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<?xml version="1.0" encoding="UTF-8"?>
<!--***********************************************************
*
* 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
*
* Unless required by applicable law or agreed to in writing,
* software distributed under the License is distributed on an
* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied. See the License for the
* specific language governing permissions and limitations
* under the License.
*
***********************************************************-->
<!--
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(interger 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="$x"/>) greate then 1 !</xsl:message>
</xsl:when>
<xsl:otherwise>
<xsl:call-template name="atan2">
<xsl:with-param name="x" select="$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="$x"/>) greate then 1 !</xsl:message>
</xsl:when>
<xsl:otherwise>
<xsl:call-template name="atan2">
<xsl:with-param name="y" select="$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 then 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>