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<DIV dir=ltr align=left><FONT color=#0000ff size=2 face=Arial><SPAN
class=293440409-23092020>[Couldn't resist 'grabbing' e-mail 1776 ...
:-)]</SPAN></FONT></DIV>
<DIV> </DIV>
<DIV><SPAN class=293440409-23092020></SPAN><FONT face=Arial><FONT
color=#0000ff><FONT size=2>M<SPAN
class=293440409-23092020>ike</SPAN></FONT></FONT></FONT><BR></DIV>
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<FONT size=2 face=Tahoma><B>From:</B> Cfp-interest
[mailto:cfp-interest-bounces@oakapple.net] <B>On Behalf Of </B>Jim
Thomas<BR><B>Sent:</B> 22 September 2020 23:43<BR><B>To:</B> Fred J.
Tydeman<BR><B>Cc:</B> CFP<BR><B>Subject:</B> [Cfp-interest 1773] Re: Exact
subnormal results<BR></FONT><BR></DIV>
<DIV></DIV><BR>
<DIV><BR>
<BLOCKQUOTE type="cite">
<DIV>On Sep 1, 2020, at 12:09 PM, Fred J. Tydeman <<A
href="mailto:tydeman@tybor.com">tydeman@tybor.com</A>> wrote:</DIV><BR
class=Apple-interchange-newline>
<DIV><SPAN
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: normal; FONT-STYLE: normal; DISPLAY: inline !important; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">Attached
is the rewrite on range errors and exact subnormal results.</SPAN><BR
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px"><BR
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px"><BR
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px"><SPAN
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: normal; FONT-STYLE: normal; DISPLAY: inline !important; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">---</SPAN><BR
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px"><SPAN
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: normal; FONT-STYLE: normal; DISPLAY: inline !important; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">Fred
J. Tydeman Tydeman
Consulting</SPAN><BR
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px"><A
style="FONT-SIZE: 12px; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; font-variant-caps: normal; -webkit-text-stroke-width: 0px; -webkit-text-size-adjust: auto"
href="mailto:tydeman@tybor.com">tydeman@tybor.com</A><SPAN
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: normal; FONT-STYLE: normal; DISPLAY: inline !important; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px"><SPAN
class=Apple-converted-space> </SPAN> Testing,
numerics, programming</SPAN><BR
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px"><SPAN
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: normal; FONT-STYLE: normal; DISPLAY: inline !important; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">+1
(702) 608-6093 Vice-chair of PL22.11 (ANSI
"C")</SPAN><BR
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px"><SPAN
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: normal; FONT-STYLE: normal; DISPLAY: inline !important; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">Sample
C99+FPCE tests:<SPAN class=Apple-converted-space> </SPAN></SPAN><A
style="FONT-SIZE: 12px; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; font-variant-caps: normal; -webkit-text-stroke-width: 0px; -webkit-text-size-adjust: auto"
href="http://www.tybor.com/">http://www.tybor.com</A><BR
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px"><SPAN
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: normal; FONT-STYLE: normal; DISPLAY: inline !important; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">Savers
sleep well, investors eat well, spenders work forever.</SPAN><BR
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px"><BR
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">
<P
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px"><BR><B>Submitter:</B>CFP
group<BR><B>Submission Date:</B><SPAN
class=Apple-converted-space> </SPAN>2020-??-??<BR><B>Document:</B><SPAN
class=Apple-converted-space> </SPAN>WG14 N25??<BR><B>Title:</B><SPAN
class=Apple-converted-space> </SPAN>N25??: Exact subnormal
results<BR><B>Reference Documents:</B>N2506</P>
<P
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">Summary</P>
<P
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">This
is a follow on to N2506 that was accepted (except for three math functions).
Those three functions [fmod(), remainder(), and remquo()] can produce exact
subnormal results and there was a question on should they underflow.</P>
<P
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">7.12.1
Treatment of error conditions has two "requirements" related to this
issue.</P>
<P
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">#4
has:</P>
<BLOCKQUOTE
style='FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; MARGIN: 1em 40px; DISPLAY: block; LETTER-SPACING: normal; BACKGROUND-COLOR: lightgray; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px'>Likewise,
a range error occurs if and only if the mathematical result of the
function cannot be represented in an object of the specified type, due to
extreme magnitude.</BLOCKQUOTE>
<P
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">#6
has:</P>
<BLOCKQUOTE
style='FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; MARGIN: 1em 40px; DISPLAY: block; LETTER-SPACING: normal; BACKGROUND-COLOR: lightgray; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px'>The
result underflows if the magnitude of the mathematical result is nonzero
and less than the minimum normal number in the type.243)</BLOCKQUOTE>
<P
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">So,
if an exact subnormal result is produced, is it an underflow range
error?</P>
<P
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">Since
it is exact, it is representable, so does not meet the condition in
paragraph 4.</P>
<P
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">Since
it is subnormal, it meets the condition of paragraph 6.</P>
<P
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">So
what is it?</P>
<P
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">Assuming
exact subnormal results are underflow, here are proposed wording changes to
the C standard.</P>
<P
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">Note:
Since what happens on underflow is implementation defined, these changes do
not cause any existing implementation to change.</P>
<P
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">C2x
changes:</P>
<UL
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">
<LI>7.12.1 Treatment of error conditions
<P>Add to 7.12.1#4 after the first sentance.</P>
<BLOCKQUOTE
style='FONT-FAMILY: "Times New Roman"; MARGIN: 1em 40px; DISPLAY: block; BACKGROUND-COLOR: lightgray'><INS
style="FONT-WEIGHT: bold; BACKGROUND-COLOR: rgb(160,255,160)">Also, a
range error occurs if the mathematical result is beyond the range where
all values can be represented in an object of the specified type, to the
full precision of the type.footnote</INS>
<P><INS
style="FONT-WEIGHT: bold; BACKGROUND-COLOR: rgb(160,255,160)">footnote:
Exact subnormal results are a range
error.</INS></P></BLOCKQUOTE></LI></UL></DIV></BLOCKQUOTE>
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Bullet 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Number 5"/>
<w:LsdException Locked="false" Priority="10" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Closing"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Signature"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="true"
UnhideWhenUsed="true" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="List Continue 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Message Header"/>
<w:LsdException Locked="false" Priority="11" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Salutation"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Date"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text First Indent"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text First Indent 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Note Heading"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Body Text Indent 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Block Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Hyperlink"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="FollowedHyperlink"/>
<w:LsdException Locked="false" Priority="22" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Document Map"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Plain Text"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="E-mail Signature"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Top of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Bottom of Form"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal (Web)"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Acronym"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Address"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Cite"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Code"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Definition"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Keyboard"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Preformatted"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Sample"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Typewriter"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="HTML Variable"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Normal Table"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="annotation subject"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="No List"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Outline List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Simple 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Classic 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Colorful 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Columns 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Grid 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 4"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 5"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 6"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 7"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table List 8"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table 3D effects 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Contemporary"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Elegant"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Professional"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Subtle 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Subtle 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 1"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 2"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Web 3"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Balloon Text"/>
<w:LsdException Locked="false" Priority="39" Name="Table Grid"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
Name="Table Theme"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" QFormat="true" Name="No Spacing"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
<w:LsdException Locked="false" Priority="0" QFormat="true"
Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" QFormat="true"
Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" QFormat="true"
Name="Subtle Emphasis"/>
<w:LsdException Locked="false" Priority="21" QFormat="true"
Name="Intense Emphasis"/>
<w:LsdException Locked="false" Priority="31" QFormat="true"
Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" QFormat="true"
Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" SemiHidden="true"
UnhideWhenUsed="true" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
<w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
<w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
<w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
<w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
<w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
<w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 1"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 1"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 2"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 2"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 3"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 3"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 4"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 4"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 5"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 5"/>
<w:LsdException Locked="false" Priority="46"
Name="Grid Table 1 Light Accent 6"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
<w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
<w:LsdException Locked="false" Priority="51"
Name="Grid Table 6 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="52"
Name="Grid Table 7 Colorful Accent 6"/>
<w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
<w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
<w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
<w:LsdException Locked="false" Priority="46"
Name="List Table 1 Light Accent 1"/>
<w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
<w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
<w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
<w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
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<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: Arial, sans-serif">Consider changing the
footnote to “A range error occurs if the function result is subnormal, even if
the mathematical result is represented exactly in the type.”</SPAN></P>
<DIV><BR></DIV>
<DIV>- Jim Thomas</DIV></DIV>
<BLOCKQUOTE type="cite">
<DIV>
<UL
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: normal; FONT-STYLE: normal; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">
<LI>The fmod functions
<P>Add to 7.12.10.1#2</P>
<BLOCKQUOTE
style='FONT-FAMILY: "Times New Roman"; MARGIN: 1em 40px; DISPLAY: block; BACKGROUND-COLOR: lightgray'><INS
style="FONT-WEIGHT: bold; BACKGROUND-COLOR: rgb(160,255,160)">A range
error occurs if x is finite, both x and y are nonzero, and either is too
close to zero.</INS></BLOCKQUOTE>
<LI>The remainder functions
<P>Add to 7.12.10.2#2</P>
<BLOCKQUOTE
style='FONT-FAMILY: "Times New Roman"; MARGIN: 1em 40px; DISPLAY: block; BACKGROUND-COLOR: lightgray'><INS
style="FONT-WEIGHT: bold; BACKGROUND-COLOR: rgb(160,255,160)">A range
error occurs if x is finite, both x and y are nonzero, and either is too
close to zero.</INS></BLOCKQUOTE>
<LI>The fdim functions
<P>Change 7.12.12.1#2</P>
<BLOCKQUOTE
style='FONT-FAMILY: "Times New Roman"; MARGIN: 1em 40px; DISPLAY: block; BACKGROUND-COLOR: lightgray'>A
range error may occur.</BLOCKQUOTE>
<P>to:</P>
<BLOCKQUOTE
style='FONT-FAMILY: "Times New Roman"; MARGIN: 1em 40px; DISPLAY: block; BACKGROUND-COLOR: lightgray'>A
range error<SPAN class=Apple-converted-space> </SPAN><DEL
style="FONT-WEIGHT: bold; BACKGROUND-COLOR: rgb(255,160,160)">may
occur</DEL><INS
style="FONT-WEIGHT: bold; BACKGROUND-COLOR: rgb(160,255,160)">occurs if
positive finite x-y is either too large or too close to
zero</INS>.</BLOCKQUOTE>
<P>Change F.10.9.1 The fdim functions</P>
<BLOCKQUOTE
style='FONT-FAMILY: "Times New Roman"; MARGIN: 1em 40px; DISPLAY: block; BACKGROUND-COLOR: lightgray'>No
aditional requirements.</BLOCKQUOTE>
<P>to:</P>
<BLOCKQUOTE
style='FONT-FAMILY: "Times New Roman"; MARGIN: 1em 40px; DISPLAY: block; BACKGROUND-COLOR: lightgray'><DEL
style="FONT-WEIGHT: bold; BACKGROUND-COLOR: rgb(255,160,160)">No
aditional requirements.</DEL><SPAN
class=Apple-converted-space> </SPAN><INS
style="FONT-WEIGHT: bold; BACKGROUND-COLOR: rgb(160,255,160)">When
subnormal results are supported, the returned value is exact and is
independent of the current rounding direction
mode.</INS></BLOCKQUOTE></LI></UL><SPAN
style="FONT-SIZE: 12px; TEXT-DECORATION: none; FONT-FAMILY: Helvetica; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: normal; FONT-STYLE: normal; DISPLAY: inline !important; LETTER-SPACING: normal; TEXT-INDENT: 0px; caret-color: rgb(0, 0, 0); font-variant-caps: normal; -webkit-text-stroke-width: 0px">_______________________________________________</SPAN><BR
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