Re: [boost][multiprecision/mpc][math/quadrature] Why boost::multiprecision::exp gets stuck when evaluating complex-valued integral?

From: John Maddock (jz.maddock_at_[hidden])
Date: 2021-08-05 16:54:36

> I have encountered a problem while using Boost C++ libraries ( 
> multiprecision/mpc.hpp, math/quadrature) which I cannot resolve.
>
> This problems appears when running the following piece of code
>
> ||

OK, the value that triggers the issue is 
-6.275135555002646369320950230099689165841342351751646e-118909138 - 
6.275135555002646369320950230099689165841342351751646e-118909138i

And this appears to be an exponent range issue - basically mpc_exp gets 
slower and slower as the exponents approach -INF and eventually grinds 
to a halt.

I'm not yet sure if this is a bug in MPC, or if you've just hit a 
stupidly hard value to compute - wolframalpha dies as well with this case.

For the purposes of calculating the integral, guess you could just 
return 1 from your functor whenever the exponent is sufficiently small?

HTH, John.

> |#include <boost/math/constants/constants.hpp> #include 
> <boost/math/quadrature/exp_sinh.hpp> #include 
> <boost/multiprecision/mpc.hpp> #include 
> <boost/multiprecision/mpfr.hpp> #include 
> <boost/math/special_functions/fpclassify.hpp> namespace mpns = 
> boost::multiprecision; typedef 
> mpns::number<boost::multiprecision::mpc_complex_backend <50> > 
> mpc_type ; typedef mpc_type::value_type mp_type ; int main() { using 
> boost::math::constants::root_pi ; mpc_type z{mp_type(1),mp_type(1)} ; 
> auto f = [&](mp_type x) { //actually I did not test if all these 
> conditions are needed... if (boost::math::fpclassify<mp_type> (x) == 
> FP_ZERO) { return mpc_type(mp_type(1)) ; }; if 
> (boost::math::fpclassify<mp_type> (x) == FP_INFINITE) { return 
> mpc_type(mp_type(0)) ; }; mp_type x2 = mpns::pow(x,2U) ; if 
> (boost::math::fpclassify<mp_type> (x2) == FP_ZERO) { return 
> mpc_type(mp_type(1)) ; }; if (boost::math::fpclassify<mp_type> (x2) == 
> FP_INFINITE) { return mpc_type(mp_type(0)) ; }; mpc_type ex2 = 
> mpns::exp(-z*x2) ; if (boost::math::fpclassify<mpc_type> (ex2) == 
> FP_ZERO) { return mpc_type(mp_type(0)) ; }; return ex2 ; } ; mp_type 
> termination = boost::math::tools::root_epsilon <mp_type> () ; mp_type 
> error; mp_type L1; size_t max_halvings = 12; 
> boost::math::quadrature::exp_sinh<mp_type> integrator(max_halvings) ; 
> mpc_type res = integrator.integrate(f,termination,&error,&L1) ; 
> mpc_type div = 2U*mpns::sqrt(z) ; mpc_type result = 
> (mpc_type(root_pi<mp_type> ())/div) - res ; return 0; } |
>
> ||Namely, the problem appears when evaluating the exponent.
>
> The code is compiled without any problems, but hangs on computing
>
> |Â Â Â  mpc_type ex2 = mpns::exp(-z*x2) ;|
>
> It was possible to go into the function while debugging.
>
> It crashed eventually, when the compiler reached "unable to resolve 
> non-existing file.../src/init2.c".
>
> I let it run for a while checking the call stack. It appears that the 
> programs is stuck atcalling ___gmpn_sub_n_coreisbr().
>
> Or better, in the call stuck it appeared frequently.
>
>
> I did several tests.
>
> The real-valued version (with mpfr_backend <2000>) works without any 
> problems.
>
> cpp_complex_backend <100> works fine, but I could not test higher 
> precision yet, since it is much slower.
>
> I found a work-around which is not ideal. Namely,
>
> mpc_type ex2 = mpc_type(mpns::exp(x2)) ;
>     mpc_type ezx2 = mpns::pow(ex2,-z) ;
>
> works fine with mpc_complex_backend <2000>.
>
> The lambda-function as it is declared in the code above works and 
> yields correct numbers.
>
> The problem appears when it is called from the integrator.
>
>
> My system.
>
> I use openSUSE Tumbeleweed.
>
> I installed boost libraries as provided by 
> |boost_1_76_0-gnu-mpich-hpc-devel.|
>
> Complier -> g++, cppStandard gnu+17.
>
> I check that I have all libs, e.g. libgmp, libmpc, libmpfr and etc.
>
> All headers are present (the programs is complied without any warnings).
>
>
> Thank you in advance and
>
> Best wishes,
>
> Kirill
>
> ||
>
>
>
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