lpnorm

auto eve::lpnorm = functor<lpnorm_t>

inlineconstexpr

Defined in Header

#include <eve/module/math.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto lpnorm(floating_value auto p, floating_value auto x,floating_value auto... xs )                         noexcept; // 1
 
   // Lanes masking
   constexpr auto lpnorm[conditional_expr auto c](loating_value auto p, floating_value auto x,floating_value auto... xs)  noexcept; // 2
   constexpr auto lpnorm[logical_value auto m](loating_value auto p, floating_value auto x,floating_value auto... xs)     noexcept; // 2
 
   // Semantic options
   constexpr auto lpnorm[pedantic](/* any of the above overloads */)                                                     noexcept; // 3
   constexpr auto lpnorm[widen](/* any of the above overloads */)                                                        noexcept; // 4
   constexpr auto lpnorm[kahan](/* any of the above overloads */)                                                        noexcept; // 5
}

Parameters

• p: floating value
• x, ... xs: floating values
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. \( \left(\sum_{i = 0}^n |x_i|^p\right)^{\frac1p} \).
2. The operation is performed conditionnaly
3. returns \(\infty\) as soon as one of its parameter is infinite, regardless of possible Nan values.
4. The summation is computed in the double sized element type (if available).
5. Kahan like compensated algorithm is used in internal summation for better precision.

Example

// revision 1
#include <eve/module/math.hpp>
#include <iostream>
#include <iomanip>
 
int main()
{
  eve::wide x = {eve::nan(eve::as<float>()), 1.0f, 1.0f, 1.0f};
  eve::wide y = {-1.5f, 2.9f, 3.5f, -11.0f};
  eve::wide z = { eve::inf(eve::as(1.0f)), -2.0f, 1.0f, 15.0f};
  eve::wide p = { 3.2f, 3.0f, 2.0f, eve::inf(eve::as(1.0f))};
 
  std::cout << std::setprecision(15) << '\n';
  std::cout << "<- p                                      = " << p  << '\n';
  std::cout << "<- x                                      = " << x  << '\n';
  std::cout << "<- y                                      = " << y  << '\n';
  std::cout << "<- z                                      = " << z  << '\n';
  std::cout << "-> lpnorm(p, x, y, z)                     = " << eve::lpnorm(p, x, y, z) << '\n';
  std::cout << "-> lpnorm[pedantic](p, x, y, z)           = " << eve::lpnorm[eve::pedantic](p, x, y, z) << '\n';
  std::cout << "-> lpnorm[kahan](p, x, y, z)              = " << eve::lpnorm[eve::kahan](p, x, y, z) << '\n';
  std::cout << "-> lpnorm[kahan][pedantic](p, x, y, z)    = " << eve::lpnorm[eve::kahan][eve::pedantic](p, x, y, z) << '\n';
  std::cout << "-> lpnorm[widen](p, x, y, z)              = " << eve::lpnorm[eve::widen](p, x, y, z) << '\n';
  std::cout << "-> lpnorm[widen][pedantic](p, x, y, z)    = " << eve::lpnorm[eve::widen][eve::pedantic](p, x, y, z) << '\n';
}