TYPES, VALUES, AND VARIABLES

Floating Point Types and Values

4.2.3

second multiplication is a

long

 multiplication. The value

 727379968

 is the deci 

mal value of the low 32 bits of the mathematical result,

1000000000000

, which is

a value too large for type

int

.

Any value of any integral type may be cast to or from any numeric type. There

are no casts between integral types and the type

boolean

.

4.2.3   Floating Point Types and Values

The floating point types are

float

 and

double

, representing the single precision

32 bit and double precision 64 bit format IEEE 754 values and operations as

specified in

IEEE Standard for Binary Floating Point Arithmetic

, ANSI/IEEE

Standard 754 1985 (IEEE, New York).

The IEEE 754 standard includes not only positive and negative sign magni 

tude numbers, but also positive and negative zeros, positive and negative

infinities

,

and a special

Not a Number

(hereafter abbreviated NaN). The NaN value is used

to represent the result of certain operations such as dividing zero by zero. NaN

constants of both

float

 and

double

 type are predefined as

Float.NaN

 ( 20.9.5)

and

Double.NaN

 ( 20.10.5).

The finite nonzero values of type

float

 are of the form

s m

2

e

, where

s

 is

+1 or  1,

m

 is a positive integer less than 2

24

, and

e

 is an integer between  149

and 104, inclusive. Values of that form such that

m

 is positive but less than 2

23

and

e

 is equal to  149 are said to be

denormalized

.

The finite nonzero values of type

double

 are of the form

s m

2

e

, where

s

 is

+1 or  1,

m

 is a positive integer less than 2 , and

53

e

 is an integer between  1075

and 970, inclusive. Values of that form such that

m

 is positive but less than

52

2

and

e

 is equal to  1075 are said to be

denormalized

.

Except for NaN, floating point values are

ordered

; arranged from smallest to

largest, they are negative infinity, negative finite nonzero values, negative zero,

positive zero, positive finite nonzero values, and positive infinity.

Positive zero and negative zero compare equal; thus the result of the expres 

sion

0.0== 0.0

 is

true

 and the result of

0.0> 0.0

 is

false

. But other opera 

tions can distinguish positive and negative zero; for example,

1.0/0.0

 has the

value positive infinity, while the value of

1.0/ 0.0

 is negative infinity. The oper 

ations

Math.min

 and

Math.max

 also distinguish positive zero and negative zero.

NaN is

unordered

, so the numerical comparison operators

<

,

<=

,

>

, and

>=

return

false

 if either or both operands are NaN ( 15.19.1). The equality operator

==

 returns

false

 if either operand is NaN, and the inequality operator

!=

 returns

true

 if either operand is NaN ( 15.20.1). In particular,

x!=x

 is

true

 if and only if

x

 is NaN, and

(x=y)

 will be

false

 if

x

 or

y

 is NaN.

Any value of a floating point type may be cast to or from any numeric type.

There are no casts between floating point types and the type

boolean

.

33