C++Talk.NET C++ language newsgroups   Archives   FAQ   Search   Memberlist   Usergroups   Register   Profile   Log in to check your private messages   Log in  Formatting numbers nicely with DBL_EPSILON          C++Talk.NET Forum Index -> C++ Language (Moderated) View previous topic :: View next topic   Author Message Jodawi Guest Posted: Fri Nov 12, 2004 4:04 am    Post subject: Formatting numbers nicely with DBL_EPSILON It's common for values like 6.0 to turn into values like 5.9999999999999991 when doing floating point calculations. What's the best way to display these to users as nice numbers? I've been using DBL_EPSILON to nudge numbers for formatting purposes for a while now (see example below). It seems to work (although I haven't tested the particular code included below), but I always have a nagging feeling that there might be a better way. Or that multiplying by (1.0 + DBL_EPSILON) may not always change the value, so some repeating values may be missed. Any thoughts? ostringstream formattedString; formattedString << fixed; // Round .xxx99999999 up by adding a very small number x *= (1.0 + DBL_EPSILON); formattedString << setprecision(f.digits); formattedString << x; [ See http://www.gotw.ca/resources/clcm.htm for info about ] [ comp.lang.c++.moderated. First time posters: Do this! ] Back to top Falk Tannhäuser Guest Posted: Sun Nov 14, 2004 4:56 pm    Post subject: Re: Formatting numbers nicely with DBL_EPSILON Jodawi wrote: Quote: It's common for values like 6.0 to turn into values like 5.9999999999999991 when doing floating point calculations. What's the best way to display these to users as nice numbers? I've been using DBL_EPSILON to nudge numbers for formatting purposes for a while now (see example below). [...] ostringstream formattedString; formattedString << fixed; // Round .xxx99999999 up by adding a very small number x *= (1.0 + DBL_EPSILON); formattedString << setprecision(f.digits); formattedString << x; How can you be sure that this will not turn 6.0 into 6.00000000000000178? It does on my implementation, when I set the precision to 18. Falk [ See http://www.gotw.ca/resources/clcm.htm for info about ] [ comp.lang.c++.moderated. First time posters: Do this! ] Back to top Carl Barron Guest Posted: Sun Nov 14, 2004 4:56 pm    Post subject: Re: Formatting numbers nicely with DBL_EPSILON Jodawi <jodawi (AT) gmail (DOT) com> wrote: Quote: It's common for values like 6.0 to turn into values like 5.9999999999999991 when doing floating point calculations. What's the best way to display these to users as nice numbers? I've been using DBL_EPSILON to nudge numbers for formatting purposes for a while now (see example below). It seems to work (although I haven't tested the particular code included below), but I always have a nagging feeling that there might be a better way. Or that multiplying by (1.0 + DBL_EPSILON) may not always change the value, so some repeating values may be missed. Any thoughts? ostringstream formattedString; formattedString << fixed; // Round .xxx99999999 up by adding a very small number x *= (1.0 + DBL_EPSILON); Its not going to work in general since the expression (1.+DBL_EPSILON) == 1. , evaluates to true. so except for errors in the numeric value of DBL_EPSILON [from binary to decimal conversion, since on most modern hardware, DBL_EPSILON in the internal format is an exact number. Write the number to an ostringstream using the formating manipulators currently used on the output stream and then examine the resulting string for a trailing sequence of '9's and modify the string. Then output it. [ See http://www.gotw.ca/resources/clcm.htm for info about ] [ comp.lang.c++.moderated. First time posters: Do this! ] Back to top Jodawi Guest Posted: Mon Nov 15, 2004 11:36 am    Post subject: Re: Formatting numbers nicely with DBL_EPSILON Falk Tannhäuser <clcppm-poster (AT) this (DOT) is.invalid> wrote: Quote: Jodawi wrote: It's common for values like 6.0 to turn into values like 5.9999999999999991 when doing floating point calculations. What's the best way to display these to users as nice numbers? I've been using DBL_EPSILON to nudge numbers for formatting purposes for a while now (see example below). [...] ostringstream formattedString; formattedString << fixed; // Round .xxx99999999 up by adding a very small number x *= (1.0 + DBL_EPSILON); formattedString << setprecision(f.digits); formattedString << x; How can you be sure that this will not turn 6.0 into 6.00000000000000178? It does on my implementation, when I set the precision to 18. Because I never display that much precision. [ See http://www.gotw.ca/resources/clcm.htm for info about ] [ comp.lang.c++.moderated. First time posters: Do this! ] Back to top Falk Tannhäuser Guest Posted: Mon Nov 15, 2004 9:39 pm    Post subject: Re: Formatting numbers nicely with DBL_EPSILON Jodawi wrote: Quote: Falk Tannhäuser <clcppm-poster (AT) this (DOT) is.invalid> wrote: Jodawi wrote: It's common for values like 6.0 to turn into values like 5.9999999999999991 when doing floating point calculations. What's the best way to display these to users as nice numbers? [...] How can you be sure that this will not turn 6.0 into 6.00000000000000178? It does on my implementation, when I set the precision to 18. Because I never display that much precision. So, what is the problem you are trying to solve, then? std::cout << std::setprecision(15) << std::showpoint << 5.9999999999999991 << 'n'; already displays 6.00000000000000 (or simply 6 when omitting 'showpoint') on my platform. Only when setting the precision to 16 or 17, I get 5.999999999999999 or 5.9999999999999991 respectively. That is how it ought to be IMO - rounding in the right direction is already done by the output function. Falk [ See http://www.gotw.ca/resources/clcm.htm for info about ] [ comp.lang.c++.moderated. First time posters: Do this! ] Back to top Jodawi Guest Posted: Tue Nov 16, 2004 11:34 am    Post subject: Re: Formatting numbers nicely with DBL_EPSILON [email]cbarron3 (AT) ix (DOT) netcom.com[/email] (Carl Barron) wrote: Quote: Jodawi <jodawi (AT) gmail (DOT) com> wrote: ostringstream formattedString; formattedString << fixed; // Round .xxx99999999 up by adding a very small number x *= (1.0 + DBL_EPSILON); Its not going to work in general since the expression (1.+DBL_EPSILON) == 1. , evaluates to true. I think the meaning (if not the technical definition) of DBL_EPSILON is the smallest representable number such that (1.+DBL_EPSILON) > 1. I just tested and (1.+DBL_EPSILON) == 1. evaluates to false for my current compiler. Quote: so except for errors in the numeric value of DBL_EPSILON [from binary to decimal conversion, since on most modern hardware, DBL_EPSILON in the internal format is an exact number. Write the number to an ostringstream using the formating manipulators currently used on the output stream and then examine the resulting string for a trailing sequence of '9's and modify the string. Then output it. That's more complicated and slower than multiplying by a number that's slightly larger than 1.0, so I'd like to avoid it. Since I don't care about trying to display more than 10 or so digits of precision, I could mulitply by something like (1.0 + 10.0*DBL_EPSILON), but I don't know of a case where (1.0 + DBL_EPSILON) fails. [ See http://www.gotw.ca/resources/clcm.htm for info about ] [ comp.lang.c++.moderated. First time posters: Do this! ] Back to top Jodawi Guest Posted: Wed Nov 17, 2004 11:13 am    Post subject: Re: Formatting numbers nicely with DBL_EPSILON Falk Tannhäuser <clcppm-poster (AT) this (DOT) is.invalid> wrote: Quote: Jodawi wrote: Falk Tannhäuser <clcppm-poster (AT) this (DOT) is.invalid> wrote: Jodawi wrote: It's common for values like 6.0 to turn into values like 5.9999999999999991 when doing floating point calculations. What's the best way to display these to users as nice numbers? How can you be sure that this will not turn 6.0 into 6.00000000000000178? It does on my implementation, when I set the precision to 18. Because I never display that much precision. So, what is the problem you are trying to solve, then? std::cout << std::setprecision(15) << std::showpoint << 5.9999999999999991 << 'n'; already displays 6.00000000000000 (or simply 6 when omitting 'showpoint') on my platform. Only when setting the precision to 16 or 17, I get 5.999999999999999 or 5.9999999999999991 respectively. That is how it ought to be IMO - rounding in the right direction is already done by the output function. Your example is giving me 6.00000000000000 without '<< fixed', and 5.999999999999999 with '<< fixed', with both MS Visual C++ and MW Codewarrior. The most recent complaint was that 2.35*1.11 displayed to 3 decimal places as 2.608 instead of 2.609. (2.35*1.11==2.6085, filtering down from our GUI as 2.6084999999999998. "2.35*1.11" is a string typed in by the user and parsed.) [ See http://www.gotw.ca/resources/clcm.htm for info about ] [ comp.lang.c++.moderated. First time posters: Do this! ] Back to top velthuijsen Guest Posted: Thu Nov 18, 2004 12:24 am    Post subject: Re: Formatting numbers nicely with DBL_EPSILON Quote: That's more complicated and slower than multiplying by a number that's slightly larger than 1.0, so I'd like to avoid it. Since I don't care about trying to display more than 10 or so digits of precision, I could mulitply by something like (1.0 + 10.0*DBL_EPSILON), but I don't know of a case where (1.0 + DBL_EPSILON) fails. easy, double epsilon is defined for my compiler as 2.2204460492503131e-016 all I need to do is give you a double that doesn't get a precision of e-16 but say e-14, 101.00000000000001 would do. Adding DBL_EPSILON to that might or might not increase the tail end (most likely won't). Then there is the chance that your compiler doesn't get a smaller number like the 5.9999999999999991 one you mentioned. There is an equal chance that you get a 6.0000000000000009 value and adding DBL_EPSILON would not remove your problem. Then there is that for me adding DBL_EPSILON to 5.9999999999999991 would generate a number 5.9999999999999991. I'd need atleast 2*DBL_EPSILON (using my compiler) to get that number rounded to 6. But you've already mentioned the solution to your problem. You only need 10 places behind the point. Then only display 10 behind the point. FormattedString.precision(10); Now if I feed in 5.9999999999999991 I just get a 6 displayed. [ See http://www.gotw.ca/resources/clcm.htm for info about ] [ comp.lang.c++.moderated. First time posters: Do this! ] Back to top Falk Tannhäuser Guest Posted: Thu Nov 18, 2004 12:26 pm    Post subject: Re: Formatting numbers nicely with DBL_EPSILON Jodawi wrote: Quote: I think the meaning (if not the technical definition) of DBL_EPSILON is the smallest representable number such that (1.+DBL_EPSILON) > 1. I just tested and (1.+DBL_EPSILON) == 1. evaluates to false for my current compiler. On my platform, with double x = 1.0 + DBL_EPSILON * 0.50001; I have x > 1.0 (and x == 1.0 + DBL_EPSILON). The exact definition is "the difference between 1 and the least value greater than 1 that is representable." See § 18.2.1.2/20, DBL_EPSILON is the same as std::numeric_limits<double>::epsilon() . Falk [ See http://www.gotw.ca/resources/clcm.htm for info about ] [ comp.lang.c++.moderated. First time posters: Do this! ] Back to top Falk Tannhäuser Guest Posted: Thu Nov 18, 2004 12:27 pm    Post subject: Re: Formatting numbers nicely with DBL_EPSILON Jodawi wrote: Quote: Your example is giving me 6.00000000000000 without '<< fixed', and 5.999999999999999 with '<< fixed', with both MS Visual C++ and MW Codewarrior. Which still looks correct to me: the original value was 5.9999999999999991 (15 nines after the point), and the result without '<< fixed' is correctly rounded up since displays only 14 digits after the point, while the result with '<< fixed' displays 15 digits after the point - which is why rounding down is appropriate. Quote: The most recent complaint was that 2.35*1.11 displayed to 3 decimal places as 2.608 instead of 2.609. (2.35*1.11==2.6085, filtering down from our GUI as 2.6084999999999998. "2.35*1.11" is a string typed in by the user and parsed.) That's another matter: The exact value would lie exactly in the middle between 2.608 instead of 2.609 but is not representable in binary floating point format. It is quite easy to construct cases where rounding errors sum up enough to defeat the "multiply by (1.0 + DBL_EPSILON)" method for this one: double foo(double x) { unsigned const N = 5; // May need to adjust this to reproduce the problem double a[N]; a[0] = x; for(unsigned i=1; i for(unsigned i=N-1; i>0; --i) a[i-1] = a[i] * 3.0; return a[0]; } .... double const d = 1.0 + std::numeric_limits<double>::epsilon(); double x = foo(2.6085); std::cout << std::fixed << std::setprecision(3) << x << ' ' << x*d << 'n'; rounds down (displays "2.608 2.608") on my machine. Falk [ See http://www.gotw.ca/resources/clcm.htm for info about ] [ comp.lang.c++.moderated. 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