[www] r196972 - Adding first batch of slides.
Tanya Lattner
tonic at nondot.org
Tue Dec 10 13:40:31 PST 2013
Author: tbrethou
Date: Tue Dec 10 15:40:31 2013
New Revision: 196972
URL: http://llvm.org/viewvc/llvm-project?rev=196972&view=rev
Log:
Adding first batch of slides.
Added:
www/trunk/devmtg/2013-11/slides/
www/trunk/devmtg/2013-11/slides/Carruth-PGO.pdf (with props)
www/trunk/devmtg/2013-11/slides/Fischer-Julia.html
www/trunk/devmtg/2013-11/slides/Kleckner-ClangVisualC++.pdf (with props)
www/trunk/devmtg/2013-11/slides/Koch-FunctionMerging-Preliminary.pdf (with props)
www/trunk/devmtg/2013-11/slides/Lattner-LLVM Early Days.pdf (with props)
www/trunk/devmtg/2013-11/slides/Lattner-WelcomeTalk.pdf (with props)
www/trunk/devmtg/2013-11/slides/Riley-DebugginWithLLDB.pdf
www/trunk/devmtg/2013-11/slides/Robinson-PS4Toolchain.pdf
www/trunk/devmtg/2013-11/slides/Rotem-Vectorization.pdf (with props)
www/trunk/devmtg/2013-11/slides/Serebryany-ASAN.pdf (with props)
www/trunk/devmtg/2013-11/slides/Stellard-R600.pdf (with props)
www/trunk/devmtg/2013-11/slides/Wanderman-Milne-Cloudera.pdf (with props)
www/trunk/devmtg/2013-11/slides/Zakai-Emscripten.pdf
Added: www/trunk/devmtg/2013-11/slides/Carruth-PGO.pdf
URL: http://llvm.org/viewvc/llvm-project/www/trunk/devmtg/2013-11/slides/Carruth-PGO.pdf?rev=196972&view=auto
==============================================================================
Binary file - no diff available.
Propchange: www/trunk/devmtg/2013-11/slides/Carruth-PGO.pdf
------------------------------------------------------------------------------
svn:mime-type = application/octet-stream
Added: www/trunk/devmtg/2013-11/slides/Fischer-Julia.html
URL: http://llvm.org/viewvc/llvm-project/www/trunk/devmtg/2013-11/slides/Fischer-Julia.html?rev=196972&view=auto
==============================================================================
--- www/trunk/devmtg/2013-11/slides/Fischer-Julia.html (added)
+++ www/trunk/devmtg/2013-11/slides/Fischer-Julia.html Tue Dec 10 15:40:31 2013
@@ -0,0 +1,5716 @@
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+<style type="text/css">
+/* Overrides of notebook CSS for static HTML export */
+html {
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+.reveal {
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+
+<!-- Custom stylesheet, it must be in the same directory as the html file -->
+<link rel="stylesheet" href="custom.css">
+
+</head>
+
+<body>
+<div class="reveal">
+<div class="slides">
+<section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h1 id="Julia:-An-LLVM-based-approach-to-scientific-computing">Julia: An LLVM-based approach to scientific computing<a class="anchor-link" href="#Julia:-An-LLVM-based-approach-to-scientific-computing">¶</a></h1>
+</div>
+<aside class="notes">
+
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>Keno Fischer</p>
+</div>
+ </aside>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [1]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">run</span><span class="p">(</span><span class="sb">`git config --get user.name`</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stdout">
+<pre>
+Keno Fischer
+
+</pre>
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h1 id="Agenda">Agenda<a class="anchor-link" href="#Agenda">¶</a></h1>
+</div>
+
+<div class="text_cell_render border-box-sizing rendered_html">
+<ul>
+<li>Julia, the language</li>
+<li>A Journey through the CodeGen</li>
+</ul>
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h1 id="Is-it-any-fast?">Is it any fast?<a class="anchor-link" href="#Is-it-any-fast?">¶</a></h1>
+</div>
+<div style=display:none>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [2]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">using</span> <span class="n">Gadfly</span>
+<span class="n">using</span> <span class="n">WWWClient</span>
+<span class="n">using</span> <span class="n">DataFrames</span>
+<span class="n">const</span> <span class="n">w</span> <span class="o">=</span> <span class="n">WWWClient</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
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+</div>
+
+</div>
+</div>
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stderr">
+<pre>
+Warning: New definition
+ round(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
+is ambiguous with:
+ round(AbstractArray{T<:Real,1},) at operators.jl:236.
+To fix, define
+ round(DataArray{_<:Real,1},)
+before the new definition.
+Warning: New definition
+ round(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
+is ambiguous with:
+ round(AbstractArray{T<:Real,2},) at operators.jl:237.
+To fix, define
+ round(DataArray{_<:Real,2},)
+before the new definition.
+Warning: New definition
+ round(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
+is ambiguous with:
+ round(AbstractArray{T<:Real,1},) at operators.jl:236.
+To fix, define
+ round(AbstractDataArray{_<:Real,1},)
+before the new definition.
+Warning: New definition
+ round(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
+is ambiguous with:
+ round(AbstractArray{T<:Real,2},) at operators.jl:237.
+To fix, define
+ round(AbstractDataArray{_<:Real,2},)
+before the new definition.
+Warning: New definition
+ ceil(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
+is ambiguous with:
+ ceil(AbstractArray{T<:Real,1},) at operators.jl:236.
+To fix, define
+ ceil(DataArray{_<:Real,1},)
+before the new definition.
+Warning: New definition
+ ceil(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
+is ambiguous with:
+ ceil(AbstractArray{T<:Real,2},) at operators.jl:237.
+To fix, define
+ ceil(DataArray{_<:Real,2},)
+before the new definition.
+Warning: New definition
+ ceil(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
+is ambiguous with:
+ ceil(AbstractArray{T<:Real,1},) at operators.jl:236.
+To fix, define
+ ceil(AbstractDataArray{_<:Real,1},)
+before the new definition.
+Warning: New definition
+ ceil(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
+is ambiguous with:
+ ceil(AbstractArray{T<:Real,2},) at operators.jl:237.
+To fix, define
+ ceil(AbstractDataArray{_<:Real,2},)
+before the new definition.
+Warning: New definition
+ floor(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
+is ambiguous with:
+ floor(AbstractArray{T<:Real,1},) at operators.jl:236.
+To fix, define
+ floor(DataArray{_<:Real,1},)
+before the new definition.
+Warning: New definition
+ floor(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
+is ambiguous with:
+ floor(AbstractArray{T<:Real,2},) at operators.jl:237.
+To fix, define
+ floor(DataArray{_<:Real,2},)
+before the new definition.
+Warning: New definition
+ floor(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
+is ambiguous with:
+ floor(AbstractArray{T<:Real,1},) at operators.jl:236.
+To fix, define
+ floor(AbstractDataArray{_<:Real,1},)
+before the new definition.
+Warning: New definition
+ floor(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
+is ambiguous with:
+ floor(AbstractArray{T<:Real,2},) at operators.jl:237.
+To fix, define
+ floor(AbstractDataArray{_<:Real,2},)
+before the new definition.
+Warning: New definition
+ trunc(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
+is ambiguous with:
+ trunc(AbstractArray{T<:Real,1},) at operators.jl:236.
+To fix, define
+ trunc(DataArray{_<:Real,1},)
+before the new definition.
+Warning: New definition
+ trunc(DataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:350
+is ambiguous with:
+ trunc(AbstractArray{T<:Real,2},) at operators.jl:237.
+To fix, define
+ trunc(DataArray{_<:Real,2},)
+before the new definition.
+Warning: New definition
+ trunc(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
+is ambiguous with:
+ trunc(AbstractArray{T<:Real,1},) at operators.jl:236.
+To fix, define
+ trunc(AbstractDataArray{_<:Real,1},)
+before the new definition.
+Warning: New definition
+ trunc(AbstractDataArray{T<:Number,N},Integer...) at /Users/kfischer/.julia/DataFrames/src/operators.jl:359
+is ambiguous with:
+ trunc(AbstractArray{T<:Real,2},) at operators.jl:237.
+To fix, define
+ trunc(AbstractDataArray{_<:Real,2},)
+before the new definition.
+Warning: New definition
+ formatter(
+</pre>
+</div>
+</div>
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_display_data">
+
+<div class="output_html rendered_html">
+<script charset="utf-8">
+
+// Traverse upwards from a d3 selection to find and return the first
+// node with "plotroot" class.
+var getplotroot = function(selection) {
+ var node = selection.node();
+ while (node && node.classList && !node.classList.contains("plotroot")) {
+ node = node.parentNode;
+ }
+ return d3.select(node);
+};
+
+
+// Construct a callback for toggling geometries on/off using color groupings.
+//
+// Args:
+// colorclass: class names assigned to geometries belonging to a paricular
+// color group.
+//
+// Returns:
+// A callback function.
+//
+var guide_toggle_color = function(colorclass) {
+ var visible = true;
+ return (function() {
+ var root = getplotroot(d3.select(this));
+ if (visible) {
+ d3.select(this)
+ .transition()
+ .duration(250)
+ .style("opacity", 0.5);
+ root.selectAll(".geometry." + colorclass)
+ .transition()
+ .duration(250)
+ .style("opacity", 0);
+ visible = false;
+ } else {
+ d3.select(this)
+ .transition()
+ .duration(250)
+ .style("opacity", 1.0);
+ root.selectAll(".geometry." + colorclass)
+ .transition()
+ .duration(250)
+ .style("opacity", 1.0);
+ visible = true;
+ }
+ });
+};
+
+
+// Construct a callback used to toggle highly-visibility grid lines.
+//
+// Args:
+// color: Faded-in/faded-out color, respectively.
+//
+// Returns:
+// Callback function.
+//
+var guide_background_mouseover = function(color) {
+ return (function () {
+ var root = getplotroot(d3.select(this));
+ root.selectAll(".xgridlines, .ygridlines")
+ .transition()
+ .duration(250)
+ .attr("stroke", color);
+ });
+};
+
+var guide_background_mouseout = function(color) {
+ return (function () {
+ var root = getplotroot(d3.select(this));
+ root.selectAll(".xgridlines, .ygridlines")
+ .transition()
+ .duration(250)
+ .attr("stroke", color);
+ });
+};
+
+
+// Construct a call back used for mouseover effects in the point geometry.
+//
+// Args:
+// lw: Stroke width to transition to.
+//
+// Returns:
+// Callback function.
+//
+var geom_point_mouseover = function(lw) {
+ return (function() {
+ d3.select(this)
+ .transition()
+ .duration(100)
+ .attr("stroke-width", lw);
+ });
+};
+
+
+// Translate and scale geometry while trying to maintain scale invariance for
+// certain ellements.
+//
+// Args:
+// root: d3 selection of the root plot group node.
+// t: A transform of the form {"scale": scale}
+// old_scale: The scaling factor applied prior to t.scale.
+//
+var set_geometry_transform = function(root, t, old_scale) {
+ var xscalable = root.node().classList.contains("xscalable");
+ var yscalable = root.node().classList.contains("yscalable");
+
+ var xscale = 1.0;
+ var tx = 0.0;
+ if (xscalable) {
+ xscale = t.scale;
+ tx = t.x;
+ }
+
+ var yscale = 1.0;
+ var ty = 0.0;
+ if (yscalable) {
+ yscale = t.scale;
+ ty = t.y;
+ }
+
+ root.selectAll(".geometry")
+ .attr("transform", function() {
+ return "translate(" + [tx, ty] + ") " +
+ "scale(" + xscale + "," + yscale + ")";
+ });
+
+ var unscale_factor = old_scale / t.scale;
+
+ // unscale geometry widths, radiuses, etc.
+ var size_attribs = ["r"];
+ var size_styles = ["font-size"];
+ root.select(".plotpanel")
+ .selectAll("g, .geometry")
+ .each(function() {
+ sel = d3.select(this);
+ var i;
+ var key;
+ var val;
+ for (i in size_styles) {
+ key = size_styles[i];
+ val = sel.style(key);
+ if (val !== null) {
+ // For some reason d3 rounds things like font-sizes to the
+ // nearest integer, so we are setting styles directly instead.
+ val = parseFloat(val);
+ sel.node().style.setProperty(key, unscale_factor * val + "px", "important");
+ }
+ }
+
+ for (i in size_attribs) {
+ key = size_attribs[i];
+ val = sel.attr(key);
+ if (val !== null) {
+ sel.attr(key, unscale_factor * val);
+ }
+ }
+ });
+
+ // TODO:
+ // Is this going to work when we do things other than circles. Suppose we
+ // have plots where we have a path drawing some sort of symbol which we want
+ // to remain size-invariant. Should we be trying to place things using
+ // translate?
+
+ // move axis labels and grid lines around
+ if (xscalable) {
+ root.selectAll(".yfixed")
+ .attr("transform", function() {
+ return "translate(" + [t.x, 0.0] + ") " +
+ "scale(" + [t.scale, 1.0] + ")";
+ });
+
+ root.selectAll(".xlabels")
+ .attr("transform", function() {
+ return "translate(" + [t.x, 0.0] + ")";
+ })
+ .selectAll("text")
+ .each(function() {
+ d3.select(this).attr("x",
+ t.scale / old_scale * d3.select(this).attr("x"));
+ });
+ }
+
+ if (yscalable) {
+ root.selectAll(".xfixed")
+ .attr("transform", function() {
+ return "translate(" + [0.0, t.y] + ") " +
+ "scale(" + [1.0, t.scale] + ")";
+ });
+
+ root.selectAll(".ylabels")
+ .attr("transform", function() {
+ return "translate(" + [0.0, t.y] + ")";
+ })
+ .selectAll("text")
+ .each(function() {
+ d3.select(this).attr("y",
+ t.scale / old_scale * d3.select(this).attr("y"));
+ });
+ }
+};
+
+
+// Construct a callback used for zoombehavior.
+//
+// Args:
+// t: A transform of the form {"scale": scale} to close arround.
+//
+// Returns:
+// A zoom behavior.
+//
+var zoom_behavior = function(t) {
+ var zm = d3.behavior.zoom();
+ zm.scaleExtent([1.0/3.0, 10.0])
+ .on("zoom", function(d, i) {
+ var root = getplotroot(d3.select(this));
+ old_scale = t.scale;
+ t.scale = d3.event.scale;
+ var bbox = root.select(".guide.background")
+ .select("path").node().getBBox();
+
+ var x_min = -bbox.width * t.scale - (t.scale * bbox.width - bbox.width);
+ var x_max = bbox.width * t.scale;
+ var y_min = -bbox.height * t.scale - (t.scale * bbox.height - bbox.height);
+ var y_max = bbox.height * t.scale;
+
+ var x0 = bbox.x - t.scale * bbox.x;
+ var y0 = bbox.y - t.scale * bbox.y;
+
+ var tx = Math.max(Math.min(d3.event.translate[0] - x0, x_max), x_min);
+ var ty = Math.max(Math.min(d3.event.translate[1] - y0, y_max), y_min);
+
+ tx += x0;
+ ty += y0;
+
+ set_geometry_transform(
+ root,
+ {"x": tx,
+ "y": ty,
+ "scale": t.scale}, old_scale);
+ zm.translate([tx, ty]);
+ });
+ return zm;
+};
+
+
+</script>
+</div>
+
+</div>
+</div>
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stderr">
+<pre>
+Array{T,N},Date{C<:Calendar}...)
+is ambiguous with:
+ formatter(Array{T,N},FloatingPoint...).
+To fix, define
+ formatter(Array{T,N},)
+before the new definition.
+Warning: New definition
+ |(SynchronousStepCollection,Any) at /Users/kfischer/.julia/BinDeps/src/BinDeps.jl:283
+is ambiguous with:
+ |(Any,NAtype) at /Users/kfischer/.julia/DataFrames/src/operators.jl:385.
+To fix, define
+ |(SynchronousStepCollection,NAtype)
+before the new definition.
+Warning: New definition
+ |(Any,SynchronousStepCollection) at /Users/kfischer/.julia/BinDeps/src/BinDeps.jl:286
+is ambiguous with:
+ |(NAtype,Any) at /Users/kfischer/.julia/DataFrames/src/operators.jl:385.
+To fix, define
+ |(NAtype,SynchronousStepCollection)
+before the new definition.
+WARNING: BinDeps.find_library is deprecated, use Base.find_library instead.
+WARNING: add_library_mapping is deprecated, use push!(DL_LOAD_PATH,"/path/to/search") instead.
+Warning: New definition
+ +(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
+is ambiguous with:
+ +(DataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:201.
+To fix, define
+ +(DataArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N})
+before the new definition.
+Warning: New definition
+ +(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
+is ambiguous with:
+ +(AbstractDataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:220.
+To fix, define
+ +(AbstractDataArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N})
+before the new definition.
+Warning: New definition
+ +(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
+is ambiguous with:
+ +(AbstractArray{T,N},DataArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:201.
+To fix, define
+ +(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},DataArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N})
+before the new definition.
+Warning: New definition
+ +(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
+is ambiguous with:
+ +(AbstractArray{T,N},AbstractDataArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:220.
+To fix, define
+ +(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractDataArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N})
+before the new definition.
+Warning: New definition
+ -(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
+is ambiguous with:
+ -(DataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:201.
+To fix, define
+ -(DataArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N})
+before the new definition.
+Warning: New definition
+ -(AbstractArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N}) at operators.jl:253
+is ambiguous with:
+ -(AbstractDataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:220.
+To fix, define
+ -(AbstractDataArray{T1<:Union(AbstractCalendarDuration,CalendarTime),N},AbstractArray{T2<:Union(AbstractCalendarDuration,CalendarTime),N})
+before the new definition.
+Warning: New definition
+ *(Any,AbstractCalendarDuration) at /Users/kfischer/.julia/Calendar/src/Calendar.jl:341
+is ambiguous with:
+ *(MeasureNil,Any) at /Users/kfischer/.julia/Compose/src/measure.jl:32.
+To fix, define
+ *(MeasureNil,AbstractCalendarDuration)
+before the new definition.
+Warning: New definition
+ -(AbstractArray{T1<:CalendarTime,N},AbstractArray{T2<:CalendarTime,N}) at operators.jl:253
+is ambiguous with:
+ -(DataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:201.
+To fix, define
+ -(DataArray{T1<:CalendarTime,N},AbstractArray{T2<:CalendarTime,N})
+before the new definition.
+Warning: New definition
+ -(AbstractArray{T1<:CalendarTime,N},AbstractArray{T2<:CalendarTime,N}) at operators.jl:253
+is ambiguous with:
+ -(AbstractDataArray{T,N},AbstractArray{T,N}) at /Users/kfischer/.julia/DataFrames/src/operators.jl:220.
+To fix, define
+ -(AbstractDataArray{T1<:CalendarTime,N},AbstractArray{T2<:CalendarTime,N})
+before the new definition.
+
+</pre>
+</div>
+</div>
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[2]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+WWWClient
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+ </div><div style=display:none>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [3]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">function</span> <span class="n">DataFrames</span><span class="o">.</span><span class="n">to_io</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">URI</span><span class="p">)</span>
+ <span class="n">x</span> <span class="o">=</span> <span class="n">IOBuffer</span><span class="p">(</span><span class="n">WWWClient</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">data</span><span class="p">)</span>
+ <span class="n">x</span><span class="p">,</span><span class="n">nb_available</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+<span class="n">end</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[3]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+to_io (generic function with 2 methods)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+ </div></section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [3]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">benchmarks</span> <span class="o">=</span> <span class="n">readtable</span><span class="p">(</span><span class="n">URI</span><span class="p">(</span><span class="s">"http://julialang.org/benchmarks.csv"</span><span class="p">);</span><span class="n">header</span><span class="o">=</span><span class="n">false</span><span class="p">,</span><span class="n">colnames</span><span class="o">=</span><span class="p">[</span><span class="s">"Language"</span><span class="p">,</span><span class="s">"Benchmark"</span><span class="p">,</span><span class="s">"Time"</span><span class="p">])</span>
+<span class="n">benchmarks</span> <span class="o">=</span> <span class="n">join</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">,</span> <span class="n">subset</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">,</span> <span class="p">:(</span><span class="n">Language</span> <span class="o">.==</span> <span class="s">"c"</span><span class="p">)),</span>
+ <span class="n">on</span><span class="o">=</span><span class="s">"Benchmark"</span><span class="p">,</span> <span class="n">kind</span><span class="o">=</span><span class="p">:</span><span class="n">outer</span><span class="p">)</span>
+<span class="n">within</span><span class="err">!</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">,</span> <span class="p">:(</span><span class="n">Time</span> <span class="o">./=</span> <span class="n">Time_1</span><span class="p">));</span>
+</pre></div>
+
+</div>
+</div>
+
+</div><div style=display:none>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [3]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="c"># Some cosmetic adjustments. Not essential to the plot, so let's skip them for the sake of space</span>
+<span class="c"># Reorder factors</span>
+<span class="n">benchmarks</span><span class="p">[</span><span class="s">"Language"</span><span class="p">]</span> <span class="o">=</span> <span class="n">PooledDataArray</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">[</span><span class="s">"Language"</span><span class="p">])</span>
+<span class="n">benchmarks</span><span class="p">[</span><span class="s">"Language"</span><span class="p">]</span> <span class="o">=</span> <span class="n">reorder</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">[</span><span class="s">"Language"</span><span class="p">],</span> <span class="n">benchmarks</span><span class="p">[</span><span class="s">"Time"</span><span class="p">])</span>
+<span class="n">benchmarks</span><span class="p">[</span><span class="s">"Benchmark"</span><span class="p">]</span> <span class="o">=</span> <span class="n">PooledDataArray</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">[</span><span class="s">"Benchmark"</span><span class="p">])</span>
+<span class="n">benchmarks</span><span class="p">[</span><span class="s">"Benchmark"</span><span class="p">]</span> <span class="o">=</span> <span class="n">reorder</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">[</span><span class="s">"Benchmark"</span><span class="p">],</span> <span class="n">benchmarks</span><span class="p">[</span><span class="s">"Time"</span><span class="p">])</span>
+
+<span class="c"># Capitalize</span>
+<span class="n">capitalize</span><span class="p">(</span><span class="nb">str</span><span class="p">)</span> <span class="o">=</span> <span class="n">string</span><span class="p">(</span><span class="n">uppercase</span><span class="p">(</span><span class="nb">str</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="p">,</span> <span class="nb">str</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="n">end</span><span class="p">])</span>
+<span class="n">benchmarks</span><span class="p">[</span><span class="s">"Language"</span><span class="p">]</span> <span class="o">=</span> <span class="n">set_levels</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">[</span><span class="s">"Language"</span><span class="p">],</span>
+ <span class="n">Dict</span><span class="p">{</span><span class="n">Any</span><span class="p">,</span> <span class="n">Any</span><span class="p">}(</span><span class="n">benchmarks</span><span class="p">[</span><span class="s">"Language"</span><span class="p">],</span>
+ <span class="p">[</span><span class="n">capitalize</span><span class="p">(</span><span class="n">l</span><span class="p">)</span>
+ <span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="n">benchmarks</span><span class="p">[</span><span class="s">"Language"</span><span class="p">]]))</span>
+
+<span class="n">benchmarks</span> <span class="o">=</span> <span class="n">subset</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">,</span> <span class="p">:(</span><span class="n">Language</span> <span class="o">.!=</span> <span class="s">"C"</span><span class="p">))</span>
+
+<span class="n">set_default_plot_size</span><span class="p">(</span><span class="mi">8</span><span class="n">inch</span><span class="p">,</span><span class="mi">8</span><span class="n">inch</span><span class="o">/</span><span class="n">golden</span><span class="p">);</span>
+</pre></div>
+
+</div>
+</div>
+
+</div>
+ </div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [4]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">p</span> <span class="o">=</span> <span class="n">plot</span><span class="p">(</span><span class="n">benchmarks</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="s">"Language"</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="s">"Time"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s">"Benchmark"</span><span class="p">,</span> <span class="n">Scale</span><span class="o">.</span><span class="n">y_log10</span><span class="p">,</span>
+ <span class="n">Guide</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">"time relative to C"</span><span class="p">),</span> <span class="n">Guide</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">"smaller is better"</span><span class="p">))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_display_data">
+
+<div class="output_html rendered_html">
+<div id="gadflyplot-f3tBxMbrYQ18zjgrGj3T"></div>
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+ ["geometry color_fib","geometry color_fib","geometry color_fib","geometry color_fib","geometry color_fib","geometry color_fib","geometry color_fib","geometry color_fib","geometry color_fib","geometry color_mandel","geometry color_mandel","geometry color_mandel","geometry color_mandel","geometry color_mandel","geometry color_mandel","geometry color_mandel","geometry color_mandel","geometry color_mandel","geometry color_parse_int","geometry color_parse_int","geometry color_parse_int","geometry color_parse_int","geometry color_parse_int","geometry color_parse_int","geometry color_parse_int","geometry color_parse_int","geometry color_parse_int","geometry color_pi_sum","geometry color_pi_sum","geometry color_pi_sum","geometry color_pi_sum","geometry color_pi_sum","geometry color_pi_sum","geometry color_pi_sum","geometry color_pi_sum","geometry color_pi_sum","geometry color_printfd","geometry color_printfd","geometry color_printfd","geometry color_quicksort","geometry color_qui!
cksort","
geometry color_quicksort","geometry color_quicksort","geometry color_quicksort","geometry color_quicksort","geometry color_quicksort","geometry color_quicksort","geometry color_quicksort","geometry color_rand_mat_mul","geometry color_rand_mat_mul","geometry color_rand_mat_mul","geometry color_rand_mat_mul","geometry color_rand_mat_mul","geometry color_rand_mat_mul","geometry color_rand_mat_mul","geometry color_rand_mat_mul","geometry color_rand_mat_mul","geometry color_rand_mat_stat","geometry color_rand_mat_stat","geometry color_rand_mat_stat","geometry color_rand_mat_stat","geometry color_rand_mat_stat","geometry color_rand_mat_stat","geometry color_rand_mat_stat","geometry color_rand_mat_stat","geometry color_rand_mat_stat"],
+ ["#FF6765","#FF6765","#FF6765","#FF6765","#FF6765","#FF6765","#FF6765","#FF6765","#FF6765","#CA7EF6","#CA7EF6","#CA7EF6","#CA7EF6","#CA7EF6","#CA7EF6","#CA7EF6","#CA7EF6","#CA7EF6","#008B28","#008B28","#008B28","#008B28","#008B28","#008B28","#008B28","#008B28","#008B28","#DC2C7A","#DC2C7A","#DC2C7A","#DC2C7A","#DC2C7A","#DC2C7A","#DC2C7A","#DC2C7A","#DC2C7A","#00BA8B","#00BA8B","#00BA8B","#777777","#777777","#777777","#777777","#777777","#777777","#777777","#777777","#777777","#0096DD","#0096DD","#0096DD","#0096DD","#0096DD","#0096DD","#0096DD","#0096DD","#0096DD","#A8A200","#A8A200","#A8A200","#A8A200","#A8A200","#A8A200","#A8A200","#A8A200","#A8A200"],
+ ["#FF928B","#FF928B","#FF928B","#FF928B","#FF928B","#FF928B","#FF928B","#FF928B","#FF928B","#F6A6FF","#F6A6FF","#F6A6FF","#F6A6FF","#F6A6FF","#F6A6FF","#F6A6FF","#F6A6FF","#F6A6FF","#32B44E","#32B44E","#32B44E","#32B44E","#32B44E","#32B44E","#32B44E","#32B44E","#32B44E","#FF5EA0","#FF5EA0","#FF5EA0","#FF5EA0","#FF5EA0","#FF5EA0","#FF5EA0","#FF5EA0","#FF5EA0","#00E5B2","#00E5B2","#00E5B2","#9E9E9E","#9E9E9E","#9E9E9E","#9E9E9E","#9E9E9E","#9E9E9E","#9E9E9E","#9E9E9E","#9E9E9E","#00BFFF","#00BFFF","#00BFFF","#00BFFF","#00BFFF","#00BFFF","#00BFFF","#00BFFF","#00BFFF","#D4CA3A","#D4CA3A","#D4CA3A","#D4CA3A","#D4CA3A","#D4CA3A","#D4CA3A","#D4CA3A","#D4CA3A"]];
+
+var draw = function(parent_id) {
+ draw_with_data(data, parent_id);
+};
+
+draw("#gadflyplot-f3tBxMbrYQ18zjgrGj3T");
+</script>
+
+</div>
+
+</div>
+</div>
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[4]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+<div class="output_html rendered_html">
+
+</div>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div><aside class="notes">
+
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>Sure, but that's not the main point. So what is? What is different about Julia?</p>
+</div>
+ </aside></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="Dynamic-Multiple-Dispatch-Everywhere">Dynamic Multiple Dispatch Everywhere<a class="anchor-link" href="#Dynamic-Multiple-Dispatch-Everywhere">¶</a></h2>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [5]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">convert</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[5]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+convert (generic function with 464 methods)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [6]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="o">+</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[6]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
++ (generic function with 188 methods)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [7]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="nd">@which</span> <span class="n">convert</span><span class="p">(</span><span class="n">Float64</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="nd">@which</span> <span class="mf">1.0</span> <span class="o">+</span> <span class="mi">2</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stdout">
+<pre>
+convert(::Type{Float64},x::Int64) at float.jl:21
++(x::Number,y::Number) at promotion.jl:148
+
+</pre>
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="Basic-Dispatch">Basic Dispatch<a class="anchor-link" href="#Basic-Dispatch">¶</a></h2>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [8]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">f</span><span class="p">(</span><span class="n">a</span><span class="p">::</span><span class="n">Any</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">=</span> <span class="s">"fallback"</span>
+<span class="n">f</span><span class="p">(</span><span class="n">a</span><span class="p">::</span><span class="n">Number</span><span class="p">,</span> <span class="n">b</span><span class="p">::</span><span class="n">Number</span><span class="p">)</span> <span class="o">=</span> <span class="s">"a and b are both numbers"</span>
+<span class="n">f</span><span class="p">(</span><span class="n">a</span><span class="p">::</span><span class="n">Number</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">=</span> <span class="s">"a is a number"</span>
+<span class="n">f</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">::</span><span class="n">Number</span><span class="p">)</span> <span class="o">=</span> <span class="s">"b is a number"</span>
+<span class="n">f</span><span class="p">(</span><span class="n">a</span><span class="p">::</span><span class="n">Integer</span><span class="p">,</span> <span class="n">b</span><span class="p">::</span><span class="n">Integer</span><span class="p">)</span> <span class="o">=</span> <span class="s">"a and b are both integers"</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[8]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+f (generic function with 5 methods)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [9]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">f</span><span class="p">(</span><span class="mf">1.5</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[9]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+"a and b are both numbers"
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [10]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">f</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="s">"bar"</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[10]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+"a is a number"
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [11]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">f</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[11]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+"a and b are both integers"
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [12]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">f</span><span class="p">(</span><span class="s">"foo"</span><span class="p">,[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">])</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[12]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+"fallback"
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [13]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">methods</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[13]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+# 5 methods for generic function "f":
+f(a::Integer,b::Integer) at In[8]:5
+f(a::Number,b::Number) at In[8]:2
+f(a::Number,b) at In[8]:3
+f(a,b::Number) at In[8]:4
+f(a,b) at In[8]:1
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="Diagonal-Dispatch/Parametric-Dispatch">Diagonal Dispatch/Parametric Dispatch<a class="anchor-link" href="#Diagonal-Dispatch/Parametric-Dispatch">¶</a></h3>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [14]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">f</span><span class="p">{</span><span class="n">T</span><span class="o"><</span><span class="p">:</span><span class="n">Number</span><span class="p">}(</span><span class="n">a</span><span class="p">::</span><span class="n">T</span><span class="p">,</span> <span class="n">b</span><span class="p">::</span><span class="n">T</span><span class="p">)</span> <span class="o">=</span> <span class="s">"a and b are both $(T)s"</span>
+<span class="n">f</span><span class="p">{</span><span class="n">T</span><span class="o"><</span><span class="p">:</span><span class="n">Number</span><span class="p">}(</span><span class="n">a</span><span class="p">::</span><span class="n">Vector</span><span class="p">{</span><span class="n">T</span><span class="p">},</span> <span class="n">b</span><span class="p">::</span><span class="n">Vector</span><span class="p">{</span><span class="n">T</span><span class="p">})</span> <span class="o">=</span> <span class="s">"a and b are both vectors of $(T)s"</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[14]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+f (generic function with 7 methods)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [15]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">f</span><span class="p">(</span><span class="n">big</span><span class="p">(</span><span class="mf">1.5</span><span class="p">),</span><span class="n">big</span><span class="p">(</span><span class="mf">1.0</span><span class="p">))</span> <span class="c">#Two BigFloats</span>
+<span class="n">f</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span><span class="mf">2.0</span><span class="p">],[</span><span class="mf">3.0</span><span class="p">,</span><span class="mf">4.0</span><span class="p">])</span> <span class="c">#Two Array{Float64,1}</span>
+<span class="n">f</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">],[</span><span class="mf">3.</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span> <span class="c">#One Array{Int64,1} & One Array{Float64,1}</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[15]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+"fallback"
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [16]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">f</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="c">#Still more specific</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[16]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+"a and b are both integers"
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="That's-nice,-but-what-does-this-have-to-do-with-speed?">That's nice, but what does this have to do with speed?<a class="anchor-link" href="#That's-nice,-but-what-does-this-have-to-do-with-speed?">¶</a></h3>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [17]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="kn">import</span> <span class="nn">Base.LinAlg.det</span>
+<span class="n">function</span> <span class="n">det</span><span class="p">{</span><span class="n">T</span><span class="p">}(</span><span class="n">A</span><span class="p">::</span><span class="n">AbstractArray</span><span class="p">{</span><span class="n">T</span><span class="p">,</span><span class="mi">2</span><span class="p">})</span>
+ <span class="n">n</span> <span class="o">=</span> <span class="n">size</span><span class="p">(</span><span class="n">A</span><span class="p">)[</span><span class="mi">1</span><span class="p">]</span>
+ <span class="n">n</span> <span class="o">==</span> <span class="n">size</span><span class="p">(</span><span class="n">A</span><span class="p">)[</span><span class="mi">2</span><span class="p">]</span> <span class="o">||</span> <span class="n">error</span><span class="p">(</span><span class="s">"Only square matrices allowed"</span><span class="p">)</span>
+ <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span> <span class="o">&&</span> <span class="k">return</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span><span class="o">*</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span>
+ <span class="n">s</span> <span class="o">=</span> <span class="n">zero</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="o">=</span> <span class="mi">1</span><span class="p">:</span><span class="n">n</span>
+ <span class="n">s</span> <span class="o">+=</span> <span class="p">(</span><span class="o">-</span><span class="n">one</span><span class="p">(</span><span class="n">T</span><span class="p">))</span><span class="o">^</span><span class="p">(</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">A</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="n">i</span><span class="p">]</span><span class="o">*</span><span class="p">(</span><span class="n">det</span><span class="p">(</span><span class="n">hcat</span><span class="p">(</span><span class="n">A</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="n">end</span><span class="p">,</span><span class="mi">1</span><span class="p">:(</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">)],</span><span class="n">A</span!
><span cl
ass="p">[</span><span class="mi">2</span><span class="p">:</span><span class="n">end</span><span class="p">,(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span><span class="n">end</span><span class="p">])))</span>
+ <span class="n">end</span>
+ <span class="n">s</span>
+<span class="n">end</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[17]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+det (generic function with 17 methods)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [18]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">methods</span><span class="p">(</span><span class="n">det</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[18]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+# 17 methods for generic function "det":
+det(A::Triangular{T<:Number}) at linalg/triangular.jl:63
+det(W::Woodbury{T}) at linalg/woodbury.jl:84
+det(A::Tridiagonal{T}) at linalg/tridiag.jl:357
+det(D::Diagonal{T}) at linalg/diagonal.jl:80
+det{T<:Union(Float32,Complex{Float64},Complex{Float32},Float64)}(A::AbstractArray{T<:Union(Float32,Complex{Float64},Complex{Float32},Float64),2}) at linalg/dense.jl:416
+det(x::Number) at linalg/dense.jl:419
+det{T}(C::Cholesky{T}) at linalg/factorization.jl:44
+det{T}(C::CholeskyPivoted{T}) at linalg/factorization.jl:122
+det{T}(A::LU{T}) at linalg/factorization.jl:186
+det(A::Eigen{T,V}) at linalg/factorization.jl:533
+det{T}(lu::LUTridiagonal{T}) at linalg/tridiag.jl:353
+det{Tv<:Float64,Ti<:Int32}(lu::UmfpackLU{Tv<:Float64,Ti<:Int32}) at linalg/umfpack.jl:189
+det{Tv<:Complex{Float64},Ti<:Int32}(lu::UmfpackLU{Tv<:Complex{Float64},Ti<:Int32}) at linalg/umfpack.jl:197
+det{Tv<:Float64,Ti<:Int64}(lu::UmfpackLU{Tv<:Float64,Ti<:Int64}) at linalg/umfpack.jl:189
+det{Tv<:Complex{Float64},Ti<:Int64}(lu::UmfpackLU{Tv<:Complex{Float64},Ti<:Int64}) at linalg/umfpack.jl:197
+det(L::CholmodFactor{Tv<:Union(Float32,Complex{Float64},Complex{Float32},Float64),Ti<:Union(Int64,Int32)}) at linalg/cholmod.jl:1039
+det{T}(A::AbstractArray{T,2}) at In[17]:3
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="But-what-about-numbers??">But what about numbers??<a class="anchor-link" href="#But-what-about-numbers??">¶</a></h3>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [19]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="c"># This code is taken 1:1 from boot.jl</span>
+<span class="n">baremodule</span> <span class="n">FakeMain</span>
+<span class="n">abstract</span> <span class="n">Number</span>
+<span class="n">abstract</span> <span class="n">Real</span> <span class="o"><</span><span class="p">:</span> <span class="n">Number</span>
+<span class="n">abstract</span> <span class="n">FloatingPoint</span> <span class="o"><</span><span class="p">:</span> <span class="n">Real</span>
+<span class="n">abstract</span> <span class="n">Integer</span> <span class="o"><</span><span class="p">:</span> <span class="n">Real</span>
+<span class="n">abstract</span> <span class="n">Signed</span> <span class="o"><</span><span class="p">:</span> <span class="n">Integer</span>
+<span class="n">abstract</span> <span class="n">Unsigned</span> <span class="o"><</span><span class="p">:</span> <span class="n">Integer</span>
+
+<span class="n">bitstype</span> <span class="mi">16</span> <span class="n">Float16</span> <span class="o"><</span><span class="p">:</span> <span class="n">FloatingPoint</span>
+<span class="n">bitstype</span> <span class="mi">32</span> <span class="n">Float32</span> <span class="o"><</span><span class="p">:</span> <span class="n">FloatingPoint</span>
+<span class="n">bitstype</span> <span class="mi">64</span> <span class="n">Float64</span> <span class="o"><</span><span class="p">:</span> <span class="n">FloatingPoint</span>
+
+<span class="n">bitstype</span> <span class="mi">8</span> <span class="n">Bool</span> <span class="o"><</span><span class="p">:</span> <span class="n">Integer</span>
+<span class="n">bitstype</span> <span class="mi">32</span> <span class="n">Char</span> <span class="o"><</span><span class="p">:</span> <span class="n">Integer</span>
+
+<span class="n">bitstype</span> <span class="mi">8</span> <span class="n">Int8</span> <span class="o"><</span><span class="p">:</span> <span class="n">Signed</span>
+<span class="n">bitstype</span> <span class="mi">8</span> <span class="n">Uint8</span> <span class="o"><</span><span class="p">:</span> <span class="n">Unsigned</span>
+<span class="n">bitstype</span> <span class="mi">16</span> <span class="n">Int16</span> <span class="o"><</span><span class="p">:</span> <span class="n">Signed</span>
+<span class="n">bitstype</span> <span class="mi">16</span> <span class="n">Uint16</span> <span class="o"><</span><span class="p">:</span> <span class="n">Unsigned</span>
+<span class="n">bitstype</span> <span class="mi">32</span> <span class="n">Int32</span> <span class="o"><</span><span class="p">:</span> <span class="n">Signed</span>
+<span class="n">bitstype</span> <span class="mi">32</span> <span class="n">Uint32</span> <span class="o"><</span><span class="p">:</span> <span class="n">Unsigned</span>
+<span class="n">bitstype</span> <span class="mi">64</span> <span class="n">Int64</span> <span class="o"><</span><span class="p">:</span> <span class="n">Signed</span>
+<span class="n">bitstype</span> <span class="mi">64</span> <span class="n">Uint64</span> <span class="o"><</span><span class="p">:</span> <span class="n">Unsigned</span>
+<span class="n">bitstype</span> <span class="mi">128</span> <span class="n">Int128</span> <span class="o"><</span><span class="p">:</span> <span class="n">Signed</span>
+<span class="n">bitstype</span> <span class="mi">128</span> <span class="n">Uint128</span> <span class="o"><</span><span class="p">:</span> <span class="n">Unsigned</span>
+<span class="n">end</span>
+</pre></div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="The-promotion-system">The promotion system<a class="anchor-link" href="#The-promotion-system">¶</a></h3>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [20]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="o">+</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Number</span><span class="p">,</span> <span class="n">y</span><span class="p">::</span><span class="n">Number</span><span class="p">)</span> <span class="o">=</span> <span class="o">+</span><span class="p">(</span><span class="n">promote</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span><span class="o">...</span><span class="p">)</span>
+<span class="o">*</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Number</span><span class="p">,</span> <span class="n">y</span><span class="p">::</span><span class="n">Number</span><span class="p">)</span> <span class="o">=</span> <span class="o">*</span><span class="p">(</span><span class="n">promote</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span><span class="o">...</span><span class="p">)</span>
+<span class="o">-</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Number</span><span class="p">,</span> <span class="n">y</span><span class="p">::</span><span class="n">Number</span><span class="p">)</span> <span class="o">=</span> <span class="o">-</span><span class="p">(</span><span class="n">promote</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span><span class="o">...</span><span class="p">)</span>
+<span class="o">/</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Number</span><span class="p">,</span> <span class="n">y</span><span class="p">::</span><span class="n">Number</span><span class="p">)</span> <span class="o">=</span> <span class="o">/</span><span class="p">(</span><span class="n">promote</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span><span class="o">...</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stderr">
+<pre>
+Warning: Method definition +(Number,Number) in module Base at promotion.jl:148 overwritten in module Main at In[20]:1.
+Warning: Method definition *(Number,Number) in module Base at promotion.jl:149 overwritten in module Main at In[20]:2.
+Warning: Method definition -(Number,Number) in module Base at promotion.jl:150 overwritten in module Main at In[20]:3.
+Warning: Method definition /(Number,Number)
+</pre>
+</div>
+</div>
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[20]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+/ (generic function with 79 methods)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [21]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">baremodule</span> <span class="n">FakeBase</span>
+
+<span class="n">promote_type</span><span class="p">{</span><span class="n">T</span><span class="p">,</span><span class="n">S</span><span class="p">}(::</span><span class="n">Type</span><span class="p">{</span><span class="n">T</span><span class="p">},</span> <span class="p">::</span><span class="n">Type</span><span class="p">{</span><span class="n">S</span><span class="p">})</span> <span class="o">=</span>
+ <span class="n">promote_result</span><span class="p">(</span><span class="n">T</span><span class="p">,</span> <span class="n">S</span><span class="p">,</span> <span class="n">promote_rule</span><span class="p">(</span><span class="n">T</span><span class="p">,</span><span class="n">S</span><span class="p">),</span> <span class="n">promote_rule</span><span class="p">(</span><span class="n">S</span><span class="p">,</span><span class="n">T</span><span class="p">))</span>
+
+<span class="n">promote_rule</span><span class="p">(</span><span class="n">T</span><span class="p">,</span> <span class="n">S</span><span class="p">)</span> <span class="o">=</span> <span class="bp">None</span>
+
+<span class="n">promote_result</span><span class="p">(</span><span class="n">t</span><span class="p">,</span><span class="n">s</span><span class="p">,</span><span class="n">T</span><span class="p">,</span><span class="n">S</span><span class="p">)</span> <span class="o">=</span> <span class="n">typejoin</span><span class="p">(</span><span class="n">T</span><span class="p">,</span><span class="n">S</span><span class="p">)</span>
+<span class="c"># If no promote_rule is defined, both directions give None. In that</span>
+<span class="c"># case use typejoin on the original types instead.</span>
+<span class="n">promote_result</span><span class="p">{</span><span class="n">T</span><span class="p">,</span><span class="n">S</span><span class="p">}(::</span><span class="n">Type</span><span class="p">{</span><span class="n">T</span><span class="p">},::</span><span class="n">Type</span><span class="p">{</span><span class="n">S</span><span class="p">},::</span><span class="n">Type</span><span class="p">{</span><span class="bp">None</span><span class="p">},::</span><span class="n">Type</span><span class="p">{</span><span class="bp">None</span><span class="p">})</span> <span class="o">=</span> <span class="n">typejoin</span><span class="p">(</span><span class="n">T</span><span class="p">,</span> <span class="n">S</span><span class="p">)</span>
+
+<span class="n">end</span>
+</pre></div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="Example:-Modular-Integers">Example: Modular Integers<a class="anchor-link" href="#Example:-Modular-Integers">¶</a></h3>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [22]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">module</span> <span class="n">ModInts</span>
+<span class="n">export</span> <span class="n">ModInt</span>
+<span class="kn">import</span> <span class="nn">Base</span><span class="p">:</span> <span class="o">-</span><span class="p">,</span> <span class="o">+</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">convert</span><span class="p">,</span> <span class="n">promote_rule</span><span class="p">,</span> <span class="n">show</span><span class="p">,</span> <span class="n">showcompact</span>
+
+<span class="n">immutable</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}</span> <span class="o"><</span><span class="p">:</span> <span class="n">Integer</span>
+ <span class="n">k</span><span class="p">::</span><span class="n">Int</span>
+ <span class="n">ModInt</span><span class="p">(</span><span class="n">k</span><span class="p">)</span> <span class="o">=</span> <span class="n">new</span><span class="p">(</span><span class="n">k</span> <span class="o">%</span> <span class="n">n</span><span class="p">)</span>
+<span class="n">end</span>
+
+<span class="o">-</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">})</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="o">-</span><span class="n">a</span><span class="o">.</span><span class="n">k</span><span class="p">)</span>
+<span class="o">+</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">},</span> <span class="n">b</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">})</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="o">.</span><span class="n">k</span><span class="o">+</span><span class="n">b</span><span class="o">.</span><span class="n">k</span><span class="p">)</span>
+<span class="o">-</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">},</span> <span class="n">b</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">})</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="o">.</span><span class="n">k</span><span class="o">-</span><span class="n">b</span><span class="o">.</span><span class="n">k</span><span class="p">)</span>
+<span class="o">*</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">},</span> <span class="n">b</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">})</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">a</span><span class="o">.</span><span class="n">k</span><span class="o">*</span><span class="n">b</span><span class="o">.</span><span class="n">k</span><span class="p">)</span>
+
+<span class="n">convert</span><span class="p">{</span><span class="n">n</span><span class="p">}(::</span><span class="n">Type</span><span class="p">{</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}},</span> <span class="n">i</span><span class="p">::</span><span class="n">Int</span><span class="p">)</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">i</span><span class="p">)</span>
+<span class="n">promote_rule</span><span class="p">{</span><span class="n">n</span><span class="p">}(::</span><span class="n">Type</span><span class="p">{</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}},</span> <span class="p">::</span><span class="n">Type</span><span class="p">{</span><span class="n">Int</span><span class="p">})</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">}</span>
+
+<span class="n">show</span><span class="p">{</span><span class="n">n</span><span class="p">}(</span><span class="n">io</span><span class="p">::</span><span class="n">IO</span><span class="p">,</span> <span class="n">k</span><span class="p">::</span><span class="n">ModInt</span><span class="p">{</span><span class="n">n</span><span class="p">})</span> <span class="o">=</span> <span class="k">print</span><span class="p">(</span><span class="n">io</span><span class="p">,</span> <span class="s">"$(k.k) mod $n"</span><span class="p">)</span>
+<span class="n">showcompact</span><span class="p">(</span><span class="n">io</span><span class="p">::</span><span class="n">IO</span><span class="p">,</span> <span class="n">k</span><span class="p">::</span><span class="n">ModInt</span><span class="p">)</span> <span class="o">=</span> <span class="k">print</span><span class="p">(</span><span class="n">io</span><span class="p">,</span> <span class="n">k</span><span class="o">.</span><span class="n">k</span><span class="p">)</span>
+
+<span class="n">end</span> <span class="c"># module</span>
+
+<span class="n">using</span> <span class="n">ModInts</span>
+</pre></div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [23]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">a</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}(</span><span class="mi">11119</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[23]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+9 mod 11
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [24]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">b</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}(</span><span class="mi">12345</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[24]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+3 mod 11
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [25]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">a</span><span class="o">+</span><span class="n">b</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[25]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+1 mod 11
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [26]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">a</span><span class="o">*</span><span class="n">b</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[26]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+5 mod 11
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [27]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">n</span> <span class="o">=</span> <span class="mi">8</span>
+<span class="n">A</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">},</span> <span class="n">rand</span><span class="p">(</span><span class="mi">1</span><span class="p">:</span><span class="mi">100</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">n</span><span class="p">))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[27]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+8x8 Array{ModInt{11},2}:
+ 10 1 1 3 1 9 7 0
+ 2 4 9 3 4 3 10 4
+ 4 0 0 0 10 1 10 1
+ 10 9 5 7 2 5 7 0
+ 6 2 10 0 9 4 10 4
+ 0 9 6 2 3 4 1 2
+ 8 6 10 10 1 7 4 5
+ 9 0 7 1 5 4 1 10
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [28]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">A</span><span class="o">^</span><span class="mi">2</span> <span class="o">+</span> <span class="n">A</span> <span class="o">+</span> <span class="mi">4</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[28]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+8x8 Array{ModInt{11},2}:
+ 3 6 8 6 1 2 4 0
+ 9 5 10 2 10 10 2 2
+ 10 9 1 9 5 5 8 8
+ 4 4 2 10 2 1 4 10
+ 9 2 5 8 8 7 6 6
+ 0 5 3 1 3 6 0 5
+ 8 1 0 9 7 10 2 10
+ 5 8 3 1 0 8 4 0
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="Cailey-Hamilton">Cailey-Hamilton<a class="anchor-link" href="#Cailey-Hamilton">¶</a></h3>
+</div>
+
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>Theorem: Every Matrix satisfies its own characteristic polynomial.</p>
+<p>Let's Check</p>
+</div><div style=display:none>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [29]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">using</span> <span class="n">Polynomial</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stderr">
+<pre>
+ in module Base at promotion.jl:151 overwritten in module Main at In[20]:4.
+Warning: New definition
+ promote_rule(Type{Poly{T}},Type{T}) at /Users/kfischer/.julia/Polynomial/src/Polynomial.jl:19
+is ambiguous with:
+ promote_rule(Type{T},Type{NAtype}) at /Users/kfischer/.julia/DataFrames/src/natype.jl:32.
+To fix, define
+ promote_rule(Type{Poly{T}},Type{NAtype})
+</pre>
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+ </div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [30]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">using</span> <span class="n">Polynomial</span>
+<span class="err">λ</span> <span class="o">=</span> <span class="n">Poly</span><span class="p">(</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span>
+<span class="n">p</span><span class="o">=</span><span class="n">det</span><span class="p">(</span><span class="n">A</span><span class="o">-</span><span class="nb">map</span><span class="p">(</span><span class="n">x</span><span class="o">-></span><span class="err">λ</span><span class="o">*</span><span class="n">x</span><span class="p">,</span><span class="n">eye</span><span class="p">(</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">},</span><span class="n">n</span><span class="p">,</span><span class="n">n</span><span class="p">)))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[30]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+Poly(-7 mod 11 + 10 mod 11x^2 + -1 mod 11x^3 + -7 mod 11x^4 + 9 mod 11x^5 + -8 mod 11x^6 + -4 mod 11x^7 + x^8)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [31]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">papply</span><span class="p">(</span><span class="n">p</span><span class="p">,</span><span class="n">A</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[31]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+8x8 Array{ModInt{11},2}:
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+ 0 0 0 0 0 0 0 0
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section><section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="Or-with-Smileys">Or with Smileys<a class="anchor-link" href="#Or-with-Smileys">¶</a></h3>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [32]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="kn">import</span> <span class="nn">Base</span><span class="p">:</span> <span class="n">promote_rule</span><span class="p">,</span> <span class="n">convert</span><span class="p">,</span> <span class="n">show</span><span class="p">,</span> <span class="n">one</span><span class="p">,</span> <span class="n">zero</span>
+<span class="n">immutable</span> <span class="n">Face</span> <span class="o"><</span><span class="p">:</span> <span class="n">Number</span>
+ <span class="n">v</span><span class="p">::</span><span class="n">Bool</span>
+<span class="n">end</span>
+<span class="o">+</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Face</span><span class="p">,</span><span class="n">y</span><span class="p">::</span><span class="n">Face</span><span class="p">)</span> <span class="o">=</span> <span class="n">Face</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">v</span><span class="err">$</span><span class="n">y</span><span class="o">.</span><span class="n">v</span><span class="p">)</span>
+<span class="o">*</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Face</span><span class="p">,</span><span class="n">y</span><span class="p">::</span><span class="n">Face</span><span class="p">)</span> <span class="o">=</span> <span class="n">Face</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">v</span><span class="o">&</span><span class="n">y</span><span class="o">.</span><span class="n">v</span><span class="p">)</span>
+<span class="o">-</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Face</span><span class="p">,</span><span class="n">y</span><span class="p">::</span><span class="n">Face</span><span class="p">)</span> <span class="o">=</span> <span class="n">x</span><span class="o">+</span><span class="n">y</span>
+<span class="o">-</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">Face</span><span class="p">)</span> <span class="o">=</span> <span class="n">x</span>
+<span class="n">one</span><span class="p">(::</span><span class="n">Type</span><span class="p">{</span><span class="n">Face</span><span class="p">})</span> <span class="o">=</span> <span class="err">âº</span>
+<span class="n">zero</span><span class="p">(::</span><span class="n">Type</span><span class="p">{</span><span class="n">Face</span><span class="p">})</span> <span class="o">=</span> <span class="err">â¹</span>
+<span class="n">Base</span><span class="o">.</span><span class="n">show</span><span class="p">(</span><span class="n">io</span><span class="p">::</span><span class="n">IO</span><span class="p">,</span><span class="n">f</span><span class="p">::</span><span class="n">Face</span><span class="p">)</span> <span class="o">=</span> <span class="k">print</span><span class="p">(</span><span class="n">io</span><span class="p">,</span><span class="n">f</span><span class="o">.</span><span class="n">v</span><span class="err">?</span><span class="s">'âº'</span><span class="p">:</span><span class="s">'â¹'</span><span class="p">)</span>
+<span class="n">Base</span><span class="o">.</span><span class="n">convert</span><span class="p">(::</span><span class="n">Type</span><span class="p">{</span><span class="n">Face</span><span class="p">},</span><span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="n">Face</span><span class="p">(</span><span class="n">convert</span><span class="p">(</span><span class="n">Bool</span><span class="p">,</span><span class="n">x</span><span class="p">))</span>
+<span class="n">Base</span><span class="o">.</span><span class="n">convert</span><span class="p">(::</span><span class="n">Type</span><span class="p">{</span><span class="n">Bool</span><span class="p">},</span><span class="n">x</span><span class="p">::</span><span class="n">Face</span><span class="p">)</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">v</span>
+<span class="n">const</span> <span class="err">âº</span> <span class="o">=</span> <span class="n">Face</span><span class="p">(</span><span class="n">true</span><span class="p">)</span>
+<span class="n">const</span> <span class="err">â¹</span> <span class="o">=</span> <span class="n">Face</span><span class="p">(</span><span class="n">false</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[32]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+â¹
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [33]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">n</span><span class="o">=</span><span class="mi">8</span>
+<span class="n">A</span><span class="o">=</span><span class="nb">map</span><span class="p">(</span><span class="n">Face</span><span class="p">,</span><span class="n">randbool</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">n</span><span class="p">))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[33]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+8x8 Array{Face,2}:
+ ⹠⹠⹠⹠⹠⺠⹠â¹
+ ⺠⺠⹠⹠⹠⺠⺠â¹
+ â¹ â¹ â¹ â¹ â¹ â¹ â¹ â¹
+ ⺠⹠⹠⹠⺠⺠⹠âº
+ ⹠⹠⺠⺠⹠⹠⹠âº
+ ⺠⺠⺠⺠⺠⹠⹠âº
+ ⹠⺠⹠⺠⹠⹠⺠âº
+ ⺠⺠⺠⹠⹠⹠⹠âº
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [34]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">using</span> <span class="n">Polynomial</span>
+<span class="err">λ</span> <span class="o">=</span> <span class="n">Poly</span><span class="p">([</span><span class="err">â¹</span><span class="p">,</span><span class="err">âº</span><span class="p">])</span>
+<span class="err">λ</span><span class="n">I</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">x</span><span class="o">-></span><span class="err">λ</span><span class="o">*</span><span class="n">x</span><span class="p">,</span><span class="n">eye</span><span class="p">(</span><span class="n">Face</span><span class="p">,</span><span class="n">n</span><span class="p">,</span><span class="n">n</span><span class="p">))</span>
+<span class="n">p</span><span class="o">=</span><span class="n">det</span><span class="p">(</span><span class="n">A</span><span class="o">-</span><span class="err">λ</span><span class="n">I</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[34]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+Poly(x^3 + x^5 + x^7 + x^8)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [35]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">papply</span><span class="p">(</span><span class="n">p</span><span class="p">,</span><span class="n">A</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[35]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+8x8 Array{Face,2}:
+ â¹ â¹ â¹ â¹ â¹ â¹ â¹ â¹
+ â¹ â¹ â¹ â¹ â¹ â¹ â¹ â¹
+ â¹ â¹ â¹ â¹ â¹ â¹ â¹ â¹
+ â¹ â¹ â¹ â¹ â¹ â¹ â¹ â¹
+ â¹ â¹ â¹ â¹ â¹ â¹ â¹ â¹
+ â¹ â¹ â¹ â¹ â¹ â¹ â¹ â¹
+ â¹ â¹ â¹ â¹ â¹ â¹ â¹ â¹
+ â¹ â¹ â¹ â¹ â¹ â¹ â¹ â¹
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h1 id="How-does-it-work?">How does it work?<a class="anchor-link" href="#How-does-it-work?">¶</a></h1>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [36]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">a</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}(</span><span class="mi">11119</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[36]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+9 mod 11
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [37]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">b</span> <span class="o">=</span> <span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}(</span><span class="mi">12345</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[37]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+3 mod 11
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [38]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">a</span><span class="o">+</span><span class="n">b</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[38]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+1 mod 11
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [39]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">code_llvm</span><span class="p">(</span><span class="o">+</span><span class="p">,(</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">},</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stderr">
+<pre>
+
+before the new definition.
+
+</pre>
+</div>
+</div>
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stdout">
+<pre>
+
+; Function Attrs: sspreq
+define %ModInt @"julia_+6067"(%ModInt, %ModInt) #2 {
+top:
+ %2 = extractvalue %ModInt %0, 0, !dbg !27934
+ %3 = extractvalue %ModInt %1, 0, !dbg !27934
+ %4 = add i64 %3, %2, !dbg !27934
+ %5 = srem i64 %4, 11, !dbg !27934
+ %6 = insertvalue %ModInt undef, i64 %5, 0, !dbg !27934, !julia_type !27939
+ ret %ModInt %6, !dbg !27934
+}
+
+</pre>
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section><section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [40]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">code_native</span><span class="p">(</span><span class="o">+</span><span class="p">,</span> <span class="p">(</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">},</span><span class="n">ModInt</span><span class="p">{</span><span class="mi">11</span><span class="p">}))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stdout">
+<pre>
+ .section __TEXT,__text,regular,pure_instructions
+Filename: In[22]
+Source line: 11
+ push rbp
+ mov rbp, rsp
+ sub rsp, 16
+ mov rcx, rdi
+Source line: 11
+ movabs rdi, 4348774360
+ mov rax, qword ptr [rdi]
+ mov qword ptr [rbp - 8], rax
+ add rcx, rsi
+ movabs rdx, 3353953467947191203
+ mov rax, rcx
+ imul rdx
+ mov rax, qword ptr [rdi]
+ cmp rax, qword ptr [rbp - 8]
+ jne 29
+ mov rax, rdx
+ shr rax, 63
+ sar rdx
+ add rdx, rax
+ imul rax, rdx, 11
+ sub rcx, rax
+ mov rax, rcx
+ add rsp, 16
+ pop rbp
+ ret
+ movabs rax, 140735631254601
+ call rax
+
+</pre>
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="Parsing">Parsing<a class="anchor-link" href="#Parsing">¶</a></h3>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [41]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">poly</span> <span class="o">=</span> <span class="p">:(</span><span class="n">A</span><span class="o">^</span><span class="mi">3</span><span class="o">+</span><span class="mi">2</span><span class="n">A</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[41]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+:(-(+(^(A,3),*(2,A)),1))
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [42]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">ex</span> <span class="o">=</span> <span class="p">:(</span><span class="n">evaluate_a_polynomial</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="err">$</span><span class="n">poly</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[42]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+:(evaluate_a_polynomial(A) = -(+(^(A,3),*(2,A)),1))
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [43]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">dump</span><span class="p">(</span><span class="n">ex</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stdout">
+<pre>
+Expr
+ head: Symbol =
+ args: Array(Any,(2,))
+ 1: Expr
+ head: Symbol call
+ args: Array(Any,(2,))
+ 1: Symbol evaluate_a_polynomial
+ 2: Symbol A
+ typ: Any
+ 2: Expr
+ head: Symbol call
+ args: Array(Any,(3,))
+ 1: Symbol -
+ 2: Expr
+ head: Symbol call
+ args: Array(Any,(3,))
+ typ: Any
+ 3: Int64 1
+ typ: Any
+ typ: Any
+
+</pre>
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [44]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="nb">eval</span><span class="p">(</span><span class="n">ex</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[44]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+evaluate_a_polynomial (generic function with 1 method)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [45]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">evaluate_a_polynomial</span> <span class="o">|></span> <span class="n">methods</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[45]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+# 1 method for generic function "evaluate_a_polynomial":
+evaluate_a_polynomial(A)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [46]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">typeof</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[46]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+Array{Face,2}
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [47]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">typeof</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[47]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+ModInt{11} (constructor with 1 method)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [48]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">code_lowered</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">A</span><span class="p">),))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[48]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+1-element Array{Any,1}:
+ :($(Expr(:lambda, {:A}, {{},{{:A,:Any,0}},{}}, quote
+ return -(+(^(A,3),*(2,A)),1)
+ end)))
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [49]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">code_lowered</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">a</span><span class="p">),))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[49]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+1-element Array{Any,1}:
+ :($(Expr(:lambda, {:A}, {{},{{:A,:Any,0}},{}}, quote
+ return -(+(^(A,3),*(2,A)),1)
+ end)))
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="So-if-there's-no-difference,-why-pass-in-the-type?">So if there's no difference, why pass in the type?<a class="anchor-link" href="#So-if-there's-no-difference,-why-pass-in-the-type?">¶</a></h2>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [50]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">evaluate_a_polynomial</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">typeof</span><span class="p">(</span><span class="n">a</span><span class="p">))</span> <span class="o">=</span> <span class="mi">14</span><span class="n">x</span><span class="o">^</span><span class="mi">6</span><span class="o">+</span><span class="mi">3</span><span class="n">x</span><span class="o">^</span><span class="mi">2</span><span class="o">+</span><span class="mi">2</span><span class="n">x</span><span class="o">+</span><span class="mi">3</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[50]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+evaluate_a_polynomial (generic function with 2 methods)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [51]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">code_lowered</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">a</span><span class="p">),))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[51]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+1-element Array{Any,1}:
+ :($(Expr(:lambda, {:x}, {{},{{:x,:Any,0}},{}}, quote # In[50], line 1:
+ return +(*(14,^(x,6)),*(3,^(x,2)),*(2,x),3)
+ end)))
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [52]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">function</span> <span class="n">a_more_complicated_function</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
+ <span class="k">if</span> <span class="nb">sum</span><span class="p">(</span><span class="nb">sum</span><span class="p">(</span><span class="n">A</span><span class="p">))</span> <span class="o">></span> <span class="mi">0</span>
+ <span class="k">return</span> <span class="p">:</span><span class="n">ok</span>
+ <span class="k">else</span>
+ <span class="k">return</span> <span class="mi">0</span>
+ <span class="n">end</span>
+<span class="n">end</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[52]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+a_more_complicated_function (generic function with 1 method)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [53]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">code_lowered</span><span class="p">(</span><span class="n">a_more_complicated_function</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">A</span><span class="p">),))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[53]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+1-element Array{Any,1}:
+ :($(Expr(:lambda, {:A}, {{},{{:A,:Any,0}},{}}, quote # In[52], line 2:
+ unless >(sum(sum(A)),0) goto 0 # line 3:
+ return :ok
+ goto 1
+ 0: # In[52], line 5:
+ return 0
+ 1:
+ end)))
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h1 id="Type-inference">Type inference<a class="anchor-link" href="#Type-inference">¶</a></h1>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [54]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">code_typed</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">A</span><span class="p">),))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[54]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+1-element Array{Any,1}:
+ :($(Expr(:lambda, {:A}, {{},{{:A,Array{Face,2},0}},{}}, quote
+ return -(+(^(A::Array{Face,2},3)::Array{Face,2},.*(2,A::Array{Face,2})::None)::None,1)::None
+ end)))
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [55]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">foo</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="n">a_more_complicated_function</span><span class="p">(</span><span class="n">det</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">(</span><span class="n">A</span><span class="p">)))</span>
+<span class="n">code_typed</span><span class="p">(</span><span class="n">foo</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">A</span><span class="p">),))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[55]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+1-element Array{Any,1}:
+ :($(Expr(:lambda, {:A}, {{},{{:A,Array{Face,2},0}},{}}, quote # In[55], line 1:
+ return a_more_complicated_function(det(-(+(^(A::Array{Face,2},3)::Array{Face,2},.*(2,A::Array{Face,2})::None)::None,1)::None)::None)::None
+ end)))
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h1 id="LLVM-IR-Generation">LLVM IR Generation<a class="anchor-link" href="#LLVM-IR-Generation">¶</a></h1>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [56]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">code_llvm</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">a</span><span class="p">),))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stdout">
+<pre>
+
+; Function Attrs: sspreq
+define %ModInt @julia_evaluate_a_polynomial(%ModInt) #2 {
+top:
+ %1 = call %ModInt @julia_power_by_squaring6226(%ModInt %0, i64 6), !dbg !28559, !julia_type !28564
+ %2 = extractvalue %ModInt %1, 0, !dbg !28559
+ %3 = mul i64 %2, 3, !dbg !28559
+ %4 = srem i64 %3, 11, !dbg !28559
+ %5 = call %ModInt @julia_power_by_squaring6226(%ModInt %0, i64 2), !dbg !28559, !julia_type !28564
+ %6 = extractvalue %ModInt %5, 0, !dbg !28559
+ %7 = mul i64 %6, 3, !dbg !28559
+ %8 = srem i64 %7, 11, !dbg !28559
+ %9 = add i64 %8, %4, !dbg !28559
+ %10 = srem i64 %9, 11, !dbg !28559
+ %11 = extractvalue %ModInt %0, 0, !dbg !28559
+ %12 = shl i64 %11, 1, !dbg !28559
+ %13 = srem i64 %12, 11, !dbg !28559
+ %14 = add i64 %13, %10, !dbg !28559
+ %15 = srem i64 %14, 11, !dbg !28559
+ %16 = add i64 %15, 3, !dbg !28559
+ %17 = srem i64 %16, 11, !dbg !28559
+ %18 = insertvalue %ModInt undef, i64 %17, 0, !dbg !28559, !julia_type !28564
+ ret %ModInt %18, !dbg !28559
+}
+
+</pre>
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [57]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">code_llvm</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">A</span><span class="p">),))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stdout">
+<pre>
+
+; Function Attrs: sspreq
+define %jl_value_t* @julia_evaluate_a_polynomial6230(%jl_value_t*, %jl_value_t**, i32) #2 {
+top:
+ %3 = alloca [4 x %jl_value_t*], align 8
+ %.sub = getelementptr inbounds [4 x %jl_value_t*]* %3, i64 0, i64 0
+ %4 = getelementptr [4 x %jl_value_t*]* %3, i64 0, i64 2, !dbg !28571
+ store %jl_value_t* inttoptr (i64 4 to %jl_value_t*), %jl_value_t** %.sub, align 8
+ %5 = load %jl_value_t*** @jl_pgcstack, align 8, !dbg !28571
+ %6 = getelementptr [4 x %jl_value_t*]* %3, i64 0, i64 1, !dbg !28571
+ %.c = bitcast %jl_value_t** %5 to %jl_value_t*, !dbg !28571
+ store %jl_value_t* %.c, %jl_value_t** %6, align 8, !dbg !28571
+ store %jl_value_t** %.sub, %jl_value_t*** @jl_pgcstack, align 8, !dbg !28571
+ store %jl_value_t* null, %jl_value_t** %4, align 8
+ %7 = getelementptr [4 x %jl_value_t*]* %3, i64 0, i64 3
+ store %jl_value_t* null, %jl_value_t** %7, align 8
+ %8 = load %jl_value_t** %1, align 8, !dbg !28571
+ %9 = call %jl_value_t* @"julia_^6025"(%jl_value_t* %8, i64 3), !dbg !28571
+ store %jl_value_t* %9, %jl_value_t** %4, align 8, !dbg !28571
+ call void @"julia_.*6231"(i64 2, %jl_value_t* %8), !dbg !28571
+ store %jl_value_t* inttoptr (i64 140620606479776 to %jl_value_t*), %jl_value_t** %7, align 8, !dbg !28571
+ %10 = call %jl_value_t* @jl_apply_generic(%jl_value_t* inttoptr (i64 140620629152784 to %jl_value_t*), %jl_value_t** %4, i32 2), !dbg !28571
+ store %jl_value_t* %10, %jl_value_t** %4, align 8, !dbg !28571
+ store %jl_value_t* inttoptr (i64 140620605942320 to %jl_value_t*), %jl_value_t** %7, align 8, !dbg !28571
+ %11 = call %jl_value_t* @jl_apply_generic(%jl_value_t* inttoptr (i64 140620629567872 to %jl_value_t*), %jl_value_t** %4, i32 2), !dbg !28571
+ %12 = load %jl_value_t** %6, align 8, !dbg !28571
+ %13 = getelementptr inbounds %jl_value_t* %12, i64 0, i32 0, !dbg !28571
+ store %jl_value_t** %13, %jl_value_t*** @jl_pgcstack, align 8, !dbg !28571
+ ret %jl_value_t* %11, !dbg !28571
+}
+
+</pre>
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [58]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">code_native</span><span class="p">(</span><span class="n">evaluate_a_polynomial</span><span class="p">,(</span><span class="n">typeof</span><span class="p">(</span><span class="n">A</span><span class="p">),))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stdout">
+<pre>
+ .section __TEXT,__text,regular,pure_instructions
+Filename: no file
+Source line: 0
+ push rbp
+ mov rbp, rsp
+ push r15
+ push r14
+ push r12
+ push rbx
+ sub rsp, 48
+ movabs r14, 4348774360
+ mov rax, qword ptr [r14]
+ mov qword ptr [rbp - 40], rax
+ mov qword ptr [rbp - 72], 4
+Source line: 0
+ movabs r15, 4348775232
+ mov rax, qword ptr [r15]
+ mov qword ptr [rbp - 64], rax
+ lea rax, qword ptr [rbp - 72]
+ mov qword ptr [r15], rax
+ vxorps xmm0, xmm0, xmm0
+ vmovups xmmword ptr [rbp - 56], xmm0
+ movabs rax, 4380607552
+ mov rbx, qword ptr [rsi]
+ mov rdi, rbx
+ mov esi, 3
+ call rax
+ movabs rcx, 4380609184
+ mov qword ptr [rbp - 56], rax
+ mov edi, 2
+ mov rsi, rbx
+ call rcx
+ lea rbx, qword ptr [rbp - 56]
+ movabs r12, 4318407168
+ movabs rax, 140620606479776
+ mov qword ptr [rbp - 48], rax
+ movabs rdi, 140620629152784
+ mov rsi, rbx
+ mov edx, 2
+ call r12
+ movabs rcx, 140620605942320
+ mov qword ptr [rbp - 56], rax
+ mov qword ptr [rbp - 48], rcx
+ movabs rdi, 140620629567872
+ mov rsi, rbx
+ mov edx, 2
+ call r12
+ mov rcx, qword ptr [rbp - 64]
+ mov qword ptr [r15], rcx
+ mov rcx, qword ptr [r14]
+ cmp rcx, qword ptr [rbp - 40]
+ jne 13
+ add rsp, 48
+ pop rbx
+ pop r12
+ pop r14
+ pop r15
+ pop rbp
+ ret
+ movabs rax, 140735631254601
+ call rax
+
+</pre>
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="Calling-C-and-Fortran">Calling C and Fortran<a class="anchor-link" href="#Calling-C-and-Fortran">¶</a></h3>
+</div>
+
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [59]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">pid</span><span class="p">()</span> <span class="o">=</span> <span class="n">ccall</span><span class="p">(:</span><span class="n">getpid</span><span class="p">,</span> <span class="n">Int32</span><span class="p">,</span> <span class="p">())</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[59]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+pid (generic function with 1 method)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [60]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">pid</span><span class="p">()</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[60]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+46441
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [61]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">code_llvm</span><span class="p">(</span><span class="n">pid</span><span class="p">,())</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stdout">
+<pre>
+
+; Function Attrs: sspreq
+define i32 @julia_pid6253() #2 {
+top:
+ %0 = call i32 @getpid(), !dbg !28644
+ ret i32 %0, !dbg !28644
+}
+
+</pre>
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="text_cell_render border-box-sizing rendered_html">
+<h1 id="Integrating-LLVM-and-Julia">Integrating LLVM and Julia<a class="anchor-link" href="#Integrating-LLVM-and-Julia">¶</a></h1>
+</div>
+</section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [62]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="kn">import</span> <span class="nn">Base.llvmcall</span>
+<span class="n">simd</span><span class="p">(</span><span class="n">x</span><span class="p">::</span><span class="n">NTuple</span><span class="p">{</span><span class="mi">4</span><span class="p">,</span><span class="n">Int64</span><span class="p">})</span> <span class="o">=</span> <span class="n">llvmcall</span><span class="p">(</span>
+<span class="sd">"""</span>
+<span class="sd">%3 = add <4 x i64> %1, %0</span>
+<span class="sd">ret <4 x i64> %3</span>
+<span class="sd">"""</span><span class="p">,</span><span class="n">NTuple</span><span class="p">{</span><span class="mi">4</span><span class="p">,</span><span class="n">Int64</span><span class="p">},(</span><span class="n">NTuple</span><span class="p">{</span><span class="mi">4</span><span class="p">,</span><span class="n">Int64</span><span class="p">},</span><span class="n">NTuple</span><span class="p">{</span><span class="mi">4</span><span class="p">,</span><span class="n">Int64</span><span class="p">}),(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">),</span><span class="n">x</span><span class="p">)</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[62]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+simd (generic function with 1 method)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [63]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">simd</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt output_prompt">
+ Out[63]:</div>
+<div class="box-flex1 output_subarea output_pyout">
+
+
+<pre>
+(3,5,7,9)
+</pre>
+
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [64]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">code_llvm</span><span class="p">(</span><span class="n">simd</span><span class="p">,(</span><span class="n">NTuple</span><span class="p">{</span><span class="mi">4</span><span class="p">,</span><span class="n">Int64</span><span class="p">},))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stdout">
+<pre>
+
+; Function Attrs: sspreq
+define <4 x i64> @julia_simd6273(<4 x i64>) #2 {
+top:
+ %1 = add <4 x i64> %0, <i64 1, i64 2, i64 3, i64 4>
+ ret <4 x i64> %1, !dbg !28729
+}
+
+</pre>
+</div>
+</div>
+
+</div>
+</div>
+
+</div></section>
+ </section><section>
+ <section>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [65]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre><span class="n">code_native</span><span class="p">(</span><span class="n">simd</span><span class="p">,(</span><span class="n">NTuple</span><span class="p">{</span><span class="mi">4</span><span class="p">,</span><span class="n">Int64</span><span class="p">},))</span>
+</pre></div>
+
+</div>
+</div>
+
+<div class="output_wrapper">
+<div class="output vbox">
+
+
+<div class="output_area"><div class="prompt"></div>
+<div class="box-flex1 output_subarea output_stream output_stdout">
+<pre>
+ .section __TEXT,__text,regular,pure_instructions
+Filename: In[62]
+Source line: 2
+ push rbp
+ mov rbp, rsp
+ sub rsp, 16
+ movabs rax, 4348774360
+ mov rcx, qword ptr [rax]
+ mov qword ptr [rbp - 8], rcx
+ movabs rcx, 4624115088
+ vpaddq xmm1, xmm0, xmmword ptr [rcx]
+ mov rax, qword ptr [rax]
+ cmp rax, qword ptr [rbp - 8]
+ jne 32
+ vextractf128 xmm0, ymm0, 1
+ movabs rax, 4624115072
+ vpaddq xmm0, xmm0, xmmword ptr [rax]
+ vinsertf128 ymm0, ymm1, xmm0, 1
+Source line: 2
+ add rsp, 16
+ pop rbp
+ ret
+ movabs rax, 140735631254601
+ vzeroupper
+ call rax
+
+</pre>
+</div>
+</div>
+
+</div>
+</div>
+
+</div>
+<div class="cell border-box-sizing code_cell vbox">
+<div class="input">
+<div class="prompt input_prompt">
+In [66]:
+</div>
+<div class="input_area box-flex1">
+<div class="highlight"><pre>
+</pre></div>
+
+</div>
+</div>
+
+</div></section>
+ </section>
+</div>
+</div>
+
+<script src="reveal.js/lib/js/head.min.js"></script>
+
+<script src="reveal.js/js/reveal.js"></script>
+
+<script>
+
+// Full list of configuration options available here: https://github.com/hakimel/reveal.js#configuration
+Reveal.initialize({
+controls: true,
+progress: true,
+history: true,
+
+theme: Reveal.getQueryHash().theme, // available themes are in /css/theme
+transition: Reveal.getQueryHash().transition || 'linear', // default/cube/page/concave/zoom/linear/none
+
+// Optional libraries used to extend on reveal.js
+dependencies: [
+{ src: "reveal.js/lib/js/classList.js", condition: function() { return !document.body.classList; } },
+{ src: "reveal.js/plugin/highlight/highlight.js", async: true, callback: function() { hljs.initHighlightingOnLoad(); } },
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+ "HTML-CSS": {
+ styles: {'.MathJax_Display': {"margin": 0}}
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+
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+
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Added: www/trunk/devmtg/2013-11/slides/Zakai-Emscripten.pdf
URL: http://llvm.org/viewvc/llvm-project/www/trunk/devmtg/2013-11/slides/Zakai-Emscripten.pdf?rev=196972&view=auto
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Binary files www/trunk/devmtg/2013-11/slides/Zakai-Emscripten.pdf (added) and www/trunk/devmtg/2013-11/slides/Zakai-Emscripten.pdf Tue Dec 10 15:40:31 2013 differ
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