By the way, almost 30 years ago, I already knew that calculators never use
Taylor series (CORDIC algorithms were written in 1959)... Even if they are
mathematically correct, they require too many iterations for small systems
and managing huge numbers such as factorials is not always possible. I'm
interested in XSLT at browser side and speed is important.
I must comment on one other mis-statement here: " Even if they are
mathematically correct, they require too many iterations for small
systems and managing huge numbers such as factorials is not always
possible"
I want to assure our readers that nowhere in the FXSL implementation
of sin() (or any other Taylor series - based implementation), there
are " huge numbers such as factorials".
I don't think even a naive freshman implementation would use
"factorials". To be up to the point, the following 25 lines contain
the most significant template that carries out the sin() calculation
-- do you see a factorial anywhere?
<xsl:template name="_sineIter">
<xsl:param name="pX2"/>
<xsl:param name="pRslt"/>
<xsl:param name="pElem"/>
<xsl:param name="pN"/>
<xsl:param name="pEps"/>
<xsl:variable name="vnextN" select="$pN+2"/>
<xsl:variable name="vnewElem" select="-$pElem*$pX2 div
($vnextN*($vnextN - 1))"/>
<xsl:variable name="vnewResult" select="$pRslt + $vnewElem"/>
<xsl:variable name="vdiffResult" select="$vnewResult - $pRslt"/>
<xsl:choose>
<xsl:when test="$vdiffResult > $pEps or $vdiffResult < -$pEps">
<xsl:call-template name="_sineIter">
<xsl:with-param name="pX2" select="$pX2"/>
<xsl:with-param name="pRslt" select="$vnewResult"/>
<xsl:with-param name="pElem" select="$vnewElem"/>
<xsl:with-param name="pN" select="$vnextN"/>
<xsl:with-param name="pEps" select="$pEps"/>
</xsl:call-template>
</xsl:when>
<xsl:otherwise>
<xsl:value-of select="$vnewResult"/>
</xsl:otherwise>
</xsl:choose>
</xsl:template>
The full code may be viewed here:
http://fxsl.cvs.sourceforge.net/viewvc/fxsl/fxsl-xslt2/f/func-trignm.xsl?revision=1.3&view=markup
--
Cheers,
Dimitre Novatchev
---------------------------------------
Truly great madness cannot be achieved without significant intelligence.
---------------------------------------
To invent, you need a good imagination and a pile of junk
-------------------------------------
Never fight an inanimate object
-------------------------------------
You've achieved success in your field when you don't know whether what
you're doing is work or play
On Wed, Mar 3, 2010 at 10:49 AM, COUTHURES Alain
<alain(_dot_)couthures(_at_)agencexml(_dot_)com> wrote:
Dimitre,
Unfortunately, FXSL is not in first results listed by Google when searching
"xslt sin" or "xslt cos".
By the way, almost 30 years ago, I already knew that calculators never use
Taylor series (CORDIC algorithms were written in 1959)... Even if they are
mathematically correct, they require too many iterations for small systems
and managing huge numbers such as factorials is not always possible. I'm
interested in XSLT at browser side and speed is important.
So, if FXSL users consider it good enough for their requirements, it's good
to know. Do you know if they are working at client-side or at server-side ?
Because I spent no more than one day to find algorithms and less than one
another to implement the ones I need, it wasn't for me a costly effort,
anyway.
If only Microsoft had already implemented XSLT 2.0, XPath 2.x, SVG,
XForms,... more efforts would have been saved...
Best regards,
-Alain
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