Re: limited accuracy for tanh-sinh integrator

From: John Maddock (jz.maddock_at_[hidden])
Date: 2020-08-16 20:23:39

On 16/08/2020 21:15, Anirban Pal via Boost-users wrote:
>
> Hello,
>
> I’m using the tanh-sinh integrator to integrate a simple function f(x) 
> = 0.26*x from 3.0 to 4.0.
> The exact result is 0.91. With the integrator I’m getting a result 
> accurate to only 10^-18 with cpp_bin_float_100 multiprecision.
>
You have the double precision constant 0.26 in your code, and since this 
is an inexact binary value, everything that depends on that constant is 
inherently limited to double precision.  Try constructing it as Real(26) 
/ 100.

> |typedef boost::multiprecision::cpp_bin_float_100 Real; int main(int 
> argc, char **argv) { using namespace boost::math::quadrature; using 
> namespace std::placeholders; tanh_sinh<Real> integrator; auto f2 = 
> [](Real x) { Real a = 0.26; return x*a; }; std::cout << 
> std::setprecision(std::numeric_limits<Real>::max_digits10) << "Comp.: 
> " << integrator.integrate(f2, (Real) 3.0, (Real) 4.0) << std::endl; 
> return 0; } |
> I'm getting an output of
>
> Comp.: 
> 0.9100000000000000310862446895043831318616867065429687499999999999999999999999999999999999999999999999429
>
> which I'm a bit curious about. I was wondering if I can improve the 
> result.
>
> Thank you.
>
>
> -- 
> Anirban Pal
>
>
>
>
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