two_prod

eve::two_prod = {}

inlineconstexpr

Computes the elementwise pair of product and error,.

Defined in Header

#include <eve/module/core.hpp>

Callable Signatures

namespace eve
{
   template< eve::floating_value T, eve::floating_value U  >
   auto two_prod(T x, U y) noexcept;
}

Parameters

• x, y : argument.

Return value

Computes elementwise a pair of values [a,e] such that:

• a is x*y
• e is a value such that a \(\oplus\)e is equal to x \(\otimes\)y

where \(\oplus\) (resp. \(\otimes\)) adds (resp. multiplies) its two parameters with infinite precision.

Example

#include <eve/module/core.hpp>
#include <eve/wide.hpp>
#include <iostream>
#include <iomanip>
 
using wide_ft = eve::wide<float, eve::fixed<4>>;
 
int main()
{
  float ep = eve::eps(eve::as<float>());
  wide_ft pf = {1.0f+ep, 0.5f*(1.0f+ep*4), -1.3f,   1.0f+4*ep};
  wide_ft qf = {1.0f-ep, 0.5f,             -1.3f,   1.0f-ep/2};
 
 
  auto [a, e]  = eve::two_prod(pf, qf);
  std::cout << "---- simd" << std::setprecision(10) << '\n'
            << "<- pf                = " << pf << '\n'
            << "<- qf                = " << qf << '\n'
            << "-> two_prod(pf, qf)  = [" << '\n'
            << "                      " << a << ", \n"
            << "                      " << e << '\n'
            << "                      ]\n";
 
  float xf = 1+ep, yf = 1-ep;
  auto [sa, se] =  eve::two_prod(xf, yf);
 
  std::cout << "---- scalar" << '\n'
            << "<- xf               =  " << xf << '\n'
            << "<- yf               =  " << yf << '\n'
            << "-> two_prod(xf, yf) = [" << sa << ", " << se << "]\n";
  return 0;
}