two_fma_approx

auto eve::two_fma_approx = functor<two_fma_approx_t>

inlineconstexpr

Defined in Header

#include <eve/module/core.hpp>

Callable Signatures

namespace eve
{
  constexpr auto two_fma_approx(floating_value auto a, floating_value auto b, floating_value auto c) noexcept;
}

Parameters

• a, b, 'c': floating arguments.

Return value

Computes elementwise a pair of values [f, e1] such that:

• f is fma(a, x, y)
• \f$ a\otimes x\oplus y = r1\oplus e1\f$ with a very small error (less than 14*eps)

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

External references

• Exact and Approximated error of the FMA

Example

// revision 0
#include <eve/module/core.hpp>
#include <iostream>
#include <iomanip>
 
int main()
{
  eve::wide a = {1.0, 2.0, 3.0, 1.0e8};
  eve::wide x = {0.1, 0.2, 0.3, 1.0e-8};
  eve::wide y = {1.0e-20, 1.0, 2.0, 1.0};
 
  std::cout << std::setprecision(20);
  std::cout << "<- a                        = " << a << "\n";
  std::cout << "<- x                        = " << x << "\n";
  std::cout << "<- y                        = " << y << "\n";
 
  auto [f, e1] = eve::two_fma_approx(a, x, y);
  std::cout << "-> f  (the fma itself)      = " << f  << "\n";
  std::cout << "-> e1 (the rounding error)  = " << e1 << "\n";
}