hypot

auto eve::hypot = functor<hypot_t>

inlineconstexpr

Header file

#include <eve/module/math.hpp>

Callable Signatures

namespace eve
{
   // Regular overloads
   constexpr auto hypot(value auto x, value auto ... xs)                          noexcept; // 1
   constexpr auto hypot(eve::non_empty_product_type auto const& tup)             noexcept; // 2
 
   // Lanes masking
   constexpr auto hypot[conditional_expr auto c](/*any of the above overloads*/)  noexcept; // 3
   constexpr auto hypot[logical_value auto m](/*any of the above overloads*/)     noexcept; // 3
 
   // Semantic options
   constexpr auto hypot[raw](/*any of the above overloads*/)                      noexcept; // 4
   constexpr auto hypot[pedantic](/*any of the above overloads*/)                 noexcept; // 5
   constexpr auto hypot[kahan](/*any of the above overloads*/)                    noexcept; // 6
   constexpr auto hypot[widen](/*any of the above overloads*/)                    noexcept; // 7
}

Parameters

• x, ...xs: real arguments.
• tup: non empty tuple of arguments.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. Returns \(\displaystyle\sqrt{\sum_1^n |x_i|^2}\). (naive formula) The result type is the common value type of the absolute values of the parameters. (Some appropriate scaling is done to enhance precision and avoid overflows.
2. equivalent to the call on the elements of the tuple.
3. The operation is performed conditionnaly
4. the naive formula is used.This option is speedier, but does not care about avoiding overflows or treating 'Nans' in special ways.
5. The pedantic option. returns \(\infty\) as soon as after disabling possible Nan parameters the result is \(\infty\), and computes the result without undue overflows or underflows. at intermediate stages of the computation.
6. A kahan like compensated algorithm is used internal for more accurate results.
7. The computation is done in the double sized element type (if available).

External references

• C++ standard reference
• Wikipedia

Example

// revision 1
#include <eve/module/math.hpp>
#include <iostream>
 
int main()
{
//   eve::wide pf = {-1.0, 2.0, -3.0, eve::valmax(eve::as<double>())};
//   eve::wide qf = {-4.0, 3.0, -2.0, eve::inf(eve::as<double>())};
//   eve::wide rf = {-40.0, 0.03, -2.0, eve::nan(eve::as<double>())};
//   kumi::tuple wt{pf, qf};
 
//    std::cout << "<- pf = " << pf << "\n";
//    std::cout << "<- qf = " << qf << "\n";
//    std::cout << "<- rf = " << rf << "\n";
//    std::cout << "<- wt = " << wt << "\n";
 
//    std::cout << "-> hypot(pf,qf)                = " << eve::hypot(pf,qf) << "\n";
//    std::cout << "-> hypot(wt)                   = " << eve::hypot(wt) << "\n";
//    std::cout << "-> hypot[ignore_last(2)](pf,qf)= " << eve::hypot[eve::ignore_last(2)](pf,qf) << "\n";
//    std::cout << "-> hypot[pf > 0.0](pf,qf)      = " << eve::hypot[pf > 0.0](pf,qf) << "\n";
//    std::cout << "-> hypot[pedantic](pf,qf)      = " << eve::hypot[eve::pedantic](pf,qf) << "\n";
//    std::cout << "-> hypot(pf,qf,rf)             = " << eve::hypot(pf,qf,rf) << "\n";
//    std::cout << "-> hypot[pedantic](pf,qf,rf)   = " << eve::hypot[eve::pedantic](pf,qf,rf) << "\n";
 
  float o = 1.0f;
  float i = eve::inf(eve::as(o));
  float n = eve::nan(eve::as(o));
  float v = eve::valmax(eve::as(o));
  float m = (v/3)*2;
  std::cout << "<- o                               = " << o << "\n";
  std::cout << "-> i                               = " << i << "\n";
  std::cout << "-> n                               = " << n << "\n";
  std::cout << "-> m                               = " << m << "\n";
  std::cout << "-> hypot(i, o, -i)                 = " << eve::hypot(i, o, -i) << "\n";
  std::cout << "-> hypot(i, o, n)                  = " << eve::hypot(i, o,  n) << "\n";
  std::cout << "-> hypot[pedantic](i, o, -i)       = " << eve::hypot[eve::pedantic](i, o, -i) << "\n";
  std::cout << "-> hypot[pedantic](i, o, n)        = " << eve::hypot[eve::pedantic](i, o,  n) << "\n";
  std::cout << "-> hypot[pedantic](o, o, n)        = " << eve::hypot[eve::pedantic](o, o, n) << "\n";
  std::cout << "-> hypot[pedantic](o, n, o)        = " << eve::hypot[eve::pedantic](o, n, o) << "\n";
  std::cout << "-> hypot[pedantic](n, o, o)        = " << eve::hypot[eve::pedantic](n, o, o) << "\n";
  std::cout << "-> hypot          (o, o, n)        = " << eve::hypot(o, o, n) << "\n";
  std::cout << "-> hypot          (o, n, o)        = " << eve::hypot(o, n, o) << "\n";
  std::cout << "-> hypot          (n, o, o)        = " << eve::hypot(n, o, o) << "\n";
  std::cout << "-> hypot(n, n, n)                  = " << eve::hypot(n, n, n) << "\n";
  std::cout << "-> hypot(m, o, o)                  = " << eve::hypot(m, o, o)<< "\n";
  std::cout << "-> hypot(m, m, n)                  = " << eve::hypot(m, m, n)<< "\n";
  std::cout << "-> hypot(i, n)                     = " << eve::hypot(i, n) << "\n";
  std::cout << "-> hypot[pedantic](m, m)           = " << eve::hypot[eve::pedantic](m, m)<< "\n";
  std::cout << "-> hypot[pedantic](m, m, n)        = " << eve::hypot[eve::pedantic](m, m, n)<< "\n";
  std::cout << "-> hypot[pedantic](i, n)           = " << eve::hypot[eve::pedantic](i, n) << "\n";
  std::cout << "-> hypot[pedantic](v, v, n)        = " << eve::hypot[eve::pedantic](v, v, n)<< "\n";
  std::cout << "-> hypot[pedantic](m, m)           = " << eve::hypot[eve::pedantic](m, m)<< "\n";
  std::cout << "-> hypot(m, m, n)                  = " << eve::hypot(m, m, n)<< "\n";
  std::cout << "-> hypot(i, n, n)                  = " << eve::hypot(i, n, n) << "\n";
  std::cout << "-> hypot(i, n)                     = " << eve::hypot(i, n)    << "\n";
  std::cout << "-> hypot(v, v, n)                  = " << eve::hypot(v, v, n)<< "\n";
}