Dear all, I am trying to understand why I am getting different numerical results with the interval library depending on the optimization level of the compiler. I am attaching the smallest example I have been able to create: # On my Mac laptop Apple LLVM version 9.0.0 (clang-900.0.39.2) boost 1.66 (installed via homebrew) $ g++ foo.cpp -o foo $ ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000000000 v1 = (0.9999999999999998889776975374843459576368331909179687500000000000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (0.9999999999999998889776975374843459576368331909179687500000000000,1.0000000000000000000000000000000000000000000000000000000000000000) $ g++ -O2 foo.cpp -o foo $ ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000000000 v1 = (1.0000000000000000000000000000000000000000000000000000000000000000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (1.0000000000000000000000000000000000000000000000000000000000000000,1.0000000000000000000000000000000000000000000000000000000000000000) I would expect to get the same output in both cases, but the lower end-points are different in the second case, and seem wrong to me since third2 * 3.0 < 1.0. # On my Linux machine the effect is different: gcc version 5.4.0 20160609 boost 1.58 on Ubuntu 16.04.9 $ g++ foo.cpp -o foo $ ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000000000 v1 = (0.9999999999999998889776975374843459576368331909179687500000000000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (0.9999999999999998889776975374843459576368331909179687500000000000,1.0000000000000000000000000000000000000000000000000000000000000000) $ g++ -O2 foo.cpp -o foo $ ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000000000 v1 = (0.9999999999999998889776975374843459576368331909179687500000000000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (1.0000000000000000000000000000000000000000000000000000000000000000,1.0000000000000000000000000000000000000000000000000000000000000000) Can anyone explain what is going on? Thanks in advance, Tim -- Tim van Erven<tim@timvanerven.nl> www.timvanerven.nl
I'm not sure what's going on (seems like maybe a fast but error prone floating point rounding), but comparing the optimization flags enabled between -O0 and -O2 might help shed some light on it. You can get the explicit optimization flags enabled for your compiler via: g++ -Q -O2 --help=optimizers g++ -Q -O0 --help=optimizers Regards, Nate On Fri, Mar 2, 2018 at 10:17 AM, Tim van Erven via Boost-users < boost-users@lists.boost.org> wrote:
Dear all,
I am trying to understand why I am getting different numerical results with the interval library depending on the optimization level of the compiler.
I am attaching the smallest example I have been able to create:
# On my Mac laptop Apple LLVM version 9.0.0 (clang-900.0.39.2) boost 1.66 (installed via homebrew) $ g++ foo.cpp -o foo $ ./foo third1 = 0.333333333333333314829616256247390992939472198486328125000000 0000 third2 = 0.333333333333333314829616256247390992939472198486328125000000 0000 v1 = (0.999999999999999888977697537484345957636833190917968750000000 0000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (0.999999999999999888977697537484345957636833190917968750000000 0000,1.0000000000000000000000000000000000000000000000000000000000000000)
$ g++ -O2 foo.cpp -o foo $ ./foo third1 = 0.333333333333333314829616256247390992939472198486328125000000 0000 third2 = 0.333333333333333314829616256247390992939472198486328125000000 0000 v1 = (1.000000000000000000000000000000000000000000000000000000000000 0000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (1.000000000000000000000000000000000000000000000000000000000000 0000,1.0000000000000000000000000000000000000000000000000000000000000000)
I would expect to get the same output in both cases, but the lower end-points are different in the second case, and seem wrong to me since third2 * 3.0 < 1.0.
# On my Linux machine the effect is different: gcc version 5.4.0 20160609 boost 1.58 on Ubuntu 16.04.9
$ g++ foo.cpp -o foo $ ./foo third1 = 0.333333333333333314829616256247390992939472198486328125000000 0000 third2 = 0.333333333333333314829616256247390992939472198486328125000000 0000 v1 = (0.999999999999999888977697537484345957636833190917968750000000 0000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (0.999999999999999888977697537484345957636833190917968750000000 0000,1.0000000000000000000000000000000000000000000000000000000000000000)
$ g++ -O2 foo.cpp -o foo $ ./foo third1 = 0.333333333333333314829616256247390992939472198486328125000000 0000 third2 = 0.333333333333333314829616256247390992939472198486328125000000 0000 v1 = (0.999999999999999888977697537484345957636833190917968750000000 0000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (1.000000000000000000000000000000000000000000000000000000000000 0000,1.0000000000000000000000000000000000000000000000000000000000000000)
Can anyone explain what is going on?
Thanks in advance,
Tim
-- Tim van Erven <tim@timvanerven.nl> <tim@timvanerven.nl>www.timvanerven.nl
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Hi Nate, Thanks for your help. Below is the output from gcc 7.2.0 on mac os. Apparently the difference already happens between -O0 and -O1. To summarize: - gcc on linux with boost 1.58 - clang and gcc 7.2.0 on mac os with boost 1.66 all give wrong (or at least inconsistent) output depending on optimization options. (Since third1 and third2 are both < 1/3, multiplying them by 3 should give an interval with lower end-point < 1, but it sometimes doesn't.) I am attaching the outputs of g++-7 -Q -O0 --help=optimizers > o0.txt $ g++-7 -Q -O1 --help=optimizers > o1.txt $ g++-7 foo.cpp -o foo $ ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000000000 v1 = (0.9999999999999998889776975374843459576368331909179687500000000000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (0.9999999999999998889776975374843459576368331909179687500000000000,1.0000000000000000000000000000000000000000000000000000000000000000) $ g++-7 -O1 foo.cpp -o foo ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000000000 v1 = (0.9999999999999998889776975374843459576368331909179687500000000000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (1.0000000000000000000000000000000000000000000000000000000000000000,1.0000000000000000000000000000000000000000000000000000000000000000) Best, Tim On 02/03/2018 18:23, Nathan Ernst wrote:
I'm not sure what's going on (seems like maybe a fast but error prone floating point rounding), but comparing the optimization flags enabled between -O0 and -O2 might help shed some light on it.
You can get the explicit optimization flags enabled for your compiler via: g++ -Q -O2 --help=optimizers g++ -Q -O0 --help=optimizers
Regards, Nate
On Fri, Mar 2, 2018 at 10:17 AM, Tim van Erven via Boost-users <boost-users@lists.boost.org <mailto:boost-users@lists.boost.org>> wrote:
Dear all,
I am trying to understand why I am getting different numerical results with the interval library depending on the optimization level of the compiler.
I am attaching the smallest example I have been able to create:
# On my Mac laptop Apple LLVM version 9.0.0 (clang-900.0.39.2) boost 1.66 (installed via homebrew) $ g++ foo.cpp -o foo $ ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000000000 v1 = (0.9999999999999998889776975374843459576368331909179687500000000000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (0.9999999999999998889776975374843459576368331909179687500000000000,1.0000000000000000000000000000000000000000000000000000000000000000)
$ g++ -O2 foo.cpp -o foo $ ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000000000 v1 = (1.0000000000000000000000000000000000000000000000000000000000000000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (1.0000000000000000000000000000000000000000000000000000000000000000,1.0000000000000000000000000000000000000000000000000000000000000000)
I would expect to get the same output in both cases, but the lower end-points are different in the second case, and seem wrong to me since third2 * 3.0 < 1.0.
# On my Linux machine the effect is different: gcc version 5.4.0 20160609 boost 1.58 on Ubuntu 16.04.9
$ g++ foo.cpp -o foo $ ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000000000 v1 = (0.9999999999999998889776975374843459576368331909179687500000000000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (0.9999999999999998889776975374843459576368331909179687500000000000,1.0000000000000000000000000000000000000000000000000000000000000000)
$ g++ -O2 foo.cpp -o foo $ ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000000000 v1 = (0.9999999999999998889776975374843459576368331909179687500000000000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (1.0000000000000000000000000000000000000000000000000000000000000000,1.0000000000000000000000000000000000000000000000000000000000000000)
Can anyone explain what is going on?
Thanks in advance,
Tim
-- Tim van Erven<tim@timvanerven.nl> <mailto:tim@timvanerven.nl> www.timvanerven.nl <http://www.timvanerven.nl>
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-- Tim van Erven <tim@timvanerven.nl> www.timvanerven.nl
I'm not really an expert in this space, but the one (rather tedious) exercise I could suggest is that for each differing option between -O0 and -O2, add the corresponding explicit option until you get the deviation you're exhibiting. I did do a diff on your settings, and I didn't really see anything that stood out to me, hence why I'm suggesting the switch-by-switch test. I'm not a boost contributor just a user and rare bug reporter. This does feel like a floating-point optimization switch, though, at least to me. Regards, Nate On Sat, Mar 3, 2018 at 2:08 PM, Tim van Erven <tim@timvanerven.nl> wrote:
Hi Nate,
Thanks for your help.
Below is the output from gcc 7.2.0 on mac os. Apparently the difference already happens between -O0 and -O1. To summarize: - gcc on linux with boost 1.58 - clang and gcc 7.2.0 on mac os with boost 1.66 all give wrong (or at least inconsistent) output depending on optimization options. (Since third1 and third2 are both < 1/3, multiplying them by 3 should give an interval with lower end-point < 1, but it sometimes doesn't.)
I am attaching the outputs of g++-7 -Q -O0 --help=optimizers > o0.txt $ g++-7 -Q -O1 --help=optimizers > o1.txt
$ g++-7 foo.cpp -o foo $ ./foo third1 = 0.333333333333333314829616256247390992939472198486328125000000 0000 third2 = 0.333333333333333314829616256247390992939472198486328125000000 0000 v1 = (0.999999999999999888977697537484345957636833190917968750000000 0000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (0.999999999999999888977697537484345957636833190917968750000000 0000,1.0000000000000000000000000000000000000000000000000000000000000000)
$ g++-7 -O1 foo.cpp -o foo ./foo third1 = 0.333333333333333314829616256247390992939472198486328125000000 0000 third2 = 0.333333333333333314829616256247390992939472198486328125000000 0000 v1 = (0.999999999999999888977697537484345957636833190917968750000000 0000,1.0000000000000000000000000000000000000000000000000000000000000000) v2 = (1.000000000000000000000000000000000000000000000000000000000000 0000,1.0000000000000000000000000000000000000000000000000000000000000000)
Best, Tim
On 02/03/2018 18:23, Nathan Ernst wrote:
I'm not sure what's going on (seems like maybe a fast but error prone floating point rounding), but comparing the optimization flags enabled between -O0 and -O2 might help shed some light on it.
You can get the explicit optimization flags enabled for your compiler via: g++ -Q -O2 --help=optimizers g++ -Q -O0 --help=optimizers
Regards, Nate
On Fri, Mar 2, 2018 at 10:17 AM, Tim van Erven via Boost-users < boost-users@lists.boost.org> wrote:
Dear all,
I am trying to understand why I am getting different numerical results with the interval library depending on the optimization level of the compiler.
I am attaching the smallest example I have been able to create:
# On my Mac laptop Apple LLVM version 9.0.0 (clang-900.0.39.2) boost 1.66 (installed via homebrew) $ g++ foo.cpp -o foo $ ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000 000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000 000000 v1 = (0.999999999999999888977697537484345957636833190917968750000 0000000,1.00000000000000000000000000000000000000000000000000 00000000000000) v2 = (0.999999999999999888977697537484345957636833190917968750000 0000000,1.00000000000000000000000000000000000000000000000000 00000000000000)
$ g++ -O2 foo.cpp -o foo $ ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000 000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000 000000 v1 = (1.000000000000000000000000000000000000000000000000000000000 0000000,1.00000000000000000000000000000000000000000000000000 00000000000000) v2 = (1.000000000000000000000000000000000000000000000000000000000 0000000,1.00000000000000000000000000000000000000000000000000 00000000000000)
I would expect to get the same output in both cases, but the lower end-points are different in the second case, and seem wrong to me since third2 * 3.0 < 1.0.
# On my Linux machine the effect is different: gcc version 5.4.0 20160609 boost 1.58 on Ubuntu 16.04.9
$ g++ foo.cpp -o foo $ ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000 000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000 000000 v1 = (0.999999999999999888977697537484345957636833190917968750000 0000000,1.00000000000000000000000000000000000000000000000000 00000000000000) v2 = (0.999999999999999888977697537484345957636833190917968750000 0000000,1.00000000000000000000000000000000000000000000000000 00000000000000)
$ g++ -O2 foo.cpp -o foo $ ./foo third1 = 0.3333333333333333148296162562473909929394721984863281250000 000000 third2 = 0.3333333333333333148296162562473909929394721984863281250000 000000 v1 = (0.999999999999999888977697537484345957636833190917968750000 0000000,1.00000000000000000000000000000000000000000000000000 00000000000000) v2 = (1.000000000000000000000000000000000000000000000000000000000 0000000,1.00000000000000000000000000000000000000000000000000 00000000000000)
Can anyone explain what is going on?
Thanks in advance,
Tim
-- Tim van Erven <tim@timvanerven.nl> <tim@timvanerven.nl>www.timvanerven.nl
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-- Tim van Erven <tim@timvanerven.nl> <tim@timvanerven.nl>www.timvanerven.nl
On 6 March 2018 at 20:43, Nathan Ernst via Boost-users < boost-users@lists.boost.org> wrote:
This does feel like a floating-point optimization switch, though, at least to me.
Additionally, the optimization level it self could interfere with the order of calculation, leading to possibly different results. degski
Not sure this "random" aswer explains it: 1/3 it's a recurring decimal (https://en.wikipedia.org/ wiki/Repeating_decimal), that means it is not possible to represent it within a limited number of bits (even in 64 bits). So your "bug" example, I would say that it's not a bug. Using optimization in one of the cases the compiler can figure out, that the value is 1, by analyzing constant values assigned to v2 and lazy expanding the expression (template expansions, etc), (which is correct math value). The other option v1, uses memory storage, and because of that, it cannot lazy expand the expression at the function call, so because you cannot store 1/3 perfectly in 64 bits, after multiplying it, it always results in a number lower 1. On Wed, Mar 7, 2018 at 11:54 AM, degski via Boost-users < boost-users@lists.boost.org> wrote:
On 6 March 2018 at 20:43, Nathan Ernst via Boost-users < boost-users@lists.boost.org> wrote:
This does feel like a floating-point optimization switch, though, at least to me.
Additionally, the optimization level it self could interfere with the order of calculation, leading to possibly different results.
degski
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Hi Degski, But if I assign 1/3 to a double and then print that to the console, then I would expect the compiler to be committed to the value shown in the console, but apparently it isn't, and still does optimization. Best, Tim On 07/03/2018 15:53, Mário Costa via Boost-users wrote:
Not sure this "random" aswer explains it:
1/3 it's a recurring decimal (https://en.wikipedia.org/wiki/Repeating_decimal <https://en.wikipedia.org/wiki/Repeating_decimal>), that means it is not possible to represent it within a limited number of bits (even in 64 bits).
So your "bug" example, I would say that it's not a bug. Using optimization in one of the cases the compiler can figure out, that the value is 1, by analyzing constant values assigned to v2 and lazy expanding the expression (template expansions, etc), (which is correct math value). The other option v1, uses memory storage, and because of that, it cannot lazy expand the expression at the function call, so because you cannot store 1/3 perfectly in 64 bits, after multiplying it, it always results in a number lower 1.
On Wed, Mar 7, 2018 at 11:54 AM, degski via Boost-users <boost-users@lists.boost.org <mailto:boost-users@lists.boost.org>> wrote:
On 6 March 2018 at 20:43, Nathan Ernst via Boost-users <boost-users@lists.boost.org <mailto:boost-users@lists.boost.org>> wrote:
This does feel like a floating-point optimization switch, though, at least to me.
Additionally, the optimization level it self could interfere with the order of calculation, leading to possibly different results.
degski
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I don't really understand what you mean. lets say you have double v1 = 1.0/3.0; double computation = v1 * 3; Using, O2, the compiler might resolve, by performing expression analisys at compile time, that you have always a constant value of 1/3 * 3 = 1. Now using O0, it might not optimize, and compute the value at runtime (just as an example). Because 1/3 does not fit into any number of bits without lossing precision (unless you'd be using some symbolic library), multiplying v1 * 3, will result in a value diferent from 1, that will be the rule. Another issue Degski mentions, its the error propagation associated with the order the expressions are evaluated/executed ... On Wed, Mar 7, 2018 at 5:09 PM, Tim van Erven via Boost-users < boost-users@lists.boost.org> wrote:
Hi Degski,
But if I assign 1/3 to a double and then print that to the console, then I would expect the compiler to be committed to the value shown in the console, but apparently it isn't, and still does optimization.
Best, Tim
On 07/03/2018 15:53, Mário Costa via Boost-users wrote:
Not sure this "random" aswer explains it:
1/3 it's a recurring decimal (https://en.wikipedia.org/wiki /Repeating_decimal), that means it is not possible to represent it within a limited number of bits (even in 64 bits).
So your "bug" example, I would say that it's not a bug. Using optimization in one of the cases the compiler can figure out, that the value is 1, by analyzing constant values assigned to v2 and lazy expanding the expression (template expansions, etc), (which is correct math value). The other option v1, uses memory storage, and because of that, it cannot lazy expand the expression at the function call, so because you cannot store 1/3 perfectly in 64 bits, after multiplying it, it always results in a number lower 1.
On Wed, Mar 7, 2018 at 11:54 AM, degski via Boost-users < boost-users@lists.boost.org> wrote:
On 6 March 2018 at 20:43, Nathan Ernst via Boost-users < boost-users@lists.boost.org> wrote:
This does feel like a floating-point optimization switch, though, at least to me.
Additionally, the optimization level it self could interfere with the order of calculation, leading to possibly different results.
degski
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-- Tim van Erven <tim@timvanerven.nl> <tim@timvanerven.nl>www.timvanerven.nl
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Hi Mário, My (somewhat naive) view of compilers is that they can only do optimization that has no visible effects on the behavior of the program. What I meant is: double v1 = 1.0/3.0; printf("%f", v1); double computation = v1 * 3; Then the print statement will show the user some value for v1 that fits in a double. So I would expect that it is then no longer free to treat v1 as exactly 1/3, because the use has already observed a different value. Best, TIm On 07/03/2018 18:43, Mário Costa wrote:
I don't really understand what you mean.
lets say you have
double v1 = 1.0/3.0;
double computation = v1 * 3;
Using, O2, the compiler might resolve, by performing expression analisys at compile time, that you have always a constant value of 1/3 * 3 = 1.
Now using O0, it might not optimize, and compute the value at runtime (just as an example).
Because 1/3 does not fit into any number of bits without lossing precision (unless you'd be using some symbolic library), multiplying v1 * 3, will result in a value diferent from 1, that will be the rule.
Another issue Degski mentions, its the error propagation associated with the order the expressions are evaluated/executed ...
On Wed, Mar 7, 2018 at 5:09 PM, Tim van Erven via Boost-users <boost-users@lists.boost.org <mailto:boost-users@lists.boost.org>> wrote:
Hi Degski,
But if I assign 1/3 to a double and then print that to the console, then I would expect the compiler to be committed to the value shown in the console, but apparently it isn't, and still does optimization.
Best, Tim
On 07/03/2018 15:53, Mário Costa via Boost-users wrote:
Not sure this "random" aswer explains it:
1/3 it's a recurring decimal (https://en.wikipedia.org/wiki/Repeating_decimal <https://en.wikipedia.org/wiki/Repeating_decimal>), that means it is not possible to represent it within a limited number of bits (even in 64 bits).
So your "bug" example, I would say that it's not a bug. Using optimization in one of the cases the compiler can figure out, that the value is 1, by analyzing constant values assigned to v2 and lazy expanding the expression (template expansions, etc), (which is correct math value). The other option v1, uses memory storage, and because of that, it cannot lazy expand the expression at the function call, so because you cannot store 1/3 perfectly in 64 bits, after multiplying it, it always results in a number lower 1.
On Wed, Mar 7, 2018 at 11:54 AM, degski via Boost-users <boost-users@lists.boost.org <mailto:boost-users@lists.boost.org>> wrote:
On 6 March 2018 at 20:43, Nathan Ernst via Boost-users <boost-users@lists.boost.org <mailto:boost-users@lists.boost.org>> wrote:
This does feel like a floating-point optimization switch, though, at least to me.
Additionally, the optimization level it self could interfere with the order of calculation, leading to possibly different results.
degski
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-- Tim van Erven<tim@timvanerven.nl> <mailto:tim@timvanerven.nl> www.timvanerven.nl <http://www.timvanerven.nl>
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-- Tim van Erven <tim@timvanerven.nl> www.timvanerven.nl
Hello
My (somewhat naive) view of compilers is that they can only do optimization that has no visible effects on the behavior of the program.
I wouldn't be surprised if ieee floating point is an exception to that, especially with optimizations enabled.
What I meant is: double v1 = 1.0/3.0; printf("%f", v1); double computation = v1 * 3; Then the print statement will show the user some value for v1 that fits in a double. So I would expect that it is then no longer free to treat v1 as exactly 1/3, because the use has already observed a different value.
I think in order to show the number to the user it would have to be copied to memory or at least a regular register but further computation could continue to use the more accurate floating point register. And the compiler might still optimize the computation away and just show you the result of printf(..., 1.0/3.0). I don't know if writing constexpr double v1 = 1.0/3.0 would change anything, at least if particular optimizations are enabled and/or disabled. Ilja
Ilja, Paul, Degski, Thanks for your help. I think that Ilja's comment below explains what's going on: compilers don't strictly respect IEEE floating point when they have optimizations turned on (see also the explanation here: https://stackoverflow.com/questions/7517588/different-floating-point-result-...). @Degski: I am not actually interested in fractions. The background is that I am using the interval library to compare the numerical accuracy of various statistical algorithms in a setting where we know that some of the methods will run out of precision for large data sets, and I am getting incorrect intervals (that do not contain the correct answer) when compiling with clang, but everything works when compiling with gcc. When trying to debug this I found that the numerical results diverged right from the first interval calculations and I could not understand why. I think I have a better handle on this now. Best, Tim On 08/03/2018 09:49, Ilja Honkonen wrote:
Hello
My (somewhat naive) view of compilers is that they can only do optimization that has no visible effects on the behavior of the program.
I wouldn't be surprised if ieee floating point is an exception to that, especially with optimizations enabled.
What I meant is: double v1 = 1.0/3.0; printf("%f", v1); double computation = v1 * 3; Then the print statement will show the user some value for v1 that fits in a double. So I would expect that it is then no longer free to treat v1 as exactly 1/3, because the use has already observed a different value.
I think in order to show the number to the user it would have to be copied to memory or at least a regular register but further computation could continue to use the more accurate floating point register. And the compiler might still optimize the computation away and just show you the result of printf(..., 1.0/3.0). I don't know if writing constexpr double v1 = 1.0/3.0 would change anything, at least if particular optimizations are enabled and/or disabled.
Ilja
-- Tim van Erven <tim@timvanerven.nl> www.timvanerven.nl
On Mon, Mar 12, 2018 at 10:08 AM, Tim van Erven via Boost-users <boost-users@lists.boost.org> wrote:
Ilja, Paul, Degski,
Thanks for your help. I think that Ilja's comment below explains what's going on: compilers don't strictly respect IEEE floating point when they have optimizations turned on (see also the explanation here: https://stackoverflow.com/questions/7517588/different-floating-point-result-...).
@Degski: I am not actually interested in fractions. The background is that I am using the interval library to compare the numerical accuracy of various statistical algorithms in a setting where we know that some of the methods will run out of precision for large data sets, and I am getting incorrect intervals (that do not contain the correct answer) when compiling with clang, but everything works when compiling with gcc. When trying to debug this I found that the numerical results diverged right from the first interval calculations and I could not understand why. I think I have a better handle on this now.
Indeed, getting deterministic results using floating point numbers is hard (and even more so if you move between compilers, processors, architectures, etc.). If you want to achieve it, you will want a very, very, very through test suite to feel confident about the results :-) There are some good articles/books on the topic -- for instance, you can look for advice from some multiplayer games which implemented deterministic physics simulations between machines. However, note that those don't care about the error, as long as it is the same error everywhere. If you need proper results, then you can save yourself a lot of trouble using a library that allows you to use arbitrary precision numbers (specially if later on you need higher precision for something else). See for instance the GMP (Multiple Precision Arithmetic), MPFR (Multiple Precision Floating-Point Reliable) and MPC (Multiple Precision Complex) libraries, used by GCC itself. For an example of how to implement complex algorithms ensuring *exact* results by increasing the precision as needed, see the CGAL (Computational Geometry Algorithms Library). Hope that helps! Miguel
Would it help to use constexpr double v1 and constexpr computation, to see what the compiler can compute at compile-time and to use a better print method std::cout.precision(std::numeric_limits<double>::max_digits10); std::cout << v1 << “ “ << computation << std::endl; to see the ‘true’ results of both your doubles? godbolt.org may also help you see what assembler is produced. Paul --- Paul A. Bristow Prizet Farmhouse Kendal UK LA8 8AB +44 (0) 1539 561830 From: Boost-users [mailto:boost-users-bounces@lists.boost.org] On Behalf Of Tim van Erven via Boost-users Sent: 08 March 2018 08:36 To: Mário Costa; boost-users@lists.boost.org Cc: Tim van Erven Subject: Re: [Boost-users] [Interval] Help debugging compiler optimization Hi Mário, My (somewhat naive) view of compilers is that they can only do optimization that has no visible effects on the behavior of the program. What I meant is: double v1 = 1.0/3.0; printf("%f", v1); double computation = v1 * 3; Then the print statement will show the user some value for v1 that fits in a double. So I would expect that it is then no longer free to treat v1 as exactly 1/3, because the use has already observed a different value. Best, TIm On 07/03/2018 18:43, Mário Costa wrote: I don't really understand what you mean. lets say you have double v1 = 1.0/3.0; double computation = v1 * 3; Using, O2, the compiler might resolve, by performing expression analisys at compile time, that you have always a constant value of 1/3 * 3 = 1. Now using O0, it might not optimize, and compute the value at runtime (just as an example). Because 1/3 does not fit into any number of bits without lossing precision (unless you'd be using some symbolic library), multiplying v1 * 3, will result in a value diferent from 1, that will be the rule. Another issue Degski mentions, its the error propagation associated with the order the expressions are evaluated/executed ... On Wed, Mar 7, 2018 at 5:09 PM, Tim van Erven via Boost-users <boost-users@lists.boost.org> wrote: Hi Degski, But if I assign 1/3 to a double and then print that to the console, then I would expect the compiler to be committed to the value shown in the console, but apparently it isn't, and still does optimization. Best, Tim On 07/03/2018 15:53, Mário Costa via Boost-users wrote: Not sure this "random" aswer explains it: 1/3 it's a recurring decimal (https://en.wikipedia.org/wiki/Repeating_decimal), that means it is not possible to represent it within a limited number of bits (even in 64 bits). So your "bug" example, I would say that it's not a bug. Using optimization in one of the cases the compiler can figure out, that the value is 1, by analyzing constant values assigned to v2 and lazy expanding the expression (template expansions, etc), (which is correct math value). The other option v1, uses memory storage, and because of that, it cannot lazy expand the expression at the function call, so because you cannot store 1/3 perfectly in 64 bits, after multiplying it, it always results in a number lower 1. On Wed, Mar 7, 2018 at 11:54 AM, degski via Boost-users <boost-users@lists.boost.org> wrote: On 6 March 2018 at 20:43, Nathan Ernst via Boost-users <boost-users@lists.boost.org> wrote: This does feel like a floating-point optimization switch, though, at least to me. Additionally, the optimization level it self could interfere with the order of calculation, leading to possibly different results. degski _______________________________________________ Boost-users mailing list Boost-users@lists.boost.org https://lists.boost.org/mailman/listinfo.cgi/boost-users _______________________________________________ Boost-users mailing list Boost-users@lists.boost.org https://lists.boost.org/mailman/listinfo.cgi/boost-users -- Tim van Erven <mailto:tim@timvanerven.nl> <tim@timvanerven.nl> www.timvanerven.nl _______________________________________________ Boost-users mailing list Boost-users@lists.boost.org https://lists.boost.org/mailman/listinfo.cgi/boost-users -- Tim van Erven <mailto:tim@timvanerven.nl> <tim@timvanerven.nl> www.timvanerven.nl
On 8 March 2018 at 02:36, Tim van Erven via Boost-users < boost-users@lists.boost.org> wrote:
My (somewhat naive) view of compilers is that they can only do optimization that has no visible effects on the behavior of the program.
Here is what the different floating point behaviors (strict/fast/precise) mean with VC (I realize you're on linux, but the same must count/exist on linux as these are CPU features). As you can see, it's intricate. In general what you are trying to do is not possible (that way), you'll need to allow for some delta between values that if the difference is smaller that delta, this qualifies them as being equal. So far so good so. We have our friends FLT_EPSILON and DBL_EPSILON from the STL <http://en.cppreference.com/w/cpp/types/climits>. These don't help you much, the delta defined by those two is the difference between 2 consecutive floats on the interval from 1. to 2.. So towards 0., the EPSILON is getting smaller, over 2. it's getting bigger, suggesting different approaches are needed for different parts of the real numbers line. Daniel Lemire <https://lemire.me/blog/2017/02/28/how-many-floating-point-numbers-are-in-the-interval-01/> has written about this subject and has suggested solutions in the past (search the blog for more articles pertaining to this subject), for only to (partially) revert those opinions later. It's quite a problem really. In case you are really working with fractions (as in your example 3 * (1/3)), it would be better to use a fractions library. The above assumes IEEE754 floating point numbers <https://en.wikipedia.org/wiki/Floating-point_arithmetic#IEEE_754:_floating_point_in_modern_computers> . degski
From: Boost-users [mailto:boost-users-bounces@lists.boost.org] On Behalf Of degski via Boost-users Sent: 08 March 2018 13:03 To: boost-users@lists.boost.org Cc: degski Subject: Re: [Boost-users] [Interval] Help debugging compiler optimization On 8 March 2018 at 02:36, Tim van Erven via Boost-users <boost-users@lists.boost.org> wrote: My (somewhat naive) view of compilers is that they can only do optimization that has no visible effects on the behavior of the program. Here is what the different floating point behaviors (strict/fast/precise) mean with VC (I realize you're on linux, but the same must count/exist on linux as these are CPU features). As you can see, it's intricate. In general what you are trying to do is not possible (that way), you'll need to allow for some delta between values that if the difference is smaller that delta, this qualifies them as being equal. So far so good so. We have our friends FLT_EPSILON and DBL_EPSILON from the STL <http://en.cppreference.com/w/cpp/types/climits> . These don't help you much, the delta defined by those two is the difference between 2 consecutive floats on the interval from 1. to 2.. So towards 0., the EPSILON is getting smaller, over 2. it's getting bigger, suggesting different approaches are needed for different parts of the real numbers line. Daniel Lemire <https://lemire.me/blog/2017/02/28/how-many-floating-point-numbers-are-in-the-interval-01/> has written about this subject and has suggested solutions in the past (search the blog for more articles pertaining to this subject), for only to (partially) revert those opinions later. It's quite a problem really. In case you are really working with fractions (as in your example 3 * (1/3)), it would be better to use a fractions library. The above assumes IEEE754 floating point numbers <https://en.wikipedia.org/wiki/Floating-point_arithmetic#IEEE_754:_floating_point_in_modern_computers> . Boost.math function float_distance http://www.boost.org/doc/libs/1_66_0/libs/math/doc/html/math_toolkit/next_fl... will show you the ‘(signed) numbers of bits different’ between two values (or any floating point type) or more formally “Returns the distance between a and b: the result is always a signed integer value (stored in floating-point type FPT) representing the number of distinct representations between a and b.” This more helpful than std::numeric_limits<FPT>::epsilon() You can also use the related functions float_next and float_prior (and next_after) to show how the values are shown in decimal. But if you really, really want rationals, then you probably should use the rationals library? http://www.boost.org/doc/libs/1_66_0/libs/rational/index.html HTH Paul --- Paul A. Bristow Prizet Farmhouse Kendal UK LA8 8AB +44 (0) 1539 561830
participants (7)
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degski -
Ilja Honkonen -
Miguel Ojeda -
Mário Costa -
Nathan Ernst -
Paul A. Bristow -
Tim van Erven