E.V.E
v2023.02.15
 
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◆ airy_ai

auto eve::airy_ai = functor<airy_ai_t>
inlineconstexpr

It is the solution of the differential equation \(y''-xy = 0\) satisfying \(Ai(0) = \frac1{3^{2/3}\Gamma(2/3)}\) and \(Ai'(0) =\frac1{3^{1/3}\Gamma(1/3)}\).

Header file

#include <eve/module/bessel.hpp>

Callable Signatures

namespace eve
{
// Regular overload
constexpr auto airy_ai(floating_value auto x) -> decltype(x) noexcept; // 1
// Lanes masking
constexpr auto airy_ai[conditional_expr auto c](floating_value auto x) noexcept; // 2
constexpr auto airy_ai[logical_value auto m](floating_value auto x) noexcept; // 2
}
Specifies that a type is a Conditional Expression.
Definition conditional.hpp:28
The concept floating_value<T> is satisfied if and only if T satisfies eve::value and the element type...
Definition value.hpp:116
The concept logical_value<T> is satisfied if and only if T satisfies eve::value and the element type ...
Definition value.hpp:132
constexpr auto airy_ai
elementwise_callable object computing the airy function .
Definition airy_ai.hpp:74
EVE Main Namespace.
Definition abi.hpp:18

Parameters

Return value

  1. The value of \( \displaystyle Ai(x)=\frac1{\pi} \int_{0}^{\infty}\cos \left( \frac{t^3}{3}+xt \right) \,dt\) is returned.
  2. The operation is performed conditionnaly..

External references

Example

// revision 1
#include <eve/module/bessel.hpp>
#include <iostream>
eve::wide<double> wf0([](auto i, auto c)->double{ return 2*(i-c/2);});
eve::wide wf1{0.5, -1.5, 0.1, -1.0, 19.0, 25.0, 21.5, 10000.0};
int main()
{
std::cout << "<- wf0 = " << wf0 << "\n";
std::cout << "<- wf1 = " << wf1 << "\n";
std::cout << "-> airy_ai(wf0) = " << eve::airy_ai(wf0) << "\n";
std::cout << "-> airy_ai[ignore_last(2)](wf0)= " << eve::airy_ai[eve::ignore_last(2)](wf0) << "\n";
std::cout << "-> airy_ai[wf0 != -2.0f](wf0) = " << eve::airy_ai[wf0 != -2.0f](wf0) << "\n";
std::cout << "-> airy_ai(wf1) = " << eve::airy_ai(wf1) << "\n";
}
Conditional expression ignoring the k last lanes from a eve::simd_value.
Definition conditional.hpp:332
Wrapper for SIMD registers.
Definition wide.hpp:70