src/cmd/trace/mmu.go - go - Git at Google

 // Copyright 2017 The Go Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.

 // Minimum mutator utilization (MMU) graphing.

 // TODO:
 //
 // In worst window list, show break-down of GC utilization sources
 // (STW, assist, etc). Probably requires a different MutatorUtil
 // representation.
 //
 // When a window size is selected, show a second plot of the mutator
 // utilization distribution for that window size.
 //
 // Render plot progressively so rough outline is visible quickly even
 // for very complex MUTs. Start by computing just a few window sizes
 // and then add more window sizes.
 //
 // Consider using sampling to compute an approximate MUT. This would
 // work by sampling the mutator utilization at randomly selected
 // points in time in the trace to build an empirical distribution. We
 // could potentially put confidence intervals on these estimates and
 // render this progressively as we refine the distributions.

 package main

 import (
 	"encoding/json"
 	"fmt"
 	"internal/trace"
 	"log"
 	"math"
 	"net/http"
 	"strconv"
 	"strings"
 	"sync"
 	"time"
 )

 func init() {
 	http.HandleFunc("/mmu", httpMMU)
 	http.HandleFunc("/mmuPlot", httpMMUPlot)
 	http.HandleFunc("/mmuDetails", httpMMUDetails)
 }

 var utilFlagNames = map[string]trace.UtilFlags{
 	"perProc":    trace.UtilPerProc,
 	"stw":        trace.UtilSTW,
 	"background": trace.UtilBackground,
 	"assist":     trace.UtilAssist,
 	"sweep":      trace.UtilSweep,
 }

 type mmuCacheEntry struct {
 	init     sync.Once
 	util     [][]trace.MutatorUtil
 	mmuCurve *trace.MMUCurve
 	err      error
 }

 var mmuCache struct {
 	m    map[trace.UtilFlags]*mmuCacheEntry
 	lock sync.Mutex
 }

 func init() {
 	mmuCache.m = make(map[trace.UtilFlags]*mmuCacheEntry)
 }

 func getMMUCurve(r *http.Request) ([][]trace.MutatorUtil, *trace.MMUCurve, error) {
 	var flags trace.UtilFlags
 	for _, flagStr := range strings.Split(r.FormValue("flags"), "|") {
 		flags |= utilFlagNames[flagStr]
 	}

 	mmuCache.lock.Lock()
 	c := mmuCache.m[flags]
 	if c == nil {
 		c = new(mmuCacheEntry)
 		mmuCache.m[flags] = c
 	}
 	mmuCache.lock.Unlock()

 	c.init.Do(func() {
 		events, err := parseEvents()
 		if err != nil {
 			c.err = err
 		} else {
 			c.util = trace.MutatorUtilization(events, flags)
 			c.mmuCurve = trace.NewMMUCurve(c.util)
 		}
 	})
 	return c.util, c.mmuCurve, c.err
 }

 // httpMMU serves the MMU plot page.
 func httpMMU(w http.ResponseWriter, r *http.Request) {
 	http.ServeContent(w, r, "", time.Time{}, strings.NewReader(templMMU))
 }

 // httpMMUPlot serves the JSON data for the MMU plot.
 func httpMMUPlot(w http.ResponseWriter, r *http.Request) {
 	mu, mmuCurve, err := getMMUCurve(r)
 	if err != nil {
 		http.Error(w, fmt.Sprintf("failed to parse events: %v", err), http.StatusInternalServerError)
 		return
 	}

 	var quantiles []float64
 	for _, flagStr := range strings.Split(r.FormValue("flags"), "|") {
 		if flagStr == "mut" {
 			quantiles = []float64{0, 1 - .999, 1 - .99, 1 - .95}
 			break
 		}
 	}

 	// Find a nice starting point for the plot.
 	xMin := time.Second
 	for xMin > 1 {
 		if mmu := mmuCurve.MMU(xMin); mmu < 0.0001 {
 			break
 		}
 		xMin /= 1000
 	}
 	// Cover six orders of magnitude.
 	xMax := xMin * 1e6
 	// But no more than the length of the trace.
 	minEvent, maxEvent := mu[0][0].Time, mu[0][len(mu[0])-1].Time
 	for _, mu1 := range mu[1:] {
 		if mu1[0].Time < minEvent {
 			minEvent = mu1[0].Time
 		}
 		if mu1[len(mu1)-1].Time > maxEvent {
 			maxEvent = mu1[len(mu1)-1].Time
 		}
 	}
 	if maxMax := time.Duration(maxEvent - minEvent); xMax > maxMax {
 		xMax = maxMax
 	}
 	// Compute MMU curve.
 	logMin, logMax := math.Log(float64(xMin)), math.Log(float64(xMax))
 	const samples = 100
 	plot := make([][]float64, samples)
 	for i := 0; i < samples; i++ {
 		window := time.Duration(math.Exp(float64(i)/(samples-1)*(logMax-logMin) + logMin))
 		if quantiles == nil {
 			plot[i] = make([]float64, 2)
 			plot[i][1] = mmuCurve.MMU(window)
 		} else {
 			plot[i] = make([]float64, 1+len(quantiles))
 			copy(plot[i][1:], mmuCurve.MUD(window, quantiles))
 		}
 		plot[i][0] = float64(window)
 	}

 	// Create JSON response.
 	err = json.NewEncoder(w).Encode(map[string]interface{}{"xMin": int64(xMin), "xMax": int64(xMax), "quantiles": quantiles, "curve": plot})
 	if err != nil {
 		log.Printf("failed to serialize response: %v", err)
 		return
 	}
 }

 var templMMU = `<!doctype html>
 <html>
   <head>
     <meta charset="utf-8">
     <script type="text/javascript" src="https://www.gstatic.com/charts/loader.js"></script>
     <script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
     <script type="text/javascript">
       google.charts.load('current', {'packages':['corechart']});
       var chartsReady = false;
       google.charts.setOnLoadCallback(function() { chartsReady = true; refreshChart(); });

       var chart;
       var curve;

       function niceDuration(ns) {
           if (ns < 1e3) { return ns + 'ns'; }
           else if (ns < 1e6) { return ns / 1e3 + 'µs'; }
           else if (ns < 1e9) { return ns / 1e6 + 'ms'; }
           else { return ns / 1e9 + 's'; }
       }

       function niceQuantile(q) {
         return 'p' + q*100;
       }

       function mmuFlags() {
         var flags = "";
         $("#options input").each(function(i, elt) {
           if (elt.checked)
             flags += "|" + elt.id;
         });
         return flags.substr(1);
       }

       function refreshChart() {
         if (!chartsReady) return;
         var container = $('#mmu_chart');
         container.css('opacity', '.5');
         refreshChart.count++;
         var seq = refreshChart.count;
         $.getJSON('/mmuPlot?flags=' + mmuFlags())
          .fail(function(xhr, status, error) {
            alert('failed to load plot: ' + status);
          })
          .done(function(result) {
            if (refreshChart.count === seq)
              drawChart(result);
          });
       }
       refreshChart.count = 0;

       function drawChart(plotData) {
         curve = plotData.curve;
         var data = new google.visualization.DataTable();
         data.addColumn('number', 'Window duration');
         data.addColumn('number', 'Minimum mutator utilization');
         if (plotData.quantiles) {
           for (var i = 1; i < plotData.quantiles.length; i++) {
             data.addColumn('number', niceQuantile(1 - plotData.quantiles[i]) + ' MU');
           }
         }
         data.addRows(curve);
         for (var i = 0; i < curve.length; i++) {
           data.setFormattedValue(i, 0, niceDuration(curve[i][0]));
         }

         var options = {
           chart: {
             title: 'Minimum mutator utilization',
           },
           hAxis: {
             title: 'Window duration',
             scaleType: 'log',
             ticks: [],
           },
           vAxis: {
             title: 'Minimum mutator utilization',
             minValue: 0.0,
             maxValue: 1.0,
           },
           legend: { position: 'none' },
           focusTarget: 'category',
           width: 900,
           height: 500,
           chartArea: { width: '80%', height: '80%' },
         };
         for (var v = plotData.xMin; v <= plotData.xMax; v *= 10) {
           options.hAxis.ticks.push({v:v, f:niceDuration(v)});
         }
         if (plotData.quantiles) {
           options.vAxis.title = 'Mutator utilization';
           options.legend.position = 'in';
         }

         var container = $('#mmu_chart');
         container.empty();
         container.css('opacity', '');
         chart = new google.visualization.LineChart(container[0]);
         chart = new google.visualization.LineChart(document.getElementById('mmu_chart'));
         chart.draw(data, options);

         google.visualization.events.addListener(chart, 'select', selectHandler);
         $('#details').empty();
       }

       function selectHandler() {
         var items = chart.getSelection();
         if (items.length === 0) {
           return;
         }
         var details = $('#details');
         details.empty();
         var windowNS = curve[items[0].row][0];
         var url = '/mmuDetails?window=' + windowNS + '&flags=' + mmuFlags();
         $.getJSON(url)
          .fail(function(xhr, status, error) {
             details.text(status + ': ' + url + ' could not be loaded');
          })
          .done(function(worst) {
             details.text('Lowest mutator utilization in ' + niceDuration(windowNS) + ' windows:');
             for (var i = 0; i < worst.length; i++) {
               details.append($('<br/>'));
               var text = worst[i].MutatorUtil.toFixed(3) + ' at time ' + niceDuration(worst[i].Time);
               details.append($('<a/>').text(text).attr('href', worst[i].URL));
             }
          });
       }

       $.when($.ready).then(function() {
         $("#options input").click(refreshChart);
       });
     </script>
     <style>
       .help {
         display: inline-block;
         position: relative;
         width: 1em;
         height: 1em;
         border-radius: 50%;
         color: #fff;
         background: #555;
         text-align: center;
         cursor: help;
       }
       .help > span {
         display: none;
       }
       .help:hover > span {
         display: block;
         position: absolute;
         left: 1.1em;
         top: 1.1em;
         background: #555;
         text-align: left;
         width: 20em;
         padding: 0.5em;
         border-radius: 0.5em;
         z-index: 5;
       }
     </style>
   </head>
   <body>
     <div style="position: relative">
       <div id="mmu_chart" style="width: 900px; height: 500px; display: inline-block; vertical-align: top">Loading plot...</div>
       <div id="options" style="display: inline-block; vertical-align: top">
         <p>
           <b>View</b><br/>
           <input type="radio" name="view" id="system" checked><label for="system">System</label>
           <span class="help">?<span>Consider whole system utilization. For example, if one of four procs is available to the mutator, mutator utilization will be 0.25. This is the standard definition of an MMU.</span></span><br/>
           <input type="radio" name="view" id="perProc"><label for="perProc">Per-goroutine</label>
           <span class="help">?<span>Consider per-goroutine utilization. When even one goroutine is interrupted by GC, mutator utilization is 0.</span></span><br/>
         </p>
         <p>
           <b>Include</b><br/>
           <input type="checkbox" id="stw" checked><label for="stw">STW</label>
           <span class="help">?<span>Stop-the-world stops all goroutines simultaneously.</span></span><br/>
           <input type="checkbox" id="background" checked><label for="background">Background workers</label>
           <span class="help">?<span>Background workers are GC-specific goroutines. 25% of the CPU is dedicated to background workers during GC.</span></span><br/>
           <input type="checkbox" id="assist" checked><label for="assist">Mark assist</label>
           <span class="help">?<span>Mark assists are performed by allocation to prevent the mutator from outpacing GC.</span></span><br/>
           <input type="checkbox" id="sweep"><label for="sweep">Sweep</label>
           <span class="help">?<span>Sweep reclaims unused memory between GCs. (Enabling this may be very slow.).</span></span><br/>
         </p>
         <p>
           <b>Display</b><br/>
           <input type="checkbox" id="mut"><label for="mut">Show percentiles</label>
           <span class="help">?<span>Display percentile mutator utilization in addition to minimum. E.g., p99 MU drops the worst 1% of windows.</span></span><br/>
         </p>
       </div>
     </div>
     <div id="details">Select a point for details.</div>
   </body>
 </html>
 `

 // httpMMUDetails serves details of an MMU graph at a particular window.
 func httpMMUDetails(w http.ResponseWriter, r *http.Request) {
 	_, mmuCurve, err := getMMUCurve(r)
 	if err != nil {
 		http.Error(w, fmt.Sprintf("failed to parse events: %v", err), http.StatusInternalServerError)
 		return
 	}

 	windowStr := r.FormValue("window")
 	window, err := strconv.ParseUint(windowStr, 10, 64)
 	if err != nil {
 		http.Error(w, fmt.Sprintf("failed to parse window parameter %q: %v", windowStr, err), http.StatusBadRequest)
 		return
 	}
 	worst := mmuCurve.Examples(time.Duration(window), 10)

 	// Construct a link for each window.
 	var links []linkedUtilWindow
 	for _, ui := range worst {
 		links = append(links, newLinkedUtilWindow(ui, time.Duration(window)))
 	}

 	err = json.NewEncoder(w).Encode(links)
 	if err != nil {
 		log.Printf("failed to serialize trace: %v", err)
 		return
 	}
 }

 type linkedUtilWindow struct {
 	trace.UtilWindow
 	URL string
 }

 func newLinkedUtilWindow(ui trace.UtilWindow, window time.Duration) linkedUtilWindow {
 	// Find the range containing this window.
 	var r Range
 	for _, r = range ranges {
 		if r.EndTime > ui.Time {
 			break
 		}
 	}
 	return linkedUtilWindow{ui, fmt.Sprintf("%s#%v:%v", r.URL(), float64(ui.Time)/1e6, float64(ui.Time+int64(window))/1e6)}
 }
	// Copyright 2017 The Go Authors. All rights reserved.
	// Use of this source code is governed by a BSD-style
	// license that can be found in the LICENSE file.

	// Minimum mutator utilization (MMU) graphing.

	// TODO:
	//
	// In worst window list, show break-down of GC utilization sources
	// (STW, assist, etc). Probably requires a different MutatorUtil
	// representation.
	//
	// When a window size is selected, show a second plot of the mutator
	// utilization distribution for that window size.
	//
	// Render plot progressively so rough outline is visible quickly even
	// for very complex MUTs. Start by computing just a few window sizes
	// and then add more window sizes.
	//
	// Consider using sampling to compute an approximate MUT. This would
	// work by sampling the mutator utilization at randomly selected
	// points in time in the trace to build an empirical distribution. We
	// could potentially put confidence intervals on these estimates and
	// render this progressively as we refine the distributions.

	package main

	import (
	"encoding/json"
	"fmt"
	"internal/trace"
	"log"
	"math"
	"net/http"
	"strconv"
	"strings"
	"sync"
	"time"
	)

	func init() {
	http.HandleFunc("/mmu", httpMMU)
	http.HandleFunc("/mmuPlot", httpMMUPlot)
	http.HandleFunc("/mmuDetails", httpMMUDetails)
	}

	var utilFlagNames = map[string]trace.UtilFlags{
	"perProc": trace.UtilPerProc,
	"stw": trace.UtilSTW,
	"background": trace.UtilBackground,
	"assist": trace.UtilAssist,
	"sweep": trace.UtilSweep,
	}

	type mmuCacheEntry struct {
	init sync.Once
	util [][]trace.MutatorUtil
	mmuCurve *trace.MMUCurve
	err error
	}

	var mmuCache struct {
	m map[trace.UtilFlags]*mmuCacheEntry
	lock sync.Mutex
	}

	func init() {
	mmuCache.m = make(map[trace.UtilFlags]*mmuCacheEntry)
	}

	func getMMUCurve(r http.Request) ([][]trace.MutatorUtil, trace.MMUCurve, error) {
	var flags trace.UtilFlags
	for _, flagStr := range strings.Split(r.FormValue("flags"), "\|") {
	flags \|= utilFlagNames[flagStr]
	}

	mmuCache.lock.Lock()
	c := mmuCache.m[flags]
	if c == nil {
	c = new(mmuCacheEntry)
	mmuCache.m[flags] = c
	}
	mmuCache.lock.Unlock()

	c.init.Do(func() {
	events, err := parseEvents()
	if err != nil {
	c.err = err
	} else {
	c.util = trace.MutatorUtilization(events, flags)
	c.mmuCurve = trace.NewMMUCurve(c.util)
	}
	})
	return c.util, c.mmuCurve, c.err
	}

	// httpMMU serves the MMU plot page.
	func httpMMU(w http.ResponseWriter, r *http.Request) {
	http.ServeContent(w, r, "", time.Time{}, strings.NewReader(templMMU))
	}

	// httpMMUPlot serves the JSON data for the MMU plot.
	func httpMMUPlot(w http.ResponseWriter, r *http.Request) {
	mu, mmuCurve, err := getMMUCurve(r)
	if err != nil {
	http.Error(w, fmt.Sprintf("failed to parse events: %v", err), http.StatusInternalServerError)
	return
	}

	var quantiles []float64
	for _, flagStr := range strings.Split(r.FormValue("flags"), "\|") {
	if flagStr == "mut" {
	quantiles = []float64{0, 1 - .999, 1 - .99, 1 - .95}
	break
	}
	}

	// Find a nice starting point for the plot.
	xMin := time.Second
	for xMin > 1 {
	if mmu := mmuCurve.MMU(xMin); mmu < 0.0001 {
	break
	}
	xMin /= 1000
	}
	// Cover six orders of magnitude.
	xMax := xMin * 1e6
	// But no more than the length of the trace.
	minEvent, maxEvent := mu[0][0].Time, mu[0][len(mu[0])-1].Time
	for _, mu1 := range mu[1:] {
	if mu1[0].Time < minEvent {
	minEvent = mu1[0].Time
	}
	if mu1[len(mu1)-1].Time > maxEvent {
	maxEvent = mu1[len(mu1)-1].Time
	}
	}
	if maxMax := time.Duration(maxEvent - minEvent); xMax > maxMax {
	xMax = maxMax
	}
	// Compute MMU curve.
	logMin, logMax := math.Log(float64(xMin)), math.Log(float64(xMax))
	const samples = 100
	plot := make([][]float64, samples)
	for i := 0; i < samples; i++ {
	window := time.Duration(math.Exp(float64(i)/(samples-1)*(logMax-logMin) + logMin))
	if quantiles == nil {
	plot[i] = make([]float64, 2)
	plot[i][1] = mmuCurve.MMU(window)
	} else {
	plot[i] = make([]float64, 1+len(quantiles))
	copy(plot[i][1:], mmuCurve.MUD(window, quantiles))
	}
	plot[i][0] = float64(window)
	}

	// Create JSON response.
	err = json.NewEncoder(w).Encode(map[string]interface{}{"xMin": int64(xMin), "xMax": int64(xMax), "quantiles": quantiles, "curve": plot})
	if err != nil {
	log.Printf("failed to serialize response: %v", err)
	return
	}
	}

	var templMMU = `<!doctype html>
	<html>
	<head>
	<meta charset="utf-8">
	<script type="text/javascript" src="https://www.gstatic.com/charts/loader.js"></script>
	<script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
	<script type="text/javascript">
	google.charts.load('current', {'packages':['corechart']});
	var chartsReady = false;
	google.charts.setOnLoadCallback(function() { chartsReady = true; refreshChart(); });

	var chart;
	var curve;

	function niceDuration(ns) {
	if (ns < 1e3) { return ns + 'ns'; }
	else if (ns < 1e6) { return ns / 1e3 + 'µs'; }
	else if (ns < 1e9) { return ns / 1e6 + 'ms'; }
	else { return ns / 1e9 + 's'; }
	}

	function niceQuantile(q) {
	return 'p' + q*100;
	}

	function mmuFlags() {
	var flags = "";
	$("#options input").each(function(i, elt) {
	if (elt.checked)
	flags += "\|" + elt.id;
	});
	return flags.substr(1);
	}

	function refreshChart() {
	if (!chartsReady) return;
	var container = $('#mmu_chart');
	container.css('opacity', '.5');
	refreshChart.count++;
	var seq = refreshChart.count;
	$.getJSON('/mmuPlot?flags=' + mmuFlags())
	.fail(function(xhr, status, error) {
	alert('failed to load plot: ' + status);
	})
	.done(function(result) {
	if (refreshChart.count === seq)
	drawChart(result);
	});
	}
	refreshChart.count = 0;

	function drawChart(plotData) {
	curve = plotData.curve;
	var data = new google.visualization.DataTable();
	data.addColumn('number', 'Window duration');
	data.addColumn('number', 'Minimum mutator utilization');
	if (plotData.quantiles) {
	for (var i = 1; i < plotData.quantiles.length; i++) {
	data.addColumn('number', niceQuantile(1 - plotData.quantiles[i]) + ' MU');
	}
	}
	data.addRows(curve);
	for (var i = 0; i < curve.length; i++) {
	data.setFormattedValue(i, 0, niceDuration(curve[i][0]));
	}

	var options = {
	chart: {
	title: 'Minimum mutator utilization',
	},
	hAxis: {
	title: 'Window duration',
	scaleType: 'log',
	ticks: [],
	},
	vAxis: {
	title: 'Minimum mutator utilization',
	minValue: 0.0,
	maxValue: 1.0,
	},
	legend: { position: 'none' },
	focusTarget: 'category',
	width: 900,
	height: 500,
	chartArea: { width: '80%', height: '80%' },
	};
	for (var v = plotData.xMin; v <= plotData.xMax; v *= 10) {
	options.hAxis.ticks.push({v:v, f:niceDuration(v)});
	}
	if (plotData.quantiles) {
	options.vAxis.title = 'Mutator utilization';
	options.legend.position = 'in';
	}

	var container = $('#mmu_chart');
	container.empty();
	container.css('opacity', '');
	chart = new google.visualization.LineChart(container[0]);
	chart = new google.visualization.LineChart(document.getElementById('mmu_chart'));
	chart.draw(data, options);

	google.visualization.events.addListener(chart, 'select', selectHandler);
	$('#details').empty();
	}

	function selectHandler() {
	var items = chart.getSelection();
	if (items.length === 0) {
	return;
	}
	var details = $('#details');
	details.empty();
	var windowNS = curve[items[0].row][0];
	var url = '/mmuDetails?window=' + windowNS + '&flags=' + mmuFlags();
	$.getJSON(url)
	.fail(function(xhr, status, error) {
	details.text(status + ': ' + url + ' could not be loaded');
	})
	.done(function(worst) {
	details.text('Lowest mutator utilization in ' + niceDuration(windowNS) + ' windows:');
	for (var i = 0; i < worst.length; i++) {
	details.append($('<br/>'));
	var text = worst[i].MutatorUtil.toFixed(3) + ' at time ' + niceDuration(worst[i].Time);
	details.append($('<a/>').text(text).attr('href', worst[i].URL));
	}
	});
	}

	$.when($.ready).then(function() {
	$("#options input").click(refreshChart);
	});
	</script>
	<style>
	.help {
	display: inline-block;
	position: relative;
	width: 1em;
	height: 1em;
	border-radius: 50%;
	color: #fff;
	background: #555;
	text-align: center;
	cursor: help;
	}
	.help > span {
	display: none;
	}
	.help:hover > span {
	display: block;
	position: absolute;
	left: 1.1em;
	top: 1.1em;
	background: #555;
	text-align: left;
	width: 20em;
	padding: 0.5em;
	border-radius: 0.5em;
	z-index: 5;
	}
	</style>
	</head>
	<body>
	<div style="position: relative">
	<div id="mmu_chart" style="width: 900px; height: 500px; display: inline-block; vertical-align: top">Loading plot...</div>
	<div id="options" style="display: inline-block; vertical-align: top">
	<p>
	<b>View</b><br/>
	<input type="radio" name="view" id="system" checked><label for="system">System</label>
	<span class="help">?<span>Consider whole system utilization. For example, if one of four procs is available to the mutator, mutator utilization will be 0.25. This is the standard definition of an MMU.</span></span><br/>
	<input type="radio" name="view" id="perProc"><label for="perProc">Per-goroutine</label>
	<span class="help">?<span>Consider per-goroutine utilization. When even one goroutine is interrupted by GC, mutator utilization is 0.</span></span><br/>
	</p>
	<p>
	<b>Include</b><br/>
	<input type="checkbox" id="stw" checked><label for="stw">STW</label>
	<span class="help">?<span>Stop-the-world stops all goroutines simultaneously.</span></span><br/>
	<input type="checkbox" id="background" checked><label for="background">Background workers</label>
	<span class="help">?<span>Background workers are GC-specific goroutines. 25% of the CPU is dedicated to background workers during GC.</span></span><br/>
	<input type="checkbox" id="assist" checked><label for="assist">Mark assist</label>
	<span class="help">?<span>Mark assists are performed by allocation to prevent the mutator from outpacing GC.</span></span><br/>
	<input type="checkbox" id="sweep"><label for="sweep">Sweep</label>
	<span class="help">?<span>Sweep reclaims unused memory between GCs. (Enabling this may be very slow.).</span></span><br/>
	</p>
	<p>
	<b>Display</b><br/>
	<input type="checkbox" id="mut"><label for="mut">Show percentiles</label>
	<span class="help">?<span>Display percentile mutator utilization in addition to minimum. E.g., p99 MU drops the worst 1% of windows.</span></span><br/>
	</p>
	</div>
	</div>
	<div id="details">Select a point for details.</div>
	</body>
	</html>
	`

	// httpMMUDetails serves details of an MMU graph at a particular window.
	func httpMMUDetails(w http.ResponseWriter, r *http.Request) {
	_, mmuCurve, err := getMMUCurve(r)
	if err != nil {
	http.Error(w, fmt.Sprintf("failed to parse events: %v", err), http.StatusInternalServerError)
	return
	}

	windowStr := r.FormValue("window")
	window, err := strconv.ParseUint(windowStr, 10, 64)
	if err != nil {
	http.Error(w, fmt.Sprintf("failed to parse window parameter %q: %v", windowStr, err), http.StatusBadRequest)
	return
	}
	worst := mmuCurve.Examples(time.Duration(window), 10)

	// Construct a link for each window.
	var links []linkedUtilWindow
	for _, ui := range worst {
	links = append(links, newLinkedUtilWindow(ui, time.Duration(window)))
	}

	err = json.NewEncoder(w).Encode(links)
	if err != nil {
	log.Printf("failed to serialize trace: %v", err)
	return
	}
	}

	type linkedUtilWindow struct {
	trace.UtilWindow
	URL string
	}

	func newLinkedUtilWindow(ui trace.UtilWindow, window time.Duration) linkedUtilWindow {
	// Find the range containing this window.
	var r Range
	for _, r = range ranges {
	if r.EndTime > ui.Time {
	break
	}
	}
	return linkedUtilWindow{ui, fmt.Sprintf("%s#%v:%v", r.URL(), float64(ui.Time)/1e6, float64(ui.Time+int64(window))/1e6)}
	}