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Molecular mechanics - Revision history
2024-03-29T15:34:20Z
Revision history for this page on the wiki
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https://en.formulasearchengine.com/index.php?title=Molecular_mechanics&diff=231955&oldid=prev
en>Anand guddu at 09:30, 16 July 2014
2014-07-16T09:30:31Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:30, 16 July 2014</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Luke Bryan is actually a superstar during the making as well as vocation expansion initially second to his 3rd restaurant recording, & , may be the proof</del>. <del style="font-weight: bold; text-decoration: none;">He burst open on the [http://www.hotelsedinburgh.org concerts for luke bryan] scene in 2004 together with his funny blend of straight down-residence accessibility, motion picture celebrity fantastic appearance and lines, is placed t inside </del>a <del style="font-weight: bold; text-decoration: none;">key way. The brand new record Top on the country graph or chart </del>and <del style="font-weight: bold; text-decoration: none;">#2 around the put graphs, producing it the 2nd greatest very first at that time of 2000 for the country designer</del>. <del style="font-weight: bold; text-decoration: none;"><br><br><br><br>The son of your , </del>is <del style="font-weight: bold; text-decoration: none;">aware perseverance and determination are important elements </del>with <del style="font-weight: bold; text-decoration: none;">regards to an excellent occupation- </del>. <del style="font-weight: bold; text-decoration: none;">His very first album, Keep Me, made the best reaches “All </del>My <del style="font-weight: bold; text-decoration: none;">Girlfriends “Country </del>and <del style="font-weight: bold; text-decoration: none;">Say” Man,” while his work, Doin’ Point, located the performer-3 right No. 6 single people: In addition Calling Is usually a Excellent Point.”<br><br>Within the tumble of 2013, Tour: Luke And which had an impressive listing of , including Metropolitan. “It’s much like you are getting a acceptance </del>to <del style="font-weight: bold; text-decoration: none;">travel </del>to <del style="font-weight: bold; text-decoration: none;">the next level, claims all those designers which were an element of the Concert toursabove </del>in <del style="font-weight: bold; text-decoration: none;">to </del>a <del style="font-weight: bold; text-decoration: none;">bigger amount of musicians</del>.<del style="font-weight: bold; text-decoration: none;">” It twisted as among the [</del>http://<del style="font-weight: bold; text-decoration: none;">www.banburycrossonline.com is the luke bryan concert sold out] most successful tours within its twenty-season record</del>.<br><br><del style="font-weight: bold; text-decoration: none;">Have a look at </del>my <del style="font-weight: bold; text-decoration: none;">blog</del>: [http://<del style="font-weight: bold; text-decoration: none;">lukebryantickets</del>.<del style="font-weight: bold; text-decoration: none;">lazintechnologies</del>.<del style="font-weight: bold; text-decoration: none;">com luke bryan tickets houston</del>]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">They call me Gabrielle</ins>. <ins style="font-weight: bold; text-decoration: none;">I am </ins>a <ins style="font-weight: bold; text-decoration: none;">very cashier </ins>and <ins style="font-weight: bold; text-decoration: none;">I'm charging pretty good financially</ins>. <ins style="font-weight: bold; text-decoration: none;">As a definite girl what I sincerely like </ins>is <ins style="font-weight: bold; text-decoration: none;">going in the market to karaoke but I do not have made a dime </ins>with <ins style="font-weight: bold; text-decoration: none;">it</ins>. My <ins style="font-weight: bold; text-decoration: none;">husband </ins>and <ins style="font-weight: bold; text-decoration: none;">I decided upon </ins>to <ins style="font-weight: bold; text-decoration: none;">reside in Guam but I will gain </ins>to <ins style="font-weight: bold; text-decoration: none;">move </ins>in a <ins style="font-weight: bold; text-decoration: none;">suitable year or two</ins>. <ins style="font-weight: bold; text-decoration: none;">See what's new on my website here: </ins>http://<ins style="font-weight: bold; text-decoration: none;">prometeu</ins>.<ins style="font-weight: bold; text-decoration: none;">net</ins><br><br><ins style="font-weight: bold; text-decoration: none;">Also visit </ins>my <ins style="font-weight: bold; text-decoration: none;">page :</ins>: [http://<ins style="font-weight: bold; text-decoration: none;">prometeu</ins>.<ins style="font-weight: bold; text-decoration: none;">net clash of clans hacker v 1</ins>.<ins style="font-weight: bold; text-decoration: none;">3</ins>]</div></td></tr>
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en>Anand guddu
https://en.formulasearchengine.com/index.php?title=Molecular_mechanics&diff=231954&oldid=prev
en>Second Quantization: per molecular dynamics talkpage. Disparate topic
2014-02-20T09:27:50Z
<p>per molecular dynamics talkpage. Disparate topic</p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:27, 20 February 2014</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">'''Global value numbering''' (GVN) </del>is a <del style="font-weight: bold; text-decoration: none;">[[compiler optimization]] based on </del>the <del style="font-weight: bold; text-decoration: none;">[[SSA (compilers)|SSA]] intermediate representation. It sometimes helps eliminate [[redundant code]] that [[common subexpression elimination]] (CSE) does not. </del> <del style="font-weight: bold; text-decoration: none;">At the same time</del>, <del style="font-weight: bold; text-decoration: none;">however, CSE </del>may <del style="font-weight: bold; text-decoration: none;">eliminate code that GVN does not, so both are often found in modern compilers</del>. <del style="font-weight: bold; text-decoration: none;"> Global value numbering is distinct from </del>[<del style="font-weight: bold; text-decoration: none;">[local value numbering]</del>] in <del style="font-weight: bold; text-decoration: none;">that the value</del>-<del style="font-weight: bold; text-decoration: none;">number mappings hold across basic block boundaries as well</del>, and <del style="font-weight: bold; text-decoration: none;">different algorithms are used to compute the mappings.</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Luke Bryan </ins>is <ins style="font-weight: bold; text-decoration: none;">actually </ins>a <ins style="font-weight: bold; text-decoration: none;">superstar during </ins>the <ins style="font-weight: bold; text-decoration: none;">making as well as vocation expansion initially second to his 3rd restaurant recording, </ins> <ins style="font-weight: bold; text-decoration: none;">& </ins>, may <ins style="font-weight: bold; text-decoration: none;">be the proof</ins>. <ins style="font-weight: bold; text-decoration: none;">He burst open on the </ins>[<ins style="font-weight: bold; text-decoration: none;">http://www.hotelsedinburgh.org concerts for luke bryan</ins>] <ins style="font-weight: bold; text-decoration: none;">scene </ins>in <ins style="font-weight: bold; text-decoration: none;">2004 together with his funny blend of straight down</ins>-<ins style="font-weight: bold; text-decoration: none;">residence accessibility</ins>, <ins style="font-weight: bold; text-decoration: none;">motion picture celebrity fantastic appearance </ins>and <ins style="font-weight: bold; text-decoration: none;"> lines, is placed t inside </ins>a <ins style="font-weight: bold; text-decoration: none;">key way</ins>. <ins style="font-weight: bold; text-decoration: none;">The brand new record </ins> <ins style="font-weight: bold; text-decoration: none;">Top on the country graph or chart </ins>and <ins style="font-weight: bold; text-decoration: none;">#2 around </ins>the <ins style="font-weight: bold; text-decoration: none;">put graphs</ins>, <ins style="font-weight: bold; text-decoration: none;">producing it </ins>the <ins style="font-weight: bold; text-decoration: none;">2nd greatest very first at that time of 2000 for </ins>the <ins style="font-weight: bold; text-decoration: none;">country designer. </ins><<ins style="font-weight: bold; text-decoration: none;">br</ins>><<ins style="font-weight: bold; text-decoration: none;">br</ins>><<ins style="font-weight: bold; text-decoration: none;">br</ins>><<ins style="font-weight: bold; text-decoration: none;">br</ins>><ins style="font-weight: bold; text-decoration: none;">The son of your </ins>, <ins style="font-weight: bold; text-decoration: none;"> is aware perseverance </ins>and <ins style="font-weight: bold; text-decoration: none;">determination are important elements with regards </ins>to <ins style="font-weight: bold; text-decoration: none;">an excellent occupation- </ins>. <ins style="font-weight: bold; text-decoration: none;">His very first album, </ins> <ins style="font-weight: bold; text-decoration: none;">Keep Me</ins>, <ins style="font-weight: bold; text-decoration: none;">made </ins>the <ins style="font-weight: bold; text-decoration: none;">best reaches “All My Girlfriends “Country and Say” Man</ins>,<ins style="font-weight: bold; text-decoration: none;">” while his work</ins>, <ins style="font-weight: bold; text-decoration: none;">Doin’ Point</ins>, <ins style="font-weight: bold; text-decoration: none;">located the performer</ins>-<ins style="font-weight: bold; text-decoration: none;">3 right No</ins>. <ins style="font-weight: bold; text-decoration: none;">6 single people</ins>: <ins style="font-weight: bold; text-decoration: none;">In addition Calling Is usually a Excellent Point.”</ins><<ins style="font-weight: bold; text-decoration: none;">br</ins>><<ins style="font-weight: bold; text-decoration: none;">br</ins>><ins style="font-weight: bold; text-decoration: none;">Within </ins>the <ins style="font-weight: bold; text-decoration: none;">tumble of 2013</ins>, <ins style="font-weight: bold; text-decoration: none;">Tour</ins>: <ins style="font-weight: bold; text-decoration: none;">Luke </ins> <ins style="font-weight: bold; text-decoration: none;">And which had an impressive listing of , including Metropolitan. “It’s much like you are getting </ins>a <ins style="font-weight: bold; text-decoration: none;"> acceptance </ins>to <ins style="font-weight: bold; text-decoration: none;">travel </ins>to <ins style="font-weight: bold; text-decoration: none;">the next level</ins>, <ins style="font-weight: bold; text-decoration: none;">claims all those designers which were an element </ins>of the <ins style="font-weight: bold; text-decoration: none;">Concert toursabove in to a bigger amount </ins>of <ins style="font-weight: bold; text-decoration: none;">musicians</ins>.<ins style="font-weight: bold; text-decoration: none;">” It twisted as among </ins>the <ins style="font-weight: bold; text-decoration: none;"> </ins>[<ins style="font-weight: bold; text-decoration: none;">http://www</ins>.<ins style="font-weight: bold; text-decoration: none;">banburycrossonline</ins>.<ins style="font-weight: bold; text-decoration: none;">com is the luke bryan concert sold out] most successful tours within its twenty</ins>-<ins style="font-weight: bold; text-decoration: none;">season record</ins>.<ins style="font-weight: bold; text-decoration: none;"><br><br>Have a look at my blog</ins>: <ins style="font-weight: bold; text-decoration: none;">[http</ins>:<ins style="font-weight: bold; text-decoration: none;">//lukebryantickets.lazintechnologies</ins>.<ins style="font-weight: bold; text-decoration: none;">com luke bryan tickets houston</ins>]</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Global value numbering works by assigning </del>a <del style="font-weight: bold; text-decoration: none;">[[value number]] to variables and expressions</del>. <del style="font-weight: bold; text-decoration: none;">To those variables </del>and <del style="font-weight: bold; text-decoration: none;">expressions which are provably equivalent, </del>the <del style="font-weight: bold; text-decoration: none;">same value number is assigned. For instance</del>, <del style="font-weight: bold; text-decoration: none;">in </del>the <del style="font-weight: bold; text-decoration: none;">following code:</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> w := 3</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> x := 3</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> y := x + 4</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> z := w + 4</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">a good GVN routine would assign </del>the <del style="font-weight: bold; text-decoration: none;">same value number to </del><<del style="font-weight: bold; text-decoration: none;">code</del>><del style="font-weight: bold; text-decoration: none;">w</del><<del style="font-weight: bold; text-decoration: none;">/code</del>> <del style="font-weight: bold; text-decoration: none;">and </del><<del style="font-weight: bold; text-decoration: none;">code</del>><del style="font-weight: bold; text-decoration: none;">x</del><<del style="font-weight: bold; text-decoration: none;">/code</del>>, and <del style="font-weight: bold; text-decoration: none;">the same value number </del>to <del style="font-weight: bold; text-decoration: none;"><code>y</code> and <code>z</code></del>. <del style="font-weight: bold; text-decoration: none;">For instance</del>, the <del style="font-weight: bold; text-decoration: none;">map <math>[{w} \mapsto 1</del>, <del style="font-weight: bold; text-decoration: none;">{x} \mapsto 1</del>, <del style="font-weight: bold; text-decoration: none;">{y} \mapsto 2</del>, <del style="font-weight: bold; text-decoration: none;">{z} \mapsto 2]</math> would constitute an optimal value</del>-<del style="font-weight: bold; text-decoration: none;">number mapping for this block</del>.</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Using this information, the previous code fragment may be safely transformed into</del>:</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> <del style="font-weight: bold; text-decoration: none;">w := 3</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> x := w</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> y := w + 4</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> z := y</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Depending on the code following this fragment, [[copy propagation]] may be able to remove the assignments to </del><<del style="font-weight: bold; text-decoration: none;">code</del>><del style="font-weight: bold; text-decoration: none;">x</del><<del style="font-weight: bold; text-decoration: none;">/code> and to <code>z</code</del>></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">The reason that GVN is sometimes more powerful than CSE comes from </del>the <del style="font-weight: bold; text-decoration: none;">fact that CSE matches lexically identical expressions whereas the GVN tries to determine an underlying equivalence. For instance</del>, <del style="font-weight: bold; text-decoration: none;">in the code</del>:</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> a <del style="font-weight: bold; text-decoration: none;">:= c × d</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> e := c</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> f := e × d</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Without copy propagation, CSE would ''not'' eliminate the recomputation assigned </del>to <del style="font-weight: bold; text-decoration: none;"><code>f</code>, but even a poor GVN algorithm should discover and eliminate this redundancy.</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">SSA form is required </del>to <del style="font-weight: bold; text-decoration: none;">perform GVN{{Citation needed|date=June 2011}} so that false {variable name → value name} mappings are not created.</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">== References ==</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">*G.A. Kildall</del>, <del style="font-weight: bold; text-decoration: none;">"A Unified Approach to Global Program Optimization." Proceedings </del>of the <del style="font-weight: bold; text-decoration: none;">First ACM Symposium on Principles of Programming Languages,194-206, 1973.</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">* Alpern, Bowen, Wegman, Mark N., and Zadeck, F. Kenneth. </del> <del style="font-weight: bold; text-decoration: none;">"Detecting Equality </del>of <del style="font-weight: bold; text-decoration: none;">Variables in Programs</del>.<del style="font-weight: bold; text-decoration: none;">", ''Conference Record of </del>the <del style="font-weight: bold; text-decoration: none;">Fifteenth Annual ACM Symposium on Principles of Programming Languages'' (</del>[<del style="font-weight: bold; text-decoration: none;">[POPL]]), ACM Press, San Diego, CA, USA, January 1988, pages 1–11</del>.</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">* L</del>. <del style="font-weight: bold; text-decoration: none;">Taylor Simpson, "Value</del>-<del style="font-weight: bold; text-decoration: none;">Driven Redundancy Elimination</del>.<del style="font-weight: bold; text-decoration: none;">" Technical Report 96-308, Computer Science Department, Rice University, 1996. (Author's Ph.D. thesis)</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">* Muchnick, Steven S. ''Advanced Compiler Design and Implementation''. Morgan Kaufmann. 1997.</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">* P. Briggs, K.D. Cooper, L.T. Simpson,"Value Numbering." Software-Practice and Experience, 27</del>:<del style="font-weight: bold; text-decoration: none;">6, pages </del>:<del style="font-weight: bold; text-decoration: none;">701-724, 1997</del>.</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">[[Category:Compiler optimizations]</del>]</div></td><td colspan="2" class="diff-side-added"></td></tr>
</table>
en>Second Quantization
https://en.formulasearchengine.com/index.php?title=Molecular_mechanics&diff=5504&oldid=prev
en>Monkbot: Fix CS1 deprecated date parameter errors
2014-01-26T20:50:30Z
<p>Fix <a href="/index.php?title=Help:CS1_errors&action=edit&redlink=1" class="new" title="Help:CS1 errors (page does not exist)">CS1 deprecated date parameter errors</a></p>
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It sometimes helps eliminate [[redundant code]] that [[common subexpression elimination]] (CSE) does not. At the same time, however, CSE may eliminate code that GVN does not, so both are often found in modern compilers. Global value numbering </ins>is <ins style="font-weight: bold; text-decoration: none;">distinct from [[local value numbering]] in that the value-number mappings hold across basic block boundaries as well, and different algorithms are used to compute the mappings.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Global value numbering works </ins>by <ins style="font-weight: bold; text-decoration: none;">assigning a [[value number]] to variables and expressions</ins>. <ins style="font-weight: bold; text-decoration: none;"> To those variables </ins>and <ins style="font-weight: bold; text-decoration: none;">expressions which are provably equivalent, </ins>the <ins style="font-weight: bold; text-decoration: none;">same value number is assigned</ins>. <ins style="font-weight: bold; text-decoration: none;"> For instance, in </ins>the <ins style="font-weight: bold; text-decoration: none;">following code:</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> w := 3</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> x := 3</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> y := x + 4</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> z := w + 4</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">a good GVN routine would assign </ins>the <ins style="font-weight: bold; text-decoration: none;">same value number to <code>w</code> and </ins><<ins style="font-weight: bold; text-decoration: none;">code</ins>><ins style="font-weight: bold; text-decoration: none;">x</ins><<ins style="font-weight: bold; text-decoration: none;">/code</ins>>, and the <ins style="font-weight: bold; text-decoration: none;">same value </ins>number to <ins style="font-weight: bold; text-decoration: none;"><code>y</code> and <code>z</code></ins>. <ins style="font-weight: bold; text-decoration: none;"> For instance, the map </ins><<ins style="font-weight: bold; text-decoration: none;">math</ins>><ins style="font-weight: bold; text-decoration: none;">[{w} \mapsto 1, {x} \mapsto 1, {y} \mapsto 2, {z} \mapsto 2]</ins><<ins style="font-weight: bold; text-decoration: none;">/math</ins>> <ins style="font-weight: bold; text-decoration: none;">would constitute </ins>an <ins style="font-weight: bold; text-decoration: none;">optimal value-number mapping </ins>for <ins style="font-weight: bold; text-decoration: none;">this block</ins>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Using this information</ins>, <ins style="font-weight: bold; text-decoration: none;">the previous code fragment may be safely transformed into:</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> w := 3</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> x := w</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> y := w + 4</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> z := y</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Depending on the code following this fragment</ins>, <ins style="font-weight: bold; text-decoration: none;">[[copy propagation]] may be able to remove </ins>the <ins style="font-weight: bold; text-decoration: none;">assignments to <code>x</code> and </ins>to <ins style="font-weight: bold; text-decoration: none;"><code>z</code></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The reason that GVN is sometimes more powerful than CSE comes from </ins>the <ins style="font-weight: bold; text-decoration: none;">fact </ins>that <ins style="font-weight: bold; text-decoration: none;">CSE matches lexically identical expressions whereas the GVN tries </ins>to <ins style="font-weight: bold; text-decoration: none;">determine an underlying equivalence</ins>. <ins style="font-weight: bold; text-decoration: none;"> For instance</ins>, <ins style="font-weight: bold; text-decoration: none;">in </ins>the <ins style="font-weight: bold; text-decoration: none;">code:</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> a := c × d</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> e := c</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> f := e × d</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Without copy propagation</ins>, <ins style="font-weight: bold; text-decoration: none;">CSE would ''not'' eliminate </ins>the <ins style="font-weight: bold; text-decoration: none;">recomputation assigned to </ins><<ins style="font-weight: bold; text-decoration: none;">code</ins>><ins style="font-weight: bold; text-decoration: none;">f</ins><<ins style="font-weight: bold; text-decoration: none;">/code</ins>><ins style="font-weight: bold; text-decoration: none;">, but even </ins>a <ins style="font-weight: bold; text-decoration: none;">poor GVN algorithm should discover </ins>and <ins style="font-weight: bold; text-decoration: none;">eliminate this redundancy</ins>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">SSA form </ins>is <ins style="font-weight: bold; text-decoration: none;">required to perform GVN{{Citation needed|date=June 2011}} so that false {variable name → value name} mappings are </ins>not <ins style="font-weight: bold; text-decoration: none;">created.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== References ==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*G.A</ins>. <ins style="font-weight: bold; text-decoration: none;">Kildall</ins>, <ins style="font-weight: bold; text-decoration: none;">"A Unified Approach </ins>to <ins style="font-weight: bold; text-decoration: none;">Global Program Optimization</ins>.<ins style="font-weight: bold; text-decoration: none;">" Proceedings of the First ACM Symposium on Principles of Programming Languages,194</ins>-<ins style="font-weight: bold; text-decoration: none;">206, 1973</ins>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* Alpern</ins>, <ins style="font-weight: bold; text-decoration: none;">Bowen</ins>, <ins style="font-weight: bold; text-decoration: none;">Wegman</ins>, <ins style="font-weight: bold; text-decoration: none;">Mark N.</ins>, and <ins style="font-weight: bold; text-decoration: none;">Zadeck, F. Kenneth. "Detecting Equality of Variables </ins>in <ins style="font-weight: bold; text-decoration: none;">Programs</ins>.<ins style="font-weight: bold; text-decoration: none;">"</ins>, '<ins style="font-weight: bold; text-decoration: none;">'Conference Record of </ins>the <ins style="font-weight: bold; text-decoration: none;">Fifteenth Annual ACM Symposium on Principles </ins>of <ins style="font-weight: bold; text-decoration: none;">Programming Languages'' ([[POPL]]), ACM Press, San Diego, CA, USA, January 1988</ins>, <ins style="font-weight: bold; text-decoration: none;">pages 1–11</ins>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* L</ins>. <ins style="font-weight: bold; text-decoration: none;">Taylor Simpson, "Value</ins>-<ins style="font-weight: bold; text-decoration: none;">Driven Redundancy Elimination</ins>.<ins style="font-weight: bold; text-decoration: none;">" Technical Report 96-308, </ins>Computer <ins style="font-weight: bold; text-decoration: none;">Science Department</ins>, <ins style="font-weight: bold; text-decoration: none;">Rice University</ins>, <ins style="font-weight: bold; text-decoration: none;">1996. (Author's Ph.D</ins>. <ins style="font-weight: bold; text-decoration: none;">thesis)</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* Muchnick</ins>, <ins style="font-weight: bold; text-decoration: none;">Steven S. ''Advanced Compiler Design and Implementation'</ins>'. <ins style="font-weight: bold; text-decoration: none;"> Morgan Kaufmann. 1997.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* P. Briggs, K.D</ins>. <ins style="font-weight: bold; text-decoration: none;">Cooper, L</ins>.<ins style="font-weight: bold; text-decoration: none;">T</ins>. <ins style="font-weight: bold; text-decoration: none;">Simpson</ins>,<ins style="font-weight: bold; text-decoration: none;">"Value Numbering." Software-Practice </ins>and <ins style="font-weight: bold; text-decoration: none;">Experience, 27:6</ins>, <ins style="font-weight: bold; text-decoration: none;">pages :701-724</ins>, <ins style="font-weight: bold; text-decoration: none;">1997</ins>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Compiler optimizations]]</ins></div></td></tr>
</table>
en>Monkbot
https://en.formulasearchengine.com/index.php?title=Molecular_mechanics&diff=231953&oldid=prev
112.196.2.230 at 06:59, 28 August 2012
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