Efficient Random Number Generation

[jonathan]

What is the best way to produce (pseudo)-random numbers on an XCore?

Any views?

In this case I am interested in both "best" (mathematically) and "best" (efficiency-wise). It's possible though not inevitable that these will be mutually exclusive.

[jonathan]

Note that the Mersenne Twister algorithm below does - quite usefully - compile already. Haven't checked but suspect it's a very inefficient way of generating pseudo-random numbers. Has anyone else looked at this? I can see if we can easily parallelize this Mersenne Twister.

Code: Select all

/* 
   A C-program for MT19937, with initialization improved 2002/1/26.
   Coded by Takuji Nishimura and Makoto Matsumoto.

   Before using, initialize the state by using init_genrand(seed)  
   or init_by_array(init_key, key_length).

   Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
   All rights reserved.                          

   Redistribution and use in source and binary forms, with or without
   modification, are permitted provided that the following conditions
   are met:

     1. Redistributions of source code must retain the above copyright
        notice, this list of conditions and the following disclaimer.

     2. Redistributions in binary form must reproduce the above copyright
        notice, this list of conditions and the following disclaimer in the
        documentation and/or other materials provided with the distribution.

     3. The names of its contributors may not be used to endorse or promote 
        products derived from this software without specific prior written 
        permission.

   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
   "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
   LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
   A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
   CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
   EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
   PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.


   Any feedback is very welcome.
   http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
   email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
*/

#include <stdio.h>

/* Period parameters */  
#define N 624
#define M 397
#define MATRIX_A 0x9908b0dfUL   /* constant vector a */
#define UPPER_MASK 0x80000000UL /* most significant w-r bits */
#define LOWER_MASK 0x7fffffffUL /* least significant r bits */

static unsigned long mt[N]; /* the array for the state vector  */
static int mti=N+1; /* mti==N+1 means mt[N] is not initialized */

/* initializes mt[N] with a seed */
void init_genrand(unsigned long s)
{
    mt[0]= s & 0xffffffffUL;
    for (mti=1; mti<N; mti++) {
        mt[mti] = 
	    (1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti); 
        /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
        /* In the previous versions, MSBs of the seed affect   */
        /* only MSBs of the array mt[].                        */
        /* 2002/01/09 modified by Makoto Matsumoto             */
        mt[mti] &= 0xffffffffUL;
        /* for >32 bit machines */
    }
}

/* initialize by an array with array-length */
/* init_key is the array for initializing keys */
/* key_length is its length */
/* slight change for C++, 2004/2/26 */
void init_by_array(unsigned long init_key[], int key_length)
{
    int i, j, k;
    init_genrand(19650218UL);
    i=1; j=0;
    k = (N>key_length ? N : key_length);
    for (; k; k--) {
        mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1664525UL))
          + init_key[j] + j; /* non linear */
        mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
        i++; j++;
        if (i>=N) { mt[0] = mt[N-1]; i=1; }
        if (j>=key_length) j=0;
    }
    for (k=N-1; k; k--) {
        mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941UL))
          - i; /* non linear */
        mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
        i++;
        if (i>=N) { mt[0] = mt[N-1]; i=1; }
    }

    mt[0] = 0x80000000UL; /* MSB is 1; assuring non-zero initial array */ 
}

/* generates a random number on [0,0xffffffff]-interval */
unsigned long genrand_int32(void)
{
    unsigned long y;
    static unsigned long mag01[2]={0x0UL, MATRIX_A};
    /* mag01[x] = x * MATRIX_A  for x=0,1 */

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

        if (mti == N+1)   /* if init_genrand() has not been called, */
            init_genrand(5489UL); /* a default initial seed is used */

        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 & 0x1UL];
        }
        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 & 0x1UL];
        }
        y = (mt[N-1]&UPPER_MASK)|(mt[0]&LOWER_MASK);
        mt[N-1] = mt[M-1] ^ (y >> 1) ^ mag01[y & 0x1UL];

        mti = 0;
    }
  
    y = mt[mti++];

    /* Tempering */
    y ^= (y >> 11);
    y ^= (y << 7) & 0x9d2c5680UL;
    y ^= (y << 15) & 0xefc60000UL;
    y ^= (y >> 18);

    return y;
}

/* generates a random number on [0,0x7fffffff]-interval */
long genrand_int31(void)
{
    return (long)(genrand_int32()>>1);
}

/* generates a random number on [0,1]-real-interval */
double genrand_real1(void)
{
    return genrand_int32()*(1.0/4294967295.0); 
    /* divided by 2^32-1 */ 
}

/* generates a random number on [0,1)-real-interval */
double genrand_real2(void)
{
    return genrand_int32()*(1.0/4294967296.0); 
    /* divided by 2^32 */
}

/* generates a random number on (0,1)-real-interval */
double genrand_real3(void)
{
    return (((double)genrand_int32()) + 0.5)*(1.0/4294967296.0); 
    /* divided by 2^32 */
}

/* generates a random number on [0,1) with 53-bit resolution*/
double genrand_res53(void) 
{ 
    unsigned long a=genrand_int32()>>5, b=genrand_int32()>>6; 
    return(a*67108864.0+b)*(1.0/9007199254740992.0); 
} 
/* These real versions are due to Isaku Wada, 2002/01/09 added */

int main(void)
{
    int i;
    unsigned long init[4]={0x123, 0x234, 0x345, 0x456}, length=4;
    init_by_array(init, length);
    printf("1000 outputs of genrand_int32()\n");
    for (i=0; i<1000; i++) {
      printf("%10lu ", genrand_int32());
      if (i%5==4) printf("\n");
    }
    printf("\n1000 outputs of genrand_real2()\n");
    for (i=0; i<1000; i++) {
      printf("%10.8f ", genrand_real2());
      if (i%5==4) printf("\n");
    }
    return 0;
}

[Berni]

Well when i needed random numbers i just used that simplest method thats used in most programming language as a random routine. The method is very fast and only needs 1 line of code. You just take the seed value and multiply it and also add a certain number. The result is then let to overflow (performing a mod operation) and thats it. Its not a very good method if you need very good random numbers, but its more than good enough for most uses.

Best random generation is always done with the help of external hardware. In small devices its common to use the PN junction noise of a diode and on PCs we can use online services that generate random numbers from listening to radio noise from space and such.

[leon_heller]

These Quantis units are very good:

http://www.idquantique.com/index.php/co ... cle/9.html

They aren't all that expensive.

Leon

[shawn]

I'm all over this!http://www.wolframscience.com/nksonline/section-7.2!Shawn

[jonathan]

Quick pseudo-random number generation using CRC.

Code: Select all

#include <stdio.h>
#include <xs1.h>

void requestor(chanend a);
void random_number_gen(chanend a);

int main() {
  chan a; 
  par {
    random_number_gen(a);
    requestor(a);
  }
} 

void requestor(chanend a) {
  int num_gen;
  while (1) {
    a :> num_gen;
    printf("%i\n",num_gen);
  }
}

void random_number_gen(chanend a) {
  unsigned int random = 1; // Seed
  while (1) {
    crc32(random,0xffffffff,0xEDB88320);
    a <: random;
  }
}

[andrew]

what do you want the random numbers for?

[jonathan]

what do you want the random numbers for?

Lol, did you see the other code I posted? The SIC emulator...

Anyone any ideas what I can do with random numbers and a SIC emulator? Hint: will be using an XMP-64.

I'm pretty sure it won't work, but I'm willing to give it a go.

[andrew]

Please tell me, I can't work it out. Sorry. I took a look but couldn't figure out how the two are related.

Thanks

[andrew]

On the L1 you could use the ring oscillator to generate random numbers. These would be pretty good.