Java Reference
In-Depth Information
3.Thethirdfieldiscalledthesignificand,orthefractionfield.InIEEEfor-
mats,thisfieldhasanimplied1-bittotheleftofanalsoimpliedbinary
point.However,thestandardvalidatesencodingsintheextendedformatin
whichthesignificand'sleadingbitisexplicitlyrepresented.
Figure21-1
showsthebitstructureandfieldsinthesingleanddouble
formatoftheIEEE754Standard.
IEEE 754 BASIC SINGLE FORMAT
31
bits
30
22
0
exponent
significand
8
23
sign
63
IEEE 754 BASIC DOUBLE FORMAT
bits
62
51
0
exponent
significand
11
52
sign
Figure21-1IEEE754SingleandDoubleFormat
IEEE754leavesconsiderablefreedomofimplementationintheex-
tendedformats.Theseformatsaredefinedashavingaminimumnumber
The standard states that the developer may encode values redundantly,
and reserve bit strings for purposes not described. The standard requires
that all implementations support the single format and recommends that
at least one extended format be implemented for the widest basic format
used. This means that an implementation that supports the single basic
formats, should also have an extended single encoding. By the same to-
ken, an implementation that supports the basic double format should also
have an extended double. The intention of this recommendation is that
the extended formats be used for storing intermediate results with more
precision than the format used for the result. This scheme serves to im-
prove computational accuracy.
![](JAVA-Programming-for-Engineers_images/img-gen1971.png)
![](JAVA-Programming-for-Engineers_images/img-gen1972.png)
![](JAVA-Programming-for-Engineers_images/img-gen1973.png)
![](JAVA-Programming-for-Engineers_images/img-gen1974.png)
![](JAVA-Programming-for-Engineers_images/img-gen1975.png)
![](JAVA-Programming-for-Engineers_images/img-gen1976.png)
![](JAVA-Programming-for-Engineers_images/img-gen1977.png)
![](JAVA-Programming-for-Engineers_images/img-gen1978.png)
![](JAVA-Programming-for-Engineers_images/img-gen1979.png)
![](JAVA-Programming-for-Engineers_images/img-gen1980.png)