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<?xml version="1.0" encoding="UTF-8"?> <!-- * This file is part of the LibreOffice project. * * This Source Code Form is subject to the terms of the Mozilla Public * License, v. 2.0. If a copy of the MPL was not distributed with this * file, You can obtain one at http://mozilla.org/MPL/2.0/. * * This file incorporates work covered by the following license notice: * * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed * with this work for additional information regarding copyright * ownership. The ASF licenses this file to you under the Apache * License, Version 2.0 (the "License"); you may not use this file * except in compliance with the License. You may obtain a copy of * the License at http://www.apache.org/licenses/LICENSE-2.0 . --> <!-- xslt math lib by Wind Li Public Functions sin(x,rounding-factor=100) cos(x,rounding-factor=100) tan(x,rounding-factor=100) ctan(x,rounding-factor=100) atan2(x, y ,rounding-factor=100) atan(x,rounding-factor=100) acos(x,rounding-factor=100) asin(x,rounding-factor=100) abs(x) max(x1,x2) min(x1,x2) power(x,power(integer only), rounding-factor=100) sqrt(x, rounding-factor=100) convert2radian(x,rounding-factor=100) convert2degree(x,rounding-factor=100) convert2fd(x,rounding-factor=100) --> <xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform" xmlns:draw="http://openoffice.org/2000/drawing" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:svg="urn:oasis:names:tc:opendocument:xmlns:svg-compatible:1.0" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:w10="urn:schemas-microsoft-com:office:word" xmlns:w="http://schemas.microsoft.com/office/word/2003/wordml" xmlns:text="http://openoffice.org/2000/text" xmlns:style="http://openoffice.org/2000/style" xmlns:fo="urn:oasis:names:tc:opendocument:xmlns:xsl-fo-compatible:1.0" xmlns:office="http://openoffice.org/2000/office" exclude-result-prefixes="draw svg style office fo text"> <xsl:variable name="pi" select="3.1416"/> <xsl:template name="math-test"> sin(34.8) <xsl:call-template name="sin"> <xsl:with-param name="x" select="34.8"/> <xsl:with-param name="rounding-factor" select="100000"/> </xsl:call-template> cos(34.8) <xsl:call-template name="cos"> <xsl:with-param name="x" select="34.8"/> <xsl:with-param name="rounding-factor" select="100000"/> </xsl:call-template> atan(2.74) <xsl:call-template name="atan"> <xsl:with-param name="x" select="2.74"/> <xsl:with-param name="rounding-factor" select="100000"/> </xsl:call-template> acos(0.5) <xsl:call-template name="acos"> <xsl:with-param name="x" select="0.5"/> <xsl:with-param name="rounding-factor" select="100000"/> </xsl:call-template> asin(0.5) <xsl:call-template name="asin"> <xsl:with-param name="x" select="0.5"/> <xsl:with-param name="rounding-factor" select="100000"/> </xsl:call-template> sqrt(1328.3414) <xsl:call-template name="sqrt"> <xsl:with-param name="x" select="1328.3414"/> <xsl:with-param name="rounding-factor" select="100000"/> </xsl:call-template> </xsl:template> <!-- public functions start --> <xsl:template name="sin"> <xsl:param name="x" select="0"/> <xsl:param name="rounding-factor" select="100"/> <xsl:variable name="angle" select="$x * 180 div $pi "/> <xsl:variable name="mod-angle" select="$angle mod 360"/> <xsl:variable name="sinx"> <xsl:call-template name="sin-private"> <xsl:with-param name="x" select=" ( $angle mod 360 ) * $pi div 180 "/> </xsl:call-template> </xsl:variable> <xsl:value-of select=" round ( number($sinx) * $rounding-factor ) div $rounding-factor"/> </xsl:template> <xsl:template name="cos"> <xsl:param name="x" select="0"/> <xsl:param name="rounding-factor" select="100"/> <xsl:variable name="angle" select="$x * 180 div $pi "/> <xsl:variable name="mod-angle" select="$angle mod 360"/> <xsl:variable name="cosx"> <xsl:call-template name="cos-private"> <xsl:with-param name="x" select=" ( $angle mod 360 ) * $pi div 180 "/> </xsl:call-template> </xsl:variable> <xsl:value-of select=" round ( number($cosx) * $rounding-factor ) div $rounding-factor"/> </xsl:template> <xsl:template name="tan"> <xsl:param name="x" select="0"/> <xsl:param name="rounding-factor" select="100"/> <xsl:variable name="sinx"> <xsl:call-template name="sin"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="rounding-factor" select="$rounding-factor * 10"/> </xsl:call-template> </xsl:variable> <xsl:variable name="cosx"> <xsl:call-template name="cos"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="rounding-factor" select="$rounding-factor * 10"/> </xsl:call-template> </xsl:variable> <xsl:choose> <xsl:when test=" $cosx = 0 "> <xsl:message>tan error : tan(<xsl:value-of select="$x"/>) is infinite!</xsl:message> <xsl:value-of select="63535"/> </xsl:when> <xsl:otherwise> <xsl:value-of select=" round( $sinx div $cosx * $rounding-factor) div $rounding-factor"/> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="ctan"> <xsl:param name="x" select="0"/> <xsl:param name="rounding-factor" select="100"/> <xsl:variable name="sinx"> <xsl:call-template name="sin"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="rounding-factor" select="$rounding-factor * 10"/> </xsl:call-template> </xsl:variable> <xsl:variable name="cosx"> <xsl:call-template name="cos"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="rounding-factor" select="$rounding-factor * 10"/> </xsl:call-template> </xsl:variable> <xsl:choose> <xsl:when test=" $sinx = 0 "> <xsl:message>tan error : tan(<xsl:value-of select="$x"/>) is infinite!</xsl:message> <xsl:value-of select="63535"/> </xsl:when> <xsl:otherwise> <xsl:value-of select=" round( $cosx div $sinx * $rounding-factor) div $rounding-factor"/> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="atan"> <xsl:param name="x" select="0"/> <xsl:param name="rounding-factor" select="100"/> <xsl:choose> <xsl:when test="$x = 0"> <xsl:value-of select="0"/> </xsl:when> <xsl:when test="$x < 0"> <xsl:variable name="atan-x"> <xsl:call-template name="atan"> <xsl:with-param name="x" select=" -1 * $x"/> <xsl:with-param name="rounding-factor" select="$rounding-factor"/> </xsl:call-template> </xsl:variable> <xsl:value-of select="-1 * $atan-x"/> </xsl:when> <xsl:when test="$x > 1"> <xsl:variable name="atan-div-x"> <xsl:call-template name="atan"> <xsl:with-param name="x" select="1 div $x "/> <xsl:with-param name="rounding-factor" select="$rounding-factor"/> </xsl:call-template> </xsl:variable> <xsl:value-of select=" $pi div 2 - $atan-div-x"/> </xsl:when> <xsl:otherwise> <xsl:variable name="arctanx"> <xsl:call-template name="atan-private"> <xsl:with-param name="x" select=" $x "/> </xsl:call-template> </xsl:variable> <xsl:value-of select=" round ( number($arctanx) * $rounding-factor ) div $rounding-factor"/> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="atan2"> <xsl:param name="x"/> <xsl:param name="y"/> <xsl:param name="rounding-factor" select="100"/> <xsl:choose> <xsl:when test="$x = 0"> <xsl:value-of select=" $pi div 2"/> </xsl:when> <xsl:otherwise> <xsl:call-template name="atan"> <xsl:with-param name="x" select="$y div $x"/> <xsl:with-param name="rounding-factor" select="$rounding-factor"/> </xsl:call-template> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="acos"> <xsl:param name="x"/> <xsl:param name="rounding-factor" select="100"/> <xsl:variable name="abs-x"> <xsl:call-template name="abs"> <xsl:with-param name="x" select="$x"/> </xsl:call-template> </xsl:variable> <xsl:choose> <xsl:when test="$abs-x > 1"> <xsl:message>acos error : abs(<xsl:value-of select="$x"/>) greater than 1 !</xsl:message> </xsl:when> <xsl:otherwise> <xsl:call-template name="atan2"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="y"> <xsl:call-template name="sqrt"> <xsl:with-param name="x" select="1 - $x * $x"/> <xsl:with-param name="rounding-factor" select=" concat($rounding-factor,'0') "/> </xsl:call-template> </xsl:with-param> </xsl:call-template> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="asin"> <xsl:param name="x"/> <xsl:param name="rounding-factor" select="100"/> <xsl:variable name="abs-x"> <xsl:call-template name="abs"> <xsl:with-param name="x" select="$x"/> </xsl:call-template> </xsl:variable> <xsl:choose> <xsl:when test="$abs-x > 1"> <xsl:message>asin error : abs(<xsl:value-of select="$x"/>) greater than 1 !</xsl:message> </xsl:when> <xsl:otherwise> <xsl:call-template name="atan2"> <xsl:with-param name="y" select="$x"/> <xsl:with-param name="x"> <xsl:call-template name="sqrt"> <xsl:with-param name="x" select="1 - $x * $x"/> <xsl:with-param name="rounding-factor" select=" concat($rounding-factor,'0') "/> </xsl:call-template> </xsl:with-param> </xsl:call-template> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="abs"> <xsl:param name="x"/> <xsl:choose> <xsl:when test="$x > 0"> <xsl:value-of select="$x"/> </xsl:when> <xsl:otherwise> <xsl:value-of select="$x * -1"/> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="max"> <xsl:param name="x1"/> <xsl:param name="x2"/> <xsl:choose> <xsl:when test="$x1 > $x2"> <xsl:value-of select="$x1"/> </xsl:when> <xsl:otherwise> <xsl:value-of select="$x2"/> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="min"> <xsl:param name="x1"/> <xsl:param name="x2"/> <xsl:choose> <xsl:when test="$x1 < $x2"> <xsl:value-of select="$x1"/> </xsl:when> <xsl:otherwise> <xsl:value-of select="$x2"/> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="power"> <xsl:param name="x"/> <xsl:param name="y" select="1"/> <xsl:param name="rounding-factor" select="100"/> <!-- z is a private param --> <xsl:param name="z" select="1"/> <xsl:choose> <xsl:when test="$y > 0"> <xsl:call-template name="power"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="y" select="$y - 1"/> <xsl:with-param name="z" select="$z * $x"/> <xsl:with-param name="rounding-factor" select="$rounding-factor"/> </xsl:call-template> </xsl:when> <xsl:otherwise> <xsl:value-of select=" round( $z * $rounding-factor) div $rounding-factor"/> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="sqrt"> <xsl:param name="x"/> <xsl:param name="rounding-factor" select="100"/> <xsl:choose> <xsl:when test="$x = 0">0</xsl:when> <xsl:when test="$x < 0"> <xsl:message>sqrt error : <xsl:value-of select="$x"/> less than 0!</xsl:message> </xsl:when> <xsl:otherwise> <xsl:call-template name="sqrt-private"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="rounding-factor" select="$rounding-factor"/> </xsl:call-template> </xsl:otherwise> </xsl:choose> </xsl:template> <!-- public functions end --> <!-- Private functions: sin-private cos-private atan-private sqrt-private integer-sqrt Sqrt-GetOneDigit --> <xsl:template name="sin-private"> <xsl:param name="x" select="0"/> <xsl:param name="n" select="0"/> <xsl:param name="nx" select="1"/> <xsl:param name="sign" select="1"/> <xsl:param name="max-n" select="20"/> <xsl:param name="sinx" select="0"/> <xsl:choose> <xsl:when test="not ($max-n > $n) or $nx = 0 "> <xsl:value-of select="$sinx"/> </xsl:when> <xsl:when test="$n = 0"> <xsl:call-template name="sin-private"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="n" select="$n + 1"/> <xsl:with-param name="sign" select="$sign * -1"/> <xsl:with-param name="max-n" select="$max-n"/> <xsl:with-param name="nx" select="$x "/> <xsl:with-param name="sinx" select="$sinx + $x"/> </xsl:call-template> </xsl:when> <xsl:otherwise> <xsl:variable name="new-nx" select="($nx * $x * $x) div ( 2 * $n ) div ( 2 * $n + 1) "/> <xsl:call-template name="sin-private"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="n" select="$n + 1"/> <xsl:with-param name="sign" select="$sign * -1"/> <xsl:with-param name="max-n" select="$max-n"/> <xsl:with-param name="nx" select=" $new-nx "/> <xsl:with-param name="sinx" select="$sinx + $new-nx * $sign"/> </xsl:call-template> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="cos-private"> <xsl:param name="x" select="0"/> <xsl:param name="n" select="0"/> <xsl:param name="nx" select="1"/> <xsl:param name="sign" select="1"/> <xsl:param name="max-n" select="20"/> <xsl:param name="cosx" select="0"/> <xsl:choose> <xsl:when test="not ($max-n > $n) or $nx = 0 "> <xsl:value-of select="$cosx"/> </xsl:when> <xsl:when test="$n = 0"> <xsl:call-template name="cos-private"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="n" select="$n + 1"/> <xsl:with-param name="sign" select="$sign * -1"/> <xsl:with-param name="max-n" select="$max-n"/> <xsl:with-param name="nx" select=" 1 "/> <xsl:with-param name="cosx" select="1"/> </xsl:call-template> </xsl:when> <xsl:otherwise> <xsl:variable name="new-nx" select="($nx * $x * $x) div ( 2 * $n -1 ) div ( 2 * $n ) "/> <xsl:call-template name="cos-private"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="n" select="$n + 1"/> <xsl:with-param name="sign" select="$sign * -1"/> <xsl:with-param name="max-n" select="$max-n"/> <xsl:with-param name="nx" select=" $new-nx "/> <xsl:with-param name="cosx" select="$cosx + $new-nx * $sign"/> </xsl:call-template> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="atan-private"> <xsl:param name="x" select="0"/> <xsl:param name="n" select="0"/> <xsl:param name="nx" select="1"/> <xsl:param name="sign" select="1"/> <xsl:param name="max-n" select="40"/> <xsl:param name="arctanx" select="0"/> <xsl:choose> <xsl:when test="not ($max-n > $n) or $nx = 0 "> <xsl:value-of select="$arctanx"/> </xsl:when> <xsl:when test="$n = 0"> <xsl:call-template name="atan-private"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="n" select="$n + 1"/> <xsl:with-param name="sign" select="$sign * -1"/> <xsl:with-param name="max-n" select="$max-n"/> <xsl:with-param name="nx" select="$x "/> <xsl:with-param name="arctanx" select="$arctanx + $x"/> </xsl:call-template> </xsl:when> <xsl:otherwise> <xsl:variable name="new-nx" select=" $nx * $x * $x "/> <xsl:call-template name="atan-private"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="n" select="$n + 1"/> <xsl:with-param name="sign" select="$sign * -1"/> <xsl:with-param name="max-n" select="$max-n"/> <xsl:with-param name="nx" select=" $new-nx "/> <xsl:with-param name="arctanx" select="$arctanx + $new-nx div (2 * $n +1) * $sign"/> </xsl:call-template> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="sqrt-private"> <xsl:param name="x"/> <xsl:param name="rounding-factor" select="100"/> <xsl:variable name="shift" select="string-length( $rounding-factor)"/> <xsl:variable name="power"> <xsl:call-template name="power"> <xsl:with-param name="x" select="100"/> <xsl:with-param name="y" select="$shift"/> <xsl:with-param name="rounding-factor" select="1"/> </xsl:call-template> </xsl:variable> <xsl:variable name="integer-x" select=" round( $power * $x )"/> <xsl:variable name="integer-quotient"> <xsl:call-template name="integer-sqrt"> <xsl:with-param name="x" select="$integer-x"/> <xsl:with-param name="length" select=" string-length( $integer-x ) "/> <xsl:with-param name="curr-pos" select=" 2 - (round (string-length( $integer-x ) div 2 ) * 2 - string-length( $integer-x ) ) "/> </xsl:call-template> </xsl:variable> <xsl:variable name="power-10"> <xsl:call-template name="power"> <xsl:with-param name="x" select="10"/> <xsl:with-param name="y" select="$shift - 1"/> <xsl:with-param name="rounding-factor" select="1"/> </xsl:call-template> </xsl:variable> <xsl:value-of select=" round( $integer-quotient div 10) div $power-10 "/> </xsl:template> <xsl:template name="integer-sqrt"> <xsl:param name="x"/> <xsl:param name="length"/> <xsl:param name="curr-pos"/> <xsl:param name="last-quotient" select="0"/> <xsl:choose> <xsl:when test="$curr-pos > $length"> <xsl:value-of select="$last-quotient"/> </xsl:when> <xsl:otherwise> <xsl:variable name="curr-x" select="substring( $x, 1, $curr-pos )"/> <xsl:variable name="new-quotient"> <xsl:call-template name="get-one-sqrt-digit"> <xsl:with-param name="x" select="$curr-x"/> <xsl:with-param name="last-quotient" select="$last-quotient"/> <xsl:with-param name="n" select="5"/> <xsl:with-param name="direct" select="0"/> </xsl:call-template> </xsl:variable> <xsl:call-template name="integer-sqrt"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="length" select="$length"/> <xsl:with-param name="curr-pos" select="$curr-pos + 2"/> <xsl:with-param name="last-quotient" select="number($new-quotient)"/> </xsl:call-template> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="get-one-sqrt-digit"> <xsl:param name="x"/> <xsl:param name="last-quotient"/> <xsl:param name="n"/> <xsl:param name="direct" select="1"/> <xsl:variable name="quotient" select=" concat( $last-quotient, $n) "/> <xsl:variable name="accumulate" select="$quotient * $quotient "/> <xsl:choose> <xsl:when test="$accumulate = $x"> <xsl:value-of select="concat($last-quotient , $n )"/> </xsl:when> <xsl:when test="$direct = 0 and $accumulate < $x"> <xsl:call-template name="get-one-sqrt-digit"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="last-quotient" select="$last-quotient"/> <xsl:with-param name="n" select="$n + 1"/> <xsl:with-param name="direct" select="1"/> </xsl:call-template> </xsl:when> <xsl:when test="$direct = 0 and $accumulate > $x"> <xsl:call-template name="get-one-sqrt-digit"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="last-quotient" select="$last-quotient"/> <xsl:with-param name="n" select="$n - 1"/> <xsl:with-param name="direct" select="-1"/> </xsl:call-template> </xsl:when> <xsl:when test=" $accumulate * $direct < $x * $direct "> <xsl:call-template name="get-one-sqrt-digit"> <xsl:with-param name="x" select="$x"/> <xsl:with-param name="last-quotient" select="$last-quotient"/> <xsl:with-param name="n" select="$n+ $direct"/> <xsl:with-param name="direct" select="$direct"/> </xsl:call-template> </xsl:when> <xsl:when test="not($n < 9) or $n = -1"> <xsl:value-of select="concat($last-quotient , $n - $direct) "/> </xsl:when> <xsl:when test="$direct = 1"> <xsl:value-of select="concat($last-quotient , $n - 1) "/> </xsl:when> <xsl:otherwise> <xsl:value-of select="concat($last-quotient , $n) "/> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="convert2redian"> <xsl:param name="x" select="'0'"/> <xsl:param name="rounding-factor" select="100"/> <xsl:choose> <xsl:when test="contains($x,'deg')"> <xsl:value-of select="round($rounding-factor * number(substring-before($x, 'deg') div 180 * $pi)) div $rounding-factor"/> </xsl:when> <xsl:when test="contains($x,'fd')"> <xsl:value-of select="round($rounding-factor * number(substring-before($x, 'fd') div 180 div 65536 * $pi)) div $rounding-factor"/> </xsl:when> <xsl:otherwise> <xsl:value-of select="round($rounding-factor * number($x) div 180 * $pi) div $rounding-factor"/> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="convert2degree"> <xsl:param name="x" select="'0'"/> <xsl:param name="rounding-factor" select="100"/> <xsl:choose> <xsl:when test="contains($x,'deg')"> <xsl:value-of select="round($rounding-factor * substring-before($x,'deg')) div $rounding-factor"/> </xsl:when> <xsl:when test="contains($x,'fd')"> <xsl:value-of select="round($rounding-factor * number(substring-before($x, 'fd')) div 65536 ) div $rounding-factor"/> </xsl:when> <xsl:otherwise> <xsl:value-of select="round($rounding-factor * number($x) * 180 div $pi) div $rounding-factor"/> </xsl:otherwise> </xsl:choose> </xsl:template> <xsl:template name="convert2fd"> <xsl:param name="x" select="'0'"/> <xsl:param name="rounding-factor" select="100"/> <xsl:choose> <xsl:when test="contains($x,'deg')"> <xsl:value-of select="round($rounding-factor * number(substring-before($x, 'deg') * 65535)) div $rounding-factor"/> </xsl:when> <xsl:when test="contains($x,'fd')"> <xsl:value-of select="round($rounding-factor * number(substring-before($x, 'fd'))) div $rounding-factor"/> </xsl:when> <xsl:otherwise> <xsl:value-of select="round($rounding-factor * number($x) * 180 div $pi * 65535) div $rounding-factor"/> </xsl:otherwise> </xsl:choose> </xsl:template> </xsl:stylesheet>