three_fma

auto eve::three_fma = functor<three_fma_t>

inlineconstexpr

Defined in Header

#include <eve/module/core.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
  constexpr auto three_fma(floating_value auto a, floating_value auto b, floating_value auto c) noexcept; //1
 
   // Semantic options
   constexpr auto three_fma[pedantic](floating_value auto x, floating_value auto y)  noexcept;            //2
}

Parameters

• a, b, 'c': floating arguments.

Return value

1. Computes elementwise a triplet of values [f, r1, r2] such that:
   • f is fma(a, x, y)
   • \f$ a\otimes x\oplus y = r1\oplus r2\oplus r3\f$ exactly
   • \( |r1 \oplus r2| \le ulp(r1)/2\)
   • \f$ |r2| \le ulp(r2)/2\f$
2. take care of overflow

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

External references

• [Error free transformations](https://www-pequan.lip6.fr/~graillat/papers/nolta07.pdf
• Exact and Approximated error of the FMA

Example

// revision 1
#include <eve/module/core.hpp>
#include <iostream>
 
int main()
{
  eve::wide wf0 = {30.0, 2.5, -32.7, 1.0};
  eve::wide wf1 = {4.2, 1.5, -100.834, eve::eps(eve::as<double>())/2};
  eve::wide wf2 = {2.0, 1.234, -2.0,  eve::eps(eve::as<double>())/2};
 
  std::cout << "<- wf0                      = " << wf0 << "\n";
  std::cout << "<- wf1                      = " << wf1 << "\n";
  std::cout << "<- wf2                      = " << wf2 << "\n";
 
  std::cout << "-> three_fma(wf0, wf1, wf2) = " << eve::three_fma(wf0, wf1, wf2) << "\n";
  using f_t =  eve::float16_t;
  f_t aa(1000);
  auto [a, b, c] = eve::three_fma(aa, aa, -aa);
  std::cout << float(a) << " " << float(b) << " " << float(c) << std::endl;
}