lrising_factorial

eve::lrising_factorial = functor<lrising_factorial_t>

inlineconstexpr

Header file

#include <eve/module/special.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   template<typename I, typename T> constexpr as_wide_as_t<T, I> lrising_factorial(I a, T x) noexcept; // 1
 
   // Lanes masking
   constexpr auto lrising_factorial[conditional_expr auto c](/*any of the above overloads*/) noexcept; // 2
   constexpr auto lrising_factorial[logical_value auto m](/*any of the above overloads*/)    noexcept; // 2
 
   // Semantic options
   constexpr auto lrising_factoriale[raw]/*any of the above overloads*/)                     noexcept; // 3
   constexpr auto lrising_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 natural logarithm 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, and in fact computes the logarithm of the absolute value of the Pochammer symbol \(\log\left|\frac{\Gamma(x+a)}{\Gamma(x)}\right|\) returning nan only 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

#include <eve/module/special.hpp>
#include <eve/wide.hpp>
#include <iostream>
#include <iomanip>
 
int main()
{
  using w32_t = eve::wide<std::int32_t, eve::fixed<4>>;
  using wf_t = eve::wide<float, eve::fixed<4>>;
  w32_t n = {1, 2, -3, 7};
  wf_t x = {1.0f,  1.5f, 2.0f, 2.5f};
 
  std::cout << "---- simd" << std::setprecision(17) << '\n'
            << " <- n                                   = " << n << '\n'
            << " <- x                                   = " << x << '\n'
            << " -> lrising_factorial(n, x)             = " << eve::lrising_factorial(n, x) << '\n';
 
  double xi = 1.8;
  std::cout << "---- scalar" << '\n'
            << " xi                           = " << xi << '\n'
            << " -> lrising_factorial(7, xi)  = " << eve::lrising_factorial(7, xi) << '\n';
 
 
  return 0;
}