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 = 0.3333333333333333148296162562473909929394721984863281250000000000
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> 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>
www.timvanerven.nl

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-- 
Tim van Erven <tim@timvanerven.nl>
www.timvanerven.nl