fma

eve::fma = functor<fma_t>

inlineconstexpr

Header file

#include <eve/module/core.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto fma(value auto x, value auto y, value auto z)                          noexcept; // 1
 
   // Lanes masking
   constexpr auto fma[conditional_expr auto c](value auto x, value auto y, value auto z) noexcept; // 2
   constexpr auto fma[logical_value auto m](value auto x, value auto y, value auto z)    noexcept; // 2
 
   // Semantic option
   constexpr auto fma[pedantic](value auto x, value auto y, value auto z)                noexcept; // 3
   constexpr auto fma[promote](value auto x, value auto y, value auto z)                 noexcept; // 4
   constexpr auto add[lower](value auto x, value auto y, value auto z)                   noexcept; // 5
   constexpr auto add[upper](value auto x, value auto y, value auto z)                   noexcept; // 6
   constexpr auto fma[lower][srict](value auto x, value auto y, value auto z)            noexcept; // 5
   constexpr auto fma[upper][srict](value auto x, value auto y, value auto z)            noexcept; // 6
}

Parameters

• x, y, z : values.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. The value of x*y+z as if calculated to infinite precision and rounded once is returned, but only if the hardware is in capacity to do it at reasonable cost.
2. The operation is performed conditionnaly
3. pedantic option always ensures the full compliance to fam properties. This can be very expensive if the system has no hardware capability.
4. The operation is performed as if the parameters where promoted to the common type of the three parameters.
5. The operation is computed in a 'round toward \(-\infty\) mode. The result is guaranted to be less or equal to the exact one (except for Nans). Combined with strict the option ensures generally faster computation, but strict inequality.
6. The operation is computed in a 'round toward \(\infty\) mode. The result is guaranted to be greater or equal to the exact one (except for Nans). Combined with strict the option ensures generally faster computation, but strict inequality.

Note

• lowerand upper can be associated with raw to provide a correct, faster but less accurate version

External references

• C++ standard reference

Example

// revision 0
#include <eve/module/core.hpp>
#include <iostream>
#include <iomanip>
int main()
{
  eve::wide wf0{0.0, 1.0, 2.0, 3.0, -1.0, -2.0, -3.0, -4.0};
  eve::wide wf1{0.0, -4.0, 1.0, -1.0, 2.0, -2.0, 3.0, -3.0};
  eve::wide wf2{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0};
  eve::wide wi0{0, 1, 2, 3, -1, -2, -3, -4};
  eve::wide wi1{0, -4, 1, -1, 2, -2, 3, -3};
  eve::wide wi2{0, 1, 2 ,3, 4, 5, 6, 7};
  eve::wide wu0{0u, 1u, 2u, 3u, 4u, 5u, 6u, 7u};
  eve::wide wu1{7u, 6u, 5u, 4u, 3u, 2u, 1u, 0u};
  eve::wide wu2{0u, 2u, 4u, 6u, 1u, 3u, 5u, 7u};
 
  std::cout << "<- wf0                                = " << wf0 << "\n";
  std::cout << "<- wf1                                = " << wf1 << "\n";
  std::cout << "<- wf2                                = " << wf2 << "\n";
  std::cout << "<- wi0                                = " << wi0 << "\n";
  std::cout << "<- wi1                                = " << wi1 << "\n";
  std::cout << "<- wi2                                = " << wi2 << "\n";
  std::cout << "<- wu0                                = " << wu0 << "\n";
  std::cout << "<- wu1                                = " << wu1 << "\n";
  std::cout << "<- wu2                                = " << wu2 << "\n";
 
  std::cout << "-> fma(wf0, wf1, wf2)                 = " << eve::fma(wf0, wf1, wf2) << "\n";
  std::cout << "-> fma[ignore_last(2)](wf0, wf1, wf2) = " << eve::fma[eve::ignore_last(2)](wf0, wf1, wf2) << "\n";
  std::cout << "-> fma[wf0 != 0](wf0, wf1, wf2)       = " << eve::fma[wf0 != 0](wf0, wf1, wf2) << "\n";
  std::cout << "-> fma[pedantic](wf0, wf1, wf2)       = " << eve::fma[eve::pedantic](wf0, wf1, wf2) << "\n";
  std::cout << "-> fma[promote](wf0, wf1, wf2)        = " << eve::fma[eve::promote](wf0, wf1, wf2) << "\n";
  std::cout << "-> fma(wu0, wu1, wu2)                 = " << eve::fma(wu0, wu1, wu2) << "\n";
  std::cout << "-> fma[ignore_last(2)](wu0, wu1, wu2) = " << eve::fma[eve::ignore_last(2)](wu0, wu1, wu2) << "\n";
  std::cout << "-> fma[wu0 != 0](wu0, wu1, wu2)       = " << eve::fma[wu0 != 0](wu0, wu1, wu2) << "\n";
  std::cout << "-> fma[pedantic](wu0, wu1, wu2)       = " << eve::fma[eve::pedantic](wu0, wu1, wu2) << "\n";
  std::cout << "-> fma[promote](wu0, wu1, wu2)        = " << eve::fma[eve::promote](wu0, wu1, wu2) << "\n";
  std::cout << "-> fma(wi0, wi1, wi2)                 = " << eve::fma(wi0, wi1, wi2) << "\n";
  std::cout << "-> fma[ignore_last(2)](wi0, wi1, wi2) = " << eve::fma[eve::ignore_last(2)](wi0, wi1, wi2) << "\n";
  std::cout << "-> fma[wi0 != 0](wi0, wi1, wi2)       = " << eve::fma[wi0 != 0](wi0, wi1, wi2) << "\n";
  std::cout << "-> fma[pedantic](wi0, wi1, wi2)       = " << eve::fma[eve::pedantic](wi0, wi1, wi2) << "\n";
  std::cout << "-> fma[promote](wi0, wi1, wi2)        = " << eve::fma[eve::promote](wi0, wi1, wi2) << "\n";
 
  std::cout << std::setprecision(20) << "-> fma(wf0, wf1, wf2)          = " << eve::fma(wf0, wf1, wf2) << "\n";
  std::cout << std::setprecision(20) << "-> fma[lower](wf0, wf1, wf2)   = " << eve::fma[eve::lower](wf0, wf1, wf2) << "\n";
  std::cout << std::setprecision(20) << "-> fma[upper](wf0, wf1, wf2)   = " << eve::fma[eve::upper](wf0, wf1, wf2) << "\n";
  std::cout << std::setprecision(20) << "-> fma[lower][strict](wf0, wf1, wf2)   = " << eve::fma[eve::lower][eve::strict](wf0, wf1, wf2) << "\n";
  std::cout << std::setprecision(20) << "-> fma[upper][strict](wf0, wf1, wf2)   = " << eve::fma[eve::upper][eve::strict](wf0, wf1, wf2) << "\n";
}