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CHAPTER 11 NAMED TEMPLATES, STYLESHEET FUNCTIONS, AND RECURSION
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<xsl:function name="private-math:product" as="xs:double"> <xsl:param name="numbers" as="xs:double*" /> <xsl:param name="product" as="xs:double" /> <xsl:sequence select="if (exists($numbers)) then private-math:product($numbers[position() > 1], $product * $numbers[1]) else $product" /> </xsl:function> The user-interface function that wraps this helper function needs to accept a sequence of numbers and, as long as that sequence actually contains some numbers, return the result of calling the helper template with <xsl:function name="math:product" as="xs:double"> <xsl:param name="numbers" as="xs:double*" /> <xsl:sequence select="if (exists($numbers)) then private-math:product($numbers, 1) else ()" /> </xsl:function> For example, you could call the math:product() function with the following call: math:product((2, 3, 4)) This would return 2 * 3 * 4 24.
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Summary XSLT and XPath have good support for operations that would usually involve iteration over a sequence. Where an operation is not supported, you can use a recursive template or function that uses the predicates to pull out the first item on which to operate and the rest of the items on which to recurse.
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Tail Recursion
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Recursion can be computationally expensive. When a processor comes across a loop in procedural programming languages, it can assign a particular set of resources to hold the values of the variables that are updated within the loop. However, with a recursive process, the processor may have to assign different resources to hold the values of the parameters each time the template is called. For example, when working through a string containing the alphabet, the processor might have to assign one byte for every letter in the alphabet, so 26 bytes for the alphabet to start with. With a loop, those same 26 bytes can be reused again and again. However, with a recursive template or function, the parameter has different resources assigned to it each time the template or function is called, so the total memory consumption is more like 26 + 25 + 24 + ... + 3 + 2 + 1 = 351 bytes. The fact that a processor has to assign new resources on each recursion means that it has to keep track of where it is within the program by recording which function called this function, and which function called that function, and so on up to the very first call that started the
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CHAPTER 11 NAMED TEMPLATES, STYLESHEET FUNCTIONS, AND RECURSION
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program running. This record of functions calling other functions is known as the stack. When you use recursive templates or functions, the stack can get very large; each time a template or function calls itself, it adds another level to the stack. So in the example of working through the alphabet letter by letter, on the last recursion you re 26 levels deeper than you were in the first recursion. All processors have a limit to the size of the stack, and therefore a limit to the depth that the recursion can reach. If you have a template that has to call itself a lot of times, you might reach the stack limit; at that point the process stops altogether, and the stylesheet generates an error. Fortunately, most processors are clever enough to recognize when they can reuse the resources that are assigned to a recursive template or function and so don t need to add another level to the stack. In particular, if you write a template or function so that it only calls itself once, and the recursive call is the last thing that s done by a template or function, then the processor can interpret the recursive instructions exactly as if they were specified in a loop. Templates or functions that call themselves as the very last thing they do are known as tail recursive.
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Note Different processors are built in different ways and optimize different aspects of XSLT and XPath. If
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you need to improve the speed of your stylesheet, then you should try out different ways of solving the same problem to see which one gives you the best performance with your data and your processor.
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Summary Tail recursive templates are more efficient than recursive templates that are not tail recursive.
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When you are writing a recursive template or function that will need to call itself lots of times, then it is worthwhile trying to make it tail recursive. The two things that you need to ensure are Within every branch of the instructions inside the template or function, the template or function only calls itself once. Within every branch of the instructions inside the template or function, the recursive call is the last thing the processor needs to do. We ll look at an alternative design for a template working out the product of a sequence of numbers to illustrate these issues. First, look at the private-math:product() helper function from the last section (the recursive call is highlighted): <xsl:function name="private-math:product" as="xs:double"> <xsl:param name="numbers" as="xs:double*" /> <xsl:param name="product" as="xs:double" /> <xsl:sequence select="if (exists($numbers)) then private-math:product($numbers[position() > 1], $product * $numbers[1]) else $product" /> </xsl:function>
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