ceil

eve::ceil = {}

inlineconstexpr

Computes the smallest integer not less than the input.

Defined in Header

#include <eve/module/core.hpp>

Callable Signatures

namespace eve
{
   template< eve::value T >
   T ceil(T x) noexcept;
}

Parameters

• x : real or complex argument.

Return value

The smallest integer not less than x.

The standard proposes 4 rounding modes namely: FE_TONEAREST, FE_DOWNWARD, FE_UPWARD, FE_TOWARDZERO. This function object implements the FE_UPWARD version.

For complex inputs the ceil operation is applied to both real and imaginary parts.

Example

#include <eve/module/core.hpp>
#include <eve/wide.hpp>
#include <iostream>
 
using wide_ft = eve::wide<float, eve::fixed<8>>;
 
int main()
{
  wide_ft pf = {-1.0f, -1.3f, -1.5f, -1.7f, 2.0f, 2.3f, 2.5f, 2.7f};
 
  std::cout << "---- simd" << '\n'
            << "<- pf             = " << pf << '\n'
            << "-> ceil(pf)       = " << eve::ceil(pf) << '\n';
 
  float xf = -32.768f;
 
  std::cout << "---- scalar" << '\n'
            << "<- xf       = " << xf << '\n'
            << "-> ceil(xf) = " << eve::ceil(xf) << '\n';
  return 0;
}

Semantic Modifiers

• Masked Call

  The call eve;ceil[mask](x) provides a masked version of eve::ceil which is equivalent to if_else (mask, ceil(x), x).

  Example

  #include <eve/module/core.hpp>
  #include <eve/wide.hpp>
  #include <iostream>
   
  using wide_ft = eve::wide<float, eve::fixed<8>>;
   
  int main()
  {
    wide_ft pf = {-1.0f, -1.3f, -1.5f, -1.7f, 2.0f, 2.3f, 2.5f, 2.7f};
   
    std::cout << "---- simd" << '\n'
              << "<- pf             = " << pf << '\n'
              << "-> ceil[pf > -1.5f](pf)       = " << eve::ceil[pf > -1.5f](pf) << '\n';
    return 0;
  }

• eve::tolerant

  The expression tolerant(ceil)(x, tol) computes a tolerant ceil value for x, where x must be a floating value.

  • If tol is a floating value, computes the floor with a tolerance tol using Hagerty's FL5 function.
  • If tol is an integral value n, computes the floor of the next nth representable value in the x type.
  • If tol is omitted, the tolerance is taken to 3 times the machine \(\epsilon\) in the x type (3*eve::eps (eve::as (x))).

  #include <eve/module/core.hpp>
  #include <eve/wide.hpp>
  #include <iostream>
  #include <iomanip>
   
  using wide_ft = eve::wide<float, eve::fixed<8>>;
   
  int main()
  {
    wide_ft pf = {-1.0f, -1.3f, -1.5f, -1.7f, 2.0f, 2.3f, 2.5f, 2.7f};
    pf += 3*eve::eps(eve::as<float>());
   
    std::cout << "---- simd" << std::setprecision(8) << '\n'
              << "<- pf                     = " << pf << '\n'
              << "-> ceil(pf)               = " << eve::ceil(pf) << '\n'
              << "-> tolerant(ceil)(pf)     = " << eve::tolerant(eve::ceil)(pf) << '\n'
              << "-> tolerant(ceil)(pf, 1)  = " << eve::tolerant(eve::ceil)(pf, 1) << '\n';
    return 0;
  }