Random number from a seed

问题:

I have an application where it becomes extremely noticeable if my program uses an RNG that has patterns based on its seed, as it builds landscapes based on the x coordinate of the landscape. While Random works well if you're calling Next() every time, I need to be able to have the same output every time I use the same input, and thus can't rely on Next(). Instead, I attempted to simply make a new Random every time with the input seed. Not a very good idea, I know, and it showed. The patterns were extremely obvious, with alternating high and low values, and an noticeable overall trend across the entire landscape. I'd prefer not to be making new generators every time, but even so, I looked into the cryptographically secure RandomNumberGenerator to see if I could at least use it temporarily. As expected, though, I can't seed it, leaving me without any sort of reproducible output (which is rather the point of the RandomNumberGenerator).

In short, neither of the two common RNGs appear to suit my purpose. I need to be able to take in a a number and return a random number based on that value without noticeable patterns in the output. Is there another way to use the above two, or is there a third I haven't used before that would better suit my purpose?

For clarity, the method I'm trying to write looks like so:

public int RandomInt(int input)
{
    int randomOutput;
    //Be random
    return randomOutput;
}

That will return the same value every time the same input is given.

回答1:

A Mersenne Twister might give better results.

Here's a sample implementation that you should be able to try out fairly quickly:

using System;

namespace Random
{
    /* C# Version Copyright (C) 2001 Akihilo Kramot (Takel).       */
    /* C# porting from a C-program for MT19937, originaly coded by */
    /* Takuji Nishimura, considering the suggestions by            */
    /* Topher Cooper and Marc Rieffel in July-Aug. 1997.           */
    /* This library is free software under the Artistic license:   */
    /*                                                             */
    /* You can find the original C-program at                      */
    /* http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html    */
    /*                                                             */

    /// <summary>
    /// Implements a Mersenne Twister Random Number Generator. This class provides the same interface
    /// as the standard System.Random number generator, plus some additional functions.
    /// </summary>

    public class MersenneTwister: System.Random
    {
        /* Period parameters */
        private const int N = 624;
        private const int M = 397;
        private const uint MATRIX_A = 0x9908b0df; /* constant vector a */
        private const uint UPPER_MASK = 0x80000000; /* most significant w-r bits */
        private const uint LOWER_MASK = 0x7fffffff; /* least significant r bits */

        /* Tempering parameters */
        private const uint TEMPERING_MASK_B = 0x9d2c5680;
        private const uint TEMPERING_MASK_C = 0xefc60000;

        private static uint TEMPERING_SHIFT_U( uint y ) { return ( y >> 11 ); }
        private static uint TEMPERING_SHIFT_S( uint y ) { return ( y << 7 ); }
        private static uint TEMPERING_SHIFT_T( uint y ) { return ( y << 15 ); }
        private static uint TEMPERING_SHIFT_L( uint y ) { return ( y >> 18 ); }

        private uint[] mt = new uint[N]; /* the array for the state vector  */

        private uint seed_;
        private short mti;

        private static uint[] mag01 = { 0x0, MATRIX_A };

        /// <summary>
        /// Create a twister with the specified seed. All sequences started with the same seed will contain
        /// the same random numbers in the same order.
        /// </summary>
        /// <param name="seed">The seed with which to start the twister.</param>

        public MersenneTwister( uint seed )
        {
            Seed = seed;
        }


        /// <summary>
        /// Create a twister seeded from the system clock to make it as random as possible.
        /// </summary>

        public MersenneTwister()
            : this( ( (uint) DateTime.Now.Ticks ) )  // A random initial seed is used.
        {
        }


        /// <summary>
        /// The seed that was used to start the random number generator.
        /// Setting the seed resets the random number generator with the new seed.
        /// All sequences started with the same seed will contain the same random numbers in the same order.
        /// </summary>

        public uint Seed
        {
            set
            {
                seed_ = value;

                /* setting initial seeds to mt[N] using         */
                /* the generator Line 25 of Table 1 in          */
                /* [KNUTH 1981, The Art of Computer Programming */
                /*    Vol. 2 (2nd Ed.), pp102]                  */

                mt[0] = seed_ & 0xffffffffU;
                for ( mti = 1; mti < N; mti++ )
                {
                    mt[mti] = ( 69069 * mt[mti - 1] ) & 0xffffffffU;
                }
            }

            get
            {
                return seed_;
            }
        }


        /// <summary>
        /// Generate a random uint.
        /// </summary>
        /// <returns>A random uint.</returns>

        protected uint GenerateUInt()
        {
            uint y;

            /* mag01[x] = x * MATRIX_A  for x=0,1 */

            if ( mti >= N ) /* generate N words at one time */
            {
                short kk;

                for ( kk = 0; kk < N - M; kk++ )
                {
                    y = ( mt[kk] & UPPER_MASK ) | ( mt[kk + 1] & LOWER_MASK );
                    mt[kk] = mt[kk + M] ^ ( y >> 1 ) ^ mag01[y & 0x1];
                }

                for ( ; kk < N - 1; kk++ )
                {
                    y = ( mt[kk] & UPPER_MASK ) | ( mt[kk + 1] & LOWER_MASK );
                    mt[kk] = mt[kk + ( M - N )] ^ ( y >> 1 ) ^ mag01[y & 0x1];
                }

                y = ( mt[N - 1] & UPPER_MASK ) | ( mt[0] & LOWER_MASK );
                mt[N - 1] = mt[M - 1] ^ ( y >> 1 ) ^ mag01[y & 0x1];

                mti = 0;
            }

            y = mt[mti++];
            y ^= TEMPERING_SHIFT_U( y );
            y ^= TEMPERING_SHIFT_S( y ) & TEMPERING_MASK_B;
            y ^= TEMPERING_SHIFT_T( y ) & TEMPERING_MASK_C;
            y ^= TEMPERING_SHIFT_L( y );

            return y;
        }


        /// <summary>
        /// Returns the next uint in the random sequence.
        /// </summary>
        /// <returns>The next uint in the random sequence.</returns>

        public virtual uint NextUInt()
        {
            return this.GenerateUInt();
        }


        /// <summary>
        /// Returns a random number between 0 and a specified maximum.
        /// </summary>
        /// <param name="maxValue">The upper bound of the random number to be generated. maxValue must be greater than or equal to zero.</param>
        /// <returns>A 32-bit unsigned integer greater than or equal to zero, and less than maxValue; that is, the range of return values includes zero but not MaxValue.</returns>

        public virtual uint NextUInt( uint maxValue )
        {
            return (uint) ( this.GenerateUInt() / ( (double) uint.MaxValue / maxValue ) );
        }


        /// <summary>
        /// Returns an unsigned random number from a specified range.
        /// </summary>
        /// <param name="minValue">The lower bound of the random number returned.</param>
        /// <param name="maxValue">The upper bound of the random number returned. maxValue must be greater than or equal to minValue.</param>
        /// <returns>A 32-bit signed integer greater than or equal to minValue and less than maxValue;
        /// that is, the range of return values includes minValue but not MaxValue.
        /// If minValue equals maxValue, minValue is returned.</returns>

        public virtual uint NextUInt( uint minValue, uint maxValue ) /* throws ArgumentOutOfRangeException */
        {
            if (minValue >= maxValue)
            {
                if (minValue == maxValue)
                {
                    return minValue;
                }
                else
                {
                    throw new ArgumentOutOfRangeException("minValue", "NextUInt() called with minValue >= maxValue");
                }
            }

            return (uint) ( this.GenerateUInt() / ( (double) uint.MaxValue / ( maxValue - minValue ) ) + minValue );
        }


        /// <summary>
        /// Returns a nonnegative random number.
        /// </summary>
        /// <returns>A 32-bit signed integer greater than or equal to zero and less than int.MaxValue.</returns>

        public override int Next()
        {
            return (int) ( this.GenerateUInt() / 2 );
        }


        /// <summary>
        /// Returns a nonnegative random number less than the specified maximum.
        /// </summary>
        /// <param name="maxValue">The upper bound of the random number to be generated. maxValue must be greater than or equal to zero.</param>
        /// <returns>A 32-bit signed integer greater than or equal to zero, and less than maxValue;
        /// that is, the range of return values includes zero but not MaxValue.</returns>

        public override int Next( int maxValue ) /* throws ArgumentOutOfRangeException */
        {
            if ( maxValue <= 0 )
            {
                if ( maxValue == 0 )
                    return 0;
                else
                    throw new ArgumentOutOfRangeException( "maxValue", "Next() called with a negative parameter" );
            }

            return (int) ( this.GenerateUInt() / ( uint.MaxValue / maxValue ) );
        }


        /// <summary>
        /// Returns a signed random number from a specified range.
        /// </summary>
        /// <param name="minValue">The lower bound of the random number returned.</param>
        /// <param name="maxValue">The upper bound of the random number returned. maxValue must be greater than or equal to minValue.</param>
        /// <returns>A 32-bit signed integer greater than or equal to minValue and less than maxValue;
        /// that is, the range of return values includes minValue but not MaxValue.
        /// If minValue equals maxValue, minValue is returned.</returns>

        public override int Next( int minValue, int maxValue ) /* ArgumentOutOfRangeException */
        {
            if (minValue >= maxValue)
            {
                if (minValue == maxValue)
                {
                    return minValue;
                }
                else
                {
                    throw new ArgumentOutOfRangeException("minValue", "Next() called with minValue > maxValue");
                }
            }

            return (int) ( this.GenerateUInt() / ( (double) uint.MaxValue / ( maxValue - minValue ) ) + minValue );
        }


        /// <summary>
        /// Fills an array of bytes with random numbers from 0..255
        /// </summary>
        /// <param name="buffer">The array to be filled with random numbers.</param>

        public override void NextBytes( byte[] buffer ) /* throws ArgumentNullException*/
        {
            int bufLen = buffer.Length;

            if ( buffer == null )
                throw new ArgumentNullException("buffer");

            for ( int idx = 0; idx < bufLen; idx++ )
                buffer[idx] = (byte) ( this.GenerateUInt() / ( uint.MaxValue / byte.MaxValue ) );
        }


        /// <summary>
        /// Returns a double-precision random number in the range [0..1[
        /// </summary>
        /// <returns>A random double-precision floating point number greater than or equal to 0.0, and less than 1.0.</returns>

        public override double NextDouble()
        {
            return (double) this.GenerateUInt() / uint.MaxValue;
        }
    }
}

回答2:

I hate to answer my own question, but a friend of mine made this suggestion off StackOverflow, and I feel that it'd be best to include it here for posterity.

What's being asked for is actually just a hashing function. If you run the input through a suitable strong hashing algorithm and convert the output to an int, random output values that correspond to their inputs will be generated.

回答3:

If you are trying to make the output reproducible then you simply need to seed Random once with a fixed seed.

You could make this seed another input in your program. That way you will know that the sequence of numbers returned by Next will be identical in two executions of your program (that use the same seed).

You should definitely not reinitialize the random generator every time.

    Random rnd1 = new Random(12);
    Random rnd2 = new Random(12);

These two generators will always output the same results when Next is called. It does not matter where in the code they are declared. Or when. The only thing that matters is that the seed (here 12) is the same.

If you want another reproducible set of values, identical to the one that results from rnd1 all you need to do is instantiate rnd2.

回答4:

A possible way seems to store random.Next() values for one run, and map them to each input. Have these values on a datastore, cache them on the next application run, and start serving them. In effect, you'll get the same random output given an input.

回答5:

If you want 'same seed -> same num'. look at this.

This is very simple.

class MyRandom
{
    private static Random Rand = new Random();
    private static Dictionary<int, int> LookupTable = new Dictionary<int, int>();

    public static int RandomInt( int seed )
    {
        try
        {
            return LookupTable[ seed ];
        }
        catch ( Exception e )
        {
            int retNum = Rand.Next();
            LookupTable.Add( seed, retNum );
            return retNum;
        }
    }
}

class Program
{
    static void Main( string[] args )
    {
        Console.WriteLine( MyRandom.RandomInt( 3 ) );
        Console.WriteLine( MyRandom.RandomInt( 1 ) );
        Console.WriteLine( MyRandom.RandomInt( 3 ) );
    }
}

回答6:

Perlin Noise or newer Simplex Noise works well for landscape generation.

If I understand the algorithm correctly, it works by adding together noise gradients (linear interpolation between random points) of different frequencies. I also found a more detailed explanation.

I found a Simplex Noise library on Google Code,

And the implementation:

// SimplexNoise for C#
// Author: Heikki Törmälä

//This is free and unencumbered software released into the public domain.

//Anyone is free to copy, modify, publish, use, compile, sell, or
//distribute this software, either in source code form or as a compiled
//binary, for any purpose, commercial or non-commercial, and by any
//means.

//In jurisdictions that recognize copyright laws, the author or authors
//of this software dedicate any and all copyright interest in the
//software to the public domain. We make this dedication for the benefit
//of the public at large and to the detriment of our heirs and
//successors. We intend this dedication to be an overt act of
//relinquishment in perpetuity of all present and future rights to this
//software under copyright law.

//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 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.

//For more information, please refer to <http://unlicense.org/>


namespace SimplexNoise
{
    /// <summary>
    /// Implementation of the Perlin simplex noise, an improved Perlin noise algorithm.
    /// Based loosely on SimplexNoise1234 by Stefan Gustavson <http://staffwww.itn.liu.se/~stegu/aqsis/aqsis-newnoise/>
    /// 
    /// </summary>
    public class Noise
    {
        /// <summary>
        /// 1D simplex noise
        /// </summary>
        /// <param name="x"></param>
        /// <returns></returns>
        public static float Generate(float x)
        {
            int i0 = FastFloor(x);
            int i1 = i0 + 1;
            float x0 = x - i0;
            float x1 = x0 - 1.0f;

            float n0, n1;

            float t0 = 1.0f - x0*x0;
            t0 *= t0;
            n0 = t0 * t0 * grad(perm[i0 & 0xff], x0);

            float t1 = 1.0f - x1*x1;
            t1 *= t1;
            n1 = t1 * t1 * grad(perm[i1 & 0xff], x1);
            // The maximum value of this noise is 8*(3/4)^4 = 2.53125
            // A factor of 0.395 scales to fit exactly within [-1,1]
            return 0.395f * (n0 + n1);
        }

        /// <summary>
        /// 2D simplex noise
        /// </summary>
        /// <param name="x"></param>
        /// <param name="y"></param>
        /// <returns></returns>
        public static float Generate(float x, float y)
        {
            const float F2 = 0.366025403f; // F2 = 0.5*(sqrt(3.0)-1.0)
            const float G2 = 0.211324865f; // G2 = (3.0-Math.sqrt(3.0))/6.0

            float n0, n1, n2; // Noise contributions from the three corners

            // Skew the input space to determine which simplex cell we're in
            float s = (x+y)*F2; // Hairy factor for 2D
            float xs = x + s;
            float ys = y + s;
            int i = FastFloor(xs);
            int j = FastFloor(ys);

            float t = (float)(i+j)*G2;
            float X0 = i-t; // Unskew the cell origin back to (x,y) space
            float Y0 = j-t;
            float x0 = x-X0; // The x,y distances from the cell origin
            float y0 = y-Y0;

            // For the 2D case, the simplex shape is an equilateral triangle.
            // Determine which simplex we are in.
            int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
            if(x0>y0) {i1=1; j1=0;} // lower triangle, XY order: (0,0)->(1,0)->(1,1)
            else {i1=0; j1=1;}      // upper triangle, YX order: (0,0)->(0,1)->(1,1)

            // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
            // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
            // c = (3-sqrt(3))/6

            float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
            float y1 = y0 - j1 + G2;
            float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
            float y2 = y0 - 1.0f + 2.0f * G2;

            // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
            int ii = i % 256;
            int jj = j % 256;

            // Calculate the contribution from the three corners
            float t0 = 0.5f - x0*x0-y0*y0;
            if(t0 < 0.0f) n0 = 0.0f;
            else {
                t0 *= t0;
                n0 = t0 * t0 * grad(perm[ii+perm[jj]], x0, y0); 
            }

            float t1 = 0.5f - x1*x1-y1*y1;
            if(t1 < 0.0f) n1 = 0.0f;
            else {
                t1 *= t1;
                n1 = t1 * t1 * grad(perm[ii+i1+perm[jj+j1]], x1, y1);
            }

            float t2 = 0.5f - x2*x2-y2*y2;
            if(t2 < 0.0f) n2 = 0.0f;
            else {
                t2 *= t2;
                n2 = t2 * t2 * grad(perm[ii+1+perm[jj+1]], x2, y2);
            }

            // Add contributions from each corner to get the final noise value.
            // The result is scaled to return values in the interval [-1,1].
            return 40.0f * (n0 + n1 + n2); // TODO: The scale factor is preliminary!
        }


        public static float Generate(float x, float y, float z)
        {
            // Simple skewing factors for the 3D case
            const float F3 = 0.333333333f;
            const float G3 = 0.166666667f;

            float n0, n1, n2, n3; // Noise contributions from the four corners

            // Skew the input space to determine which simplex cell we're in
            float s = (x+y+z)*F3; // Very nice and simple skew factor for 3D
            float xs = x+s;
            float ys = y+s;
            float zs = z+s;
            int i = FastFloor(xs);
            int j = FastFloor(ys);
            int k = FastFloor(zs);

            float t = (float)(i+j+k)*G3; 
            float X0 = i-t; // Unskew the cell origin back to (x,y,z) space
            float Y0 = j-t;
            float Z0 = k-t;
            float x0 = x-X0; // The x,y,z distances from the cell origin
            float y0 = y-Y0;
            float z0 = z-Z0;

            // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
            // Determine which simplex we are in.
            int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
            int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords

            /* This code would benefit from a backport from the GLSL version! */
            if(x0>=y0) {
                if(y0>=z0)
                { i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; } // X Y Z order
                else if(x0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; } // X Z Y order
                else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; } // Z X Y order
                }
            else { // x0<y0
                if(y0<z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; } // Z Y X order
                else if(x0<z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; } // Y Z X order
                else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; } // Y X Z order
            }

            // A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
            // a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
            // a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
            // c = 1/6.

            float x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
            float y1 = y0 - j1 + G3;
            float z1 = z0 - k1 + G3;
            float x2 = x0 - i2 + 2.0f*G3; // Offsets for third corner in (x,y,z) coords
            float y2 = y0 - j2 + 2.0f*G3;
            float z2 = z0 - k2 + 2.0f*G3;
            float x3 = x0 - 1.0f + 3.0f*G3; // Offsets for last corner in (x,y,z) coords
            float y3 = y0 - 1.0f + 3.0f*G3;
            float z3 = z0 - 1.0f + 3.0f*G3;

            // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
            int ii = i % 256;
            int jj = j % 256;
            int kk = k % 256;

            // Calculate the contribution from the four corners
            float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0;
            if(t0 < 0.0f) n0 = 0.0f;
            else {
                t0 *= t0;
                n0 = t0 * t0 * grad(perm[ii+perm[jj+perm[kk]]], x0, y0, z0);
            }

            float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1;
            if(t1 < 0.0f) n1 = 0.0f;
            else {
                t1 *= t1;
                n1 = t1 * t1 * grad(perm[ii+i1+perm[jj+j1+perm[kk+k1]]], x1, y1, z1);
            }

            float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2;
            if(t2 < 0.0f) n2 = 0.0f;
            else {
                t2 *= t2;
                n2 = t2 * t2 * grad(perm[ii+i2+perm[jj+j2+perm[kk+k2]]], x2, y2, z2);
            }

            float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3;
            if(t3<0.0f) n3 = 0.0f;
            else {
                t3 *= t3;
                n3 = t3 * t3 * grad(perm[ii+1+perm[jj+1+perm[kk+1]]], x3, y3, z3);
            }

            // Add contributions from each corner to get the final noise value.
            // The result is scaled to stay just inside [-1,1]
            return 32.0f * (n0 + n1 + n2 + n3); // TODO: The scale factor is preliminary!
        }

        private static byte[] perm = new byte[512] { 151,160,137,91,90,15,
              131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
              190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
              88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
              77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
              102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
              135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
              5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
              223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
              129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
              251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
              49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
              138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180,
              151,160,137,91,90,15,
              131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
              190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
              88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
              77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
              102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
              135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
              5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
              223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
              129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
              251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
              49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
              138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180 
            };

        private static int FastFloor(float x)
        {
            return (x > 0) ? ((int)x) : (((int)x) - 1);
        }

        private static float grad( int hash, float x )
        {
            int h = hash & 15;
            float grad = 1.0f + (h & 7);   // Gradient value 1.0, 2.0, ..., 8.0
            if ((h & 8) != 0) grad = -grad;         // Set a random sign for the gradient
            return ( grad * x );           // Multiply the gradient with the distance
        }

        private static float grad( int hash, float x, float y )
        {
            int h = hash & 7;      // Convert low 3 bits of hash code
            float u = h<4 ? x : y;  // into 8 simple gradient directions,
            float v = h<4 ? y : x;  // and compute the dot product with (x,y).
            return ((h&1) != 0 ? -u : u) + ((h&2) != 0 ? -2.0f*v : 2.0f*v);
        }

        private static float grad( int hash, float x, float y , float z ) {
            int h = hash & 15;     // Convert low 4 bits of hash code into 12 simple
            float u = h<8 ? x : y; // gradient directions, and compute dot product.
            float v = h<4 ? y : h==12||h==14 ? x : z; // Fix repeats at h = 12 to 15
            return ((h&1) != 0 ? -u : u) + ((h&2) != 0 ? -v : v);
        }

        private static float grad( int hash, float x, float y, float z, float t ) {
            int h = hash & 31;      // Convert low 5 bits of hash code into 32 simple
            float u = h<24 ? x : y; // gradient directions, and compute dot product.
            float v = h<16 ? y : z;
            float w = h<8 ? z : t;
            return ((h&1) != 0 ? -u : u) + ((h&2) != 0 ? -v : v) + ((h&4) != 0 ? -w : w);
        }
    }
}