manhattan

auto eve::manhattan = functor<manhattan_t>

inlineconstexpr

Example

// revision 0
#include <eve/module/core.hpp>
#include <iostream>
#include <iomanip>
 
 
int main()
{
  eve::wide wf0{0.01, 1.01, 2.01, 3.01, -1.01, -2.01, -3.01, -4.01};
  eve::wide wf1{0.01, -4.01, 1.01, -1.01, 2.01, -2.01, 3.01, -3.01};
  eve::wide wi0{0, 1, 2, 3, -1, -2, -3, -4};
  eve::wide wi1{0, -4, 1, -1, 2, -2, 3, -3};
  eve::wide wu0{0u, 1u, 2u, 3u, 4u, 5u, 6u, 7u};
  eve::wide wu1{7u, 6u, 5u, 4u, 3u, 2u, 1u, 0u};
 
  std::cout << "<- wf0                                 = " << wf0 << "\n";
  std::cout << "<- wf1                                 = " << wf1 << "\n";
  std::cout << "<- wi0                                 = " << wi0 << "\n";
  std::cout << "<- wi1                                 = " << wi1 << "\n";
  std::cout << "<- wu0                                 = " << wu0 << "\n";
  std::cout << "<- wu1                                 = " << wu1 << "\n";
 
  std::cout << "-> manhattan(wf0, wf1)                 = " << eve::manhattan(wf0, wf1) << "\n";
  std::cout << "-> manhattan[ignore_last(2)](wf0, wf1) = " << eve::manhattan[eve::ignore_last(2)](wf0, wf1) << "\n";
  std::cout << "-> manhattan[wf0 != 0](wf0, wf1)       = " << eve::manhattan[wf0 != 0](wf0, wf1) << "\n";
  std::cout << "-> manhattan[pedantic](wf0, wf1)       = " << eve::manhattan[eve::pedantic](wf0, wf1) << "\n";
  std::cout << "-> manhattan(wu0, wu1)                 = " << eve::manhattan(wu0, wu1) << "\n";
  std::cout << "-> manhattan(wi0, wi1)                 = " << eve::manhattan(wi0, wi1) << "\n";
 
  std::cout << std::hexfloat;
  std::cout << "-> manhattan[lower][strict](wf0, wf1)  = " << eve::manhattan[eve::lower][eve::strict](wf0, wf1) << "\n";
  std::cout << "-> manhattan[lower](wf0, wf1)          = " << eve::manhattan[eve::lower](wf0, wf1) << "\n";
  std::cout << "-> manhattan(wf0, wf1)                 = " << eve::manhattan(wf0, wf1) << "\n";
  std::cout << "-> manhattan[upper](wf0, wf1)          = " << eve::manhattan[eve::upper](wf0, wf1) << "\n";
  std::cout << "-> manhattan[upper][strict](wf0, wf1)  = " << eve::manhattan[eve::upper][eve::strict](wf0, wf1) << "\n";
 
  auto eps_2 = eve::eps(eve::as<float>())/2;
  auto tup = kumi::tuple{1.0f, eps_2, eps_2, eps_2};
  std::cout << "-> manhattan[kahan](tup)   = " << eve::manhattan[eve::kahan](tup) << "\n";
 
 
  float o = 1.0f;
  float i = eve::inf(eve::as(o));
  float n = eve::nan(eve::as(o));
  float m = (eve::valmax(eve::as(o))/3)*2;
  std::cout << "<- o                                   = " << o << "\n";
  std::cout << "-> i                                   = " << i << "\n";
  std::cout << "-> n                                   = " << n << "\n";
  std::cout << "-> manhattan(i, o, -i)                 = " << eve::manhattan(i, o, -i) << "\n";
  std::cout << "-> manhattan(i, o, n)                  = " << eve::manhattan(i, o,  n) << "\n";
  std::cout << "-> manhattan[pedantic](i, o, -i)       = " << eve::manhattan[eve::pedantic](i, o, -i) << "\n";
  std::cout << "-> manhattan[pedantic](i, o, n)        = " << eve::manhattan[eve::pedantic](i, o,  n) << "\n";
  std::cout << "-> manhattan[pedantic](o, o, n)        = " << eve::manhattan[eve::pedantic](o, o, n) << "\n";
  std::cout << "-> manhattan[pedantic](o, n, o)        = " << eve::manhattan[eve::pedantic](o, n, o) << "\n";
  std::cout << "-> manhattan[pedantic](n, o, o)        = " << eve::manhattan[eve::pedantic](n, o, o) << "\n";
  std::cout << "-> manhattan          (o, o, n)        = " << eve::manhattan(o, o, n) << "\n";
  std::cout << "-> manhattan          (o, n, o)        = " << eve::manhattan(o, n, o) << "\n";
  std::cout << "-> manhattan          (n, o, o)        = " << eve::manhattan(n, o, o) << "\n";
  std::cout << "-> manhattan(n, n, n)                  = " << eve::manhattan(n, n, n) << "\n";
  std::cout << "-> manhattan(m, o, o)                  = " << eve::manhattan(m, o, o)<< "\n";
  std::cout << "-> manhattan(m, m, n)                  = " << eve::manhattan(m, m, n)<< "\n";
  std::cout << "-> manhattan(i, n)                     = " << eve::manhattan(i, n) << "\n";
  std::cout << "-> manhattan[pedantic](m, m, n)        = " << eve::manhattan[eve::pedantic](m, m, n)<< "\n";
  std::cout << "-> manhattan[pedantic](i, n)           = " << eve::manhattan[eve::pedantic](i, n) << "\n";
}

Header file

#include <eve/module/core.hpp>

Callable Signatures

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

Parameters

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

Return value

1. The value of the sum of the absolute value of the arguments is returned.
2. equivalent to the call on the elements of the tuple.
3. The operation is performed conditionnaly
4. internally uses saturated options.
5. returns \(\infty\) as soon as after disabling possible Nan parameters the result is \(\infty\).
6. uses kahan like compensated algorithm for better accuracy.

External references

• Wikipedia taxicab norm