rising_factorial

auto eve::rising_factorial = functor<rising_factorial_t>

inlineconstexpr

Defined in header

#include <eve/module/special.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   template<typename I, typename T> constexpr as_wide_as_t<T, I> rising_factorial(I a, T x) noexcept; // 1
 
   // Lanes masking
   constexpr auto rising_factorial[conditional_expr auto c](/*any of the above overloads*/) noexcept; // 2
   constexpr auto rising_factorial[logical_value auto m](/*any of the above overloads*/)    noexcept; // 2
 
   // Semantic options
   constexpr auto rising_factoriale[raw]/*any of the above overloads*/)                     noexcept; // 3
   constexpr auto rising_factorialee[pedantic](/*any of the above overloads*/)              noexcept; // 4
}

Parameters

• a: value.
• x: floating value.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. The value of the rising_factorial is returned( a and x must be strictly positive).
2. The operation is performed conditionnaly.
3. The raw option uses the crude formula with all its limitations and inacurracies and return a Nan if a and a+x are not both positive.
4. The pedantic option uses reflection tricks and computes the function for all real a and x, returning nan if the result is really undefined.

External references

• Wolfram MathWorld: Rising Factorial
• [Wikipedia: Falling and rising factorials](https://en.wikipedia.org/wiki/Falling_and_rising_factorials

Example

// revision 1
#include <eve/module/special.hpp>
#include <iostream>
 
int main()
{
  eve::wide n = {1, 2, -3, 7};
  eve::wide p = {1.0f,  1.5f, 2.0f, 2.5f};
 
  std::cout << "<- n                                     = " << n << "\n";
  std::cout << "<- p                                     = " << p << "\n";
 
  std::cout << "-> rising_factorial(n, p)                = " << eve::rising_factorial(n, p) << "\n";
  std::cout << "-> rising_factorial[ignore_last(2)](n, p)= " << eve::rising_factorial[eve::ignore_last(2)](n, p) << "\n";
  std::cout << "-> rising_factorial[n != 2.0f](n, p)     = " << eve::rising_factorial[n != 2.0f](n, p) << "\n";
  std::cout << "-> rising_factorial[raw](n, p)           = " << eve::rising_factorial[eve::raw](n, p) << "\n";
  std::cout << "-> rising_factorial[pedantic](n, p)      = " << eve::rising_factorial[eve::pedantic](n, p) << "\n";
}