graph.go

     1  // Copyright 2014 Google Inc. All Rights Reserved.
     2  //
     3  // Licensed under the Apache License, Version 2.0 (the "License");
     4  // you may not use this file except in compliance with the License.
     5  // You may obtain a copy of the License at
     6  //
     7  //     http://www.apache.org/licenses/LICENSE-2.0
     8  //
     9  // Unless required by applicable law or agreed to in writing, software
    10  // distributed under the License is distributed on an "AS IS" BASIS,
    11  // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    12  // See the License for the specific language governing permissions and
    13  // limitations under the License.
    14  
    15  // Package graph collects a set of samples into a directed graph.
    16  package graph
    17  
    18  import (
    19  	"fmt"
    20  	"math"
    21  	"path/filepath"
    22  	"regexp"
    23  	"sort"
    24  	"strconv"
    25  	"strings"
    26  
    27  	"github.com/google/pprof/profile"
    28  )
    29  
    30  var (
    31  	// Removes package name and method arguments for Java method names.
    32  	// See tests for examples.
    33  	javaRegExp = regexp.MustCompile(`^(?:[a-z]\w*\.)*([A-Z][\w\$]*\.(?:<init>|[a-z][\w\$]*(?:\$\d+)?))(?:(?:\()|$)`)
    34  	// Removes package name and method arguments for Go function names.
    35  	// See tests for examples.
    36  	goRegExp = regexp.MustCompile(`^(?:[\w\-\.]+\/)+([^.]+\..+)`)
    37  	// Removes potential module versions in a package path.
    38  	goVerRegExp = regexp.MustCompile(`^(.*?)/v(?:[2-9]|[1-9][0-9]+)([./].*)$`)
    39  	// Strips C++ namespace prefix from a C++ function / method name.
    40  	// NOTE: Make sure to keep the template parameters in the name. Normally,
    41  	// template parameters are stripped from the C++ names but when
    42  	// -symbolize=demangle=templates flag is used, they will not be.
    43  	// See tests for examples.
    44  	cppRegExp                = regexp.MustCompile(`^(?:[_a-zA-Z]\w*::)+(_*[A-Z]\w*::~?[_a-zA-Z]\w*(?:<.*>)?)`)
    45  	cppAnonymousPrefixRegExp = regexp.MustCompile(`^\(anonymous namespace\)::`)
    46  )
    47  
    48  // Graph summarizes a performance profile into a format that is
    49  // suitable for visualization.
    50  type Graph struct {
    51  	Nodes Nodes
    52  }
    53  
    54  // Options encodes the options for constructing a graph
    55  type Options struct {
    56  	SampleValue       func(s []int64) int64      // Function to compute the value of a sample
    57  	SampleMeanDivisor func(s []int64) int64      // Function to compute the divisor for mean graphs, or nil
    58  	FormatTag         func(int64, string) string // Function to format a sample tag value into a string
    59  	ObjNames          bool                       // Always preserve obj filename
    60  	OrigFnNames       bool                       // Preserve original (eg mangled) function names
    61  
    62  	CallTree     bool // Build a tree instead of a graph
    63  	DropNegative bool // Drop nodes with overall negative values
    64  
    65  	KeptNodes NodeSet // If non-nil, only use nodes in this set
    66  }
    67  
    68  // Nodes is an ordered collection of graph nodes.
    69  type Nodes []*Node
    70  
    71  // Node is an entry on a profiling report. It represents a unique
    72  // program location.
    73  type Node struct {
    74  	// Info describes the source location associated to this node.
    75  	Info NodeInfo
    76  
    77  	// Function represents the function that this node belongs to. On
    78  	// graphs with sub-function resolution (eg line number or
    79  	// addresses), two nodes in a NodeMap that are part of the same
    80  	// function have the same value of Node.Function. If the Node
    81  	// represents the whole function, it points back to itself.
    82  	Function *Node
    83  
    84  	// Values associated to this node. Flat is exclusive to this node,
    85  	// Cum includes all descendents.
    86  	Flat, FlatDiv, Cum, CumDiv int64
    87  
    88  	// In and out Contains the nodes immediately reaching or reached by
    89  	// this node.
    90  	In, Out EdgeMap
    91  
    92  	// LabelTags provide additional information about subsets of a sample.
    93  	LabelTags TagMap
    94  
    95  	// NumericTags provide additional values for subsets of a sample.
    96  	// Numeric tags are optionally associated to a label tag. The key
    97  	// for NumericTags is the name of the LabelTag they are associated
    98  	// to, or "" for numeric tags not associated to a label tag.
    99  	NumericTags map[string]TagMap
   100  }
   101  
   102  // FlatValue returns the exclusive value for this node, computing the
   103  // mean if a divisor is available.
   104  func (n *Node) FlatValue() int64 {
   105  	if n.FlatDiv == 0 {
   106  		return n.Flat
   107  	}
   108  	return n.Flat / n.FlatDiv
   109  }
   110  
   111  // CumValue returns the inclusive value for this node, computing the
   112  // mean if a divisor is available.
   113  func (n *Node) CumValue() int64 {
   114  	if n.CumDiv == 0 {
   115  		return n.Cum
   116  	}
   117  	return n.Cum / n.CumDiv
   118  }
   119  
   120  // AddToEdge increases the weight of an edge between two nodes. If
   121  // there isn't such an edge one is created.
   122  func (n *Node) AddToEdge(to *Node, v int64, residual, inline bool) {
   123  	n.AddToEdgeDiv(to, 0, v, residual, inline)
   124  }
   125  
   126  // AddToEdgeDiv increases the weight of an edge between two nodes. If
   127  // there isn't such an edge one is created.
   128  func (n *Node) AddToEdgeDiv(to *Node, dv, v int64, residual, inline bool) {
   129  	if n.Out[to] != to.In[n] {
   130  		panic(fmt.Errorf("asymmetric edges %v %v", *n, *to))
   131  	}
   132  
   133  	if e := n.Out[to]; e != nil {
   134  		e.WeightDiv += dv
   135  		e.Weight += v
   136  		if residual {
   137  			e.Residual = true
   138  		}
   139  		if !inline {
   140  			e.Inline = false
   141  		}
   142  		return
   143  	}
   144  
   145  	info := &Edge{Src: n, Dest: to, WeightDiv: dv, Weight: v, Residual: residual, Inline: inline}
   146  	n.Out[to] = info
   147  	to.In[n] = info
   148  }
   149  
   150  // NodeInfo contains the attributes for a node.
   151  type NodeInfo struct {
   152  	Name              string
   153  	OrigName          string
   154  	Address           uint64
   155  	File              string
   156  	StartLine, Lineno int
   157  	Columnno          int
   158  	Objfile           string
   159  }
   160  
   161  // PrintableName calls the Node's Formatter function with a single space separator.
   162  func (i *NodeInfo) PrintableName() string {
   163  	return strings.Join(i.NameComponents(), " ")
   164  }
   165  
   166  // NameComponents returns the components of the printable name to be used for a node.
   167  func (i *NodeInfo) NameComponents() []string {
   168  	var name []string
   169  	if i.Address != 0 {
   170  		name = append(name, fmt.Sprintf("%016x", i.Address))
   171  	}
   172  	if fun := i.Name; fun != "" {
   173  		name = append(name, fun)
   174  	}
   175  
   176  	switch {
   177  	case i.Lineno != 0:
   178  		s := fmt.Sprintf("%s:%d", i.File, i.Lineno)
   179  		if i.Columnno != 0 {
   180  			s += fmt.Sprintf(":%d", i.Columnno)
   181  		}
   182  		// User requested line numbers, provide what we have.
   183  		name = append(name, s)
   184  	case i.File != "":
   185  		// User requested file name, provide it.
   186  		name = append(name, i.File)
   187  	case i.Name != "":
   188  		// User requested function name. It was already included.
   189  	case i.Objfile != "":
   190  		// Only binary name is available
   191  		name = append(name, "["+filepath.Base(i.Objfile)+"]")
   192  	default:
   193  		// Do not leave it empty if there is no information at all.
   194  		name = append(name, "<unknown>")
   195  	}
   196  	return name
   197  }
   198  
   199  // NodeMap maps from a node info struct to a node. It is used to merge
   200  // report entries with the same info.
   201  type NodeMap map[NodeInfo]*Node
   202  
   203  // NodeSet is a collection of node info structs.
   204  type NodeSet map[NodeInfo]bool
   205  
   206  // NodePtrSet is a collection of nodes. Trimming a graph or tree requires a set
   207  // of objects which uniquely identify the nodes to keep. In a graph, NodeInfo
   208  // works as a unique identifier; however, in a tree multiple nodes may share
   209  // identical NodeInfos. A *Node does uniquely identify a node so we can use that
   210  // instead. Though a *Node also uniquely identifies a node in a graph,
   211  // currently, during trimming, graphs are rebuilt from scratch using only the
   212  // NodeSet, so there would not be the required context of the initial graph to
   213  // allow for the use of *Node.
   214  type NodePtrSet map[*Node]bool
   215  
   216  // FindOrInsertNode takes the info for a node and either returns a matching node
   217  // from the node map if one exists, or adds one to the map if one does not.
   218  // If kept is non-nil, nodes are only added if they can be located on it.
   219  func (nm NodeMap) FindOrInsertNode(info NodeInfo, kept NodeSet) *Node {
   220  	if kept != nil {
   221  		if _, ok := kept[info]; !ok {
   222  			return nil
   223  		}
   224  	}
   225  
   226  	if n, ok := nm[info]; ok {
   227  		return n
   228  	}
   229  
   230  	n := &Node{
   231  		Info:        info,
   232  		In:          make(EdgeMap),
   233  		Out:         make(EdgeMap),
   234  		LabelTags:   make(TagMap),
   235  		NumericTags: make(map[string]TagMap),
   236  	}
   237  	nm[info] = n
   238  	if info.Address == 0 && info.Lineno == 0 {
   239  		// This node represents the whole function, so point Function
   240  		// back to itself.
   241  		n.Function = n
   242  		return n
   243  	}
   244  	// Find a node that represents the whole function.
   245  	info.Address = 0
   246  	info.Lineno = 0
   247  	info.Columnno = 0
   248  	n.Function = nm.FindOrInsertNode(info, nil)
   249  	return n
   250  }
   251  
   252  // EdgeMap is used to represent the incoming/outgoing edges from a node.
   253  type EdgeMap map[*Node]*Edge
   254  
   255  // Edge contains any attributes to be represented about edges in a graph.
   256  type Edge struct {
   257  	Src, Dest *Node
   258  	// The summary weight of the edge
   259  	Weight, WeightDiv int64
   260  
   261  	// residual edges connect nodes that were connected through a
   262  	// separate node, which has been removed from the report.
   263  	Residual bool
   264  	// An inline edge represents a call that was inlined into the caller.
   265  	Inline bool
   266  }
   267  
   268  // WeightValue returns the weight value for this edge, normalizing if a
   269  // divisor is available.
   270  func (e *Edge) WeightValue() int64 {
   271  	if e.WeightDiv == 0 {
   272  		return e.Weight
   273  	}
   274  	return e.Weight / e.WeightDiv
   275  }
   276  
   277  // Tag represent sample annotations
   278  type Tag struct {
   279  	Name          string
   280  	Unit          string // Describe the value, "" for non-numeric tags
   281  	Value         int64
   282  	Flat, FlatDiv int64
   283  	Cum, CumDiv   int64
   284  }
   285  
   286  // FlatValue returns the exclusive value for this tag, computing the
   287  // mean if a divisor is available.
   288  func (t *Tag) FlatValue() int64 {
   289  	if t.FlatDiv == 0 {
   290  		return t.Flat
   291  	}
   292  	return t.Flat / t.FlatDiv
   293  }
   294  
   295  // CumValue returns the inclusive value for this tag, computing the
   296  // mean if a divisor is available.
   297  func (t *Tag) CumValue() int64 {
   298  	if t.CumDiv == 0 {
   299  		return t.Cum
   300  	}
   301  	return t.Cum / t.CumDiv
   302  }
   303  
   304  // TagMap is a collection of tags, classified by their name.
   305  type TagMap map[string]*Tag
   306  
   307  // SortTags sorts a slice of tags based on their weight.
   308  func SortTags(t []*Tag, flat bool) []*Tag {
   309  	ts := tags{t, flat}
   310  	sort.Sort(ts)
   311  	return ts.t
   312  }
   313  
   314  // New summarizes performance data from a profile into a graph.
   315  func New(prof *profile.Profile, o *Options) *Graph {
   316  	if o.CallTree {
   317  		return newTree(prof, o)
   318  	}
   319  	g, _ := newGraph(prof, o)
   320  	return g
   321  }
   322  
   323  // newGraph computes a graph from a profile. It returns the graph, and
   324  // a map from the profile location indices to the corresponding graph
   325  // nodes.
   326  func newGraph(prof *profile.Profile, o *Options) (*Graph, map[uint64]Nodes) {
   327  	nodes, locationMap := CreateNodes(prof, o)
   328  	seenNode := make(map[*Node]bool)
   329  	seenEdge := make(map[nodePair]bool)
   330  	for _, sample := range prof.Sample {
   331  		var w, dw int64
   332  		w = o.SampleValue(sample.Value)
   333  		if o.SampleMeanDivisor != nil {
   334  			dw = o.SampleMeanDivisor(sample.Value)
   335  		}
   336  		if dw == 0 && w == 0 {
   337  			continue
   338  		}
   339  		for k := range seenNode {
   340  			delete(seenNode, k)
   341  		}
   342  		for k := range seenEdge {
   343  			delete(seenEdge, k)
   344  		}
   345  		var parent *Node
   346  		// A residual edge goes over one or more nodes that were not kept.
   347  		residual := false
   348  
   349  		labels := joinLabels(sample)
   350  		// Group the sample frames, based on a global map.
   351  		for i := len(sample.Location) - 1; i >= 0; i-- {
   352  			l := sample.Location[i]
   353  			locNodes := locationMap[l.ID]
   354  			for ni := len(locNodes) - 1; ni >= 0; ni-- {
   355  				n := locNodes[ni]
   356  				if n == nil {
   357  					residual = true
   358  					continue
   359  				}
   360  				// Add cum weight to all nodes in stack, avoiding double counting.
   361  				if _, ok := seenNode[n]; !ok {
   362  					seenNode[n] = true
   363  					n.addSample(dw, w, labels, sample.NumLabel, sample.NumUnit, o.FormatTag, false)
   364  				}
   365  				// Update edge weights for all edges in stack, avoiding double counting.
   366  				if _, ok := seenEdge[nodePair{n, parent}]; !ok && parent != nil && n != parent {
   367  					seenEdge[nodePair{n, parent}] = true
   368  					parent.AddToEdgeDiv(n, dw, w, residual, ni != len(locNodes)-1)
   369  				}
   370  				parent = n
   371  				residual = false
   372  			}
   373  		}
   374  		if parent != nil && !residual {
   375  			// Add flat weight to leaf node.
   376  			parent.addSample(dw, w, labels, sample.NumLabel, sample.NumUnit, o.FormatTag, true)
   377  		}
   378  	}
   379  
   380  	return selectNodesForGraph(nodes, o.DropNegative), locationMap
   381  }
   382  
   383  func selectNodesForGraph(nodes Nodes, dropNegative bool) *Graph {
   384  	// Collect nodes into a graph.
   385  	gNodes := make(Nodes, 0, len(nodes))
   386  	for _, n := range nodes {
   387  		if n == nil {
   388  			continue
   389  		}
   390  		if n.Cum == 0 && n.Flat == 0 {
   391  			continue
   392  		}
   393  		if dropNegative && isNegative(n) {
   394  			continue
   395  		}
   396  		gNodes = append(gNodes, n)
   397  	}
   398  	return &Graph{gNodes}
   399  }
   400  
   401  type nodePair struct {
   402  	src, dest *Node
   403  }
   404  
   405  func newTree(prof *profile.Profile, o *Options) (g *Graph) {
   406  	parentNodeMap := make(map[*Node]NodeMap, len(prof.Sample))
   407  	for _, sample := range prof.Sample {
   408  		var w, dw int64
   409  		w = o.SampleValue(sample.Value)
   410  		if o.SampleMeanDivisor != nil {
   411  			dw = o.SampleMeanDivisor(sample.Value)
   412  		}
   413  		if dw == 0 && w == 0 {
   414  			continue
   415  		}
   416  		var parent *Node
   417  		labels := joinLabels(sample)
   418  		// Group the sample frames, based on a per-node map.
   419  		for i := len(sample.Location) - 1; i >= 0; i-- {
   420  			l := sample.Location[i]
   421  			lines := l.Line
   422  			if len(lines) == 0 {
   423  				lines = []profile.Line{{}} // Create empty line to include location info.
   424  			}
   425  			for lidx := len(lines) - 1; lidx >= 0; lidx-- {
   426  				nodeMap := parentNodeMap[parent]
   427  				if nodeMap == nil {
   428  					nodeMap = make(NodeMap)
   429  					parentNodeMap[parent] = nodeMap
   430  				}
   431  				n := nodeMap.findOrInsertLine(l, lines[lidx], o)
   432  				if n == nil {
   433  					continue
   434  				}
   435  				n.addSample(dw, w, labels, sample.NumLabel, sample.NumUnit, o.FormatTag, false)
   436  				if parent != nil {
   437  					parent.AddToEdgeDiv(n, dw, w, false, lidx != len(lines)-1)
   438  				}
   439  				parent = n
   440  			}
   441  		}
   442  		if parent != nil {
   443  			parent.addSample(dw, w, labels, sample.NumLabel, sample.NumUnit, o.FormatTag, true)
   444  		}
   445  	}
   446  
   447  	nodes := make(Nodes, 0, len(prof.Location))
   448  	for _, nm := range parentNodeMap {
   449  		nodes = append(nodes, nm.nodes()...)
   450  	}
   451  	return selectNodesForGraph(nodes, o.DropNegative)
   452  }
   453  
   454  // ShortenFunctionName returns a shortened version of a function's name.
   455  func ShortenFunctionName(f string) string {
   456  	f = cppAnonymousPrefixRegExp.ReplaceAllString(f, "")
   457  	f = goVerRegExp.ReplaceAllString(f, `${1}${2}`)
   458  	for _, re := range []*regexp.Regexp{goRegExp, javaRegExp, cppRegExp} {
   459  		if matches := re.FindStringSubmatch(f); len(matches) >= 2 {
   460  			return strings.Join(matches[1:], "")
   461  		}
   462  	}
   463  	return f
   464  }
   465  
   466  // TrimTree trims a Graph in forest form, keeping only the nodes in kept. This
   467  // will not work correctly if even a single node has multiple parents.
   468  func (g *Graph) TrimTree(kept NodePtrSet) {
   469  	// Creates a new list of nodes
   470  	oldNodes := g.Nodes
   471  	g.Nodes = make(Nodes, 0, len(kept))
   472  
   473  	for _, cur := range oldNodes {
   474  		// A node may not have multiple parents
   475  		if len(cur.In) > 1 {
   476  			panic("TrimTree only works on trees")
   477  		}
   478  
   479  		// If a node should be kept, add it to the new list of nodes
   480  		if _, ok := kept[cur]; ok {
   481  			g.Nodes = append(g.Nodes, cur)
   482  			continue
   483  		}
   484  
   485  		// If a node has no parents, then delete all of the in edges of its
   486  		// children to make them each roots of their own trees.
   487  		if len(cur.In) == 0 {
   488  			for _, outEdge := range cur.Out {
   489  				delete(outEdge.Dest.In, cur)
   490  			}
   491  			continue
   492  		}
   493  
   494  		// Get the parent. This works since at this point cur.In must contain only
   495  		// one element.
   496  		if len(cur.In) != 1 {
   497  			panic("Get parent assertion failed. cur.In expected to be of length 1.")
   498  		}
   499  		var parent *Node
   500  		for _, edge := range cur.In {
   501  			parent = edge.Src
   502  		}
   503  
   504  		parentEdgeInline := parent.Out[cur].Inline
   505  
   506  		// Remove the edge from the parent to this node
   507  		delete(parent.Out, cur)
   508  
   509  		// Reconfigure every edge from the current node to now begin at the parent.
   510  		for _, outEdge := range cur.Out {
   511  			child := outEdge.Dest
   512  
   513  			delete(child.In, cur)
   514  			child.In[parent] = outEdge
   515  			parent.Out[child] = outEdge
   516  
   517  			outEdge.Src = parent
   518  			outEdge.Residual = true
   519  			// If the edge from the parent to the current node and the edge from the
   520  			// current node to the child are both inline, then this resulting residual
   521  			// edge should also be inline
   522  			outEdge.Inline = parentEdgeInline && outEdge.Inline
   523  		}
   524  	}
   525  	g.RemoveRedundantEdges()
   526  }
   527  
   528  func joinLabels(s *profile.Sample) string {
   529  	if len(s.Label) == 0 {
   530  		return ""
   531  	}
   532  
   533  	var labels []string
   534  	for key, vals := range s.Label {
   535  		for _, v := range vals {
   536  			labels = append(labels, key+":"+v)
   537  		}
   538  	}
   539  	sort.Strings(labels)
   540  	return strings.Join(labels, `\n`)
   541  }
   542  
   543  // isNegative returns true if the node is considered as "negative" for the
   544  // purposes of drop_negative.
   545  func isNegative(n *Node) bool {
   546  	switch {
   547  	case n.Flat < 0:
   548  		return true
   549  	case n.Flat == 0 && n.Cum < 0:
   550  		return true
   551  	default:
   552  		return false
   553  	}
   554  }
   555  
   556  // CreateNodes creates graph nodes for all locations in a profile. It
   557  // returns set of all nodes, plus a mapping of each location to the
   558  // set of corresponding nodes (one per location.Line).
   559  func CreateNodes(prof *profile.Profile, o *Options) (Nodes, map[uint64]Nodes) {
   560  	locations := make(map[uint64]Nodes, len(prof.Location))
   561  	nm := make(NodeMap, len(prof.Location))
   562  	for _, l := range prof.Location {
   563  		lines := l.Line
   564  		if len(lines) == 0 {
   565  			lines = []profile.Line{{}} // Create empty line to include location info.
   566  		}
   567  		nodes := make(Nodes, len(lines))
   568  		for ln := range lines {
   569  			nodes[ln] = nm.findOrInsertLine(l, lines[ln], o)
   570  		}
   571  		locations[l.ID] = nodes
   572  	}
   573  	return nm.nodes(), locations
   574  }
   575  
   576  func (nm NodeMap) nodes() Nodes {
   577  	nodes := make(Nodes, 0, len(nm))
   578  	for _, n := range nm {
   579  		nodes = append(nodes, n)
   580  	}
   581  	return nodes
   582  }
   583  
   584  func (nm NodeMap) findOrInsertLine(l *profile.Location, li profile.Line, o *Options) *Node {
   585  	var objfile string
   586  	if m := l.Mapping; m != nil && m.File != "" {
   587  		objfile = m.File
   588  	}
   589  
   590  	if ni := nodeInfo(l, li, objfile, o); ni != nil {
   591  		return nm.FindOrInsertNode(*ni, o.KeptNodes)
   592  	}
   593  	return nil
   594  }
   595  
   596  func nodeInfo(l *profile.Location, line profile.Line, objfile string, o *Options) *NodeInfo {
   597  	if line.Function == nil {
   598  		return &NodeInfo{Address: l.Address, Objfile: objfile}
   599  	}
   600  	ni := &NodeInfo{
   601  		Address:  l.Address,
   602  		Lineno:   int(line.Line),
   603  		Columnno: int(line.Column),
   604  		Name:     line.Function.Name,
   605  	}
   606  	if fname := line.Function.Filename; fname != "" {
   607  		ni.File = filepath.Clean(fname)
   608  	}
   609  	if o.OrigFnNames {
   610  		ni.OrigName = line.Function.SystemName
   611  	}
   612  	if o.ObjNames || (ni.Name == "" && ni.OrigName == "") {
   613  		ni.Objfile = objfile
   614  		ni.StartLine = int(line.Function.StartLine)
   615  	}
   616  	return ni
   617  }
   618  
   619  type tags struct {
   620  	t    []*Tag
   621  	flat bool
   622  }
   623  
   624  func (t tags) Len() int      { return len(t.t) }
   625  func (t tags) Swap(i, j int) { t.t[i], t.t[j] = t.t[j], t.t[i] }
   626  func (t tags) Less(i, j int) bool {
   627  	if !t.flat {
   628  		if t.t[i].Cum != t.t[j].Cum {
   629  			return abs64(t.t[i].Cum) > abs64(t.t[j].Cum)
   630  		}
   631  	}
   632  	if t.t[i].Flat != t.t[j].Flat {
   633  		return abs64(t.t[i].Flat) > abs64(t.t[j].Flat)
   634  	}
   635  	return t.t[i].Name < t.t[j].Name
   636  }
   637  
   638  // Sum adds the flat and cum values of a set of nodes.
   639  func (ns Nodes) Sum() (flat int64, cum int64) {
   640  	for _, n := range ns {
   641  		flat += n.Flat
   642  		cum += n.Cum
   643  	}
   644  	return
   645  }
   646  
   647  func (n *Node) addSample(dw, w int64, labels string, numLabel map[string][]int64, numUnit map[string][]string, format func(int64, string) string, flat bool) {
   648  	// Update sample value
   649  	if flat {
   650  		n.FlatDiv += dw
   651  		n.Flat += w
   652  	} else {
   653  		n.CumDiv += dw
   654  		n.Cum += w
   655  	}
   656  
   657  	// Add string tags
   658  	if labels != "" {
   659  		t := n.LabelTags.findOrAddTag(labels, "", 0)
   660  		if flat {
   661  			t.FlatDiv += dw
   662  			t.Flat += w
   663  		} else {
   664  			t.CumDiv += dw
   665  			t.Cum += w
   666  		}
   667  	}
   668  
   669  	numericTags := n.NumericTags[labels]
   670  	if numericTags == nil {
   671  		numericTags = TagMap{}
   672  		n.NumericTags[labels] = numericTags
   673  	}
   674  	// Add numeric tags
   675  	if format == nil {
   676  		format = defaultLabelFormat
   677  	}
   678  	for k, nvals := range numLabel {
   679  		units := numUnit[k]
   680  		for i, v := range nvals {
   681  			var t *Tag
   682  			if len(units) > 0 {
   683  				t = numericTags.findOrAddTag(format(v, units[i]), units[i], v)
   684  			} else {
   685  				t = numericTags.findOrAddTag(format(v, k), k, v)
   686  			}
   687  			if flat {
   688  				t.FlatDiv += dw
   689  				t.Flat += w
   690  			} else {
   691  				t.CumDiv += dw
   692  				t.Cum += w
   693  			}
   694  		}
   695  	}
   696  }
   697  
   698  func defaultLabelFormat(v int64, key string) string {
   699  	return strconv.FormatInt(v, 10)
   700  }
   701  
   702  func (m TagMap) findOrAddTag(label, unit string, value int64) *Tag {
   703  	l := m[label]
   704  	if l == nil {
   705  		l = &Tag{
   706  			Name:  label,
   707  			Unit:  unit,
   708  			Value: value,
   709  		}
   710  		m[label] = l
   711  	}
   712  	return l
   713  }
   714  
   715  // String returns a text representation of a graph, for debugging purposes.
   716  func (g *Graph) String() string {
   717  	var s []string
   718  
   719  	nodeIndex := make(map[*Node]int, len(g.Nodes))
   720  
   721  	for i, n := range g.Nodes {
   722  		nodeIndex[n] = i + 1
   723  	}
   724  
   725  	for i, n := range g.Nodes {
   726  		name := n.Info.PrintableName()
   727  		var in, out []int
   728  
   729  		for _, from := range n.In {
   730  			in = append(in, nodeIndex[from.Src])
   731  		}
   732  		for _, to := range n.Out {
   733  			out = append(out, nodeIndex[to.Dest])
   734  		}
   735  		s = append(s, fmt.Sprintf("%d: %s[flat=%d cum=%d] %x -> %v ", i+1, name, n.Flat, n.Cum, in, out))
   736  	}
   737  	return strings.Join(s, "\n")
   738  }
   739  
   740  // DiscardLowFrequencyNodes returns a set of the nodes at or over a
   741  // specific cum value cutoff.
   742  func (g *Graph) DiscardLowFrequencyNodes(nodeCutoff int64) NodeSet {
   743  	return makeNodeSet(g.Nodes, nodeCutoff)
   744  }
   745  
   746  // DiscardLowFrequencyNodePtrs returns a NodePtrSet of nodes at or over a
   747  // specific cum value cutoff.
   748  func (g *Graph) DiscardLowFrequencyNodePtrs(nodeCutoff int64) NodePtrSet {
   749  	cutNodes := getNodesAboveCumCutoff(g.Nodes, nodeCutoff)
   750  	kept := make(NodePtrSet, len(cutNodes))
   751  	for _, n := range cutNodes {
   752  		kept[n] = true
   753  	}
   754  	return kept
   755  }
   756  
   757  func makeNodeSet(nodes Nodes, nodeCutoff int64) NodeSet {
   758  	cutNodes := getNodesAboveCumCutoff(nodes, nodeCutoff)
   759  	kept := make(NodeSet, len(cutNodes))
   760  	for _, n := range cutNodes {
   761  		kept[n.Info] = true
   762  	}
   763  	return kept
   764  }
   765  
   766  // getNodesAboveCumCutoff returns all the nodes which have a Cum value greater
   767  // than or equal to cutoff.
   768  func getNodesAboveCumCutoff(nodes Nodes, nodeCutoff int64) Nodes {
   769  	cutoffNodes := make(Nodes, 0, len(nodes))
   770  	for _, n := range nodes {
   771  		if abs64(n.Cum) < nodeCutoff {
   772  			continue
   773  		}
   774  		cutoffNodes = append(cutoffNodes, n)
   775  	}
   776  	return cutoffNodes
   777  }
   778  
   779  // TrimLowFrequencyTags removes tags that have less than
   780  // the specified weight.
   781  func (g *Graph) TrimLowFrequencyTags(tagCutoff int64) {
   782  	// Remove nodes with value <= total*nodeFraction
   783  	for _, n := range g.Nodes {
   784  		n.LabelTags = trimLowFreqTags(n.LabelTags, tagCutoff)
   785  		for s, nt := range n.NumericTags {
   786  			n.NumericTags[s] = trimLowFreqTags(nt, tagCutoff)
   787  		}
   788  	}
   789  }
   790  
   791  func trimLowFreqTags(tags TagMap, minValue int64) TagMap {
   792  	kept := TagMap{}
   793  	for s, t := range tags {
   794  		if abs64(t.Flat) >= minValue || abs64(t.Cum) >= minValue {
   795  			kept[s] = t
   796  		}
   797  	}
   798  	return kept
   799  }
   800  
   801  // TrimLowFrequencyEdges removes edges that have less than
   802  // the specified weight. Returns the number of edges removed
   803  func (g *Graph) TrimLowFrequencyEdges(edgeCutoff int64) int {
   804  	var droppedEdges int
   805  	for _, n := range g.Nodes {
   806  		for src, e := range n.In {
   807  			if abs64(e.Weight) < edgeCutoff {
   808  				delete(n.In, src)
   809  				delete(src.Out, n)
   810  				droppedEdges++
   811  			}
   812  		}
   813  	}
   814  	return droppedEdges
   815  }
   816  
   817  // SortNodes sorts the nodes in a graph based on a specific heuristic.
   818  func (g *Graph) SortNodes(cum bool, visualMode bool) {
   819  	// Sort nodes based on requested mode
   820  	switch {
   821  	case visualMode:
   822  		// Specialized sort to produce a more visually-interesting graph
   823  		g.Nodes.Sort(EntropyOrder)
   824  	case cum:
   825  		g.Nodes.Sort(CumNameOrder)
   826  	default:
   827  		g.Nodes.Sort(FlatNameOrder)
   828  	}
   829  }
   830  
   831  // SelectTopNodePtrs returns a set of the top maxNodes *Node in a graph.
   832  func (g *Graph) SelectTopNodePtrs(maxNodes int, visualMode bool) NodePtrSet {
   833  	set := make(NodePtrSet)
   834  	for _, node := range g.selectTopNodes(maxNodes, visualMode) {
   835  		set[node] = true
   836  	}
   837  	return set
   838  }
   839  
   840  // SelectTopNodes returns a set of the top maxNodes nodes in a graph.
   841  func (g *Graph) SelectTopNodes(maxNodes int, visualMode bool) NodeSet {
   842  	return makeNodeSet(g.selectTopNodes(maxNodes, visualMode), 0)
   843  }
   844  
   845  // selectTopNodes returns a slice of the top maxNodes nodes in a graph.
   846  func (g *Graph) selectTopNodes(maxNodes int, visualMode bool) Nodes {
   847  	if maxNodes > 0 {
   848  		if visualMode {
   849  			var count int
   850  			// If generating a visual graph, count tags as nodes. Update
   851  			// maxNodes to account for them.
   852  			for i, n := range g.Nodes {
   853  				tags := countTags(n)
   854  				if tags > maxNodelets {
   855  					tags = maxNodelets
   856  				}
   857  				if count += tags + 1; count >= maxNodes {
   858  					maxNodes = i + 1
   859  					break
   860  				}
   861  			}
   862  		}
   863  	}
   864  	if maxNodes > len(g.Nodes) {
   865  		maxNodes = len(g.Nodes)
   866  	}
   867  	return g.Nodes[:maxNodes]
   868  }
   869  
   870  // countTags counts the tags with flat count. This underestimates the
   871  // number of tags being displayed, but in practice is close enough.
   872  func countTags(n *Node) int {
   873  	count := 0
   874  	for _, e := range n.LabelTags {
   875  		if e.Flat != 0 {
   876  			count++
   877  		}
   878  	}
   879  	for _, t := range n.NumericTags {
   880  		for _, e := range t {
   881  			if e.Flat != 0 {
   882  				count++
   883  			}
   884  		}
   885  	}
   886  	return count
   887  }
   888  
   889  // RemoveRedundantEdges removes residual edges if the destination can
   890  // be reached through another path. This is done to simplify the graph
   891  // while preserving connectivity.
   892  func (g *Graph) RemoveRedundantEdges() {
   893  	// Walk the nodes and outgoing edges in reverse order to prefer
   894  	// removing edges with the lowest weight.
   895  	for i := len(g.Nodes); i > 0; i-- {
   896  		n := g.Nodes[i-1]
   897  		in := n.In.Sort()
   898  		for j := len(in); j > 0; j-- {
   899  			e := in[j-1]
   900  			if !e.Residual {
   901  				// Do not remove edges heavier than a non-residual edge, to
   902  				// avoid potential confusion.
   903  				break
   904  			}
   905  			if isRedundantEdge(e) {
   906  				delete(e.Src.Out, e.Dest)
   907  				delete(e.Dest.In, e.Src)
   908  			}
   909  		}
   910  	}
   911  }
   912  
   913  // isRedundantEdge determines if there is a path that allows e.Src
   914  // to reach e.Dest after removing e.
   915  func isRedundantEdge(e *Edge) bool {
   916  	src, n := e.Src, e.Dest
   917  	seen := map[*Node]bool{n: true}
   918  	queue := Nodes{n}
   919  	for len(queue) > 0 {
   920  		n := queue[0]
   921  		queue = queue[1:]
   922  		for _, ie := range n.In {
   923  			if e == ie || seen[ie.Src] {
   924  				continue
   925  			}
   926  			if ie.Src == src {
   927  				return true
   928  			}
   929  			seen[ie.Src] = true
   930  			queue = append(queue, ie.Src)
   931  		}
   932  	}
   933  	return false
   934  }
   935  
   936  // nodeSorter is a mechanism used to allow a report to be sorted
   937  // in different ways.
   938  type nodeSorter struct {
   939  	rs   Nodes
   940  	less func(l, r *Node) bool
   941  }
   942  
   943  func (s nodeSorter) Len() int           { return len(s.rs) }
   944  func (s nodeSorter) Swap(i, j int)      { s.rs[i], s.rs[j] = s.rs[j], s.rs[i] }
   945  func (s nodeSorter) Less(i, j int) bool { return s.less(s.rs[i], s.rs[j]) }
   946  
   947  // Sort reorders a slice of nodes based on the specified ordering
   948  // criteria. The result is sorted in decreasing order for (absolute)
   949  // numeric quantities, alphabetically for text, and increasing for
   950  // addresses.
   951  func (ns Nodes) Sort(o NodeOrder) error {
   952  	var s nodeSorter
   953  
   954  	switch o {
   955  	case FlatNameOrder:
   956  		s = nodeSorter{ns,
   957  			func(l, r *Node) bool {
   958  				if iv, jv := abs64(l.Flat), abs64(r.Flat); iv != jv {
   959  					return iv > jv
   960  				}
   961  				if iv, jv := l.Info.PrintableName(), r.Info.PrintableName(); iv != jv {
   962  					return iv < jv
   963  				}
   964  				if iv, jv := abs64(l.Cum), abs64(r.Cum); iv != jv {
   965  					return iv > jv
   966  				}
   967  				return compareNodes(l, r)
   968  			},
   969  		}
   970  	case FlatCumNameOrder:
   971  		s = nodeSorter{ns,
   972  			func(l, r *Node) bool {
   973  				if iv, jv := abs64(l.Flat), abs64(r.Flat); iv != jv {
   974  					return iv > jv
   975  				}
   976  				if iv, jv := abs64(l.Cum), abs64(r.Cum); iv != jv {
   977  					return iv > jv
   978  				}
   979  				if iv, jv := l.Info.PrintableName(), r.Info.PrintableName(); iv != jv {
   980  					return iv < jv
   981  				}
   982  				return compareNodes(l, r)
   983  			},
   984  		}
   985  	case NameOrder:
   986  		s = nodeSorter{ns,
   987  			func(l, r *Node) bool {
   988  				if iv, jv := l.Info.Name, r.Info.Name; iv != jv {
   989  					return iv < jv
   990  				}
   991  				return compareNodes(l, r)
   992  			},
   993  		}
   994  	case FileOrder:
   995  		s = nodeSorter{ns,
   996  			func(l, r *Node) bool {
   997  				if iv, jv := l.Info.File, r.Info.File; iv != jv {
   998  					return iv < jv
   999  				}
  1000  				if iv, jv := l.Info.StartLine, r.Info.StartLine; iv != jv {
  1001  					return iv < jv
  1002  				}
  1003  				return compareNodes(l, r)
  1004  			},
  1005  		}
  1006  	case AddressOrder:
  1007  		s = nodeSorter{ns,
  1008  			func(l, r *Node) bool {
  1009  				if iv, jv := l.Info.Address, r.Info.Address; iv != jv {
  1010  					return iv < jv
  1011  				}
  1012  				return compareNodes(l, r)
  1013  			},
  1014  		}
  1015  	case CumNameOrder, EntropyOrder:
  1016  		// Hold scoring for score-based ordering
  1017  		var score map[*Node]int64
  1018  		scoreOrder := func(l, r *Node) bool {
  1019  			if iv, jv := abs64(score[l]), abs64(score[r]); iv != jv {
  1020  				return iv > jv
  1021  			}
  1022  			if iv, jv := l.Info.PrintableName(), r.Info.PrintableName(); iv != jv {
  1023  				return iv < jv
  1024  			}
  1025  			if iv, jv := abs64(l.Flat), abs64(r.Flat); iv != jv {
  1026  				return iv > jv
  1027  			}
  1028  			return compareNodes(l, r)
  1029  		}
  1030  
  1031  		switch o {
  1032  		case CumNameOrder:
  1033  			score = make(map[*Node]int64, len(ns))
  1034  			for _, n := range ns {
  1035  				score[n] = n.Cum
  1036  			}
  1037  			s = nodeSorter{ns, scoreOrder}
  1038  		case EntropyOrder:
  1039  			score = make(map[*Node]int64, len(ns))
  1040  			for _, n := range ns {
  1041  				score[n] = entropyScore(n)
  1042  			}
  1043  			s = nodeSorter{ns, scoreOrder}
  1044  		}
  1045  	default:
  1046  		return fmt.Errorf("report: unrecognized sort ordering: %d", o)
  1047  	}
  1048  	sort.Sort(s)
  1049  	return nil
  1050  }
  1051  
  1052  // compareNodes compares two nodes to provide a deterministic ordering
  1053  // between them. Two nodes cannot have the same Node.Info value.
  1054  func compareNodes(l, r *Node) bool {
  1055  	return fmt.Sprint(l.Info) < fmt.Sprint(r.Info)
  1056  }
  1057  
  1058  // entropyScore computes a score for a node representing how important
  1059  // it is to include this node on a graph visualization. It is used to
  1060  // sort the nodes and select which ones to display if we have more
  1061  // nodes than desired in the graph. This number is computed by looking
  1062  // at the flat and cum weights of the node and the incoming/outgoing
  1063  // edges. The fundamental idea is to penalize nodes that have a simple
  1064  // fallthrough from their incoming to the outgoing edge.
  1065  func entropyScore(n *Node) int64 {
  1066  	score := float64(0)
  1067  
  1068  	if len(n.In) == 0 {
  1069  		score++ // Favor entry nodes
  1070  	} else {
  1071  		score += edgeEntropyScore(n, n.In, 0)
  1072  	}
  1073  
  1074  	if len(n.Out) == 0 {
  1075  		score++ // Favor leaf nodes
  1076  	} else {
  1077  		score += edgeEntropyScore(n, n.Out, n.Flat)
  1078  	}
  1079  
  1080  	return int64(score*float64(n.Cum)) + n.Flat
  1081  }
  1082  
  1083  // edgeEntropyScore computes the entropy value for a set of edges
  1084  // coming in or out of a node. Entropy (as defined in information
  1085  // theory) refers to the amount of information encoded by the set of
  1086  // edges. A set of edges that have a more interesting distribution of
  1087  // samples gets a higher score.
  1088  func edgeEntropyScore(n *Node, edges EdgeMap, self int64) float64 {
  1089  	score := float64(0)
  1090  	total := self
  1091  	for _, e := range edges {
  1092  		if e.Weight > 0 {
  1093  			total += abs64(e.Weight)
  1094  		}
  1095  	}
  1096  	if total != 0 {
  1097  		for _, e := range edges {
  1098  			frac := float64(abs64(e.Weight)) / float64(total)
  1099  			score += -frac * math.Log2(frac)
  1100  		}
  1101  		if self > 0 {
  1102  			frac := float64(abs64(self)) / float64(total)
  1103  			score += -frac * math.Log2(frac)
  1104  		}
  1105  	}
  1106  	return score
  1107  }
  1108  
  1109  // NodeOrder sets the ordering for a Sort operation
  1110  type NodeOrder int
  1111  
  1112  // Sorting options for node sort.
  1113  const (
  1114  	FlatNameOrder NodeOrder = iota
  1115  	FlatCumNameOrder
  1116  	CumNameOrder
  1117  	NameOrder
  1118  	FileOrder
  1119  	AddressOrder
  1120  	EntropyOrder
  1121  )
  1122  
  1123  // Sort returns a slice of the edges in the map, in a consistent
  1124  // order. The sort order is first based on the edge weight
  1125  // (higher-to-lower) and then by the node names to avoid flakiness.
  1126  func (e EdgeMap) Sort() []*Edge {
  1127  	el := make(edgeList, 0, len(e))
  1128  	for _, w := range e {
  1129  		el = append(el, w)
  1130  	}
  1131  
  1132  	sort.Sort(el)
  1133  	return el
  1134  }
  1135  
  1136  // Sum returns the total weight for a set of nodes.
  1137  func (e EdgeMap) Sum() int64 {
  1138  	var ret int64
  1139  	for _, edge := range e {
  1140  		ret += edge.Weight
  1141  	}
  1142  	return ret
  1143  }
  1144  
  1145  type edgeList []*Edge
  1146  
  1147  func (el edgeList) Len() int {
  1148  	return len(el)
  1149  }
  1150  
  1151  func (el edgeList) Less(i, j int) bool {
  1152  	if el[i].Weight != el[j].Weight {
  1153  		return abs64(el[i].Weight) > abs64(el[j].Weight)
  1154  	}
  1155  
  1156  	from1 := el[i].Src.Info.PrintableName()
  1157  	from2 := el[j].Src.Info.PrintableName()
  1158  	if from1 != from2 {
  1159  		return from1 < from2
  1160  	}
  1161  
  1162  	to1 := el[i].Dest.Info.PrintableName()
  1163  	to2 := el[j].Dest.Info.PrintableName()
  1164  
  1165  	return to1 < to2
  1166  }
  1167  
  1168  func (el edgeList) Swap(i, j int) {
  1169  	el[i], el[j] = el[j], el[i]
  1170  }
  1171  
  1172  func abs64(i int64) int64 {
  1173  	if i < 0 {
  1174  		return -i
  1175  	}
  1176  	return i
  1177  }
  1178
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