Failure of tanh_sinh when used with mpfr_float

[duhadler]

I have recently started to use the quadrature routines of Boost Math with the mpfr_float data type of Boost Multiprecision.

To my amazement, the following routines work out of the box:

trapezoidal
gauss
exp_sinh
sinh_sinh
ooura_fourier_cos

However, tanh_sinh fails during initialization with the following error message:

Message from thrown exception was :
Error in function boost::multiprecision::itrunc<class boost::multiprecision::number<struct boost::multiprecision::backends::mpfr_float_backend<0, 1>, 1>>(class boost::multiprecision::number<struct boost::multiprecision::backends::mpfr_float_backend<0, 1>, 1>) :
Value inf can not be represented in the target integer type.

This can be fixed by making the following change in line 164 of the file

\boost\math\quadrature\detail\tanh_sinh_detail.hpp

Real l = log(sqrt(2 - x) / sqrt(x));     //Original:  Real l = log(sqrt((2 - x) / x));

[NAThompson]

@duhadler : Thanks! I was just thinking last night that I needed to add some MPFR quadrature tests; looks like this will be a good opportunity to get that done.

I have validated your fix; now I just need to produce an ulps plot to make sure that (say) (log(2-x) - log(x))/2 isn't a better option.

[NAThompson]

For future reference, I found that I had to explicitly specify the return type with MPFR:

    auto f = [](const Real& x)->Real
    {
       return 5*x + 7;
    };

or else I get compile errors on g++-10. Not quite sure why this is the case. . .

[NAThompson]

@duhadler : The issue for tanh_sinh is now fixed. I'll leave this issue open since there is a broader issue of adding tests for MPFR types that needs to be addressed on a longer timescale.