Why would rand() return a negative value when min

Question

I have a simple piece of PHP code which requires a random number to be created. However, even though the input is always positive, it sometimes returns a negative output.

Here's my debug code:

$debt = rand($this->gdp * 0.02, $this->gdp * 0.17);
echo "<p>GDP: ".$this->gdp." rand(".$this->gdp * 0.02."  , ".$this->gdp * 0.17.") = <strong>".$debt."</strong></p>";

Here's an example output:

GDP: 219254674605 rand(4385093492.1 , 37273294682.85) = 75276999

GDP: 345015694865 rand(6900313897.3 , 58652668127.05) = -1636353016

GDP: 90445390920 rand(1808907818.4 , 15375716456.4) = -165604705

GDP: 3412849650 rand(68256993 , 580184440.5) = 347516196

GDP: 2939111315 rand(58782226.3 , 499648923.55) = 119181875

GDP: 26369065 rand(527381.3 , 4482741.05) = 3632416

GDP: 215838135 rand(4316762.7 , 36692482.95) = 28784811

GDP: 511763530 rand(10235270.6 , 86999800.1) = 39954394

GDP: 42416245 rand(848324.9 , 7210761.65) = 3974882

GDP: 75090235 rand(1501804.7 , 12765339.95) = 5201966

So why would a rand() of two positive numbers give a negative return?

Any help would be much appreciated!

Answer 1

Because you're seeing an integer overflow in the arguments.

According to the rand() documentation it takes two int values as arguments. On a 32-bit machine those are 32 bit as well (at least for PHP). So when you pass arguments larger than 2³¹ − 1 they overflow and start at −2³¹ again.

Apparently, if you need larger values you'll have to code it yourself. While simply creating a 64-bit number from two 32-bit numbers works as intended, you can't simply do a modulo operation with your maximum value since that skews the distribution. For a good implementation how to generate a uniformly-distributed random integer between 0 and a certain upper bound you can take a look at java.util.Random.nextInt(int) and adapt accordingly for 64 bit integers.

mt_rand() while usually a nice choice for random numbers because it uses MT19937 instead of a poor LCG, doesn't help here either as its arguments are ints as well.

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Another option you might want to consider if you don't require every possible value to be picked eventually:

• Generate a random floating-point value between 0 and 1 by calling

  $rnd = mt_rand() / (double)mt_getrandmax()
  

• Determine the range of numbers you need:

  $min = $this->gdp * 0.02;
  $max = $this->gdp * 0.17;
  $range = $max - $min;
  

• Multiply this by the previously-obtained random floating-point value and add the minimum:

  $value = $min + $range * $rnd
  

• Now you have a random value between your chosen boundaries. It's approximately uniformly distributed, although there are discrete steps between adjacent random numbers as you are stretching 32 bits of randomness over a larger number of bits. If that's no problem for you, go ahead, though.

Answer 2

Rand takes as arguments, and returns, integers. Integers (in PHP) usually have a maximum range of 2**32.

Your double arguments are larger than this, causing an integer overflow when they are converted to integers.