Interval cosine function broken

[NAThompson]

Code to reproduce:

#include <boost/numeric/interval.hpp>

using boost::numeric::interval;
using namespace boost::numeric::interval_lib;

int main()
{
    auto x = cos(interval<double>(2.3));
    return 0;
}

Error message:

g++-7 -Wall -Wextra -Wfatal-errors -fext-numeric-literals main.cpp -o main.x -pthread
main.cpp: In function 'int main()':
main.cpp:8:10: warning: variable 'x' set but not used [-Wunused-but-set-variable]
     auto x = cos(interval<double>(2.3));
          ^
In file included from ../numeric/interval/include/boost/numeric/interval.hpp:30:0,
                 from main.cpp:1:
../numeric/interval/include/boost/numeric/interval/transc.hpp: In instantiation of 'boost::numeric::interval<T, Policies> boost::numeric::cos(const boost::numeric::interval<T, Policies>&) [with T = double; Policies = boost::numeric::interval_lib::policies<boost::numeric::interval_lib::rounded_math<double>, boost::numeric::interval_lib::checking_strict<double> >]':
main.cpp:8:39:   required from here
../numeric/interval/include/boost/numeric/interval/transc.hpp:73:18: error: 'boost::numeric::interval_lib::policies<boost::numeric::interval_lib::rounded_math<double>, boost::numeric::interval_lib::checking_strict<double> >::rounding {aka struct boost::numeric::interval_lib::rounded_math<double>}' has no member named 'cos_down'; did you mean 'conv_down'?
     return I(rnd.cos_down(u), rnd.cos_up(l), true);
              ~~~~^~~~~~~~
              conv_down
compilation terminated due to -Wfatal-errors.
make: *** [main.x] Error 1

Compiled against a fresh clone.

[mclow]

I have reproduced this locally; it appears that none of the rounding policies provide cos_down (and cos_up, and others).

[mclow]

This functionality has been missing for a long time.

[zfergus]

For transcendental functions, you need to specify the rounding policy. For example:

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;

Read more about the rounding policy for transcendental functions here.

[njezersek]

The above solution didn't work for me. But I found a working example here: https://stackoverflow.com/questions/47488323/boost-interval-with-multiprecision

#include <iostream>
#include <boost/numeric/interval.hpp>
#include <boost/numeric/interval/io.hpp>

namespace bn = boost::numeric;
namespace bni = bn::interval_lib;

template <typename T>
using Interval = bn::interval<T, bni::policies<bni::save_state<bni::rounded_transc_exact<T>>, bni::checking_base<T>>>;

int main() {
    Interval<double> x(0.1, 0.2);

    Interval<double> y = sin(x);
    std::cout << y << std::endl; // [0.0998334,0.198669]
}