PocketMine-MP/src/utils/MersenneTwister.php

<?php
/*
  Mersenne Twister, 1.1.0
  -----------------------

  This is an implementation of the Mersenne Twister.  The current version
  number is 1.1.0.

  Much of the code here was derived from the C code in the file
  mt19937ar.c, which is in the archive mt19937ar.sep.tgz, available from
  http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html.
  Some of the original C code is preserved in a few of the comments below.

  It is non-trivial to map the C code onto PHP, because PHP has no
  unsigned integer type.  What we do here is to use integers when we can,
  and floats when we must.

  Only the class `twister' is part of the API; everything else is private.
  
  http://kingfisher.nfshost.com/sw/twister/

*/

const N = 624;
const M = 397;
const MATRIX_A = 0x9908b0df;
const UPPER_MASK = 0x80000000;
const LOWER_MASK = 0x7fffffff;

  foreach (array(10, 11, 12, 14, 20, 21, 22, 26, 27, 31) as $n) {
    $val = ~((~0) << $n);
	define("MASK$n", $val);
  }

  foreach (array(16, 31, 32) as $n) {
    $val = pow(2, $n);
	define("TWO_TO_THE_$n",$val);
  }

  $val = MASK31 | (MASK31 << 1);
  define("MASK32", $val);


class twister {
  const N = N;
  # the class constant is not used anywhere in this namespace,
  # but it makes the API cleaner.

  function __construct() {
    $this->bits32 = PHP_INT_MAX == 2147483647;

    if(func_num_args() == 1) {
      $this->init_with_integer(func_get_arg(0));
    }
  }

  function init_with_integer($integer_seed) {
    $integer_seed = force_32_bit_int($integer_seed);

    $mt = &$this->mt;
    $mti = &$this->mti;

    $mt = array_fill(0, N, 0);

    $mt[0] = $integer_seed;

    for($mti = 1; $mti < N; $mti++) {
      $mt[$mti] = add_2(mul(1812433253,
        ($mt[$mti - 1] ^ (($mt[$mti - 1] >> 30) & 3))), $mti);
      /*
      mt[mti] =
          (1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti);
      */
    }
  }

  function init_with_array(array $integer_array) {
    $integer_array =
      array_map("force_32_bit_int", $integer_array);

    $mt = &$this->mt;
    $mti = &$this->mti;

    $key_length = count($integer_array);

    $this->init_with_integer(19650218);
    $i=1; $j=0;
    $k = (N>$key_length ? N : $key_length);
    for (; $k; $k--) {
        $mt[$i] = add_3($mt[$i] ^
          mul_by_1664525($mt[$i-1] ^ (($mt[$i-1] >> 30) & 3)),
          $integer_array[$j], $j);
        /*
          mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1664525UL))
            + init_key[j] + j;
        */
        $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] = sub($mt[$i] ^
          mul($mt[$i-1] ^ (($mt[$i-1] >> 30) & 3), 1566083941), $i);
        /*
          mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941UL))
            - i;
        */
        $i++;
        if ($i>=N) { $mt[0] = $mt[N-1]; $i=1; }
    }

    $mt[0] = (1 << 31); /* MSB is 1; assuring non-zero initial array */ 
  }

  function init_with_string($string) {
    $remainder = strlen($string) % 4;

    if($remainder > 0){
      $string .= str_repeat("\0", 4 - $remainder);
	}

    $integer_array = array_values(unpack("N*", $string));

    $this->init_with_array($integer_array);
  }

  function init_with_files(array $filenames, $max_ints = -1) {
    $limit_applies = $max_ints !== -1;

    if($limit_applies){
      $limit = $max_ints * 4;   # 32 bits is 4 characters
    }
    $data = "";

    foreach ($filenames as $filename) {
      $contents =
	file_get_contents($filename, FALSE, NULL, 0,
	  $limit_applies? $limit - strlen($data): -1);

      if($contents === FALSE) {
	throw new Exception("problem reading from $filename");
      } else {
	$data .= $contents;

	if($limit_applies && strlen($data) == $limit) {
	  break;
	}
      }
    }

    $this->init_with_string($data);
  }

  function init_with_file($filename, $max_ints = -1) {
    $this->init_with_files(array($filename), $max_ints);
  }

  function int32() {
    static $mag01 = array(0, MATRIX_A);

    $mt = &$this->mt;
    $mti = &$this->mti;

    if ($mti >= N) { /* generate N words all at once */
        for ($kk=0;$kk<N-M;$kk++) {
            $y = ($mt[$kk]&UPPER_MASK)|($mt[$kk+1]&LOWER_MASK);
            $mt[$kk] = $mt[$kk+M] ^ (($y >> 1) & MASK31) ^ $mag01[$y & 1];
        }
        for (;$kk<N-1;$kk++) {
            $y = ($mt[$kk]&UPPER_MASK)|($mt[$kk+1]&LOWER_MASK);
            $mt[$kk] =
              $mt[$kk+(M-N)] ^ (($y >> 1) & MASK31) ^ $mag01[$y & 1];
        }
        $y = ($mt[N-1]&UPPER_MASK)|($mt[0]&LOWER_MASK);
        $mt[N-1] = $mt[M-1] ^ (($y >> 1) & MASK31) ^ $mag01[$y & 1];

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

    /* Tempering */
    $y ^= ($y >> 11) & MASK21;
    $y ^= ($y << 7) & ((0x9d2c << 16) | 0x5680);
    $y ^= ($y << 15) & (0xefc6 << 16);
    $y ^= ($y >> 18) & MASK14;

    return $y;
  }

  function int31() {
    return $this->int32() & MASK31;
  }

  /* generates a random number on [0,1]-real-interval */
  function real_closed() {
    return signed2unsigned($this->int32()) * (1.0 / 4294967295.0); 
  }

  /* generates a random number on [0,1)-real-interval */
  function real_halfopen() {
    return signed2unsigned($this->int32()) * (1.0 / 4294967296.0); 
  }

  /* generates a random number on (0,1)-real-interval */
  function real_open() {
    return (signed2unsigned($this->int32()) + .5) * (1.0 / 4294967296.0); 
  }

  /* generates a random number on [0,1) with 53-bit resolution */
  function real_halfopen2() { 
    return ((($this->int32() & MASK27) * 67108864.0) +
        ($this->int32() & MASK26)) *
      (1.0 / 9007199254740992.0);
  } 

  function rangeint($lower_bound, $upper_bound) {
    $lower_bound = intval($lower_bound);
    $upper_bound = intval($upper_bound);

    if($this->bits32) {
      $pow_2_32 = pow(2, 32);

      $size_of_range = $upper_bound - $lower_bound + 1;

      $remainder = fmod($pow_2_32, $size_of_range);

      if($remainder == 0) {
	return $lower_bound +
	  ($this->int32() & unsigned2signed($size_of_range - 1));
      } else {
	$start_of_partial_range = $pow_2_32 - $remainder;
	$start_as_int = unsigned2signed($start_of_partial_range);
	do {
	  $rand = $this->int32();
	} while($rand >= $start_as_int && $rand < 0);

	$result = $lower_bound +
	  fmod(signed2unsigned($rand), $size_of_range);

	return intval($result);
      }
    } else {
      if($lower_bound == -PHP_INT_MAX - 1 && $upper_bound == PHP_INT_MAX) {
	return ($this->int32() << 32) & $this->int32();
      } else {
	$pow_2_32 = 1 << 32;

	$size_of_range = $upper_bound - $lower_bound + 1;

	if($size_of_range > $pow_2_32) {
	  $size_of_range >>= 32;
	  $shift = 32;
	  $low_bits = $this->int32();
	} else {
	  $shift = 0;
	  $low_bits = 0;
	}

	$remainder = $pow_2_32 % $size_of_range;

	if($remainder == 0) {
	  $high_bits = $this->int32() & ($size_of_range - 1); 
	} else {
	  $start_of_partial_range = $pow_2_32 - $remainder;
	  do {
	    $rand = $this->int32();
	  } while($rand >= $start_of_partial_range);

	  $high_bits = $rand % $size_of_range;
	}

	return $lower_bound + (($high_bits << $shift) | $low_bits);
      }
    }
  }

  /*
    in each of the next 3 functions, we loop until we have a number that
    meets the function's post-condition.  this may be more work than
    is really necessary, but i am concerned about rounding errors.

    why no rangereal_closed?  because, due to the aforementioned
    rounding errors, i am unable to guarantee that $upper_bound
    would be a possible return value of such a function.
  */

  function rangereal_open($lower_bound, $upper_bound) {
    do {
      $rand = $lower_bound +
	$this->real_open() * ($upper_bound - $lower_bound);
    } while($rand <= $lower_bound || $rand >= $upper_bound);

    return $rand;
  }

  function rangereal_halfopen($lower_bound, $upper_bound) {
    do {
      $rand = $lower_bound +
	$this->real_halfopen() * ($upper_bound - $lower_bound);
    } while($rand >= $upper_bound);
      /*
	$rand cannot go any lower than $lower_bound, because
	$this->real_halfopen() cannot go any lower than 0
      */

    return $rand;
  }

  function rangereal_halfopen2($lower_bound, $upper_bound) {
    do {
      $rand = $lower_bound +
	$this->real_halfopen2() * ($upper_bound - $lower_bound);
    } while($rand >= $upper_bound);

    return $rand;
  }
}

function signed2unsigned($signed_integer) {
  ## assert(is_integer($signed_integer));
  ## assert(($signed_integer & ~MASK32) === 0);

  return $signed_integer >= 0? $signed_integer:
    TWO_TO_THE_32 + $signed_integer;
}

function unsigned2signed($unsigned_integer) {
  ## assert($unsigned_integer >= 0);
  ## assert($unsigned_integer < pow(2, 32));
  ## assert(floor($unsigned_integer) === floatval($unsigned_integer));

  return intval($unsigned_integer < TWO_TO_THE_31? $unsigned_integer:
    $unsigned_integer - TWO_TO_THE_32);
}

function force_32_bit_int($x) {
  /*
    it would be un-PHP-like to require is_integer($x),
    so we have to handle cases like this:

      $x === pow(2, 31)
      $x === strval(pow(2, 31))

    we are also opting to do something sensible (rather than dying)
    if the seed is outside the range of a 32-bit unsigned integer.
  */

  if(is_integer($x)) {
    /* 
      we mask in case we are on a 64-bit machine and at least one
      bit is set between position 32 and position 63.
    */
    return $x & MASK32;
  } else {
    $x = floatval($x);

    $x = $x < 0? ceil($x): floor($x);

    $x = fmod($x, TWO_TO_THE_32);

    if($x < 0){
      $x += TWO_TO_THE_32;
	}

    return unsigned2signed($x);
  }
}

/*
  takes 2 integers, treats them as unsigned 32-bit integers,
  and adds them.
  
  it works by splitting each integer into
  2 "half-integers", then adding the high and low half-integers
  separately.

  a slight complication is that the sum of the low half-integers
  may not fit into 16 bits; any "overspill" is added to the sum
  of the high half-integers.
*/ 
function add_2($n1, $n2) {
  $x = ($n1 & 0xffff) + ($n2 & 0xffff);

  return (((($n1 >> 16) & 0xffff) + 
    (($n2 >> 16) & 0xffff) + 
    ($x >> 16)) << 16) | ($x & 0xffff);
}

# takes 2 integers, treats them as unsigned 32-bit integers,
# and adds them.
#
# for how it works, see the comment for add_2.
#
function add_3($n1, $n2, $n3) {
  $x = ($n1 & 0xffff) + ($n2 & 0xffff) + ($n3 & 0xffff);

  return (((($n1 >> 16) & 0xffff) + 
    (($n2 >> 16) & 0xffff) + 
    (($n3 >> 16) & 0xffff) + 
    ($x >> 16)) << 16) | ($x & 0xffff);
}

# takes 2 integers, treats them as unsigned 32-bit integers,
# and subtracts the second from the first.
#
# the explanation of why this works is too long to be
# included here, so it has been moved into the file why-sub-works.txt.
#
function sub($a, $b) {
  return (($a & MASK31) - ($b & MASK31)) ^
    (($a ^ $b) & 0x80000000);
}

function mul($a, $b) {
  /*
    a and b, considered as unsigned integers, can be expressed as follows:

      a = 2**16 * a1 + a2,

      b = 2**16 * b1 + b2,

      where

	0 <= a2 < 2**16,
	0 <= b2 < 2**16.

    given those 2 equations, what this function essentially does is to
    use the following identity:

      a * b = 2**32 * a1 * b1 + 2**16 * a1 * b2 + 2**16 * b1 * a2 + a2 * b2

    note that the first term, i.e. 2**32 * a1 * b1, is unnecessary here,
    so we don't compute it.

    we could make the following code clearer by using intermediate
    variables, but that would probably hurt performance.
  */

  return unsigned2signed(
      fmod(
	TWO_TO_THE_16 *
	  /*
	    the next line of code calculates a1 * b2,
	    the line after that calculates b1 * a2, 
	    and the line after that calculates a2 * b2.
	  */
	  ((($a >> 16) & 0xffff) * ($b & 0xffff) +
	    (($b >> 16) & 0xffff) * ($a & 0xffff)) +
	($a & 0xffff) * ($b & 0xffff),

	TWO_TO_THE_32));
}

/*
  mul_by_1664525($x) should be more efficient than mul(1664525, $x).
*/
function mul_by_1664525($n) {
  return unsigned2signed(fmod(1664525 * ($n >= 0?
    $n: (TWO_TO_THE_32 + $n)), TWO_TO_THE_32));
}

function do_bc_op($bc_op, array $numbers) {
  $modulus = pow(2, 32);

  $result =
    call_user_func_array($bc_op,
      array_map("signed2unsigned", $numbers));

  $result = bcmod($result, $modulus);

  return unsigned2signed(bccomp($result, 0) < 0?
    bcadd($result, $modulus): $result);
}

function get_random_32bit_int() {
  return rand(0, 0xffff) | (rand(0, 0xffff) << 16);
}