mersenne-twister.cpp

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/*
 * The Mersenne Twister pseudo-random number generator (PRNG)
 *
 * This is an implementation of fast PRNG called MT19937,
 * meaning it has a period of 2^19937-1, which is a Mersenne
 * prime.
 *
 * This PRNG is fast and suitable for non-cryptographic code.
 * For instance, it would be perfect for Monte Carlo simulations,
 * etc.
 *
 * For all the details on this algorithm, see the original paper:
 * http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.pdf
 *
 * Written by Christian Stigen Larsen
 * http://csl.name
 *
 * Distributed under the modified BSD license.
 *
 * 2015-02-17
 */

#include <cstdio>
#include "mersenne-twister.h"

/*
 * We have an array of 624 32-bit values, and there are
 * 31 unused bits, so we have a seed value of
 * 624*32-31 = 19937 bits.
 */
static const unsigned SIZE   = 624;
static const unsigned PERIOD = 397;
static const unsigned DIFF   = SIZE - PERIOD;

static uint32_t MT[SIZE];
static unsigned index = 0;

#define M32(x) (0x80000000 & (x)) // 32nd Most Significant Bit
#define L31(x) (0x7FFFFFFF & (x)) // 31 Least Significant Bits
#define ODD(x) ((x) & 1) // Check if number is odd

#define UNROLL(expr) \
  y = M32(MT[i]) | L31(MT[i+1]); \
  MT[i] = MT[expr] ^ (y>>1) ^ MATRIX[ODD(y)]; \
  ++i;

#define MD_UINT32_MAX std::numeric_limits<uint32_t>::max()

static inline void generate_numbers()
{
  /*
   * Originally, we had one loop with i going from [0, SIZE) and
   * two modulus operations:
   *
   * for ( register unsigned i=0; i<SIZE; ++i ) {
   *   register uint32_t y = M32(MT[i]) | L31(MT[(i+1) % SIZE]);
   *   MT[i] = MT[(i + PERIOD) % SIZE] ^ (y>>1);
   *   if ( ODD(y) ) MT[i] ^= 0x9908b0df;
   * }
   *
   * For performance reasons, we've unrolled the loop three times, thus
   * mitigating the need for any modulus operations.
   *
   * Anyway, it seems this trick is old hat:
   * http://www.quadibloc.com/crypto/co4814.htm
   *
   */

  static const uint32_t MATRIX[2] = {0, 0x9908b0df};
  uint32_t y, i = 0;

  // i = [0 ... 226]
  while ( i < ( DIFF - 1 ) )
  {
    /*
     * We're doing 226 = 113*2, an even number of steps, so we can
     * safely unroll one more step here for speed:
     */
    UNROLL( i + PERIOD );
    UNROLL( i + PERIOD );
  }

  // i = 226
  UNROLL( ( i + PERIOD ) % SIZE );

  // i = [227 ... 622]
  while ( i < ( SIZE - 1 ) )
  {
    /*
     * 623-227 = 396 = 2*2*3*3*11, so we can unroll this loop in any number
     * that evenly divides 396 (2, 4, 6, etc). Here we'll unroll 11 times.
     */
    UNROLL( i - DIFF );
    UNROLL( i - DIFF );
    UNROLL( i - DIFF );
    UNROLL( i - DIFF );
    UNROLL( i - DIFF );
    UNROLL( i - DIFF );
    UNROLL( i - DIFF );
    UNROLL( i - DIFF );
    UNROLL( i - DIFF );
    UNROLL( i - DIFF );
    UNROLL( i - DIFF );
  }

  // i = 623
  y = M32( MT[SIZE - 1] ) | L31( MT[0] );
  MT[SIZE - 1] = MT[PERIOD - 1] ^ ( y >> 1 ) ^ MATRIX[ODD( y )];
}

extern "C" void seed( uint32_t value )
{
  /*
   * The equation below is a linear congruential generator (LCG),
   * one of the oldest known pseudo-random number generator
   * algorithms, in the form X_(n+1) = = (a*X_n + c) (mod m).
   *
   * We've implicitly got m=32 (mask + word size of 32 bits), so
   * there is no need to explicitly use modulus.
   *
   * What is interesting is the multiplier a.  The one we have
   * below is 0x6c07865 --- 1812433253 in decimal, and is called
   * the Borosh-Niederreiter multiplier for modulus 2^32.
   *
   * It is mentioned in passing in Knuth's THE ART OF COMPUTER
   * PROGRAMMING, Volume 2, page 106, Table 1, line 13.  LCGs are
   * treated in the same book, pp. 10-26
   *
   * You can read the original paper by Borosh and Niederreiter
   * as well.  It's called OPTIMAL MULTIPLIERS FOR PSEUDO-RANDOM
   * NUMBER GENERATION BY THE LINEAR CONGRUENTIAL METHOD (1983) at
   * http://www.springerlink.com/content/n7765ku70w8857l7/
   *
   * You can read about LCGs at:
   * http://en.wikipedia.org/wiki/Linear_congruential_generator
   *
   * From that page, it says:
   * "A common Mersenne twister implementation, interestingly
   * enough, uses an LCG to generate seed data.",
   *
   * Since we're using 32-bits data types for our MT array, we can skip the
   * masking with 0xFFFFFFFF below.
   */

  MT[0] = value;
  index = 0;

  for ( unsigned i = 1; i < SIZE; ++i )
    MT[i] = 0x6c078965 * ( MT[i - 1] ^ MT[i - 1] >> 30 ) + i;
}

extern "C" uint32_t rand_u32()
{
  if ( !index )
    generate_numbers();

  uint32_t y = MT[index];

  // Tempering
  y ^= y >> 11;
  y ^= y << 7 & 0x9d2c5680;
  y ^= y << 15 & 0xefc60000;
  y ^= y >> 18;

  if ( ++index == SIZE )
    index = 0;

  return y;
}

extern "C" int mt_rand()
{
  /*
   * PORTABILITY WARNING:
   *
   * rand_u32() uses all 32-bits for the pseudo-random number,
   * but rand() must return a number from 0 ... MD_RAND_MAX.
   *
   * We'll just assume that rand() only uses 31 bits worth of
   * data, and that we're on a two's complement system.
   *
   * So, to output an integer compatible with rand(), we have
   * two options: Either mask off the highest (32nd) bit, or
   * shift right by one bit.  Masking with 0x7FFFFFFF will be
   * compatible with 64-bit MT[], so we'll just use that here.
   *
   */
  return static_cast<int>( 0x7FFFFFFF & rand_u32() );
}

extern "C" void mt_srand( unsigned value )
{
  seed( static_cast<uint32_t>( value ) );
}

extern "C" float randf_cc()
{
  return static_cast<float>( rand_u32() ) / MD_UINT32_MAX;
}

extern "C" float randf_co()
{
  return static_cast<float>( rand_u32() ) / ( MD_UINT32_MAX + 1.0f );
}

extern "C" float randf_oo()
{
  return ( static_cast<float>( rand_u32() ) + 0.5f ) / ( MD_UINT32_MAX + 1.0f );
}

extern "C" double randd_cc()
{
  return static_cast<double>( rand_u32() ) / MD_UINT32_MAX;
}

extern "C" double randd_co()
{
  return static_cast<double>( rand_u32() ) / ( MD_UINT32_MAX + 1.0 );
}

extern "C" double randd_oo()
{
  return ( static_cast<double>( rand_u32() ) + 0.5 ) / ( MD_UINT32_MAX + 1.0 );
}

extern "C" uint64_t rand_u64()
{
  return static_cast<uint64_t>( rand_u32() ) << 32 | rand_u32();
}