Re: [HACKERS] [OT] somebody could explain this?
yes, MAJOR goof on my part. My brain cells were not firing quite right :( For those really interested, here are some resources: http://www.cs.wisc.edu/~cs354-1/cs354/karen.notes/reps.flpt.html http://cch.loria.fr/documentation/IEEE754/ACM/goldberg.pdf http://babbage.cs.qc.edu/courses/cs341/IEEE-754references.html -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of Tom Lane Sent: Friday, November 04, 2005 11:52 AM To: [EMAIL PROTECTED] Cc: pgsql-hackers@postgresql.org Subject: Re: [OT] somebody could explain this? Otto Hirr [EMAIL PROTECTED] writes: Most notably, the IEEE rep, either single or double, most certainly has the ability to store the EXACT value for 0.1. Oh really? regards, tom lane ---(end of broadcast)--- TIP 5: don't forget to increase your free space map settings ---(end of broadcast)--- TIP 6: explain analyze is your friend
Re: [HACKERS][OT] somebody could explain this?
[snip] Floating points numbers are accurate but not precise. OK, now this one beats me... what's the difference between accurate and exact ? I thought both mean something like correct, but precise refers to some action and accurate applies to a situation or description... I'm actually curios what it means. Merriam-Webster refers for both to correct as a synonym. Cheers, Csaba. ---(end of broadcast)--- TIP 9: In versions below 8.0, the planner will ignore your desire to choose an index scan if your joining column's datatypes do not match
Re: [HACKERS][OT] somebody could explain this?
Csaba Nagy wrote: [snip] Floating points numbers are accurate but not precise. OK, now this one beats me... what's the difference between accurate and exact ? I thought both mean something like correct, but precise refers to some action and accurate applies to a situation or description... Accurate means close to the real value, precise means having a lot of detail. So 3 is more accurate than 4 as a representation of Pi, but both are not very precise. 5.32290753057207250735 is a very precise representation of Pi but totally inaccurate. This also means that the statement at the top is wrong. It should be the other way around. -- Peter Eisentraut http://developer.postgresql.org/~petere/ ---(end of broadcast)--- TIP 2: Don't 'kill -9' the postmaster
Re: [HACKERS][OT] somebody could explain this?
I think the crucial point is that the common IEEE floating point formats are unable to store an EXACT representation of common decimal fractions (such as .1) -- they can only store an APPROXIMATION. Peter Eisentraut [EMAIL PROTECTED] Csaba Nagy wrote: [snip] Floating points numbers are accurate but not precise. OK, now this one beats me... what's the difference between accurate and exact ? I thought both mean something like correct, but precise refers to some action and accurate applies to a situation or description... Accurate means close to the real value, precise means having a lot of detail. So 3 is more accurate than 4 as a representation of Pi, but both are not very precise. 5.32290753057207250735 is a very precise representation of Pi but totally inaccurate. This also means that the statement at the top is wrong. It should be the other way around. -- Peter Eisentraut http://developer.postgresql.org/~petere/ ---(end of broadcast)--- TIP 2: Don't 'kill -9' the postmaster ---(end of broadcast)--- TIP 6: explain analyze is your friend
Re: [HACKERS] [OT] somebody could explain this?
On Fri, Nov 04, 2005 at 18:30:56 +0100, Csaba Nagy [EMAIL PROTECTED] wrote: [snip] Floating points numbers are accurate but not precise. OK, now this one beats me... what's the difference between accurate and exact ? I thought both mean something like correct, but precise refers to some action and accurate applies to a situation or description... I'm actually curios what it means. Merriam-Webster refers for both to correct as a synonym. My memory from science courses a long time ago, is that precision refers to how much information you have (e.g. the number of digits in a number) and accuracy refers to how close your information is to reality. Using a precision that was much higher than justified by accuracy used to get points deducted from lab report grades. In mathematics precise has a somewhat different meaning, but isn't a synonym for accurate in that context. ---(end of broadcast)--- TIP 4: Have you searched our list archives? http://archives.postgresql.org
Re: [HACKERS] [OT] somebody could explain this?
Lets start with an agreed upon expert, Knuth. The art of computer programming. Vol2,Seminumerical Algorithms.Ed2. pg682: Precision: The number of digits in a representation. pg212: Section: Accuracy of floating point numbers. A rough (but reasonably useful) way to express the behavior of floating point arithmetic can be based upon the concept of significant figures or relative error. The float point rep is built of a exponent and fractional part. (Note mantissa means a worthless addition(pg199) Most notably, the IEEE rep, either single or double, most certainly has the ability to store the EXACT value for 0.1. The issue is how to REPRESENT an exact value in the computer. Some values may be represented exactly. Some values may not. The tricky part is then operations on these values. We may have exact representation of two values, then applying an operation that results in a theoretical value that can only have an approximate representation. Accuracy deals with the difference between the theoretical exact value and our ability to represent it. Note that Knuth's observation about add/sub v. mul/div: Roughly speaking, the operations of floating point multiplication and division do not magnify the relative error by very much; but floating point subtraction of nearly equal quantities (and floating point addition, u+v, where u is nearly equal to -v) can very greatly increase the relative error. Surprised? Things to consider: Is the value I want to represent have, shall we say, a limit to the number of digits required to fully define its value, eg 0.5, 0.9987 Is the value I want to represent have no limit to the number of digits, eg pi, etc. Does my representation provide a value that is within acceptable limits of error, between the rep and actual value. !Are the operations that I am performing introducing greater amounts of relative error! Break out the old computer book/math book and review... Lets not assume or re-invent the wheel. ..Otto I think the crucial point is that the common IEEE floating point formats are unable to store an EXACT representation of common decimal fractions (such as .1) -- they can only store an APPROXIMATION. Peter Eisentraut [EMAIL PROTECTED] Csaba Nagy wrote: [snip] Floating points numbers are accurate but not precise. OK, now this one beats me... what's the difference between accurate and exact ? I thought both mean something like correct, but precise refers to some action and accurate applies to a situation or description... Accurate means close to the real value, precise means having a lot of detail. So 3 is more accurate than 4 as a representation of Pi, but both are not very precise. 5.32290753057207250735 is a very precise representation of Pi but totally inaccurate. This also means that the statement at the top is wrong. It should be the other way around. -- Peter Eisentraut http://developer.postgresql.org/~petere/ ---(end of broadcast)--- TIP 2: Don't 'kill -9' the postmaster ---(end of broadcast)--- TIP 6: explain analyze is your friend ---(end of broadcast)--- TIP 6: explain analyze is your friend
Re: [HACKERS] [OT] somebody could explain this?
Otto Hirr [EMAIL PROTECTED] writes: Most notably, the IEEE rep, either single or double, most certainly has the ability to store the EXACT value for 0.1. Oh really? regards, tom lane ---(end of broadcast)--- TIP 5: don't forget to increase your free space map settings
Re: [HACKERS] [OT] somebody could explain this?
No, the IEEE formats can not store .1 exactly. How close it comes depends on the rest of the number. For single and double precision, respectively, the IEEE representations fall at about: 0.10001490116119384765625 0.155511151231257827021181583404541015625 Libraries must do some rounding of these approximations when formatting for display, so the error is rarely seen, except when conversions to other data types are done via truncation. The problem values from the previous example were actually stored as something close to the following. 0.11999555910790149937383830547332763671875 0.1499944488848768742172978818416595458984375 Whole numbers, on the other hand, are always accurate unless they exceed the number of significant digits for the format. -Kevin Otto Hirr [EMAIL PROTECTED] Most notably, the IEEE rep, either single or double, most certainly has the ability to store the EXACT value for 0.1. ---(end of broadcast)--- TIP 6: explain analyze is your friend
