21.9

java.util.Random

THE PACKAGE JAVA.UTIL

return (((long)next(27) << 27) + next(27))

/ (double)(1L << 54);

This might seem to be equivalent, if not better, but in fact it introduced a large

nonuniformity because of the bias in the rounding of floating point numbers: it

was three times as likely that the low order bit of the significand would be

0

 than

that it would be

1

! This nonuniformity probably doesn't matter much in practice,

but we strive for perfection.]

21.9.12

public double nextGaussian()

The general contract of

nextGaussian

 is that one

double

 value, chosen from

(approximately) the usual normal distribution with mean

0.0

 and standard devia 

tion

1.0

, is pseudorandomly generated and returned.

The method

setSeed

 is implemented by class

Random

 as follows:

synchronized public double nextGaussian() {

if (haveNextNextGaussian) {

haveNextNextGaussian = false;

return nextNextGaussian;

} else {

double v1, v2, s;

do {

v1 = 2 * nextDouble()   1; //

between

 1.0

 and

1.0

v2 = 2 * nextDouble()   1; //

between

 1.0

 and

1.0

s = v1 * v1 + v2 * v2;

} while (s >= 1);

double norm = Math.sqrt( 2 * Math.log(s)/s);

nextNextGaussian = v2 * norm;

haveNextNextGaussian = true;

return v1 * norm;

}

}

This uses the

polar method

 of G. E. P. Box, M. E. Muller, and G. Marsaglia, as

described by Donald E. Knuth in

The Art of Computer Programming

, Volume 2:

Seminumerical Algorithms

, section 3.4.1, subsection C, algorithm P. Note that it

generates two independent values at the cost of only one call to

Math.log

 and one

call to

Math.sqrt

.

 . . . who can tell what may be the event? . . .

The mind of the multitude is left at random . . .

 Thomas Paine,

Common Sense

 (1776), Appendix A

650