Data Types - Beginning Java 8 Fundamentals - page 89

For comparison purposes, +0.0 and -0.0 are considered equal. Therefore, the expression 0.0 == -0.0 always
returns true .
Why does IEEE define two zeros if they are considered equal? The sign of zero is used to determine the result
of an arithmetic expression involving multiplication and division. The result of 3.0 * 0.0 is a positive zero ( 0.0 ),
whereas the result of 3.0 * (-0.0) is a negative zero ( -0.0 ). For a floating-point number num with the values
±Infinity, the relation 1/(1/num) = num holds true only because of two signed zeros.

Signed Infinities
The IEEE floating-point format allows for two infinities: positive infinity and negative infinity. The sign bit represents
the sign of infinity. The maximum exponent value 128 (the biased exponent 255) for the single-precision format and
zero significand represents infinity. The maximum biased value 255 can be represented in 8-bit with all bits set to 1 as
11111111 . The binary representations of infinities in single-precision format are shown in Table 3-9 .

Table 3-9. Binary Representations of Positive and Negative Infinities in the Single-Precision Format

Number Sign Exponent Significand

+Infinity 0 11111111 00000000000000000000000

-Infinity 1 11111111 00000000000000000000000

NaN
NaN stands for “Not-a-Number.” NaN is the result of arithmetic operations that do not have meaningful results, such as
dividing zero by zero, the square root of a negative number, adding -Infinity to +Infinity, etc.
NaN is represented by maximum exponent value (128 for single-precision format) and non-zero significand. The
sign bit is not interpreted for NaN . What happens when NaN is one of the operands in an arithmetic expression? For
example, what is the result of NaN + 100 ? Should the execution of an arithmetic expression involving NaNs be stopped
or continued? There are two types of NaNs :

NaN • Quiet

NaN
A quiet NaN , when encountered as an operand in an arithmetic expression, quietly (i.e. without raising any trap
or exception) produces another quiet NaN as the result. In case of a quiet NaN , the expression NaN + 100 will result
in another quiet NaN . The most significant bit in the significand is set to 1 for a quiet NaN . Table 3-10 shows a binary
representation of a quiet NaN . In the table, s and b indicate a 0 or 1 bit.

• Signaling

Table 3-10. A Binary Representation of a Quiet NaN

Number Sign Exponent Significand

Quiet NaN s 11111111 1bbbbbbbbbbbbbbbbbbbbbb

When a signaling NaN is encountered as an operand in an arithmetic expression, an invalid operation exception
is signaled and a quiet NaN is delivered as the result. Signaling NaNs are generally used to initialize the uninitialized
variables in a program, so when variables are not initialized before they are used, errors can be signaled. The most
significant bit of the significand is set to 0 for a signaling NaN . Table 3-11 shows a binary representation of a signaling
NaN . In the table, s and b indicate a 0 or 1 bit.