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authorAlbert Cheng <acheng@hdfgroup.org>2004-12-15 23:21:23 (GMT)
committerAlbert Cheng <acheng@hdfgroup.org>2004-12-15 23:21:23 (GMT)
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[svn-r9672] Purpose:
New document committed. Description: Report of the Data Transform work.
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+<body lang=EN-US style='tab-interval:.5in'>
+
+<div class=Section1>
+
+<p class=MsoNormal align=center style='text-align:center'><b><span
+style='font-size:16.0pt'>Arithmetic Data Transforms<o:p></o:p></span></b></p>
+
+<p class=MsoNormal align=center style='text-align:center'>Leon Arber, Albert
+Cheng, William Wendling<a style='mso-footnote-id:ftn1' href="#_ftn1"
+name="_ftnref1" title=""><span class=MsoFootnoteReference><span
+style='mso-special-character:footnote'><![if !supportFootnotes]><span
+class=MsoFootnoteReference><span style='font-size:12.0pt;font-family:"Times New Roman";
+mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:
+EN-US;mso-bidi-language:AR-SA'>[1]</span></span><![endif]></span></span></a></p>
+
+<p class=MsoNormal align=center style='text-align:center'><st1:date Year="2004"
+Day="10" Month="12">December 10, 2004</st1:date></p>
+
+<h1>Purpose</h1>
+
+<p class=MsoNormal>Data can be stored and represented in many different
+ways.<span style='mso-spacerun:yes'>  </span>In most fields of science, for
+example, the metric system is used for storing all data.<span
+style='mso-spacerun:yes'>  </span>However, many fields of engineering still use
+the English system.<span style='mso-spacerun:yes'>  </span>In such scenarios,
+there needs to be a way to easily perform arbitrary scaling of data.<span
+style='mso-spacerun:yes'>  </span>The data transforms provide just such
+functionality.<span style='mso-spacerun:yes'>  </span>They allow arbitrary
+arithmetic expressions to be applied to a dataset during read and write
+operations.<span style='mso-spacerun:yes'>  </span>This means that data can be
+stored in Celsius in a data file, but read in and automatically converted to
+Fahrenheit.<span style='mso-spacerun:yes'>  </span>Alternatively, data that is
+obtained in Fahrenheit can be written out to the data file in Celsius.<span
+style='mso-spacerun:yes'>  </span></p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>Although a user can always manually modify the data they
+read and write, having the data transform as a property means that the user
+doesn’t have to worry about forgetting to call the conversion function or even
+writing it in the first place.</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<h1>Usage</h1>
+
+<p class=MsoNormal>The data transform functionality is implemented as a
+property that is set on a dataset transfer property list.<span
+style='mso-spacerun:yes'>  </span>There are two functions available: one for
+setting the transform and another for finding out what transform, if any, is
+currently set.</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>The function for setting the transform is:</p>
+
+<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'>herr_t
+H5Pset_data_transform(hid_t plist_id, const char* expression)<o:p></o:p></span></p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'>plist_id
+</span>is the identifier of the dataset transfer property list on which the
+data transform property should be set.</p>
+
+<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'>expression
+</span>is a pointer to a string of the form “(5/9.0)*(x-32)” which describes
+the transform.</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>The function for getting the transform is: </p>
+
+<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'>ssize_t
+H5Pget_data_transform(hid_t plist_id, char* expression, size_t size)<o:p></o:p></span></p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'>plist_id
+</span>is the identifier of the dataset transfer property list which will be
+queried for its data transform property.</p>
+
+<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'>expression
+</span>is either NULL or a pointer to memory where the data transform string,
+if present, will be copied.</p>
+
+<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'>size
+</span>is the number of bytes to copy from the transform string into
+expression. <span style='mso-spacerun:yes'> </span>H5Pget_data_transform will
+never copy more than the length of the transform expression.</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<h1>Data Transform Expressions</h1>
+
+<p class=MsoNormal>Data transforms are set by passing a pointer to a string,
+which is the data transform expression.<span style='mso-spacerun:yes'> 
+</span>This string describes what sort of arithmetic transform should be done
+during data transfer of read or write.<span style='mso-spacerun:yes'> 
+</span>The string is a standard mathematical expression, as would be entered
+into a something like MATLAB.<span style='mso-spacerun:yes'>  </span></p>
+
+<p class=MsoNormal>Expressions are defined by the following context-free
+grammar:</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>expr:=<span style='mso-spacerun:yes'>  </span>term | term +
+term | term - term</p>
+
+<p class=MsoNormal>term := factor | factor * factor | factor / factor</p>
+
+<p class=MsoNormal>factor :=<span style='mso-spacerun:yes'>  </span>number |
+symbol | - factor | + factor | ( expr )</p>
+
+<p class=MsoNormal>symbol := [a-zA-Z][a-zA-Z0-9]*</p>
+
+<p class=MsoNormal>number := INT | FLOAT</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>where INT is interpreted as a C long int and FLOAT is interpreted
+as a C double</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>This grammar allows for order of operations (multiplication
+and dividision take precedence over addition and subtraction), floating and
+integer constants, and grouping of terms by way of parentheses.<span
+style='mso-spacerun:yes'>  </span>Although the grammar allows symbols to be
+arbitrary strings, this documentation will always use ‘x’ for symbols.</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>Within a transform expression, the symbol represents a
+variable which contains the data to be manipulated.<span
+style='mso-spacerun:yes'>  </span>For this reason, the terms symbol and
+variable will be used interchangeably.<span style='mso-spacerun:yes'> 
+</span>Furthermore, in the current implementation of data transforms, all
+symbols appearing in an expression are interpreted as referring to the same
+dataset.<span style='mso-spacerun:yes'>  </span>So, an expression such as
+“alpha + 5” is equivalent to “x+5” and an expression such as “alpha + 3*beta +
+5” is equivalent to “alpha + 3*alpha + 5” which is equivalent to “4*x +
+5”.<span style='mso-spacerun:yes'>    </span></p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<h1>Data Transform Implementation</h1>
+
+<p class=MsoNormal>When the data transform property of a dataset transfer
+property list is set, a parse tree of the expression is immediately generated
+and its root is saved in the property list.<span style='mso-spacerun:yes'> 
+</span>The generation of the parse involves several steps.</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>First, the expression is reduced, so as to simply the final
+parse and speed up the transform operations.<span style='mso-spacerun:yes'> 
+</span>Expressions such as “(5/9.0) * (x-32)” will be reduced to
+“.555555*(x-32).”<span style='mso-spacerun:yes'>  </span>While further
+simplification is algebraically possible, the data transform code will only
+reduce simple trivial arithmetic operations.<span style='mso-spacerun:yes'> 
+</span></p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>Then, this reduced expression is parsed into a set of
+tokens, from which the parse tree is generated.<span style='mso-spacerun:yes'> 
+</span>From the expression “(5/9.0)*(x-32),” for example, the following parse
+tree would be created:</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal><span style='mso-tab-count:4'>                                          </span><span
+style='mso-spacerun:yes'>     </span>*</p>
+
+<p class=MsoNormal><span style='mso-tab-count:4'>                                          </span>/<span
+style='mso-tab-count:1'>          </span>\<span style='mso-spacerun:yes'> 
+</span></p>
+
+<p class=MsoNormal><span style='mso-tab-count:3'>                                </span><span
+style='mso-spacerun:yes'>       </span>.555555<span
+style='mso-spacerun:yes'>     </span>-</p>
+
+<p class=MsoNormal><span style='mso-tab-count:5'>                                                     </span>/<span
+style='mso-spacerun:yes'>   </span>\<span style='mso-tab-count:5'>                                                </span></p>
+
+<p class=MsoNormal><span style='mso-tab-count:4'>                                          </span><span
+style='mso-spacerun:yes'>           </span>x<span style='mso-spacerun:yes'> 
+</span>32</p>
+
+<p class=MsoNormal><span style='mso-tab-count:1'>           </span></p>
+
+<h2>HDread with Data Transform Expressions</h2>
+
+<p class=MsoNormal>When a read is performed with a dataset transfer property
+list that has the data transform property set, the following sequence of events
+occurs:</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<ol style='margin-top:0in' start=1 type=1>
+ <li class=MsoNormal style='mso-list:l2 level1 lfo3;tab-stops:list .5in'>A
+ piece of the file is read into memory</li>
+ <li class=MsoNormal style='mso-list:l2 level1 lfo3;tab-stops:list .5in'>The
+ data transform is performed on this piece of memory</li>
+ <li class=MsoNormal style='mso-list:l2 level1 lfo3;tab-stops:list .5in'>This piece
+ of memory is then copied to the user</li>
+ <li class=MsoNormal style='mso-list:l2 level1 lfo3;tab-stops:list .5in'>Steps
+ 1 – 3 are repeated until the read is complete.</li>
+</ol>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>Step 2 works like this:</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<ol style='margin-top:0in' start=1 type=1>
+ <li class=MsoNormal style='mso-list:l1 level1 lfo6;tab-stops:list .5in'>The
+ function responsible for doing the transform is passed a buffer and is
+ informed what type of data is inside this buffer and how many elements
+ there are.</li>
+ <li class=MsoNormal style='mso-list:l1 level1 lfo6;tab-stops:list .5in'>This
+ buffer is then treated as the variable in the data transform expression
+ and the transform expression is applied.</li>
+ <li class=MsoNormal style='mso-list:l1 level1 lfo6;tab-stops:list .5in'>The
+ transformed buffer is returned to the library.</li>
+</ol>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>If the transform expression is “(5/9.0)*(x-32),” with the
+parse tree shown above and the buffer contains [-10 0 10 50 100], then the
+intermediate steps involved in the transform are:</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<ol style='margin-top:0in' start=1 type=1>
+ <li class=MsoNormal style='mso-pagination:widow-orphan lines-together;
+ page-break-after:avoid;mso-list:l5 level1 lfo9;mso-hyphenate:none;
+ tab-stops:list .5in'>First, the (x-32) subexpression is evaluated.<span
+ style='mso-spacerun:yes'>  </span>Now the buffer would contain<span
+ style='mso-spacerun:yes'>           </span>[-42 -32 -22 18 68]</li>
+ <li class=MsoNormal style='mso-list:l5 level1 lfo9;tab-stops:list .5in'>Then,
+ the .55555 * part of the expression is evaluated.<span
+ style='mso-spacerun:yes'>  </span>Now the buffer would contain: [-23.3333
+ -17.7777 -12.2222 9.9999 37.7777]</li>
+ <li class=MsoNormal style='mso-list:l5 level1 lfo9;tab-stops:list .5in'>Now,
+ the transform would be completed and the resulting buffer returned.</li>
+</ol>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>Note that the original data in the file was not modified. </p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<h2>HDwrite with Data Transform Expressions</h2>
+
+<p class=MsoNormal>The process of a write works much the same way, but in the
+reverse order.<span style='mso-spacerun:yes'>  </span>When a file is written
+out with a dataset transfer property list that has the data transform property
+set:</p>
+
+<p class=MsoNormal><span style='mso-spacerun:yes'>  </span></p>
+
+<ol style='margin-top:0in' start=1 type=1>
+ <li class=MsoNormal style='mso-list:l4 level1 lfo12;tab-stops:list .5in'>The
+ user passes a buffer to HDwrite, along with the type and number of
+ elements.</li>
+ <li class=MsoNormal style='mso-list:l4 level1 lfo12;tab-stops:list .5in'>The
+ data transform is performed on a copy of this piece of memory.</li>
+ <li class=MsoNormal style='mso-list:l4 level1 lfo12;tab-stops:list .5in'>This
+ copy with the transformed data is then written out to the file.</li>
+</ol>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>Step 2 works exactly as in the read example.<span
+style='mso-spacerun:yes'>  </span>Note that the user’s data is not modified. <span
+style='mso-spacerun:yes'> </span>Also, since the transform property is not
+saved with the dataset, in order to recover the original data, a user must know
+the inverse of the transform that was applied in order to recover it.<span
+style='mso-spacerun:yes'>  </span>In the case of “(5/9.0)*(x-32)” this inverse
+would be “(9/5.0)*x + 32”.<span style='mso-spacerun:yes'>  </span>Reading from
+a data file that had previously been written out with a transform string of
+“(5/9.0)*(x-32)” with a transform string of “(9/5.0)*x + 32” would effectively
+recover the original data the author of the file had been using.<a
+style='mso-footnote-id:ftn2' href="#_ftn2" name="_ftnref2" title=""><span
+class=MsoFootnoteReference><span style='mso-special-character:footnote'><![if !supportFootnotes]><span
+class=MsoFootnoteReference><span style='font-size:12.0pt;font-family:"Times New Roman";
+mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:
+EN-US;mso-bidi-language:AR-SA'>[2]</span></span><![endif]></span></span></a></p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<h1>Mixed Mode and Truncation</h1>
+
+<p class=MsoNormal>Because the data transform sits and modifies data between
+the file space and the memory space, various effects can occur that are the
+result of the typecasting that may be involved in the operations.<span
+style='mso-spacerun:yes'>   </span>In addition, because constants in the data
+transform expression can be either INT or FLOAT, the data transform itself can
+be a source of truncation.</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>In the example above, the reason that the transform
+expression is always written as “(5/9.0)*(x-32)” is because, if it were written
+without a floating point constant, it would always evaluate to 0.<span
+style='mso-spacerun:yes'>  </span>The expression “(5/9)*(x-32)” would, when
+set, get reduced to “0*(x-32)” because both 5 and 9 would get read as C long
+ints and, when divided, the result would get truncated to 0.<span
+style='mso-spacerun:yes'>  </span>This resulting expression, “0*(x-32),” would
+cause any data read or written to be saved as an array of all 0’s.<span
+style='mso-spacerun:yes'>  </span></p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>Another source of unpredictability caused by truncation
+occurs when intermediate data is of a type that is more precise than the
+destination memory type.<span style='mso-spacerun:yes'>  </span>For example, if
+the transform expression “(1/2.0)*x” is applied to data read from a file that
+is being read into an integer memory buffer, the results can be
+unpredictable.<span style='mso-spacerun:yes'>  </span>If the source array is [1
+2 3 4], then the resulting array could be either [0 1 1 2] or [0 0 1 1],
+depending on the floating point unit of the processors.<span
+style='mso-spacerun:yes'>  </span>Note that this result is independent of the
+source data type.<span style='mso-spacerun:yes'>  </span>It doesn’t matter if
+the source data is integer or floating point because the 2.0 in the data
+transform expression will cause everything to be evaluated in a floating-point
+context.</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>When setting transform expressions, care must be taken to
+ensure that the truncation does not adversely affect the data.<span
+style='mso-spacerun:yes'>  </span>A workaround for the possible effects of a
+transform such as “(1/2.0) * x” would be to used the transform expression
+“(1/2.0)*x + 0.5” instead of the original.<span style='mso-spacerun:yes'> 
+</span>This will ensure that all truncation rounds up, with the possible
+exception of a boundary condition.</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<h1>Data Transform Example</h1>
+
+<p class=MsoNormal>The following code snippet shows an example using data
+transform, where the data transform property is set and a write is
+performed.<span style='mso-spacerun:yes'>  </span>Then, a read is performed
+with no data transform property set.<span style='mso-spacerun:yes'>  </span>It
+is assumed that <span style='font-family:Courier'>dataset </span>is a dataset
+that has been opened and <span style='font-family:Courier'>windchillF </span>and
+<span style='font-family:Courier'>windchillC </span>are both arrays that hold
+floating point data.<span style='mso-spacerun:yes'>  </span>The result of this
+snippet is to fill <span style='font-family:Courier'>windchillC </span>with the
+data in <span style='font-family:Courier'>windchillF</span>, converted to
+Celcius.</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal><span style='font-family:Courier'>hid_t dxpl_id_c_to_f;<o:p></o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'>const char* c_to_f =
+“(9/5.0)*x + 32”;<o:p></o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'><o:p>&nbsp;</o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'>/* Create the dataset
+transfer property list */<o:p></o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'><span
+style='mso-spacerun:yes'>    </span>dxpl_id_c_to_f =
+H5Pcreate(H5P_DATASET_XFER);<o:p></o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'><o:p>&nbsp;</o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'>/* Set the data transform
+to be used on the read*/<o:p></o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'><span
+style='mso-spacerun:yes'>    </span>H5Pset_data_transform(dxpl_id_c_to_f,
+c_to_f);<o:p></o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'><o:p>&nbsp;</o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'><span
+style='mso-spacerun:yes'>    </span><o:p></o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'>/*<o:p></o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'>* Write the data to the
+dataset using the f_to_c transform<o:p></o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'>*/<o:p></o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'><span
+style='mso-spacerun:yes'>    </span>status = H5Dwrite(dataset, H5T_NATIVE_FLOAT,
+H5S_ALL, H5S_ALL, dxpl_id_f_to_c, windchillF);<o:p></o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'><span
+style='mso-spacerun:yes'>    </span><o:p></o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'>/* Read the data with the
+c_to_f data transform */<o:p></o:p></span></p>
+
+<p class=MsoNormal><span style='font-family:Courier'><span
+style='mso-spacerun:yes'>    </span>H5Dread(dataset, H5T_NATIVE_FLOAT, H5S_ALL,
+H5S_ALL, H5P_DEFAULT, windchillC);<o:p></o:p></span></p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<h1>H5Pget_data_transform Details</h1>
+
+<p class=MsoNormal>Querying the data transform string of a dataset transfer
+property list requires the use of the H5Pget_data_transform function.<span
+style='mso-spacerun:yes'>  </span>This function provides the ability to both
+query the size of the string stored and retrieve part or all of it.<span
+style='mso-spacerun:yes'>  </span>Note that H5Pget_data_transform will return
+the expression that was set by H5Pset_data_transform.<span
+style='mso-spacerun:yes'>  </span>The reduced transform string, computed when
+H5Pset_data_transform is called, is not stored in string form and is not
+available to the user.</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>In order to ascertain the size of the string, a NULL <span
+style='font-family:Courier'>expression</span> should be passed to the
+function.<span style='mso-spacerun:yes'>  </span>This will make the function
+return the length of the transform string (not including the terminated ‘\0’
+character).</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>To actually retrieve the string, a pointer to a valid memory
+location should be passed in for <span style='font-family:Courier'>expression </span>and
+the number of bytes from the string that should be copied to that memory
+location should be passed in as <span style='font-family:Courier'>size</span>.</p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<h1>Further Work</h1>
+
+<p class=MsoNormal>Some additional functionality can still be added to the data
+transform.<span style='mso-spacerun:yes'>  </span>Currently the most important
+feature lacking is the addition of operators, such as exponentiation and the
+trigonometric functions.<span style='mso-spacerun:yes'>  </span>Although
+exponentiation can be explicitly carried with a transform expression such as
+“x*x*x” it may be easier to support expression like “x^3.” Also lacking are the
+commonly used trigonometric functions, such as sin, cos, and tan.<span
+style='mso-spacerun:yes'>  </span></p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>Popular constants could also be added, such as &#960; or
+e.<span style='mso-spacerun:yes'>  </span></p>
+
+<p class=MsoNormal><o:p>&nbsp;</o:p></p>
+
+<p class=MsoNormal>More advanced functionality, such as the ability to perform
+a transform on multiple datasets is also a possibility, but is a feature is
+more a completely new addition than an extension to data transforms.<span
+style='mso-spacerun:yes'>  </span></p>
+
+</div>
+
+<div style='mso-element:footnote-list'><![if !supportFootnotes]><br clear=all>
+
+<hr align=left size=1 width="33%">
+
+<![endif]>
+
+<div style='mso-element:footnote' id=ftn1>
+
+<p class=MsoFootnoteText><a style='mso-footnote-id:ftn1' href="#_ftnref1"
+name="_ftn1" title=""><span class=MsoFootnoteReference><span style='mso-special-character:
+footnote'><![if !supportFootnotes]><span class=MsoFootnoteReference><span
+style='font-size:10.0pt;font-family:"Times New Roman";mso-fareast-font-family:
+"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:EN-US;
+mso-bidi-language:AR-SA'>[1]</span></span><![endif]></span></span></a> Mr.
+Wendling, who involved in the initial design and implemented the expression
+parser, has left NCSA.</p>
+
+</div>
+
+<div style='mso-element:footnote' id=ftn2>
+
+<p class=MsoFootnoteText><a style='mso-footnote-id:ftn2' href="#_ftnref2"
+name="_ftn2" title=""><span class=MsoFootnoteReference><span style='mso-special-character:
+footnote'><![if !supportFootnotes]><span class=MsoFootnoteReference><span
+style='font-size:10.0pt;font-family:"Times New Roman";mso-fareast-font-family:
+"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:EN-US;
+mso-bidi-language:AR-SA'>[2]</span></span><![endif]></span></span></a> See the
+h5_dtransform.c example in the examples directory of the hdf5 library for just
+such an illustration.</p>
+
+</div>
+
+</div>
+
+</body>
+
+</html>