Random number from a seed

Question

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.

Answer 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;
        }
    }
}

Answer 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.

Answer 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.