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documentation on NaN
2011-10-24 21:57:44 +05:30
<!-- DFUM_035.HTML continuation of C4$:[SAVAGE.HTML.UM]DFUM.HTML -->
<html><head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<title>DIGITAL Fortran 90</title>
</head>
<body bgcolor="white">
<font color="maroon">
<h1 align="center">DIGITAL Fortran 90<br>User Manual for <br> DIGITAL UNIX Systems</h1>
</font>
<hr>
<table border="2">
<tbody><tr>
<td align="center" bgcolor="lightgoldenrodyellow" width="100"><a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_034.html#bottom_034">Previous</a>
</td><td align="center" bgcolor="cyan" width="100"><a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_contents.html">Contents</a>
</td><td align="center" bgcolor="lightskyblue" width="100"><a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_index.html">Index</a>
</td></tr></tbody></table>
<hr>
<a name="sec_complex16"><h2>9.4.6 COMPLEX (KIND=8) or COMPLEX*16 Representation</h2></a>
<a name="index_x_2968"></a>
<p>
Intrinsic COMPLEX (KIND=8) or COMPLEX*16 (same as DOUBLE COMPLEX) data
is 16 contiguous bytes containing a pair of REAL*8 values stored in
IEEE T_float format.
</p><p>
The low-order eight bytes contain REAL (KIND=8) data that represents
the real part of the complex data. The high-order eight bytes contain
REAL (KIND=8) data that represents the imaginary part of the complex
data, as shown in <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_035.html#fig_complex_16">Figure 9-10</a>.
<a name="fig_complex_16"></a>
</p><p>
<strong>Figure 9-10 COMPLEX (KIND =8) or COMPLEX*16
Representation</strong>
</p><hr>
<img src="dfum_035-Dateien/zk-9818.gif">
<p>
The limits and underflow characteristics for REAL (KIND=8) apply to the
two separate real and imaginary parts of a COMPLEX (KIND=8) or
COMPLEX*16 number. Like REAL (KIND=8) or REAL*8 numbers, the sign bit
representation is 0 (zero) for positive numbers and 1 for negative
numbers.
</p><p>
<strong>For More Information:</strong>
<br>
</p><ul>
<li>On converting unformatted data, see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_035.html#ch_conv">Chapter 10</a>.
</li><li>On defining constants and assigning values to variables, see the
<em>DIGITAL Fortran Language Reference Manual</em>.
</li><li>On intrinsic functions related to the various data types, such as
SELECTED_REAL_KIND, see the <em>DIGITAL Fortran Language Reference Manual</em>.
</li><li>On VAX (OpenVMS) floating-point data types (provided for those
converting OpenVMS data), see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_044.html#sec_fltng_pt_vax">Section A.4.3</a>.
</li><li>On the
<font size="+1"><tt>f90</tt></font>
command options that control the size of REAL and COMPLEX declarations
(without a kind parameter or size specifier), see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_011.html#sec_option_real">Section 3.63</a>.
</li><li>On the
<font size="+1"><tt>f90</tt></font>
command options that control the size of DOUBLE PRECISION declarations,
see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_008.html#sec_option_double">Section 3.25</a>.
</li><li>On IEEE binary floating-point, see ANSI/IEEE Standard 754-1985.
</li></ul>
<a name="sec_fltng_pt_exc"><h2>9.4.7 Exceptional Floating-Point Representations</h2></a>
<a name="index_x_2969"></a>
<a name="index_x_2970"></a>
<a name="index_x_2971"></a>
<a name="index_x_2972"></a>
<p>
<strong>Exceptional values</strong> usually result from a computation
and include plus infinity, minus infinity, NaN, and denormalized
numbers.
</p><p>
Floating-point numbers can be one of the following:
</p><ul>
<li><strong>Alpha finite number</strong>---A floating-point number that
represents a valid number (bit pattern) within the normalized ranges of
a particular data type, including --<em>max</em> to
--<em>min</em>,---zero, +zero, +<em>min</em> to +<em>max</em>. <br>For
any native IEEE floating-point data type, the values of <em>min</em> or
<em>max</em> are listed in <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_034.html#sec_real4">Section 9.4.2</a> (single precision),
<a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_034.html#sec_real8">Section 9.4.3</a> (double precision), and <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_034.html#sec_real16_x">Section 9.4.4</a> (extended
precision). <br>Special bit patterns that are <em>not</em> Alpha finite
numbers represent exceptional values.
</li><li><strong>Infinity</strong>---An IEEE floating-point bit pattern
<a name="index_x_2973"></a>
<a name="index_x_2974"></a>
<a name="index_x_2975"></a>
that represents plus or minus infinity. DIGITAL Fortran 90 identifies
infinity values with the letters "Infinity" or asterisks
(******) in output statements (depends on field width) or certain
hexadecimal values (fraction of 0 and exponent of all 1 values).
</li><li><strong>Not-a-Number (NaN)</strong>---An IEEE floating-point bit
pattern that
<a name="index_x_2976"></a>
<a name="index_x_2977"></a>
<a name="index_x_2978"></a>
represents something other than a number. DIGITAL Fortran 90 identifies NaN
values with the letters "NaN" in output statements. A NaN can
be a signaling NaN or a quiet NaN:
<ul>
<li>A quiet NaN might occur as a result of a calculation, such as 0./0.
and has an exponent of all 1 values and initial fraction bit of 1.
</li><li>A signaling NaN must be set intentionally (does not result from
calculations) and has an exponent of all 1 values and initial fraction
bit of 0 (with one or more other fraction bits of 1).
</li></ul>
</li><li><strong>Denormal</strong>---Identifies an IEEE floating-point bit
pattern
<a name="index_x_2979"></a>
<a name="index_x_2980"></a>
<a name="index_x_2981"></a>
<a name="index_x_2982"></a>
that represents a number whose value falls between zero and the
smallest finite (normalized) number for that data type. The exponent
field contains all zeros. <br>For negative numbers, denormalized
numbers range from the next representable value larger than minus zero
to the representable value that is one bit less than the smallest
finite (normalized) negative number. For positive numbers, denormalized
numbers range from the next representable value larger than positive
zero to the representable value that is one bit less than the smallest
finite (normalized) positive number.
<a name="index_x_2983"></a>
<a name="index_x_2984"></a>
<a name="index_x_2985"></a>
</li><li><strong>Zero</strong>---Can be the value +0 (all zero bits, also
called true zero)
<a name="index_x_2986"></a>
or -0 (all zero bits except the sign bit, such as Z<font size="+1"><tt>'</tt></font>8000000000000000<font size="+1"><tt>'</tt></font>).
</li></ul>
<p>
A NaN or infinity value might result from a calculation that contains a
divide by zero, overflow, or invalid data.
</p><p>
A denormalized number occurs when the result of a calculation falls
within the denormalized range for that data type (subnormal value).
</p><p>
To control floating-point exception handling at run time for the main
program, use the appropriate
<font size="+1"><tt>-fpe<em>n</em></tt></font>
option. The callable
<font size="+1"><tt>for_set_fpe</tt></font>
routine allows further control for subprogram use or conditional use
during program execution.
</p><p>
If an exceptional value is used in a calculation, an unrecoverable
exception can occur unless you specify the appropriate
<font size="+1"><tt>-fpe<em>n</em></tt></font>
option or use the
<font size="+1"><tt>for_set_fpe</tt></font>
routine. Denormalized numbers can be processed as is, set equal to zero
with program continuation or a program stop, and generate warning
messages (see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_008.html#sec_option_fpe">Section 3.33</a>).
</p><p>
<a name="index_x_2987"></a>
<a name="index_x_2988"></a>
<a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_035.html#tab_except">Table 9-2</a> lists the hexadecimal (hex) values of the IEEE
exceptional floating-point numbers in Alpha systems, for S_float
(single precision), T_float (double precision), and X_float (extended
precision) formats: </p><p>
<table border="3">
<caption><a name="tab_except"><strong>Table 9-2 Exceptional Floating-Point Numbers</strong></a></caption>
<tbody><tr bgcolor="lightseagreen">
<th align="center">Exceptional Number </th>
<th align="center">Hex Value </th>
</tr>
<tr bgcolor="lightseagreen">
<th colspan="2" align="left">S_float Representation </th>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Infinity (+)
</td>
<td>
Z
<font size="+1">
<tt>'</tt>
</font>
7F800000
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Infinity (--)
</td>
<td>
Z
<font size="+1">
<tt>'</tt>
</font>
FF800000
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Zero (+0)
</td>
<td>
Z
<font size="+1">
<tt>'</tt>
</font>
00000000
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Zero (--0)
</td>
<td>
Z
<font size="+1">
<tt>'</tt>
</font>
80000000
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Quiet NaN (+)
</td>
<td>
From Z
<font size="+1">
<tt>'</tt>
</font>
7FC00000
<font size="+1">
<tt>'</tt>
</font>
to Z
<font size="+1">
<tt>'</tt>
</font>
7FFFFFFF
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Quiet NaN (--)
</td>
<td>
From Z
<font size="+1">
<tt>'</tt>
</font>
FFC00000
<font size="+1">
<tt>'</tt>
</font>
to Z
<font size="+1">
<tt>'</tt>
</font>
FFFFFFFF
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Signaling NaN (+)
</td>
<td>
From Z
<font size="+1">
<tt>'</tt>
</font>
7F800001
<font size="+1">
<tt>'</tt>
</font>
to Z
<font size="+1">
<tt>'</tt>
</font>
7FBFFFFF
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Signaling NaN (--)
</td>
<td>
From Z
<font size="+1">
<tt>'</tt>
</font>
FF800001
<font size="+1">
<tt>'</tt>
</font>
to Z
<font size="+1">
<tt>'</tt>
</font>
FFBFFFFF
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="lightseagreen">
<th colspan="2" align="left">T_float Representation </th>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Infinity (+)
</td>
<td>
Z
<font size="+1">
<tt>'</tt>
</font>
7FF0000000000000
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Infinity (--)
</td>
<td>
Z
<font size="+1">
<tt>'</tt>
</font>
FFF0000000000000
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Zero (+0)
</td>
<td>
Z
<font size="+1">
<tt>'</tt>
</font>
0000000000000000
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Zero (-0)
</td>
<td>
Z
<font size="+1">
<tt>'</tt>
</font>
8000000000000000
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Quiet NaN (+)
</td>
<td>
From Z
<font size="+1">
<tt>'</tt>
</font>
7FF8000000000000
<font size="+1">
<tt>'</tt>
</font>
to Z
<font size="+1">
<tt>'</tt>
</font>
7FFFFFFFFFFFFFFF
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Quiet NaN (--)
</td>
<td>
From Z
<font size="+1">
<tt>'</tt>
</font>
FFF8000000000000
<font size="+1">
<tt>'</tt>
</font>
to Z
<font size="+1">
<tt>'</tt>
</font>
FFFFFFFFFFFFFFFF
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Signaling NaN (+)
</td>
<td>
From Z
<font size="+1">
<tt>'</tt>
</font>
7FF0000000000001
<font size="+1">
<tt>'</tt>
</font>
to Z
<font size="+1">
<tt>'</tt>
</font>
7FF7FFFFFFFFFFFF
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Signaling NaN (--)
</td>
<td>
From Z
<font size="+1">
<tt>'</tt>
</font>
FFF0000000000001
<font size="+1">
<tt>'</tt>
</font>
to Z
<font size="+1">
<tt>'</tt>
</font>
FFF7FFFFFFFFFFFF
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="lightseagreen">
<th colspan="2" align="left">X_float Representation </th>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Infinity (+)
</td>
<td>
Z
<font size="+1">
<tt>'</tt>
</font>
7FFF0000000000000000000000000000
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Infinity (--)
</td>
<td>
Z
<font size="+1">
<tt>'</tt>
</font>
FFFF0000000000000000000000000000
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Zero (+0)
</td>
<td>
Z
<font size="+1">
<tt>'</tt>
</font>
000000000000000000000000000000000
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Zero (--0)
</td>
<td>
Z
<font size="+1">
<tt>'</tt>
</font>
800000000000000000000000000000000
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Quiet NaN (+)
</td>
<td>
From Z
<font size="+1">
<tt>'</tt>
</font>
7FFF80000000000000000000000000000
<font size="+1">
<tt>'</tt>
</font>
to Z
<font size="+1">
<tt>'</tt>
</font>
7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Quiet NaN (--)
</td>
<td>
From Z
<font size="+1">
<tt>'</tt>
</font>
FFFF80000000000000000000000000000
<font size="+1">
<tt>'</tt>
</font>
to Z
<font size="+1">
<tt>'</tt>
</font>
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Signaling NaN (+)
</td>
<td>
From Z
<font size="+1">
<tt>'</tt>
</font>
7FFF00000000000000000000000000001
<font size="+1">
<tt>'</tt>
</font>
to Z
<font size="+1">
<tt>'</tt>
</font>
7FFF7FFFFFFFFFFFFFFFFFFFFFFFFFFFF
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
Signaling NaN (--)
</td>
<td>
From Z
<font size="+1">
<tt>'</tt>
</font>
FFFF00000000000000000000000000001
<font size="+1">
<tt>'</tt>
</font>
to Z
<font size="+1">
<tt>'</tt>
</font>
FFFF7FFFFFFFFFFFFFFFFFFFFFFFFFFFF
<font size="+1">
<tt>'</tt>
</font>
</td>
</tr>
</tbody></table>
</p><p>
DIGITAL Fortran 90 supports IEEE exception handling, allowing you to test
for infinity by using a comparison of floating-point data (such as
generating positive infinity by using a calculation like x=1.0/0 and
comparing x to the calculated number).
</p><p>
The appropriate
<font size="+1"><tt>f90</tt></font>
command
<font size="+1"><tt>-fpe<em>n</em></tt></font>
options or calling the
<font size="+1"><tt>for_set_fpe</tt></font>
routine with appropriate arguments allows program continuation when a
calculation results in a divide by zero, overflow, or invalid data
arithmetic exception, generating an exceptional value (a NaN or
Infinity (+ or --)).
</p><p>
<a name="index_x_2989"></a>
<a name="index_x_2990"></a>
<a name="index_x_2991"></a>
To test for a NaN when DIGITAL Fortran 90 allows continuation for
arithmetic exceptions, you can use the ISNAN intrinsic function.
</p><p>
For example, you might use the following code to test a DOUBLE
PRECISION (REAL (KIND=8)) value:
<a name="index_x_2992"></a>
</p><p>
<table border="0">
<tbody><tr>
<td bgcolor="blanchedalmond">
<br>
<font color="mediumblue"><pre> DOUBLE PRECISION A, B, F
A = 0.
B = 0.
! Perform calculations with variables A and B
.
.
.
! f contains the value to check against a particular NaN
F = A / B
IF (ISNAN(F)) THEN
WRITE (6,*) '--&gt; Variable F contains a NaN value &lt;--'
ENDIF
! Inform user that f has the hardware quiet NaN value
! Perform calculations with variable F (or stop program early)
END PROGRAM
</pre>
</font>
</td></tr></tbody></table>
</p><p>
<a name="index_x_2993"></a>
<a name="index_x_2994"></a>
<a name="index_x_2995"></a>
This program might be compiled with
<font size="+1"><tt>-fpe2</tt></font>
or
<font size="+1"><tt>-fpe4</tt></font>
to allow:
</p><ul>
<li>Continuation when a NaN (or other exceptional value) is encountered
in a calculation
</li><li>A summary message explaining the number and types of arithmetic
exceptions encountered:
<p>
<table border="0">
<tbody><tr>
<td bgcolor="blanchedalmond">
<br>
<font color="mediumblue"><pre>% <strong>f90 -fpe2 isnan.for</strong>
% <strong>a.out</strong>
forrtl: error: floating invalid
--&gt; Variable F contains a NaN value &lt;--
forrtl: info: 1 floating invalid traps
</pre>
</font>
</td></tr></tbody></table>
</p></li></ul>
<p>
The FP_CLASS intrinsic function is also available to check for
exceptional values (see the <em>DIGITAL Fortran Language Reference Manual</em> and the file
<font size="+1"><tt>/usr/include/fordef.f</tt></font>
).
</p><p>
<strong>For More Information:</strong>
<br>
</p><ul>
<li>On using the
<font size="+1"><tt>f90</tt></font>
command
<font size="+1"><tt>-fpe<em>n</em></tt></font>
options and the
<font size="+1"><tt>for_set_fpe</tt></font>
routine to control arithmetic exception handling, see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_008.html#sec_option_fpe">Section 3.33</a>.
</li><li>On Alpha exceptional values, see <em>Alpha Architecture Reference Manual</em>.
</li><li>On IEEE binary floating-point exception handling, see the <em>IEEE
Standard for Binary Floating-Point Arithmetic</em> (ANSI/IEEE Standard
754-1985) and <font size="+1"><tt>ieee(3)</tt></font>.
</li></ul>
<a name="sec_char_rep"><h1><font color="maroon">9.5 Character Representation</font></h1></a>
<a name="index_x_2996"></a>
<a name="index_x_2997"></a>
<p>
A character string is a contiguous sequence of bytes in memory, as
shown in <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_035.html#fig_character">Figure 9-11</a>.
<a name="fig_character"></a>
</p><p>
<strong>Figure 9-11 CHARACTER Data Representation</strong>
</p><hr>
<img src="dfum_035-Dateien/zk-0809.gif">
<p>
A character string is specified by two attributes: the address A of the
first byte of the string, and the length L of the string in bytes. The
length L of a string is in the range 1 through 65,535.
</p><p>
<strong>For More Information:</strong>
<br>
</p><ul>
<li>On defining constants, assigning values to variables, using
substring expressions, and concatenation, see the <em>DIGITAL Fortran Language Reference Manual</em>.
</li><li>On intrinsic functions related to the various data types, see the
<em>DIGITAL Fortran Language Reference Manual</em>.
</li></ul>
<a name="sec_holrith_rep"><h1><font color="maroon">9.6 Hollerith Representation</font></h1></a>
<a name="index_x_2998"></a>
<a name="index_x_2999"></a>
<p>
Hollerith constants are stored internally, one character per byte. When
Hollerith constants contain the ASCII representation of characters,
they resemble the storage of character data (see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_035.html#fig_character">Figure 9-11</a>).
</p><p>
When Hollerith constants store numeric data, they usually have a length
of one, two, four, or eight bytes and resemble the corresponding
numeric data type.
</p><p>
<strong>For More Information:</strong>
<br>
</p><ul>
<li>On defining constants and assigning values to variables, see the
<em>DIGITAL Fortran Language Reference Manual</em>.
</li><li>On intrinsic functions related to the various data types, see the
<em>DIGITAL Fortran Language Reference Manual</em>.
</li></ul>
<p>
</p><hr size="5">
<font color="maroon">
<a name="ch_conv"><h1>Chapter 10<br>Converting Unformatted Numeric Data</h1></a>
</font>
<p>
This chapter describes how you can use DIGITAL Fortran 90 to read and write
unformatted numeric data in certain nonnative formats, including big
endian IEEE and VAX floating-point formats.
</p><p>
On DIGITAL UNIX systems, DIGITAL Fortran 90 supports the following little
endian floating-point formats in memory:
<table border="3">
<tbody><tr bgcolor="lightseagreen">
<th align="center">Floating-Point Size </th>
<th align="center">Format in Memory </th>
</tr>
<tr bgcolor="blanchedalmond">
<td>
KIND=4
</td>
<td>
IEEE S_float
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
KIND=8
</td>
<td>
IEEE T_float
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
KIND=16
</td>
<td>
DIGITAL IEEE style X_float
</td>
</tr>
</tbody></table>
</p><p>
If your program needs to read or write unformatted data files
containing a floating-point format that differs from the format in
memory for that data size, you can request that the unformatted data be
converted.
</p><p>
Converting unformatted data is generally faster than converting
formatted data and is less likely to lose precision for floating-point
numbers.
<a name="sec_float_convert_endian"></a></p><h1><a name="sec_float_convert_endian"><font color="maroon">10.1 Endian Order of Numeric Formats</font></a></h1>
<p>
<a name="index_x_3000"></a>
<a name="index_x_3001"></a>
<a name="index_x_3002"></a>
<a name="index_x_3003"></a>
<a name="index_x_3004"></a>
<a name="index_x_3005"></a>
<a name="index_x_3006"></a>
<a name="index_x_3007"></a>
<a name="index_x_3008"></a>
<a name="index_x_3009"></a>
<a name="index_x_3010"></a>
<a name="index_x_3011"></a>
<a name="index_x_3012"></a>
Data storage in different computers use a convention of either
<strong>little endian</strong> or <strong>big endian</strong> storage.
The storage convention generally applies to numeric values that span
multiple bytes, as follows:
</p><ul>
<li><strong>Little endian</strong> storage occurs when:
<ul>
<li>The least significant bit (LSB) value is in the byte with the
lowest address.
</li><li>The most significant bit (MSB) value is in the byte with the
highest address.
</li><li>The address of the numeric value is the byte containing the LSB.
Subsequent bytes with higher addresses contain more significant bits.
</li></ul>
</li><li><strong>Big endian</strong> storage occurs when:
<ul>
<li>The least significant bit (LSB) value is in the byte with the
highest address.
</li><li>The most significant bit (MSB) value is in the byte with the lowest
address.
</li><li>The address of the numeric value is the byte containing the MSB.
Subsequent bytes with higher addresses contain less significant bits.
</li></ul>
</li></ul>
<p>
<a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_035.html#fig_endian">Figure 10-1</a> shows the difference between the two byte-ordering
schemes.
<a name="fig_endian"></a>
</p><p>
<strong>Figure 10-1 Little and Big Endian Storage of an INTEGER
Value</strong>
</p><hr>
<img src="dfum_035-Dateien/zk-6654a.gif">
<p>
Moving data files between big endian and little endian computers
requires that the data be converted.
<a name="sec_float_convert"></a></p><h1><a name="sec_float_convert"><font color="maroon">10.2 Native and Supported Nonnative Numeric Formats</font></a></h1>
<p>
<a name="index_x_3013"></a>
<a name="index_x_3014"></a>
<a name="index_x_3015"></a>
<a name="index_x_3016"></a>
<a name="index_x_3017"></a>
<a name="index_x_3018"></a>
<a name="index_x_3019"></a>
<a name="index_x_3020"></a>
<a name="index_x_3021"></a>
<a name="index_x_3022"></a>
<a name="index_x_3023"></a>
<a name="index_x_3024"></a>
<a name="index_x_3025"></a>
<a name="index_x_3026"></a>
<a name="index_x_3027"></a>
<a name="index_x_3028"></a>
DIGITAL Fortran 90 provides the capability for programs to read and write
unformatted data (originally written using unformatted I/O statements)
in
<a name="index_x_3029"></a>
several nonnative floating-point formats and in big endian INTEGER or
floating-point format.
</p><p>
When reading a nonnative unformatted format, the nonnative format on
disk must be converted to native format in memory. Similarly, native
data in memory can be written to a nonnative unformatted format. If a
converted nonnative value is outside the range of the native data type,
a run-time message appears (listed in <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_033.html#tab_runtime_errors">Table 8-2</a>).
</p><p>
Supported native and nonnative floating-point formats include:
</p><ul>
<li>Standard IEEE little endian floating-point formats<sup>1</sup> and
little endian integers. These formats are found on DIGITAL UNIX (Alpha)
systems, DIGITAL OpenVMS Alpha systems, Microsoft® Windows
NT<sup>tm</sup> systems, IBM-compatible PC systems, and DIGITAL ULTRIX
RISC systems. On DIGITAL UNIX systems, these are the native (in memory)
floating-point and integer formats.
<a name="index_x_3030"></a>
<a name="index_x_3031"></a>
<a name="index_x_3032"></a>
<a name="index_x_3033"></a>
</li><li>Standard IEEE big endian floating-point formats<sup>1</sup> and big
endian integers found on most Sun systems, most Hewlett-Packard systems
(such as HP-UX systems), and IBM's RISC System/6000 systems.
</li><li>DIGITAL VAX little endian floating-point formats and little endian
integers supported by DIGITAL Fortran for OpenVMS VAX systems and
DIGITAL Fortran for OpenVMS Alpha systems.
</li><li>Big endian proprietary floating-point formats and big endian
integers associated with CRAY (CRAY systems).
</li><li>Big endian proprietary floating-point formats and big endian
integers associated with IBM (the IBM's System\370 and similar systems).
</li></ul>
<p>
<a name="index_x_3034"></a>
<a name="index_x_3035"></a>
<a name="index_x_3036"></a>
The native memory format uses little endian integers and little endian
IEEE floating-point formats, as follows:
</p><ul>
<li>INTEGER and LOGICAL declarations of one, two, four, or eight bytes
(intrinsic kinds 1, 2, 4, and 8). You can specify the integer data
length by using an explicit data declaration (kind parameter or size
specifier). All INTEGER and LOGICAL declarations without a kind
parameter or size specifier will be four bytes in length. To request an
8-byte size for all INTEGER and LOGICAL declarations without a kind
parameter or size specifier, use an
<font size="+1"><tt>f90</tt></font>
command-line option (see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_034.html#sec_int_options">Section 9.2.1</a>).
</li><li>IEEE S_float format for single-precision 4-byte REAL and 8-byte
COMPLEX declarations (KIND=4). You can specify the real or complex data
length by using an explicit data declaration (kind parameter or size
specifier). For all REAL or COMPLEX declarations without a kind
parameter or size specifier, this is the default size unless you use an
<font size="+1"><tt>f90</tt></font>
command-line option to request double-precision sizes (see
<a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_034.html#sec_realcomplex_option">Section 9.4.1</a>).
</li><li>IEEE T_float format for double-precision 8-byte REAL and 16-byte
COMPLEX declarations (KIND=8). You can specify the real or complex data
length by using an explicit data declaration (kind parameter or size
specifier). To request double-precision sizes for all REAL or COMPLEX
declarations without a kind parameter or size specifier, you can use an
<font size="+1"><tt>f90</tt></font>
command-line option (see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_034.html#sec_realcomplex_option">Section 9.4.1</a>).
</li><li>DIGITAL IEEE style X_float format for extended-precision 16-byte
REAL declarations (KIND=16). You can specify the real data length by
using an explicit data declaration (kind parameter or size specifier).
To request extended-precision sizes for all DOUBLE PRECISION
declarations, you can use an
<font size="+1"><tt>f90</tt></font>
command-line option (see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_034.html#sec_realcomplex_option">Section 9.4.1</a>).
</li></ul>
<p>
<a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_035.html#tab_nonnative_float">Table 10-1</a> lists the keywords for the supported unformatted file
data formats. Use the appropriate keyword after the
<font size="+1"><tt>-convert</tt></font>
option (such as
<font size="+1"><tt>-convert cray</tt></font>
) or as an environment variable value (see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_036.html#sec_nonnative_method">Section 10.4</a>).
<a name="index_x_3037"></a>
<a name="index_x_3038"></a>
<a name="index_x_3039"></a>
<a name="index_x_3040"></a>
<a name="index_x_3041"></a>
<a name="index_x_3042"></a>
<a name="index_x_3043"></a>
</p><p>
<a name="index_x_3044"></a>
<table border="3">
<caption><a name="tab_nonnative_float"><strong>Table 10-1 Unformatted Numeric Formats, Keywords, and Supported Data Types</strong></a></caption>
<tbody><tr bgcolor="lightseagreen">
<th align="center">Recognized Keyword<sup>1</sup> </th>
<th align="center">Description </th>
</tr>
<tr bgcolor="blanchedalmond">
<td>
BIG_ENDIAN
</td>
<td>
Big endian integer data of the appropriate INTEGER size (one, two, or
four bytes) and big endian IEEE floating-point formats for REAL and
COMPLEX single- and double-precision numbers. INTEGER (KIND=1) or
INTEGER*1 data is the same for little endian and big endian.
<a name="index_x_3045">
</a>
<a name="index_x_3046">
</a>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
CRAY
</td>
<td>
Big endian integer data of the appropriate INTEGER size (one, two,
four, or eight bytes) and big endian CRAY proprietary floating-point
format for
<a name="index_x_3047">
</a>
REAL and COMPLEX single- and double-precision numbers.
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
FDX
</td>
<td>
Native little endian integers of the appropriate INTEGER size (one,
two, four, or eight bytes) and the following little endian DIGITAL
proprietary floating-point formats:
<ul>
<li>VAX F_float for REAL (KIND=4) and COMPLEX (KIND=4)
<a name="index_x_3048">
</a>
<a name="index_x_3049">
</a>
</li><li>VAX D_float for REAL (KIND=8) and COMPLEX (KIND=8)
</li><li>IEEE style X_float for REAL (KIND=16)
</li></ul>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
FGX
</td>
<td>
Native little endian integers of the appropriate INTEGER size (one,
two, four, or eight bytes) and the following little endian DIGITAL
proprietary floating-point formats:
<ul>
<li>VAX F_float for REAL (KIND=4) and COMPLEX (KIND=4)
<a name="index_x_3050">
</a>
<a name="index_x_3051">
</a>
</li><li>VAX G_float for REAL (KIND=8) and COMPLEX (KIND=8)
</li><li>IEEE style X_float for REAL (KIND=16)
</li></ul>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
IBM
</td>
<td>
Big endian integer data of the appropriate INTEGER size (one, two, or
four bytes) and big endian IBM proprietary (System\370 and similar)
floating-point format for
<a name="index_x_3052">
</a>
REAL and COMPLEX single- and double-precision numbers.
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
LITTLE_ENDIAN
</td>
<td>
Native little endian integers of the appropriate INTEGER size (one,
two, four, or eight bytes) and the following native little endian IEEE
floating-point formats:
<ul>
<li>S_float for REAL (KIND=4) and COMPLEX (KIND=4)
<a name="index_x_3053">
</a>
<a name="index_x_3054">
</a>
</li><li>T_float for REAL (KIND=8) and COMPLEX (KIND=8)
</li><li>IEEE style X_float for REAL (KIND=16)
</li></ul>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
NATIVE
</td>
<td>
No conversion occurs between memory and disk. This is the default for
unformatted files.
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
VAXD
</td>
<td>
Native little endian integers of the appropriate INTEGER size (one,
two, four, or eight bytes) and the following little endian VAX DIGITAL
proprietary floating-point formats:
<ul>
<li>VAX F_float for REAL (KIND=4) and COMPLEX (KIND=4)
<a name="index_x_3055">
</a>
<a name="index_x_3056">
</a>
</li><li>VAX D_float for REAL (KIND=8) and COMPLEX (KIND=8)
</li><li>VAX H_float for REAL (KIND=16)
</li></ul>
</td>
</tr>
<tr bgcolor="blanchedalmond">
<td>
VAXG
</td>
<td>
Native little endian integers of the appropriate INTEGER size (one,
two, four, or eight bytes) and the following little endian VAX DIGITAL
proprietary floating-point formats:
<ul>
<li>VAX F_float for REAL (KIND=4) and COMPLEX (KIND=4)
<a name="index_x_3057">
</a>
<a name="index_x_3058">
</a>
</li><li>VAX G_float for REAL (KIND=8) and COMPLEX (KIND=8)
</li><li>VAX H_float for REAL (KIND=16)
</li></ul>
</td>
</tr>
</tbody></table>
</p><hr>
<sup>1</sup>When using the data type as a <font size="+1"><tt>-convert</tt></font> keyword option on the <font size="+1"><tt>f90</tt></font> command line, the data type keyword must be
in lowercase, such as <font size="+1"><tt>-convert big_endian</tt></font>.
<br>
<hr>
<p>
While this solution is not expected to fulfill all floating-point
conversion needs, it provides the capability to read and write various
types of unformatted nonnative floating-point data.
</p><p>
<strong>For More Information:</strong>
<br>
</p><ul>
<li>On porting OpenVMS Fortran data files to a DIGITAL UNIX system for
use by DIGITAL Fortran 90, see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_044.html#sec_compat_vms">Section A.4</a>.
</li><li>Ranges and the format of native IEEE floating-point data types, see
<a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_034.html#tab_datatype_summ">Table 9-1</a> and <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_034.html#sec_fltng_pt">Section 9.4</a>.
</li><li>Ranges and the format of VAX floating-point data types, see
<a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_044.html#sec_fltng_pt_vax">Section A.4.3</a>.
</li><li>Specifying the size of INTEGER declarations (without a kind) using
an
<font size="+1"><tt>f90</tt></font>
command option, see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_034.html#sec_int_options">Section 9.2.1</a>.
</li><li>Specifying the size of LOGICAL declarations (without a kind) using
an
<font size="+1"><tt>f90</tt></font>
command option, see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_034.html#sec_logical_rep">Section 9.3</a>.
</li><li>Specifying the size of REAL or COMPLEX declarations (without a
kind) using an
<font size="+1"><tt>f90</tt></font>
command option, see <a href="http://www.hpc.unimelb.edu.au/doc/f90lrm/dfum_034.html#sec_realcomplex_option">Section 9.4.1</a>.
</li><li>Data declarations and other DIGITAL Fortran 90 language information,
see the <em>DIGITAL Fortran Language Reference Manual</em>.
</li></ul>
<p>
</p><center>
<table bgcolor="lightskyblue" border="0" width="75%">
<tbody><tr>
<td>
<center><font color="black" size="+2"><strong>Note </strong></font></center>
<hr noshade="noshade" size="1">
<font color="black">
<h4><strong><sup>1</sup> </strong> IEEE floating-point formats are
defined in the IEEE Standard for Binary Floating-Point Arithmetic,
ANSI/IEEE Standard 754-1985, Institute of Electrical and Electronics
Engineers, August 1985.</h4>
</font>
</td>
</tr>
</tbody></table>
</center>
<p>
<a name="bottom_035"></a>
</p><p>
</p><hr>
<table border="2">
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