From: Marnen LaibowKoser on 28 Oct 2009 14:52 Aldric Giacomoni wrote: > Matthew K. Williams wrote: >>> irb(main):016:0> 123.6  123.0 >>> => 0.599999999999994 >>> >>> That's a little strange.. Isn't it? >> >> No, it's not. Welcome to the wonderfully confusing world of floating >> point math... > > Oh, thanks. Can I have some popcorn and an introductory pamphlet before > I bash my head against the wall? :) Most languages these days use IEEE 754style floats, which leads to the imprecision you saw. http://c2.com/cgi/wiki?IeeeSevenFiftyFour Don't use floats for serious arithmetic. Best,  Marnen LaibowKoser http://www.marnen.org marnen(a)marnen.org  Posted via http://www.rubyforum.com/.
From: Robert Klemme on 28 Oct 2009 14:55 On 28.10.2009 19:21, Matthew K. Williams wrote: > On Thu, 29 Oct 2009, Aldric Giacomoni wrote: > >> Matthew K. Williams wrote: >>>> irb(main):016:0> 123.6  123.0 >>>> => 0.599999999999994 >>>> >>>> That's a little strange.. Isn't it? >>> No, it's not. Welcome to the wonderfully confusing world of floating >>> point math... >> Oh, thanks. Can I have some popcorn and an introductory pamphlet before >> I bash my head against the wall? :) > > Pamphlet > http://en.wikipedia.org/wiki/IEEE_7542008 > > Popcorn, well, it's kinda hard to transmit over the wire. ;) Easy to do with a modern email client  just needs support for POP3 and a working firewall (for the heat). :) > As a rule of thumb, if you really care about the decimals, either use > BigDecimal or integers (and keep track of where the decimal should be  > this is common for $$$$). Unfortunately, this is not limited to ruby, > either  C, Java, and a host of other languages all are subject. Absolutely: this is a common issue in *all* programming languages which are not systems for symbolic math (like Mathematica) because they do not work with real numbers but just rational numbers. Cheers robert  remember.guy do as, often as.you_can  without end http://blog.rubybestpractices.com/
From: Marnen LaibowKoser on 28 Oct 2009 15:30 Robert Klemme wrote: > On 28.10.2009 19:21, Matthew K. Williams wrote: >>> I bash my head against the wall? :) >> >> Pamphlet > http://en.wikipedia.org/wiki/IEEE_7542008 >> >> Popcorn, well, it's kinda hard to transmit over the wire. ;) > > Easy to do with a modern email client  just needs support for POP3 and > a working firewall (for the heat). :) LOL! > >> As a rule of thumb, if you really care about the decimals, either use >> BigDecimal or integers (and keep track of where the decimal should be  >> this is common for $$$$). Unfortunately, this is not limited to ruby, >> either  C, Java, and a host of other languages all are subject. > > Absolutely: this is a common issue in *all* programming languages which > are not systems for symbolic math (like Mathematica) because they do not > work with real numbers but just rational numbers. That is not the issue here  after all, BigDecimal does precise arithmetic, but only with rational numbers. The issue is rather that IEEE 754 does an inadequate job of representing arbitrary rational numbers, and the small errors are accumulated and magnified in calculations. > > Cheers > > robert Best,  Marnen LaibowKoser http://www.marnen.org marnen(a)marnen.org  Posted via http://www.rubyforum.com/.
From: Gary Wright on 28 Oct 2009 16:45 On Oct 28, 2009, at 3:30 PM, Marnen LaibowKoser wrote: > That is not the issue here  after all, BigDecimal does precise > arithmetic, but only with rational numbers. The issue is rather that > IEEE 754 does an inadequate job of representing arbitrary rational > numbers, and the small errors are accumulated and magnified in > calculations. I'd like to emphasize the fact that it is a very specific representation problem that most often leads to a thread such as this. That problem is a misunderstanding about the nature of converting between a base 10 literal and a base 2 internal value. Many people don't realize that floating point literals written in base 10 (such as 123.6) may not have an exact finite representation when converted to base 2 and similarly a finite base 2 floating point value may not have a finite representation in base 10. In the original post the floating point subtraction in the expression (123.6  123.0) is handled just fine. The problem is that 123.6 can't be represented exactly as a base 2 floating point value so the subtraction that actually gets done is 123.599999999999994315658113919198513031005859375  123.0 and the result 0.599999999999994315658113919198513031005859375 is rounded via Ruby's Float#to_s method to 0.599999999999994 Gary Wright
From: Marnen LaibowKoser on 28 Oct 2009 17:14 Gary Wright wrote: [...]. > > > Many people don't realize that floating point literals written > in base 10 (such as 123.6) may not have an exact finite > representation when converted to base 2 Right. 0.6 in binary has a repeating decimal  0.1001 repeating or something like that. > and similarly a finite > base 2 floating point value may not have a finite representation > in base 10. [...] I think not. Every number of the form 1/(2^n) has a terminating decimal in base 10. Am I wrong? The problems, of course, arise with numbers like 1/3, which doesn't terminate in either base. This is what the Rational class is good for. > Best,  Marnen LaibowKoser http://www.marnen.org marnen(a)marnen.org  Posted via http://www.rubyforum.com/.
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