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@ -44,6 +44,9 @@
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|||
<!--[if lt IE 9]>
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<script src="../reveal.js-3.1.0/lib/js/html5shiv.js"></script>
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<![endif]-->
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<script src="../vega/vega.js"></script>
|
||||
<script src="../vega/vega-lite.js"></script>
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<script src="../vega/vega-embed.js"></script>
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</head>
|
||||
|
||||
<body>
|
||||
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@ -306,8 +309,8 @@
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|||
<h3>Union Node</h3>
|
||||
<table>
|
||||
<tr><td style="text-align: right;">Visual:</td><td><img src="figs/union.svg" style="margin: 0px;"/></td></tr>
|
||||
<tr><td style="text-align: right;">UIL:</td><td>$\uplus(x: \mathbb P, y: \mathbb P)$</td></tr>
|
||||
<tr><td style="text-align: right;">Logical:</td><td>$x \uplus y$</td></tr>
|
||||
<tr><td style="text-align: right;">UIL:</td><td>$\uplus(a: \mathbb P, b: \mathbb P)$</td></tr>
|
||||
<tr><td style="text-align: right;">Logical:</td><td>$a \uplus b$</td></tr>
|
||||
</table>
|
||||
</section>
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||||
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@ -315,8 +318,8 @@
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|||
<h3>Combining Primitives: Linked List</h3>
|
||||
<table>
|
||||
<tr><td style="text-align: right;">Visual:</td><td><img src="figs/linkedlist.svg" style="margin: 0px;"/></td></tr>
|
||||
<tr><td style="text-align: right;">UIL:</td><td>\begin{align}LL :=\;&|\;U(Sng(x: \mathbb R), y: LL)\\&|\;Sng(x)\end{align}</td></tr>
|
||||
<tr><td style="text-align: right;">Logical:</td><td>$\{ x \} \uplus y$</td></tr>
|
||||
<tr><td style="text-align: right;">UIL:</td><td>\begin{align}LL :=\;&|\;U(Sng(x: \mathbb R), a: LL)\\&|\;Sng(x)\end{align}</td></tr>
|
||||
<tr><td style="text-align: right;">Logical:</td><td>$\{ x \} \uplus a$ or $\{ x \}</td></tr>
|
||||
</table>
|
||||
<p class="fragment" data-fragment-index="1" style="clear: right; font-weight: bold;">
|
||||
Existing data structures can be expressed as syntactic restrictions on this grammar.
|
||||
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@ -327,9 +330,9 @@
|
|||
<h3>Extension 1: Semantic Constraints</h3>
|
||||
<table>
|
||||
<tr><td style="text-align: right;">Visual:</td><td><img src="figs/BTreeNode.svg" style="margin: 0px;"/></td></tr>
|
||||
<tr><td style="text-align: right;">UIL:</td><td>$BT_{k: \mathbb K}(x: \mathbb P, y: \mathbb P)$</td></tr>
|
||||
<tr><td style="text-align: right;">Logical:</td><td>$x \uplus y$</td></tr>
|
||||
<tr><td style="text-align: right;">Constraint:</td><td>$\forall r \in x: r.key \lt K$<br/>$\forall r \in y: r.key \geq K$</td></tr>
|
||||
<tr><td style="text-align: right;">UIL:</td><td>$BT_{k: \mathbb K}(a: \mathbb P, b: \mathbb P)$</td></tr>
|
||||
<tr><td style="text-align: right;">Logical:</td><td>$a \uplus b$</td></tr>
|
||||
<tr><td style="text-align: right;">Constraint:</td><td>$\forall r \in a: r.key \lt K$<br/>$\forall r \in b: r.key \geq K$</td></tr>
|
||||
</table>
|
||||
<p class="fragment" data-fragment-index="1" style="clear: right; font-weight: bold;">
|
||||
Nodes can define syntactic constraints on the contents of descendents.
|
||||
|
|
@ -339,7 +342,7 @@
|
|||
<section>
|
||||
<h3 style="margin-bottom: 60px;">Combining Primitives: Binary Tree</h3>
|
||||
\begin{align}
|
||||
BinTree :=\;&|\;BT_{k: \mathbb K}(x: BinTree, y: BinTree)\\&|\;Sng(x: \mathbb R)
|
||||
BinTree :=\;&|\;BT_{k: \mathbb K}(a: BinTree, b: BinTree)\\&|\;Sng(x: \mathbb R)
|
||||
\end{align}
|
||||
</section>
|
||||
|
||||
|
|
@ -438,16 +441,16 @@
|
|||
|
||||
<section style="font-size: smaller">
|
||||
\begin{align}
|
||||
Q_{\ell,h}(\uplus(x, y)) \equiv &\;\uplus(Q_{\ell,h}(x), Q_{\ell,h}(y))\\[10px]
|
||||
Q_{\ell,h}(BT_k(x, y)) \equiv &\;
|
||||
Q_{\ell,h}(\uplus(a, b)) \rightarrow &\;\uplus(Q_{\ell,h}(a), Q_{\ell,h}(b))\\[10px]
|
||||
Q_{\ell,h}(BT_k(a, b)) \rightarrow &\;
|
||||
\begin{cases}
|
||||
Q_{\ell,h}(x) & \text{if } h \lt k\\
|
||||
Q_{\ell,h}(y) & \text{if } \ell \geq k\\
|
||||
BT_k(Q_{\ell,h}(x), Q_{\ell,h}(y)) & \text{otherwise}
|
||||
Q_{\ell,h}(a) & \text{if } h \lt k\\
|
||||
Q_{\ell,h}(b) & \text{if } \ell \geq k\\
|
||||
BT_k(Q_{\ell,h}(a), Q_{\ell,h}(b)) & \text{otherwise}
|
||||
\end{cases}\\[10px]
|
||||
Q_{\ell,h}(Array_N(x_1,\ldots,x_N)) \equiv &\;
|
||||
Q_{\ell,h}(Array_N(x_1,\ldots,x_N)) \rightarrow &\;
|
||||
Array_{|Y|}(y_1, \ldots, y_{|Y|}) \\&\;\;\text{ s.t. } Y = \{\;x_i\;|\;\ell \leq x_i \lt h\;\}\\[10px]
|
||||
Q_{\ell,h}(Sorted_N(x_1,\ldots,x_N)) \equiv &\;
|
||||
Q_{\ell,h}(Sorted_N(x_1,\ldots,x_N)) \rightarrow &\;
|
||||
Sorted_{j-i+1}(x_i, \ldots, x_j) \\&\;\;\text{ s.t. } i = argmin_i(x_i \geq \ell); \\&\;\;\;\;\;\;\;\;j = argmax_(x_j \lt h);
|
||||
\end{align}
|
||||
</section>
|
||||
|
|
@ -457,7 +460,7 @@
|
|||
$$Insert: \mathbb P \times \mathbb P \rightarrow \mathbb P$$
|
||||
<p style="font-weight: bold; margin-top: 60px" class="fragment">Do the least work possible (optimize later)</p>
|
||||
<div class="fragment" style="margin-top: 60px">
|
||||
$$Insert(x, y) \equiv \uplus(x, y)$$
|
||||
$$Insert(a, b) \rightarrow \uplus(a, b)$$
|
||||
</div>
|
||||
</section>
|
||||
<!-- Accessing Static Data Structures
|
||||
|
|
@ -483,6 +486,144 @@
|
|||
<li style="color: grey;">Optimization Policy Discovery</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p><b>Core Idea:</b> Physical layout as a compiler optimization problem. </p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Example: Organize A Hybrid Data Structure</h3>
|
||||
<img src="figs/Pushdown-Before.svg" style="vertical-align: middle;"/>
|
||||
<span class="fragment" data-fragment-index="2">➔<img src="figs/Pushdown-Step1.svg" style="vertical-align: middle;" /></span>
|
||||
<span class="fragment" data-fragment-index="3">➔<img src="figs/Pushdown-Step2.svg" style="vertical-align: middle;" /></span>
|
||||
<div class="fragment" data-fragment-index="1" style="font-size: smaller; margin-top: 30px">
|
||||
$$\uplus(Sng(x), BT_k(a, b)) \rightarrow \begin{cases} BT_k(\uplus(Sng(x), a), b) & \text{if } x.key \lt k\\ BT_k(a, \uplus(Sng(x), b)) & \text{if } x.key \geq k\end{cases}$$
|
||||
</div>
|
||||
<div class="fragment" data-fragment-index="3" style="font-size: smaller; margin-top: 30px">
|
||||
$$\uplus(Sng(x), Sorted_N(y_1, \ldots, y_N) \rightarrow Sorted_N(y_1, \ldots, y_i, x, y_{i+1}, \ldots y_N)$$
|
||||
$$\text{ where }y_i.key \leq x.key \leq y_{i+1}.key$$
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Rewrites</h3>
|
||||
|
||||
<p>A pattern/replacement pair.</p>
|
||||
|
||||
<ul>
|
||||
<li>Crack-Array</li>
|
||||
<li>Sort-Array</li>
|
||||
<li>Sort-Merge</li>
|
||||
<li>Pushdown-Array</li>
|
||||
<li>Pushdown-BT</li>
|
||||
<li>Pushdown-Sorted</li>
|
||||
<li>...</li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Events</h3>
|
||||
|
||||
<p>A trigger for applying a rewrite.</p>
|
||||
|
||||
<ul>
|
||||
<li>Before-Scan</li>
|
||||
<li>After-Scan</li>
|
||||
<li>Before-Visit</li>
|
||||
<li>After-Visit</li>
|
||||
<li>Before-Insert</li>
|
||||
<li>After-Insert</li>
|
||||
<li>Idle-Tick</li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3 style="margin-bottom:50px">Policies (Take 1)</h3>
|
||||
<p>A set of Rewrite/Event pairs.</p>
|
||||
|
||||
<div style="margin-top:50px; margin-bottom: 50px;">
|
||||
<ul>
|
||||
<li>Cracker (Implements [Idreos et.al.-CIDR 2007])</li>
|
||||
<li>Adaptive Merge (Implements [Graefe/Kano-EDBT 2010])</li>
|
||||
<li>Swap (Heuristic Hybrid: Switch after 2000 events)</li>
|
||||
<li>Transition (Heuristic Hybrid: Gradient from 1-3k events)</li>
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
<attribution><a href="https://odin.cse.buffalo.edu/papers/2015/CIDR-jitd-final.pdf">[Kennedy/Ziarek-CIDR 2015]</a>; <a href="https://github.com/UBOdin/jitd">https://github.com/UBOdin/jitd</a></attribution>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>The Entire Transition Policy</h3>
|
||||
<pre style="width: 50%"><code class="java" style="font-size: 40%; line-height: 120%;">
|
||||
package jitd;
|
||||
|
||||
import java.util.*;
|
||||
|
||||
public class TransitionMode extends Mode {
|
||||
int stepsTotal;
|
||||
int stepsTaken = 0;
|
||||
Random rand = new Random();
|
||||
Mode source, target;
|
||||
|
||||
public TransitionMode(Mode source, Mode target, int steps)
|
||||
{
|
||||
this.stepsTotal = steps;
|
||||
this.source = source;
|
||||
this.target = target;
|
||||
}
|
||||
|
||||
public Mode pick()
|
||||
{
|
||||
stepsTaken++;
|
||||
if(rand.nextInt(stepsTotal) < stepsTaken){
|
||||
return target;
|
||||
} else {
|
||||
return source;
|
||||
}
|
||||
}
|
||||
|
||||
public KeyValueIterator scan(Driver driver, long low, long high)
|
||||
{
|
||||
return pick().scan(driver, low, high);
|
||||
}
|
||||
public void insert(Driver driver, Cog values)
|
||||
{
|
||||
pick().insert(driver, values);
|
||||
}
|
||||
public void idle(Driver driver)
|
||||
{
|
||||
pick().idle(driver);
|
||||
}
|
||||
}
|
||||
</code></pre>
|
||||
<p>(40 lines of java)</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Cracker Policy</h3>
|
||||
<img src="results/1g_cracker_1write.png"/>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Adaptive Merge Policy</h3>
|
||||
<img src="results/1g_merge_1write.png"/>
|
||||
(first read: 33s)
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Swap Policy</h3>
|
||||
<img src="results/1g_swap_1write.png"/>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Transition Policy</h3>
|
||||
<img src="results/1g_transition_1write.png"/>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>Universal data structures allow us to <br/> hybridize policies "for free".</p>
|
||||
</section>
|
||||
<!-- Optimizing Static Data Structures
|
||||
- Now we're talking about purely physical state transitions
|
||||
- Pattern + Replacement Language
|
||||
|
|
@ -494,6 +635,94 @@
|
|||
-->
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<h3>Policies (Take 2)</h3>
|
||||
<p style="margin-top: 80px;"><b>Core Idea:</b> Physical layout as a <i>just-in-time</i> compiler optimization problem.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3 style="margin-bottom: 60px">Just-in-Time Data Structures</h3>
|
||||
<img src="graphics/Interface.png" height="200px" style="float: right;">
|
||||
<p style="padding-top: 40px; width: 400px;">A background thread incrementally optimizes the data structure.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Challenges</h3>
|
||||
<ol>
|
||||
<li class="fragment" style="margin-top: 30px">Which rewrite to apply?</li>
|
||||
<li class="fragment" style="margin-top: 30px">Which data to rewrite?</li>
|
||||
<li class="fragment" style="margin-top: 30px">How to rewrite safely?</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>Two simple transforms: Crack or Sort</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Crack</h3>
|
||||
\begin{align}
|
||||
Array_N(x_1, \ldots, x_N) \rightarrow BT_{x_j.key}(\;\;&Array_{|Y|}(y_1, \ldots, y_{|Y|}), \\&Array_{|Z|}(z_1, \ldots, z_{|Z|})\;\;)
|
||||
\end{align}
|
||||
<p style="font-size: smaller">
|
||||
where $j \in [1, N]$, $Y = \{x_i | x_i.key \lt x_j\}$, $Z = \{x_i | x_i.key \geq x_j\}$
|
||||
</p>
|
||||
<h3 style="margin-top: 60px">Sort</h3>
|
||||
$$Array_N(x_1, \ldots, x_N) \rightarrow Sorted_N(x_{f(1)}, \ldots, x_{f(N)})$$
|
||||
<p style="font-size: smaller">
|
||||
where $f : [N] \rightarrow [N]$ and $x_{f(i)} \leq x_{f(i+1)}$
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Crack</h3>
|
||||
<p><b>Deqeue: </b> 1x Array</p>
|
||||
<p><b>Enqueue: </b> 2x Array</p>
|
||||
|
||||
<h3 style="margin-top: 60px">Sort</h3>
|
||||
<p><b>Deqeue: </b> 1x Array</p>
|
||||
<p><b>Enqueue: </b> 1x Sorted Array</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<img src="figs/Split-Step1.svg">
|
||||
<p><b>Option 1:</b> Crack($Array_8(1 \ldots 8)$)</p>
|
||||
<p><b>Option 2:</b> Sort($Array_8(1 \ldots 8)$)</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<img src="figs/Split-Step2.svg">
|
||||
<p><b>Option 1:</b> Crack($Array_4(1 \ldots 4)$)</p>
|
||||
<p><b>Option 2:</b> Sort($Array_4(1 \ldots 4)$)</p>
|
||||
<p><b>Option 3:</b> Crack($Array_4(5 \ldots 8)$)</p>
|
||||
<p><b>Option 4:</b> Sort($Array_4(5 \ldots 8)$)</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<img src="figs/Split-Step3.svg">
|
||||
<p><b>Option 1:</b> Crack($Array_4(1 \ldots 4)$)</p>
|
||||
<p><b>Option 2:</b> Sort($Array_4(1 \ldots 4)$)</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<div id="predictions"></div>
|
||||
<script>
|
||||
vega.embed("#predictions", {
|
||||
"data": {
|
||||
"url": "results/predictions.json"
|
||||
},
|
||||
"mark": "point",
|
||||
"encoding": {}
|
||||
})
|
||||
</script>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>How to prioritize rewrites?</p>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<h2>Incremental Transitions</h2>
|
||||
|
|
|
|||
BIN
slides/talks/2017-4-Cornell-JITDs/results/1g_cracker_1write.png
Normal file
BIN
slides/talks/2017-4-Cornell-JITDs/results/1g_cracker_1write.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 255 KiB |
541
slides/talks/2017-4-Cornell-JITDs/results/1g_cracker_1write.svg
Normal file
541
slides/talks/2017-4-Cornell-JITDs/results/1g_cracker_1write.svg
Normal file
|
|
@ -0,0 +1,541 @@
|
|||
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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||||
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|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 33 KiB |
18
slides/talks/2017-4-Cornell-JITDs/results/import.rb
Normal file
18
slides/talks/2017-4-Cornell-JITDs/results/import.rb
Normal file
|
|
@ -0,0 +1,18 @@
|
|||
$:.push("~/ownCloud/CodeSnippets")
|
||||
require "csvx.rb"
|
||||
require "util.rb"
|
||||
require "json"
|
||||
|
||||
input = File.csv("predictions.csv")
|
||||
headers = input.shift.every(2, 1).map { |h| h.gsub(/[^0-9a-zA-Z]/, "_").gsub(/_+/,"_") }
|
||||
p headers
|
||||
|
||||
# outputs = Hash.new { |hash, key| hash[key] = File.new("output_#{headers[key]}.csv", "w+") }
|
||||
File.open("predictions.json", "w+") do |f|
|
||||
input.each do |l|
|
||||
(0..(l.length / 2).floor).each do |i|
|
||||
f.puts({ x: l[i*2], y: l[i*2+1], c: i }.to_json) if l[i*2] != ""
|
||||
end
|
||||
end
|
||||
end
|
||||
# outputs.values.each { |f| f.close }
|
||||
65536
slides/talks/2017-4-Cornell-JITDs/results/predictions.csv
Normal file
65536
slides/talks/2017-4-Cornell-JITDs/results/predictions.csv
Normal file
File diff suppressed because it is too large
Load diff
102974
slides/talks/2017-4-Cornell-JITDs/results/predictions.json
Normal file
102974
slides/talks/2017-4-Cornell-JITDs/results/predictions.json
Normal file
File diff suppressed because it is too large
Load diff
|
|
@ -0,0 +1,7 @@
|
|||
{
|
||||
"data": {
|
||||
"url": "output.csv"
|
||||
},
|
||||
"mark": "point",
|
||||
"encoding": {}
|
||||
}
|
||||
53
slides/talks/mathjax/MathJax.js
Normal file
53
slides/talks/mathjax/MathJax.js
Normal file
|
|
@ -0,0 +1,53 @@
|
|||
(function () {
|
||||
var newMathJax = 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js';
|
||||
var oldMathJax = 'cdn.mathjax.org/mathjax/latest/MathJax.js';
|
||||
|
||||
var replaceScript = function (script, src) {
|
||||
//
|
||||
// Make redirected script
|
||||
//
|
||||
var newScript = document.createElement('script');
|
||||
newScript.src = newMathJax + src.replace(/.*?(\?|$)/, '$1');
|
||||
//
|
||||
// Move onload and onerror handlers to new script
|
||||
//
|
||||
newScript.onload = script.onload;
|
||||
newScript.onerror = script.onerror;
|
||||
script.onload = script.onerror = null;
|
||||
//
|
||||
// Move any content (old-style configuration scripts)
|
||||
//
|
||||
while (script.firstChild) newScript.appendChild(script.firstChild);
|
||||
//
|
||||
// Copy script id
|
||||
//
|
||||
if (script.id != null) newScript.id = script.id;
|
||||
//
|
||||
// Replace original script with new one
|
||||
//
|
||||
script.parentNode.replaceChild(newScript, script);
|
||||
//
|
||||
// Issue a console warning
|
||||
//
|
||||
console.warn('WARNING: cdn.mathjax.org has been retired. Check https://www.mathjax.org/cdn-shutting-down/ for migration tips.')
|
||||
}
|
||||
|
||||
if (document.currentScript) {
|
||||
var script = document.currentScript;
|
||||
replaceScript(script, script.src);
|
||||
} else {
|
||||
//
|
||||
// Look for current script by searching for one with the right source
|
||||
//
|
||||
var n = oldMathJax.length;
|
||||
var scripts = document.getElementsByTagName('script');
|
||||
for (var i = 0; i < scripts.length; i++) {
|
||||
var script = scripts[i];
|
||||
var src = (script.src || '').replace(/.*?:\/\//,'');
|
||||
if (src.substr(0, n) === oldMathJax) {
|
||||
replaceScript(script, src);
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
})();
|
||||
1310
slides/talks/vega/vega-embed.js
Normal file
1310
slides/talks/vega/vega-embed.js
Normal file
File diff suppressed because one or more lines are too long
13011
slides/talks/vega/vega-lite.js
Normal file
13011
slides/talks/vega/vega-lite.js
Normal file
File diff suppressed because it is too large
Load diff
35329
slides/talks/vega/vega.js
Normal file
35329
slides/talks/vega/vega.js
Normal file
File diff suppressed because one or more lines are too long
Loading…
Reference in a new issue