Cosine rounding failure on macOS

[zfergus]

I am running into issues with the interval library when compiling with Clang. This is the simple failure case:

#include <iomanip>
#include <iostream>

#include <boost/numeric/interval.hpp>

typedef boost::numeric::interval<
    double,
    boost::numeric::interval_lib::policies<
        boost::numeric::interval_lib::save_state<
            boost::numeric::interval_lib::rounded_transc_std<double> >,
        boost::numeric::interval_lib::checking_base<double> > >
    Interval;

int main(int argc, char* argv[])
{
    Interval theta = Interval(0.79358805865013693);
    Interval output = cos(theta);
    std::cout << std::setprecision(std::numeric_limits<double>::digits10 + 1)
              << "[" << output.lower() << ", " << output.upper() << "]"
              << std::endl;
    std::cout << "is empty: "
              << (output.lower() > output.upper() ? "true" : "false")
              << std::endl;
}

The output when compiled with clang is:

[0.7012920012119436, 0.7012920012119435]
is empty: true

You can see that the last digit was rounded improperly resulting in an empty interval. If I try the same case but use rounded_transc_exact for the rounding policy It works as expected:

[0.7012920012119437, 0.7012920012119437]
is empty: false

My compiler info is

Apple clang version 11.0.0 (clang-1100.0.33.17)
Target: x86_64-apple-darwin19.3.0
Thread model: posix

and the example is compiled in debug mode. The examples works fine on GCC (specifically I tested on gcc (Ubuntu 9.2.1-9ubuntu2) 9.2.1 20191008)

Is this an expected failure for Clang?

[zfergus]

Debugging some more, I wanted to verify it would work for GCC on my mac. Using g++-9 (Homebrew GCC 9.2.0_3) 9.2.0, I still get the same rounding failure:

[0.7012920012119436, 0.7012920012119435]
is empty: true

Could this be a problem with the hardware implementation of the trignometric functions? Is it guaranteed that FE_DOWNWARD cos(theta) < FE_UPWARD cos(theta)?

[zfergus]

At this point, I have run it on five different machines:

1. macOS with Intel(R) Core(TM) i7-7567U CPU: fail
2. Ubuntu 19.10 with AMD EPYC 7452 32-Core Processor: pass
3. Ubuntu 18.04.3 LTS with Intel(R) Core(TM) i7-5930K CPU: pass
4. CentOS Linux with Intel(R) Xeon(R) CPU E5-2680 v4: pass
5. CentOS Linux with Intel(R) Xeon(R) CPU E5-2690 v2: pass

All compiled with GCC (of different versions ranging from 7 to 9).