fibonacci

auto eve::fibonacci = functor<fibonacci_t>

inlineconstexpr

The sequence is defined by the recurrence relations :

• \(f_0 = x\)
• \(f_1 = y\)
• \(f_{n+2} = f_{n+1} + f_{n}, n > 0\)

but is computed using the Binet formula.

Header file

#include <eve/module/combinatorial.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   template <floating_value T0,  floating_value T1, unsigned_value N>
   constexpr as_wide_as_t<common_value_t<T0, T1>, N> fibonacci(unsigned_value n,
                                                 floating_value x, floating_value y) noexcept; //1
 
   // Lanes masking
   constexpr auto fibonacci[conditional_expr auto c](/*any of the above overloads*/) noexcept; // 2
   constexpr auto fibonacci[logical_value auto m](/*any of the above overloads*/)    noexcept; // 2
}

Parameters

• n: indexes of the value to be returned.
• x, y: floating point arguments.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. The value of the nth element of the Fibonacci sequence beginning by x and y is returned.
2. The operation is performed conditionnaly.

External references

• Wikipedia: Fibonacci sequence

Example

// revision 1
#include <eve/module/combinatorial.hpp>
#include <iostream>
 
eve::wide<std::uint32_t> n([](auto i, auto )->std::uint32_t{ return i+2;});
eve::wide m{13u, 25u, 32u, 80u, 1u, 2u, 3u, 4u};
eve::wide a{1.0f, 2.0f, 3.0f, 4.0f, 0.5f, 0.33f, -4.5f, 0.0f};
eve::wide b{2.0f, 3.0f, 4.0f, 0.5f, 0.33f, -4.5f, 0.0f, 1.0f};
 
int main(){
   std::cout << "<- n   = " << n   << "\n";
   std::cout << "<- m   = " << m   << "\n";
   std::cout << "<- a   = " << a   << "\n";
   std::cout << "<- b   = " << b   << "\n";
 
   std::cout << "-> fibonacci(n, 1.0f, 1.0f)= " << eve::fibonacci(n, 1.0f, 1.0f) << "\n";
   std::cout << "-> fibonacci(m, a, b)      = " << eve::fibonacci(m, a, b) << "\n";
}