exp_int

auto eve::exp_int = functor<exp_int_t>

inlineconstexpr

Header file

#include <eve/module/special.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto exp_int(floating_value auto x)                                   noexcept; // 1
   constexpr auto exp_int(unsigned_value auto n, floating_value auto x)            noexcept; // 2
 
   // Lanes masking
   constexpr auto exp_int[conditional_expr auto c](/*any of the above overloads*/) noexcept; // 3
   constexpr auto exp_int[logical_value auto m](/*any of the above overloads*/)    noexcept; // 3
}

Parameters

• n: unsigned argument. If not present taken to be 1.
• x: real floating argument.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. The value of the exponential integral \( \mathbf{E}_n(x) = \displaystyle \int_1^\infty \frac{e^{-xt}}{t^n}\;\mbox{d}t\), is returned.
2. The operation is performed conditionnaly.

External references

• Wolfram MathWorld:Exponential Integral
• DLMF: Generalized Exponential Integral
• Wikipedia: Exponential integral

Example

// revision 1
#include <eve/module/special.hpp>
#include <iostream>
 
int main()
{
  eve::wide wf = {0.5, 1.5, 0.1, 1.0, 19.0, 25.0, 21.5, 10000.0};
  eve::wide wi  = {0, 1, 5, -2, 10, 6000, 0, 2};
 
   std::cout << "<- wf = " << wf << "\n";
   std::cout << "<- wi = " << wi << "\n";
 
   std::cout << "-> exp_int(wf)                = " << eve::exp_int(wf) << "\n";
   std::cout << "-> exp_int(wi, wf)            = " << eve::exp_int(wi, wf) << "\n";
   std::cout << "-> exp_int[ignore_last(2)](wf)= " << eve::exp_int[eve::ignore_last(2)](wf) << "\n";
   std::cout << "-> exp_int[wf< 25.0](wf)      = " << eve::exp_int[wf < 25.0](wf) << "\n";
}