//-----------------------------------------------------------------------
//-----------------------------------------------------------------------
//     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.Math
{
    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 );
        }

    }
}