TYPES, VALUES, AND VARIABLES

Floating Point Operations

4.2.4

Java requires that floating point arithmetic behave as if every floating point

operator rounded its floating point result to the result precision.

Inexact

 results

must be rounded to the representable value nearest to the infinitely precise result;

if the two nearest representable values are equally near, the one with its least sig 

nificant bit zero is chosen. This is the IEEE 754 standard's default rounding mode

known as

round to nearest

.

Java uses

round toward zero

 when converting a floating value to an integer

( 5.1.3), which acts, in this case, as though the number were truncated, discarding

the mantissa bits. Rounding toward zero chooses at its result the format's value

closest to and no greater in magnitude than the infinitely precise result.

Java floating point operators produce no exceptions ( 11). An operation that

overflows produces a signed infinity, an operation that underflows produces a

signed zero, and an operation that has no mathematically definite result produces

NaN. All numeric operations with NaN as an operand produce NaN as a result. As

has already been described, NaN is unordered, so a numeric comparison operation

involving one or two NaNs returns

false

 and any

!=

 comparison involving NaN

returns

true

, including

x!=x

 when

x

 is NaN.

The example program:

class Test {

public static void main(String[] args) {

//

An example of overflow:

double d = 1e308;

System.out.print("overflow produces infinity: ");

System.out.println(d + "*10==" + d*10);

//

An example of gradual underflow:

d = 1e 305 * Math.PI;

System.out.print("gradual underflow: " + d + "\n

");

for (int i = 0; i < 4; i++)

System.out.print(" " + (d /= 100000));

System.out.println();

//

An example of NaN:

System.out.print("0.0/0.0 is Not a Number: ");

d = 0.0/0.0;

System.out.println(d);

//

An example of inexact results and rounding:

System.out.print("inexact results with float:");

for (int i = 0; i < 100; i++) {

float z = 1.0f / i;

if (z * i != 1.0f)

System.out.print(" " + i);

}

System.out.println();

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