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CHAPTER 11 NAMED TEMPLATES, STYLESHEET FUNCTIONS, AND RECURSION
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</xsl:otherwise> </xsl:choose> </xsl:template> Recursive functions are similar, except that, as we ve seen, they can t have default values for their parameters, and the call to the function is made using a function call rather than an <xsl:call-template> instruction. The fact that the recursive call can be made in an XPath expression rather than an XSLT instruction means that you can use an if expression to test the stopping condition instead of an <xsl:choose>: <xsl:function name="functionName" as="returnType"> <xsl:param name="paramName" as="paramType" /> ... <xsl:sequence select="if (condition) then ... else ... functionName(differentValue) ..." /> </xsl:template>
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Summary A recursive template or function is a named template or stylesheet function that calls itself.
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Numeric Calculations Using Recursion
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The first type of recursion we ll look at in detail is recursion to perform a numeric calculation. XPath provides operators and functions for some numeric calculations, but not all of them. For example, XPath doesn t offer functions for getting the square root of a number or getting the power of a number.
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Note Writing stylesheet functions for these functions can be quite tricky; usually you can use an extension
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function instead, as you ll see in 14, or you can reuse utility functions such as those from EXSLT (http://www.exslt.org/math). I m really only including these functions here as examples of recursion in use.
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In these kinds of functions, you use a parameter to keep track of the value attained so far, and only emit that value when you come to the end of the recursion. This parameter is only ever used within the recursion, so there are usually two function declarations that support the function: one that provides the user interface to the function (without the extra parameter) and another that actually carries out the recursion.
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When a function parameter should never actually be used by a user, I usually put the function that Tip accepts the extra parameter in a different namespace. For example, the math:squareRoot() function would be the one that the user calls (without the extra parameter), with the private-math:squareRoot() function being the one that actually does the work (with the extra parameter).
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CHAPTER 11 NAMED TEMPLATES, STYLESHEET FUNCTIONS, AND RECURSION
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For example, the following math:squareRoot() stylesheet function (provided in squareRoot.xsl), or rather its helper function private-math:squareRoot(), gives the square root of a number by repeatedly adjusting an estimate of the square root by half of the difference between the square of the estimate and the number of which you re attempting to find the square root. We prevent infinite recursion by only using a certain precision, passed in as a parameter. The $precision parameter is used to round the number to a certain number of decimal places in conjunction with the round-half-to-even() function. If the current estimate is the same as the next estimate, to the specified precision, then you ve found the square root of the number, at least to the desired precision: <xsl:function name="math:squareRoot" as="xs:double"> <xsl:param name="number" as="xs:double" /> <xsl:sequence select="math:squareRoot($number, 4)" /> </xsl:function> <xsl:function name="math:squareRoot" as="xs:double"> <xsl:param name="number" as="xs:double" /> <xsl:param name="precision" as="xs:integer" /> <xsl:sequence select="private-math:squareRoot($number, $precision, 1)" /> </xsl:function> <xsl:function name="private-math:squareRoot" as="xs:double"> <xsl:param name="number" as="xs:double" /> <xsl:param name="precision" as="xs:integer" /> <xsl:param name="estimate" as="xs:double" /> <xsl:variable name="nextEstimate" as="xs:double" select="$estimate + (($number - $estimate * $estimate) div (2 * $estimate))" /> <xsl:variable name="roundedEstimate" as="xs:double" select="round-half-to-even($nextEstimate, $precision) " /> <xsl:sequence select="if ($estimate = $roundedEstimate) then $estimate else private-math:squareRoot($number, $precision, $roundedEstimate)" /> </xsl:function> For example, you could call the math:squareRoot() function with the following call: math:squareRoot(10) and it would return the square root of 10 to 4 decimal places (since that s the precision supplied by the version of the function with a single argument) 3.1623. In other calculating functions, the solution is adjusted a particular number of times. In a function to work out the power of a number, for example, the number needs to be multiplied by itself a certain number of times. In the math:power() function (provided in power.xsl), the $result parameter keeps track of the result and is adjusted by being multiplied by the same number (held in the $number parameter) the number of times specified by the $power parameter: <xsl:function name="math:power" as="xs:double"> <xsl:param name="number" as="xs:double" />
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