erf

auto eve::erf = functor<erf_t>

inlineconstexpr

Header file

#include <eve/module/special.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto erf(floating_value auto x)                          noexcept; // 1
 
   // Lanes masking
   // Lanes masking
   constexpr auto erf[raw](floating_value auto x)                     noexcept; // 2
   constexpr auto erf[fast](floating_value auto x)                    noexcept; // 2
   constexpr auto erf[conditional_expr auto c](floating_value auto x) noexcept; // 3
   constexpr auto erf[logical_value auto m](floating_value auto x)    noexcept; // 3
}

Parameters

• x: floating value.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. The value of the error function is returned: \( \displaystyle \mbox{erf}(x)=\frac{2}{\sqrt\pi}\int_0^{x} e^{-t^2}\mbox{d}t\). In particular:
   • If the argument is \(\pm0\), \(\pm0\) is returned.
   • If the argument is \(\pm\infty\), \(\pm1\) is returned.
   • If the argument is Nan, nan returned.
2. faster computations at accuracy price, based on atanh(erf(x)) expansion.
3. The operation is performed conditionally.

External references

• C++ standard reference: erf
• Wolfram MathWorld: Erf
• DLMF: Error Functions
• Wikipedia: Error Function

Example

// revision 1
#include <eve/module/special.hpp>
#include <iostream>
 
int main()
{
  eve::wide wf = {0.0f, -0.0f, -1.0f, 1.0f, 2.0f,
                  eve::inf(eve::as<float>()), eve::minf(eve::as<float>()), eve::nan(eve::as<float>())};
 
  std::cout << "<- wf                     = " << wf << "\n";
 
  std::cout << "-> erf(wf)                = " << eve::erf(wf) << "\n";
  std::cout << "-> erf[ignore_last(2)](wf)= " << eve::erf[eve::ignore_last(2)](wf) << "\n";
  std::cout << "-> erf[wf <= 2.0f](wf)    = " << eve::erf[wf <= 2.0f](wf) << "\n";
}