//-----------------------------------------------------------------------
// -----------------------------------------------------------------------
// file="Factorial.cs"
// Project: StgSharp
// AuthorGroup: Nitload Space
// Copyright (c) Nitload Space. All rights reserved.
//     
// Permission is hereby granted, free of charge, to any person 
// obtaining a copy of this software and associated documentation 
// files (the “Software”), to deal in the Software without restriction, 
// including without limitation the rights to use, copy, modify, merge,
// publish, distribute, sublicense, and/or sell copies of the Software, 
// and to permit persons to whom the Software is furnished to do so, 
// subject to the following conditions:
//     
// The above copyright notice and 
// this permission notice shall be included in all copies 
// or substantial portions of the Software.
//     
// THE SOFTWARE IS PROVIDED “AS IS”, 
// WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, 
// INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 
// IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, 
// DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 
// ARISING FROM, OUT OF OR IN CONNECTION WITH 
// THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
//     
// -----------------------------------------------------------------------
// -----------------------------------------------------------------------
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace StgSharp.Mathematics
{
    public static partial class Scaler
    {

        private static readonly uint[] factorialResult = [1, 1, 2, 6, 24,120,720,5040,40320,362880,3628800,39916800,479001600];

        public static unsafe ulong Factorial(int n)
        {
            ArgumentOutOfRangeException.ThrowIfLessThan(n, 0);
            if (n < 13) {
                return factorialResult[n];
            }
            if (n < 30) {
                return InternalIO.Intrinsic.factorial_simd(n);
            }
            double 
                dn = n,
                stir = Sqrt(2 * PiDouble * dn) * Pow(dn / EDouble, dn),
                correction = Exp(1 / (12 * dn));
            return (ulong)(stir * correction);
        }

    }
}