Bugs in breeze.stats.distributions.RandBasis.uniform and randLong

[Sanzo-Miyazawa]

1. The comments of breeze.stats.distributions.RandBasis.uniform indicate "Uniformly samples in [0,1]". However, I think that this comment should be corrected as "[0, 1)", because the java code finally called, org.apache.commons.math3.random.MersenneTwister.nextDouble == org.apache.commons.math3.random.BitsStreamGenerator.nextDouble , will generate [0, 1).

   public double nextDouble() {
       final long high = ((long) next(26)) << 26;
       final int  low  = next(26);
       return (high | low) * 0x1.0p-52d;
   }

   If so, "require( low <= high)" in the breeze.stats.distributions.Uniform(low, high) should be "require( low < high)".

2. Also, I think that the following codes for randLong are not correct.

   /**
   * Uniformly samples a long integer in [0,n)
   */
   def randLong(n: Long): Rand[Long] = new Rand[Long] {
    def draw() = {
     val value = generator.nextLong & Long.MaxValue
     value % n
   }
   }
   
   /**
   * Uniformly samples a long integer in [n,m)
   */
   def randLong(n: Long, m: Long): Rand[Long] = new Rand[Long] {
   def draw() = {
     val value = generator.nextLong & Long.MaxValue
     value % (m - n) + n
   }
   }

   They may be written as

   
   /**
   * Uniformly samples a long integer in [0,n)
   */
   def randLong(n: Long): Rand[Long] = new Rand[Long] {
   require(n > 0, "n > 0")
   def draw() = {
     val maxVal = Long.MaxValue - (Long.MaxValue % n) - 1
     var value = (generator.nextLong() & Long.MaxValue)
     while ( value > maxVal ) {
       value = (generator.nextLong() & Long.MaxValue)
     }
     value % n
   }
   }

/**

• Uniformly samples a long integer in [n,m) */ def randLong(n: Long, m: Long): Rand[Long] = new Rand[Long] { def draw() = randLong(m - n).draw() + n }

  Otherwise, simply,

  def randLong(n: Long): Rand[Long] = new Rand[Long] { def draw() = generator.nextLong(n) } def randLong(n: Long, m: Long): Rand[Long] = new Rand[Long] { def draw() = generator.nextLong(m - n) + n }