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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> </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 +doesnt have to worry about forgetting to call the conversion function or even +writing it in the first place.</p> + +<p class=MsoNormal><o:p> </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> </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> </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> </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> </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> </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> </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> </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> </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> </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> </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> </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> </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> </o:p></p> + +<p class=MsoNormal><o:p> </o:p></p> + +<p class=MsoNormal><o:p> </o:p></p> + +<p class=MsoNormal><o:p> </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> </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> </o:p></p> + +<p class=MsoNormal>Step 2 works like this:</p> + +<p class=MsoNormal><o:p> </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> </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> </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> </o:p></p> + +<p class=MsoNormal>Note that the original data in the file was not modified. </p> + +<p class=MsoNormal><o:p> </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> </o:p></p> + +<p class=MsoNormal>Step 2 works exactly as in the read example.<span +style='mso-spacerun:yes'> </span>Note that the users 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> </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> </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 0s.<span +style='mso-spacerun:yes'> </span></p> + +<p class=MsoNormal><o:p> </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 doesnt 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> </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> </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> </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> </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> </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> </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> </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> </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> </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> </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> </o:p></p> + +<p class=MsoNormal>Popular constants could also be added, such as π or +e.<span style='mso-spacerun:yes'> </span></p> + +<p class=MsoNormal><o:p> </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> |