding in one go. Consider the rule 'use ceiling when the first removed digit is 5'. Then 0.45 - (round to one place) - 0.5 - (round to integer) - 1 but 0.45 - (round to integer) - 0 That is of course true (and was the topic of heated discussion with my fourth grade math teacher), but does not explain 2.5 - 2. Because doing otherwise would be odd rounding. ;-) ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
(Janis, sorry for e-mailiing just for you on the first time.) On Mon, Oct 27, 2008 at 8:15 AM, Janis Voigtlaender [EMAIL PROTECTED] wrote: That is of course true (and was the topic of heated discussion with my fourth grade math teacher), but does not explain 2.5 - 2. If you round to odd instead of round to even, then 4.5 rounds to 5, which would may need rounding again and introduce double rounding errors. For a simple example, 2.45 - 2.4 - 2 2.45 - 2.5 - 3 The Wikipedia article that was linked in this thread talks about this problem as well. -- Felipe. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
Felipe Lessa wrote: On Mon, Oct 27, 2008 at 8:15 AM, Janis Voigtlaender [EMAIL PROTECTED] wrote: That is of course true (and was the topic of heated discussion with my fourth grade math teacher), but does not explain 2.5 - 2. If you round to odd instead of round to even, then 4.5 rounds to 5, Well, of course I did not learn to round to odd. I learned to round .5 to above, but not to do repeated rounding. So we would never have either of 2.45 - 2.4 - 2 2.45 - 2.5 - 3 as you suggest. Instead, always in one go: 2.45 - 2 Because of the 4, whereas any digit following it would be ignored: 2.4x - x In fact, by your explanation, you would have: 3.46 - 3.5 - 4 Which is most odd. 3.46 is definitely closer to 3 than to 4. -- Dr. Janis Voigtlaender http://wwwtcs.inf.tu-dresden.de/~voigt/ mailto:[EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
Janis Voigtlaender wrote: 2.4x - x That's supposed to be 2.4x - 2, of course. -- Dr. Janis Voigtlaender http://wwwtcs.inf.tu-dresden.de/~voigt/ mailto:[EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
On Mon, Oct 27, 2008 at 8:30 AM, Janis Voigtlaender [EMAIL PROTECTED] wrote: Well, of course I did not learn to round to odd. I learned to round .5 to above, but not to do repeated rounding. Nobody rounds in passes, of course =). I was talking about two successive rounds. In fact, by your explanation, you would have: 3.46 - 3.5 - 4 Which is most odd. 3.46 is definitely closer to 3 than to 4. If you're doing a double rounding, then this error will always happen. Round to even avoids this error when the last digit was a 5, which is good. -- Felipe. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
Henning Thielemann wrote: I think one reason is that repeated rounding should not be worse than rounding in one go. Consider the rule 'use ceiling when the first removed digit is 5'. Then 0.45 - (round to one place) - 0.5 - (round to integer) - 1 But repeated rounding *is* worse than rounding in one go, under any reasonable scheme: 3.46 - 3.5 - 4 vs. 3.46 - 3 That was actually the debate with that teacher. Unbelievable as that still is to me today, she advocated the 3.46 - 3.5 - 4 route... And yes, Henning, you are right, we didn't yet share school in fourth grade when rounding was taught. Ciao, Janis. -- Dr. Janis Voigtlaender http://wwwtcs.inf.tu-dresden.de/~voigt/ mailto:[EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
Felipe Lessa wrote: On Mon, Oct 27, 2008 at 8:30 AM, Janis Voigtlaender [EMAIL PROTECTED] wrote: Well, of course I did not learn to round to odd. I learned to round .5 to above, but not to do repeated rounding. Nobody rounds in passes, of course =). Oh, Mrs. I forgot her name actually did ;-) -- Dr. Janis Voigtlaender http://wwwtcs.inf.tu-dresden.de/~voigt/ mailto:[EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
On Mon, 27 Oct 2008, Janis Voigtlaender wrote: Henning Thielemann wrote: I think one reason is that repeated rounding should not be worse than rounding in one go. Consider the rule 'use ceiling when the first removed digit is 5'. Then 0.45 - (round to one place) - 0.5 - (round to integer) - 1 But repeated rounding *is* worse than rounding in one go, under any reasonable scheme: 3.46 - 3.5 - 4 With the rounding-to-even route this would be 3.46 - 3.4 - 3 so rounding in passes is no worse than rounding in one go for this example. vs. 3.46 - 3 That was actually the debate with that teacher. Unbelievable as that still is to me today, she advocated the 3.46 - 3.5 - 4 route ... I also know a didact which tells teachers that 1 has no prime decomposition. Oh, I see, she may have copied that from Wikipedia: http://en.wikipedia.org/wiki/Prime_factorisation ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
Janis Voigtlaender [EMAIL PROTECTED] writes: If you round to odd instead of round to even, then 4.5 rounds to 5, Well, of course I did not learn to round to odd. I learned to round .5 to above, but not to do repeated rounding. Since just about every floating point operation involves some sort of loss of precision, repeated rounding is a fact of life. Or use rationals. -k -- If I haven't seen further, it is by standing in the footprints of giants ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
Am Montag, 27. Oktober 2008 11:46 schrieb Henning Thielemann: On Mon, 27 Oct 2008, Janis Voigtlaender wrote: Henning Thielemann wrote: I think one reason is that repeated rounding should not be worse than rounding in one go. Consider the rule 'use ceiling when the first removed digit is 5'. Then 0.45 - (round to one place) - 0.5 - (round to integer) - 1 But repeated rounding *is* worse than rounding in one go, under any reasonable scheme: 3.46 - 3.5 - 4 With the rounding-to-even route this would be 3.46 - 3.4 - 3 Wait, that cannot be. 6 5, so 3.46 - 3.5 even with banker's rounding. so rounding in passes is no worse than rounding in one go for this example. Rounding in passes is bad per se, because there are pretty large intervals where that gives a different result from a direct rounding. vs. 3.46 - 3 That was actually the debate with that teacher. Unbelievable as that still is to me today, she advocated the 3.46 - 3.5 - 4 route ... I also know a didact which tells teachers that 1 has no prime decomposition. Oh, I see, she may have copied that from Wikipedia: http://en.wikipedia.org/wiki/Prime_factorisation I can believe that makes sense to somebody who considers 0 an unnatural number, an empty product must be frightening for them. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
On Mon, 27 Oct 2008, Daniel Fischer wrote: Am Montag, 27. Oktober 2008 11:46 schrieb Henning Thielemann: On Mon, 27 Oct 2008, Janis Voigtlaender wrote: Henning Thielemann wrote: I think one reason is that repeated rounding should not be worse than rounding in one go. Consider the rule 'use ceiling when the first removed digit is 5'. Then 0.45 - (round to one place) - 0.5 - (round to integer) - 1 But repeated rounding *is* worse than rounding in one go, under any reasonable scheme: 3.46 - 3.5 - 4 With the rounding-to-even route this would be 3.46 - 3.4 - 3 Wait, that cannot be. 6 5, so 3.46 - 3.5 even with banker's rounding. You are right, my oversight. So only the method helps, that the last digit is marked, whether it was generated by rounding up or down. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
Ketil Malde wrote: Janis Voigtlaender [EMAIL PROTECTED] writes: If you round to odd instead of round to even, then 4.5 rounds to 5, Well, of course I did not learn to round to odd. I learned to round .5 to above, but not to do repeated rounding. Since just about every floating point operation involves some sort of loss of precision, repeated rounding is a fact of life. Of course. But that was not the point of the discussion... -- Dr. Janis Voigtlaender http://wwwtcs.inf.tu-dresden.de/~voigt/ mailto:[EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
2008/10/27 Janis Voigtlaender [EMAIL PROTECTED]: Janis Voigtlaender wrote: 2.4x - x That's supposed to be 2.4x - 2, of course. Ah, damn it. I was hoping for a long discussion on just what math would look like with rounding like that ;-) /M -- Magnus Therning(OpenPGP: 0xAB4DFBA4) magnus＠therning．org Jabber: magnus＠therning．org http://therning.org/magnus identi.ca|twitter: magthe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
It is certainly what I learnt in school. But that was another school. On Mon, Oct 27, 2008 at 12:15 PM, Janis Voigtlaender [EMAIL PROTECTED] wrote: Henning Thielemann wrote: On Mon, 27 Oct 2008, L.Guo wrote: I think this is unresonable. then try it in GHC 6.8.3. Prelude round 3.5 4 Prelude round 2.5 2 Is there any explanation about that ? It's the definition we learnt in school ... Hmm, Henning, this is strange. The two of us went to the very same school, but I know for a fact that I learnt 2.5 to round to 3, not 2 as above. ;-) I think one reason is that repeated rounding should not be worse than rounding in one go. Consider the rule 'use ceiling when the first removed digit is 5'. Then 0.45 - (round to one place) - 0.5 - (round to integer) - 1 but 0.45 - (round to integer) - 0 That is of course true (and was the topic of heated discussion with my fourth grade math teacher), but does not explain 2.5 - 2. Ciao, Janis. -- Dr. Janis Voigtlaender http://wwwtcs.inf.tu-dresden.de/~voigt/ mailto:[EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
Lennart Augustsson wrote: It is certainly what I learnt in school. But that was another school. Hmm, on reflection, taking Neil's explanation into account and the fact that this rounding mode was referred to as banker's rounding, the point may be that it was not only another school, but another world (politically, pre-'89 ;-). -- Dr. Janis Voigtlaender http://wwwtcs.inf.tu-dresden.de/~voigt/ mailto:[EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
I can't remember the method being called anything. It was just what we were being taught. With the obvious explanation that .5 is right in the middle so always going one way would introduce a bias. This was circa 1969. On Mon, Oct 27, 2008 at 3:30 PM, Janis Voigtlaender [EMAIL PROTECTED] wrote: Lennart Augustsson wrote: It is certainly what I learnt in school. But that was another school. Hmm, on reflection, taking Neil's explanation into account and the fact that this rounding mode was referred to as banker's rounding, the point may be that it was not only another school, but another world (politically, pre-'89 ;-). -- Dr. Janis Voigtlaender http://wwwtcs.inf.tu-dresden.de/~voigt/ mailto:[EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
Lennart Augustsson wrote: I can't remember the method being called anything. It was just what we were being taught. With the obvious explanation that .5 is right in the middle so always going one way would introduce a bias. This was circa 1969. Well, I wasn't serious about the political explanation. And yes, the avoiding bias explanation makes sense, but not the this way of rounding makes repeated rounding safe explanation. -- Dr. Janis Voigtlaender http://wwwtcs.inf.tu-dresden.de/~voigt/ mailto:[EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
On Mon, Oct 27, 2008 at 9:48 AM, L.Guo [EMAIL PROTECTED] wrote: Hi all: I just read about definitions of Prelude [1], and noticing that. In 6.4.6 Coercions and Component Extraction, it discribes like this: round x returns the nearest integer to x, the even integer if x is equidistant between two integers. I think this is unresonable. then try it in GHC 6.8.3. Prelude round 3.5 4 Prelude round 2.5 2 Is there any explanation about that ? [1] The Haskell 98 Report: Predefined Types and Classes http://haskell.org/onlinereport/basic.html This behaviour is not what I expect after reading the description at http://haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html#v:round . Given that this behaviour has caused a bit of confusion I think a change to the documention might be in order. /M -- Magnus Therning(OpenPGP: 0xAB4DFBA4) magnus＠therning．org Jabber: magnus＠therning．org http://therning.org/magnus identi.ca|twitter: magthe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
On Mon, Oct 27, 2008 at 1:37 PM, Lennart Augustsson [EMAIL PROTECTED] wrote: I can't remember the method being called anything. It was just what we were being taught. With the obvious explanation that .5 is right in the middle so always going one way would introduce a bias. This was circa 1969. By the time I was in the Swedish school system that seems to have changed. I had never heard of this method of rounding before reading this thread :-) /M -- Magnus Therning(OpenPGP: 0xAB4DFBA4) magnus＠therning．org Jabber: magnus＠therning．org http://therning.org/magnus identi.ca|twitter: magthe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
[1] The Haskell 98 Report: Predefined Types and Classes http://haskell.org/onlinereport/basic.html This behaviour is not what I expect after reading the description at http://haskell.org/ghc/docs/latest/html/libraries/base/ Prelude.html#v:round . Given that this behaviour has caused a bit of confusion I think a change to the documention might be in order. Given that the documentation says round x returns the nearest integer to x, I think pretty much any behavior can be expected -- there's no single integer nearest to 2.5. The documentation certainly needs updated though. Bob___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
On 2008 Oct 27, at 6:00, Henning Thielemann wrote: On Mon, 27 Oct 2008, L.Guo wrote: I think this is unresonable. then try it in GHC 6.8.3. Prelude round 3.5 4 Prelude round 2.5 2 Is there any explanation about that ? It's the definition we learnt in school ... Maybe you did; I learned 5/9 rounding. -- brandon s. allbery [solaris,freebsd,perl,pugs,haskell] [EMAIL PROTECTED] system administrator [openafs,heimdal,too many hats] [EMAIL PROTECTED] electrical and computer engineering, carnegie mellon universityKF8NH ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
Janis Voigtlaender [EMAIL PROTECTED] writes: Since just about every floating point operation involves some sort of loss of precision, repeated rounding is a fact of life. Of course. But that was not the point of the discussion... Well, allow me to contribute to keeping the discussion on topic by stating that when I was in school, I was taught to round up. Now if you will excuse a momentary digression: The point *I* wanted to make is that we have two qualitatively different rounding modes: round up on 0.5, or round to even (or randomly, or alternating), and they make sense in different contexts. Doing computations with fixed precision, you keep losing precision, and rounding bias accumulates - thus the need to use some non-biased rounding. Doing (small scale) calculations on paper, you can avoid repeated rounding, and only round the result. In which case rounding up is okay, you don't introduce the amount of bias as with repeated rounding. And if your input happens to be truncated, rounding up becomes the right thing to do. Of course, Haskell should discard the rather tasteless IEEE754 crud, and do its calculations on infinite streams of digits. Then, rounding upwards after 'take'ing a sufficient amount of decimals will be the right thing to do. -k -- If I haven't seen further, it is by standing in the footprints of giants ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
Ketil Malde wrote: Janis Voigtlaender [EMAIL PROTECTED] writes: Since just about every floating point operation involves some sort of loss of precision, repeated rounding is a fact of life. Of course. But that was not the point of the discussion... Well, allow me to contribute to keeping the discussion on topic by stating that when I was in school, I was taught to round up. Now if you will excuse a momentary digression: The point *I* wanted to make is that we have two qualitatively different rounding modes: round up on 0.5, or round to even (or randomly, or alternating), and they make sense in different contexts. Doing computations with fixed precision, you keep losing precision, and rounding bias accumulates - thus the need to use some non-biased rounding. Doing (small scale) calculations on paper, you can avoid repeated rounding, and only round the result. In which case rounding up is okay, you don't introduce the amount of bias as with repeated rounding. And if your input happens to be truncated, rounding up becomes the right thing to do. Of course, Haskell should discard the rather tasteless IEEE754 crud, and do its calculations on infinite streams of digits. Then, rounding upwards after 'take'ing a sufficient amount of decimals will be the right thing to do. Yes, that all makes sense. And I did not intend to cut you short. -- Dr. Janis Voigtlaender http://wwwtcs.inf.tu-dresden.de/~voigt/ mailto:[EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
This behaviour is not what I expect after reading the description at http://haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html#v:round . Given that this behaviour has caused a bit of confusion I think a change to the documention might be in order. The authority here is the report which says round x returns the nearest integer to x, the even integer if x is equidistant between two integers. However I agree the haddock ought to mirror the report. Jules ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
Ketil Malde wrote: Of course, Haskell should discard the rather tasteless IEEE754 crud, and do its calculations on infinite streams of digits. Then, rounding upwards after 'take'ing a sufficient amount of decimals will be the right thing to do. Except arbitrary-precision real arithmetic is not as trivial as you make it sound, and using an infinite stream of digits is not sufficient by itself. See also: http://www.haskell.org/haskellwiki/Exact_real_arithmetic Martijn. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
It's well known from numerical analysis that you can achieve the best general behavior by rounding to even in half the cases, and rounding to odd in half the cases. It's usually deterministic by looking at the digit to the right of the round point. Regards, John A. De Goes N-BRAIN, Inc. http://www.n-brain.net [n minds are better than n-1] On Oct 27, 2008, at 10:59 AM, Jules Bean wrote: This behaviour is not what I expect after reading the description at http://haskell.org/ghc/docs/latest/html/libraries/base/ Prelude.html#v:round . Given that this behaviour has caused a bit of confusion I think a change to the documention might be in order. The authority here is the report which says round x returns the nearest integer to x, the even integer if x is equidistant between two integers. However I agree the haddock ought to mirror the report. Jules ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
L.Guo wrote: Hi all: I just read about definitions of Prelude [1], and noticing that. In 6.4.6 Coercions and Component Extraction, it discribes like this: round x returns the nearest integer to x, the even integer if x is equidistant between two integers. I think this is unresonable. then try it in GHC 6.8.3. Prelude round 3.5 4 Prelude round 2.5 2 Is there any explanation about that ? This is the same exact behavior found in the FPU of most processors, except that you usually don't notice because the rounding occurs between very small values. The reason for doing it this way is that e.g. 2.5 is exactly between 2 and 3, and rounding *up* every time would cause an uneven bias toward 3. To counteract that effect, rounding to the nearest even integer is used, which causes the half of the x.5 values to round up, and the other half to round down. Pete ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
On Mon, 27 Oct 2008, Ketil Malde wrote: Of course, Haskell should discard the rather tasteless IEEE754 crud, and do its calculations on infinite streams of digits. Then, rounding upwards after 'take'ing a sufficient amount of decimals will be the right thing to do. When I implemented just this in http://darcs.haskell.org/numericprelude/src/Number/Positional.hs I used redundant sets of digits. In a base-n number I use the digits 1-n to n-1. That is, the truncated number abc.def actually represents the interval [abc.def-0.001, abd.def+0.001]. This representation is not unique (more non-unique than standard base-n representation), but testing numbers with infinitely many places for equality is not possible anyway. So (==) is obsolete, just like for floating point numbers. The advantage is that carries are reduced considerably. It allows to compute (sqrt 2)^2, which is not possible in standard representation, because one can never decide whether the result is 2.0... or 1.9 (Pentium's division algorithm also uses digits -1, 0, 1 (we could call them mone (minus one), none, one) for reduced carries.) In this redundant representation one could simply round by truncation, the result depends on the particular sequence of digits used to represent a number, and the rounding would not become worse by repeated rounding (also because it is already worse than the Haskel 98 rounding since the error with respect to the last digit is not only 0.5 but up to 1 :-). ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
On Mon, 27 Oct 2008, Janis Voigtlaender wrote: Lennart Augustsson wrote: I can't remember the method being called anything. It was just what we were being taught. With the obvious explanation that .5 is right in the middle so always going one way would introduce a bias. This was circa 1969. Well, I wasn't serious about the political explanation. And yes, the avoiding bias explanation makes sense, but not the this way of rounding makes repeated rounding safe explanation. In measured data the .5-case should be very rare - a null set? However I assume that .5 happens more often in practice - because of prior rounding, which was shown to be bad practice in this thread. :-) ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
RE: [Haskell-cafe] Why 'round' does not just round numbers ?
G'day all. Quoting Mitchell, Neil [EMAIL PROTECTED]: With rounding to the nearest even integer for 0.5's you get 6, otherwise if you always round up you get 7. If you bias towards rounding up you get a general upwards trend as numbers are rounded, which is bad, while the even condition ensures that statistically it averages to the same thing. There are also many numeric algorithms for which the rounding pattern in the least-significant digit is somewhat systematic. A simple example might be this: x - round(x + 0.5) x - round(x - 0.5) x - round(x + 0.5) x - round(x - 0.5) ... etc If you try this procedure starting with, say, x = 1.5, you can see a clear difference between round-up and round-to-even. With round-up, the rounding error is keeps increasing as the procedure continues. With round-to-even, the error is bounded. Cheers, Andrew Bromage ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
RE: [Haskell-cafe] Why 'round' does not just round numbers ?
G'day all. Henning Thielemann suggested: In measured data the .5-case should be very rare - a null set? However I assume that .5 happens more often in practice - because of prior rounding, which was shown to be bad practice in this thread. The usual case in floating point is usually not 0.5, but some power of 0.5 just beyond the precision of the mantissa. And this is actually one of the most common cases in rounding, due to the fact that we use binary arithmetic. Cheers, Andrew Bromage ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
On 27 Oct 2008, at 11:00 pm, Henning Thielemann wrote: On Mon, 27 Oct 2008, L.Guo wrote: I think this is unresonable. then try it in GHC 6.8.3. Prelude round 3.5 4 Prelude round 2.5 2 Is there any explanation about that ? It's the definition we learnt in school ... Check http://en.wikipedia.org/wiki/Rounding where you will find that the version of rounding generally taught in elementary schools is the one used in Pascal, namely round(X) = truncate(X + 0.5*sign(X)) (The Wikipedia entry says that Pascal uses a different algorithm, but ISO 7185 says If x is positive or zero, round(x) shall be equivalent to trunc(x +0.5); otherwise, round(x) shall be equivalent to trunc(x-0.5).) I think one reason is that repeated rounding should not be worse than rounding in one go. That would be nice, but while round-to-even _reduces_ the harm from double rounding, it does not eliminate it. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why 'round' does not just round numbers ?
On 28 Oct 2008, at 11:11 am, Henning Thielemann wrote: In measured data the .5-case should be very rare - a null set? However I assume that .5 happens more often in practice - because of prior rounding, Think about money. When I was a child, farthings (1/4 of a penny) had just been dropped. (By now, our smallest coin is 10c, formerly a shilling, so in ~ 50 years the value of the smallest coin has eroded by a factor of 48.) Ha'pennies (1/2 of a penny) were still around. If you were adding up a sum of money, sums ending with 1/2 were actually quite common. When the ha'penny went the way of the farthing, one still had to round sums in pounds shillings and pence to sums in pounds and shillings, and sixpence (0.5 of a shilling) was not an unlikely amount. Now that the smallest coin is 10c, supermarkets still price things in multiples of 1c, so in order to give change, they have to round to a multuple of 10c. Sums that end with 5c are not at all unusual. Considering that the point of the thread is what should we expect rounding to do, it may be of interest that a couple of years after the death of the 5c piece, supermarkets *still* display their rounding rule at the cash registers. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
