sec

auto eve::sec = functor<sec_t>

inlineconstexpr

Header file

#include <eve/module/math.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto sec(floating_value auto x)                          noexcept; // 1
 
   // Lanes masking
   constexpr auto sec[conditional_expr auto c](floating_value auto x) noexcept; // 2
   constexpr auto sec[logical_value auto m](floating_value auto x)    noexcept; // 2
 
   // Semantic options
   constexpr auto sec[quarter_circle](floating_value auto x)          noexcept; // 3.a
   constexpr auto sec[half_circle](floating_value auto x)             noexcept; // 3.b
   constexpr auto sec[full_circle](floating_value auto x)             noexcept; // 3.c
}

Parameters

 * `x`: [floating value](@ref eve::floating_value).
 * `c`: [Conditional expression](@ref eve::conditional_expr) masking the operation.
 * `m`: [Logical value](@ref eve::logical_value) masking the operation.

Return value

1. Returns the elementwise secant of the input (inverse of the cosine). In particular:
   • If the element is \(\pm0\), \(1\) is returned.
   • If the element is \(\pm\infty\), Nan is returned.
   • If the element is a NaN, NaN is returned.
2. The operation is performed conditionnaly.
3. These are optimized calls providing a balance between speed and range limitation.
   1. assumes that the inputs elements belong to \([-\pi/4,\pi/4]\) and return NaN outside.
   2. assumes that the inputs elements belong to \([-\pi/2,\pi/2]\) and return NaN outside.
   3. assumes that the inputs elements belong to \([-\pi,\pi]\) and return NaN outside.

External references

• Wolfram MathWorld

Example

// revision 1
#include <eve/module/math.hpp>
#include <iostream>
 
int main()
{
  eve::wide wf = {0.0, 0.25, 0.5, 2.0, -0.0, -0.25, -0.5, -2.0};
  wf *= eve::pi[eve::lower](eve::as(wf));
 
  std::cout << "<- wf                     = " << wf << "\n";
 
  std::cout << "-> sec(wf)                = " << eve::sec(wf) << "\n";
  std::cout << "-> sec[ignore_last(2)](wf)= " << eve::sec[eve::ignore_last(2)](wf) << "\n";
  std::cout << "-> sec[wf > 0.0](wf)      = " << eve::sec[wf > 0.0](wf) << "\n";
  std::cout << "-> sec[quarter_circle](wf)= " << eve::sec[eve::quarter_circle](wf) << "\n";
  std::cout << "-> sec[half_circle](wf)   = " << eve::sec[eve::half_circle](wf) << "\n";
  std::cout << "-> sec[full_circle](wf)   = " << eve::sec[eve::full_circle](wf) << "\n";
}