Re: python rounding problem.
Thomas Bartkus [EMAIL PROTECTED] wrote: Grant Edwards [EMAIL PROTECTED] wrote in message news:[EMAIL PROTECTED] On 2006-05-08, Thomas Bartkus [EMAIL PROTECTED] wrote: does python support true rations, which means that 1/3 is a true one-third and not 0.3 rounded off at some arbitrary precision? At risk of being boring ;-) - Python supports both rational and irrational numbers as floating point numbers the way any language on any digital computer does - imprecisely. A true (1/3) can only be expressed as a fraction. At the risk of being both boring and overly pedantic, that's not true. In base 3, the value in question is precisely representable in floating point: 0.1 As soon as you express it as a floating point - you are in a bit of trouble because that's impossible. It's not possible in base 2 or base 10. It's perfectly possible in base 9 (used by the Nenets of Northern Russia) base 12 (popular on planets where everybody has twelve toes) or base 60 (used by th Sumerians). [I don't know if any of those peoples used floating point in those bases -- I'm just pointing out that your prejudice towards base 10 notation is showing.] You can not express (1/3) as a floating point in Python any more than you can do it with pencil and paper. That's true assuming base 2 in Python and base 10 on paper. The base used by Python is pretty much etched in stone (silicon, to be precise). There used to be articles about people working on base-3 logic gates, but base-3 logic never made it out of the lab. However, you can pick any base you want when using paper and pencil. You can be precise and write 1/3 or you can surrender to arithmetic convenience and settle for the imprecise by writing 0.3, chopping it off at some arbitrary precision. Or you can write 0.1 3 :) Ahhh! But if I need to store the value 1/10 (decimal!), what kind of a precision pickle will I then find myself while working in base 3 ? How much better for precision if we just learn our fractions and stick to storing integer numerators alongside integer denominators in big 128 bit double registers ? Even the Nenets might become more computationally precise by such means ;-) And how does a human culture come to decide on base 9 arithmetic anyway? Just guessing: * Use one thumb to point at one of the other 9 fingers * Every finger (except for the thumb) has 3 segments (and links), each of which can easily divided in three part (upper, middle, lower or left middle, right for the links) making 9 points for each finger. Even base 60 makes more sense if you like it when a lot of divisions come out nice and even. You can count to 60 using two hands: Use the right thumb to point on one of the 12 segments of the remaining 4 fingers and on the left hand one finger for each dozen. Of course this is wasting resources as you can count to 1023 with your fingers. I never heard of a culture doing so, though. Florian -- http://www.florian-diesch.de/ -- http://mail.python.org/mailman/listinfo/python-list
Re: python rounding problem.
chun ping wang [EMAIL PROTECTED] wrote: Hey i have a stupid question. How do i get python to print the result in only three decimal place... Example round (2.9954254, 3) 2.9951 but i want to get rid of all trailing 0's..how would i do that? Your problem is not a problem in real programs -- it's only a problem because of the way the interactive interpreter works: C:\WINDOWSpython Python 2.4.1 (#65, Mar 30 2005, 09:13:57) [MSC v.1310 32 bit (Intel)] on win32 Type help, copyright, credits or license for more information. round(2.99543322,3) 2.9951 print round(2.99543322,3) 2.995 -- - Tim Roberts, [EMAIL PROTECTED] Providenza Boekelheide, Inc. -- http://mail.python.org/mailman/listinfo/python-list
Re: python rounding problem.
Grant Edwards [EMAIL PROTECTED] wrote in message news:[EMAIL PROTECTED] On 2006-05-08, Thomas Bartkus [EMAIL PROTECTED] wrote: Or you can write 0.1 3 :) Ahhh! But if I need to store the value 1/10 (decimal!), what kind of a precision pickle will I then find myself while working in base 3? Then we're right back where we started. No matter what base you choose, any fixed length floating-point representation can only represent 0% of all rational numbers. So, clearly what we need are floating point objects with configurable bases -- bases that automatically adjust to maintain exact representation of calculation results. Which probably exactly the same as just storing rational numbers as numerator,denominator tuples as you suggest. How much better for precision if we just learn our fractions and stick to storing integer numerators alongside integer denominators in big 128 bit double registers ? I completely overlooked the infinite (presumably!) length integer handling in Python. You can do integer arithmetic on integers of large and arbitrary lengths and if ultimate precision were indeed so important (and I can't imagine why!) then working with numerators and denominators stored as tuples is quite practical. Anyone old enough to remember Forth might remember the arguments about how unnecessary floating point is. True enough! Floating point is merely a convenience for which we sacrifice some (insignificant!) arithmetic precision to enjoy. Even the Nenets might become more computationally precise by such means ;-) And how does a human culture come to decide on base 9 arithmetic anyway? I've no clue, whatsoever. I just stumbled across that factoid when I used Wikipedia to look up which civilizations used base-60. For some reason I can never remember whether it was one of the mesoamerican ones or one of the mesopotamian ones. I suspect a hoax or an urban legend here. A brief and casual googling brings up the Nenets but no mention of base 9 arithmetic which I would find rather astonishing. Look up the Tasaday tribe together with the word hoax. A great joke on academic anthropologists really. On the other hand, the name Nenet is full of Ns and so evocative of the number nine ;-) Even base 60 makes more sense if you like it when a lot of divisions come out nice and even. Did they actually have 60 unique number symbols and use place-weighting in a manner similar to the arabic/indian system we use? I don't know. I do know that we have 360 degrees in a circle for the simple reason that this is evenly divisible by so damned many integers. A significant and logical convenience if you have to do all your calculations on a wooden board using the chunk of charcoal you hold in your fist. Thomas Bartkus Do the Nenets amputate the left pinky as a rite of adulthood ;-) Nah, winters up there are so friggin' cold that nobody ever has more than nine digits by the time they reach adulthood. -- Grant Edwards grante Yow! Hello. Just walk at along and try NOT to think visi.comabout your INTESTINES being almost FORTY YARDS LONG!! -- http://mail.python.org/mailman/listinfo/python-list
Re: python rounding problem.
On 2006-05-09, Thomas Bartkus [EMAIL PROTECTED] wrote: Even base 60 makes more sense if you like it when a lot of divisions come out nice and even. Did they actually have 60 unique number symbols and use place-weighting in a manner similar to the arabic/indian system we use? I don't know. I googled around a while last night, and they ahd sort of a hybrid notation. The Sumerians started withindividual tic marks up to 9, and symbols for 10, 60, 600, 3600 and so on. That evolved into the Babylonian base-60 position-weighted system (without a zero symbol) that used only the 1 symbol and the 10 symbol. http://it.stlawu.edu/%7Edmelvill/mesomath/sumerian.html http://www.ancientscripts.com/sumerian.html http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_numerals.html I do know that we have 360 degrees in a circle And 60 seconds in a minute, 60 minutes in a hour (for both time and angles), and 60 minutes in a degree. -- Grant Edwards grante Yow! PARDON me, am I at speaking ENGLISH? visi.com -- http://mail.python.org/mailman/listinfo/python-list
Re: python rounding problem.
Grant Edwards wrote: ... Did they actually have 60 unique number symbols and use place-weighting in a manner similar to the arabic/indian system we use? The Bablyonians did use a place-value system, but they only had two basic numerals: a Y-like symbol for 1 and a -like symbol for ten. These were combined to make base-60 digits. For example, 59 was represented by YYY YYY YYY Zero (used as a placeholder, but not as a number in itself) was represented by a space. -- http://mail.python.org/mailman/listinfo/python-list
Re: python rounding problem.
On 2006-05-09, Dan Bishop [EMAIL PROTECTED] wrote: Grant Edwards wrote: ... Did they actually have 60 unique number symbols and use place-weighting in a manner similar to the arabic/indian system we use? The Bablyonians did use a place-value system, but they only had two basic numerals: a Y-like symbol for 1 and a -like symbol for ten. These were combined to make base-60 digits. For example, 59 was represented by YYY YYY YYY Zero (used as a placeholder, but not as a number in itself) was represented by a space. And they also (acording to the web pages I found) used base-60 floating point notation, but without an actual symbol to represent the sexagesimal point. Which seems really ambiguous -- even to somebody who does know how to use a slide rule. -- Grant Edwards grante Yow! I'm totally at DESPONDENT over the LIBYAN visi.comsituation and the price of CHICKEN... -- http://mail.python.org/mailman/listinfo/python-list
Re: python rounding problem.
Grant Edwards wrote: On 2006-05-09, Dan Bishop [EMAIL PROTECTED] wrote: Grant Edwards wrote: ... Did they actually have 60 unique number symbols and use place-weighting in a manner similar to the arabic/indian system we use? The Bablyonians did use a place-value system, but they only had two basic numerals: a Y-like symbol for 1 and a -like symbol for ten. These were combined to make base-60 digits. For example, 59 was represented by YYY YYY YYY Zero (used as a placeholder, but not as a number in itself) was represented by a space. And they also (acording to the web pages I found) used base-60 floating point notation, but without an actual symbol to represent the sexagesimal point. Which seems really ambiguous -- even to somebody who does know how to use a slide rule. Yes, it was. (Our spy's message says that Cyrus the Great has '6 ' troops. Does that mean 360 or 21,600?) -- http://mail.python.org/mailman/listinfo/python-list
Re: python rounding problem.
Gary Wessle [EMAIL PROTECTED] wrote in message news:[EMAIL PROTECTED] Erik Max Francis [EMAIL PROTECTED] writes: chun ping wang wrote: Hey i have a stupid question. How do i get python to print the result in only three decimal place... Example round (2.9954254, 3) 2.9951 but i want to get rid of all trailing 0's..how would i do that? Floating point arithmetic is inherently imprecise. This is not a Python problem. does python support true rations, which means that 1/3 is a true one-third and not 0.3 rounded off at some arbitrary precision? At risk of being boring ;-) - Python supports both rational and irrational numbers as floating point numbers the way any language on any digital computer does - imprecisely. A true (1/3) can only be expressed as a fraction. As soon as you express it as a floating point - you are in a bit of trouble because that's impossible. You can not express (1/3) as a floating point in Python any more than you can do it with pencil and paper. You can be precise and write 1/3 or you can surrender to arithmetic convenience and settle for the imprecise by writing 0.3, chopping it off at some arbitrary precision. Which is exactly what you did in your post ;-) Thomas Bartkus -- http://mail.python.org/mailman/listinfo/python-list
Re: python rounding problem.
On 2006-05-08, Thomas Bartkus [EMAIL PROTECTED] wrote: does python support true rations, which means that 1/3 is a true one-third and not 0.3 rounded off at some arbitrary precision? At risk of being boring ;-) - Python supports both rational and irrational numbers as floating point numbers the way any language on any digital computer does - imprecisely. A true (1/3) can only be expressed as a fraction. At the risk of being both boring and overly pedantic, that's not true. In base 3, the value in question is precisely representable in floating point: 0.1 As soon as you express it as a floating point - you are in a bit of trouble because that's impossible. It's not possible in base 2 or base 10. It's perfectly possible in base 9 (used by the Nenets of Northern Russia) base 12 (popular on planets where everybody has twelve toes) or base 60 (used by th Sumerians). [I don't know if any of those peoples used floating point in those bases -- I'm just pointing out that your prejudice towards base 10 notation is showing.] You can not express (1/3) as a floating point in Python any more than you can do it with pencil and paper. That's true assuming base 2 in Python and base 10 on paper. The base used by Python is pretty much etched in stone (silicon, to be precise). There used to be articles about people working on base-3 logic gates, but base-3 logic never made it out of the lab. However, you can pick any base you want when using paper and pencil. You can be precise and write 1/3 or you can surrender to arithmetic convenience and settle for the imprecise by writing 0.3, chopping it off at some arbitrary precision. Or you can write 0.1 3 :) -- Grant Edwards grante Yow! Yes, Private at DOBERMAN!! visi.com -- http://mail.python.org/mailman/listinfo/python-list
Re: python rounding problem.
Grant Edwards [EMAIL PROTECTED] wrote in message news:[EMAIL PROTECTED] On 2006-05-08, Thomas Bartkus [EMAIL PROTECTED] wrote: does python support true rations, which means that 1/3 is a true one-third and not 0.3 rounded off at some arbitrary precision? At risk of being boring ;-) - Python supports both rational and irrational numbers as floating point numbers the way any language on any digital computer does - imprecisely. A true (1/3) can only be expressed as a fraction. At the risk of being both boring and overly pedantic, that's not true. In base 3, the value in question is precisely representable in floating point: 0.1 As soon as you express it as a floating point - you are in a bit of trouble because that's impossible. It's not possible in base 2 or base 10. It's perfectly possible in base 9 (used by the Nenets of Northern Russia) base 12 (popular on planets where everybody has twelve toes) or base 60 (used by th Sumerians). [I don't know if any of those peoples used floating point in those bases -- I'm just pointing out that your prejudice towards base 10 notation is showing.] You can not express (1/3) as a floating point in Python any more than you can do it with pencil and paper. That's true assuming base 2 in Python and base 10 on paper. The base used by Python is pretty much etched in stone (silicon, to be precise). There used to be articles about people working on base-3 logic gates, but base-3 logic never made it out of the lab. However, you can pick any base you want when using paper and pencil. You can be precise and write 1/3 or you can surrender to arithmetic convenience and settle for the imprecise by writing 0.3, chopping it off at some arbitrary precision. Or you can write 0.1 3 :) Ahhh! But if I need to store the value 1/10 (decimal!), what kind of a precision pickle will I then find myself while working in base 3 ? How much better for precision if we just learn our fractions and stick to storing integer numerators alongside integer denominators in big 128 bit double registers ? Even the Nenets might become more computationally precise by such means ;-) And how does a human culture come to decide on base 9 arithmetic anyway? Even base 60 makes more sense if you like it when a lot of divisions come out nice and even. Do the Nenets amputate the left pinky as a rite of adulthood ;-) Thomas Bartkus -- http://mail.python.org/mailman/listinfo/python-list
Re: python rounding problem.
On 2006-05-08, Thomas Bartkus [EMAIL PROTECTED] wrote: Or you can write 0.1 3 :) Ahhh! But if I need to store the value 1/10 (decimal!), what kind of a precision pickle will I then find myself while working in base 3? Then we're right back where we started. No matter what base you choose, any fixed length floating-point representation can only represent 0% of all rational numbers. So, clearly what we need are floating point objects with configurable bases -- bases that automatically adjust to maintain exact representation of calculation results. Which probably exactly the same as just storing rational numbers as numerator,denominator tuples as you suggest. How much better for precision if we just learn our fractions and stick to storing integer numerators alongside integer denominators in big 128 bit double registers ? Even the Nenets might become more computationally precise by such means ;-) And how does a human culture come to decide on base 9 arithmetic anyway? I've no clue, whatsoever. I just stumbled across that factoid when I used Wikipedia to look up which civilizations used base-60. For some reason I can never remember whether it was one of the mesoamerican ones or one of the mesopotamian ones. Even base 60 makes more sense if you like it when a lot of divisions come out nice and even. Did they actually have 60 unique number symbols and use place-weighting in a manner similar to the arabic/indian system we use? Do the Nenets amputate the left pinky as a rite of adulthood ;-) Nah, winters up there are so friggin' cold that nobody ever has more than nine digits by the time they reach adulthood. -- Grant Edwards grante Yow! Hello. Just walk at along and try NOT to think visi.comabout your INTESTINES being almost FORTY YARDS LONG!! -- http://mail.python.org/mailman/listinfo/python-list
python rounding problem.
Hey i have a stupid question. How do i get python to print the result in only three decimal place... Example round (2.9954254, 3) 2.9951 but i want to get rid of all trailing 0's..how would i do that? _ Express yourself instantly with MSN Messenger! Download today - it's FREE! http://messenger.msn.click-url.com/go/onm00200471ave/direct/01/ -- http://mail.python.org/mailman/listinfo/python-list
Re: python rounding problem.
chun ping wang wrote: Hey i have a stupid question. How do i get python to print the result in only three decimal place... Example round (2.9954254, 3) 2.9951 but i want to get rid of all trailing 0's..how would i do that? Floating point arithmetic is inherently imprecise. This is not a Python problem. If you want to print it to only three digits, then use something like:: '%.3f' % 2.9954254 '2.995' -- Erik Max Francis [EMAIL PROTECTED] http://www.alcyone.com/max/ San Jose, CA, USA 37 20 N 121 53 W AIM erikmaxfrancis Whoever contends with the great sheds his own blood. -- Sa'di -- http://mail.python.org/mailman/listinfo/python-list
Re: python rounding problem.
Erik Max Francis wrote: chun ping wang wrote: Hey i have a stupid question. How do i get python to print the result in only three decimal place... Example round (2.9954254, 3) 2.9951 but i want to get rid of all trailing 0's..how would i do that? Floating point arithmetic is inherently imprecise. This is not a Python problem. http://www2.hursley.ibm.com/decimal/ (read about IEEE754 here) -- http://mail.python.org/mailman/listinfo/python-list
Re: python rounding problem.
Erik Max Francis [EMAIL PROTECTED] writes: chun ping wang wrote: Hey i have a stupid question. How do i get python to print the result in only three decimal place... Example round (2.9954254, 3) 2.9951 but i want to get rid of all trailing 0's..how would i do that? Floating point arithmetic is inherently imprecise. This is not a Python problem. does python support true rations, which means that 1/3 is a true one-third and not 0.3 rounded off at some arbitrary precision? -- http://mail.python.org/mailman/listinfo/python-list
