Java Numbers

Java Numbers

Numbers are basic to just about any computation. They’re used for array indexes,
temperatures, salaries, ratings, and an infinite variety of things. Yet they’re not as
simple as they seem. With floating-point numbers, how accurate is accurate? With
random numbers, how random is random? With strings that should contain a num-
ber, what actually constitutes a number?

Java has several built-in types that can be used to represent numbers, summarized in
Table. Note that unlike languages such as C or Perl, which don’t specify the size
or precision of numeric types, Java—with its goal of portability—specifies these
exactly and states that they are the same on all platforms.

As you can see, Java provides a numeric type for just about any purpose. There are
four sizes of signed integers for representing various sizes of whole numbers. There
are two sizes of floating-point numbers to approximate real numbers. There is also a
type specifically designed to represent and allow operations on Unicode characters.

When you read a string from user input or a text file, you need to convert it to the
appropriate type. The object wrapper classes in the second column have several

functions, but one of the most important is to provide this basic conversion functionality—replacing the C programmer’s atoi/atof family of functions and the
numeric arguments to scanf.

Going the other way, you can convert any number (indeed, anything at all in Java) to
a string just by using string concatenation. If you want a little bit of control over
numeric formatting, Recipe 5.8 shows you how to use some of the object wrappers’
conversion routines. And if you want full control, it also shows the use of
NumberFormat and its related classes to provide full control of formatting.

As the name object wrapper implies, these classes are also used to “wrap” a number
in a Java object, as many parts of the standard API are defined in terms of objects.
Later on, Recipe 10.16 shows using an Integer object to save an int ’s value to a file
using object serialization, and retrieving the value later.

But I haven’t yet mentioned the issues of floating point. Real numbers, you may
recall, are numbers with a fractional part. There is an infinity of possible real num-
bers. A floating-point number—what a computer uses to approximate a real num-
ber—is not the same as a real number. The number of floating-point numbers is
finite, with only 2^32 different bit patterns for float s, and 2^64 for double s. Thus,
most real values have only an approximate correspondence to floating point. The
result of printing the real number 0.3 works correctly, as in:

System.out.println("The real value 0.3 is " + 0.3);

results in this printout:

The real value 0.3 is 0.3

But the difference between a real value and its floating-point approximation can accumulate if the value is used in a computation; this is often called a rounding error. Continuing the previous example, the real 0.3 multiplied by 3 yields:

The real 0.3 times 3 is 0.89999999999999991

Surprised? More surprising is this: you’ll get the same output on any conforming Java implementation. I ran it on machines as disparate as a Pentium with OpenBSD, a Pentium with Windows and Sun’s JDK, and on Mac OS X with JDK 1.4.1. Always the same answer.

And what about random numbers? How random are they? You have probably heard the expression “pseudo-random numbers.” All conventional random number genera- tors, whether written in Fortran, C, or Java, generate pseudo-random numbers. That is, they’re not truly random! True randomness comes only from specially built hard- ware: an analog source of Brownian noise connected to an analog-to-digital con- verter, for example. * This is not your average PC! However, pseudo-random number generators (PRNG for short) are good enough for most purposes, so we use them. Java provides one random generator in the base library java.lang.Math , and several others; we’ll examine these in Recipe 5.13. 

The class java.lang.Math contains an entire “math library” in one class, including trigonometry, conversions (including degrees to radians and back), rounding, trun- cating, square root, minimum, and maximum. It’s all there. Check the Javadoc for java.lang.Math . 

The package java.Math contains support for “big numbers”—those larger than the normal built-in long integers, for example. See Recipe 5.19. Java works hard to ensure that your programs are reliable. 

The usual ways you’d notice this are in the common requirement to catch potential exceptions—all through the Java API—and in the need to “cast” or convert when storing a value that might or might not fit into the variable you’re trying to store it in. I’ll show examples of these. Overall, Java’s handling of numeric data fits well with the ideals of portability, reli- ability, and ease of programming. 

See Also 

The Java Language Specification. The Javadoc page for java.lang.Math .


Post a Comment