go/callgraph/rta/rta.go - tools - Git at Google

 // Copyright 2013 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.

 // This package provides Rapid Type Analysis (RTA) for Go, a fast
 // algorithm for call graph construction and discovery of reachable code
 // (and hence dead code) and runtime types.  The algorithm was first
 // described in:
 //
 // David F. Bacon and Peter F. Sweeney. 1996.
 // Fast static analysis of C++ virtual function calls. (OOPSLA '96)
 // http://doi.acm.org/10.1145/236337.236371
 //
 // The algorithm uses dynamic programming to tabulate the cross-product
 // of the set of known "address taken" functions with the set of known
 // dynamic calls of the same type.  As each new address-taken function
 // is discovered, call graph edges are added from each known callsite,
 // and as each new call site is discovered, call graph edges are added
 // from it to each known address-taken function.
 //
 // A similar approach is used for dynamic calls via interfaces: it
 // tabulates the cross-product of the set of known "runtime types",
 // i.e. types that may appear in an interface value, or be derived from
 // one via reflection, with the set of known "invoke"-mode dynamic
 // calls.  As each new "runtime type" is discovered, call edges are
 // added from the known call sites, and as each new call site is
 // discovered, call graph edges are added to each compatible
 // method.
 //
 // In addition, we must consider all exported methods of any runtime type
 // as reachable, since they may be called via reflection.
 //
 // Each time a newly added call edge causes a new function to become
 // reachable, the code of that function is analyzed for more call sites,
 // address-taken functions, and runtime types.  The process continues
 // until a fixed point is achieved.
 //
 // The resulting call graph is less precise than one produced by pointer
 // analysis, but the algorithm is much faster.  For example, running the
 // cmd/callgraph tool on its own source takes ~2.1s for RTA and ~5.4s
 // for points-to analysis.
 //
 package rta // import "golang.org/x/tools/go/callgraph/rta"

 // TODO(adonovan): test it by connecting it to the interpreter and
 // replacing all "unreachable" functions by a special intrinsic, and
 // ensure that that intrinsic is never called.

 import (
 	"fmt"
 	"go/types"

 	"golang.org/x/tools/go/callgraph"
 	"golang.org/x/tools/go/ssa"
 	"golang.org/x/tools/go/types/typeutil"
 )

 // A Result holds the results of Rapid Type Analysis, which includes the
 // set of reachable functions/methods, runtime types, and the call graph.
 //
 type Result struct {
 	// CallGraph is the discovered callgraph.
 	// It does not include edges for calls made via reflection.
 	CallGraph *callgraph.Graph

 	// Reachable contains the set of reachable functions and methods.
 	// This includes exported methods of runtime types, since
 	// they may be accessed via reflection.
 	// The value indicates whether the function is address-taken.
 	//
 	// (We wrap the bool in a struct to avoid inadvertent use of
 	// "if Reachable[f] {" to test for set membership.)
 	Reachable map[*ssa.Function]struct{ AddrTaken bool }

 	// RuntimeTypes contains the set of types that are needed at
 	// runtime, for interfaces or reflection.
 	//
 	// The value indicates whether the type is inaccessible to reflection.
 	// Consider:
 	// 	type A struct{B}
 	// 	fmt.Println(new(A))
 	// Types *A, A and B are accessible to reflection, but the unnamed
 	// type struct{B} is not.
 	RuntimeTypes typeutil.Map
 }

 // Working state of the RTA algorithm.
 type rta struct {
 	result *Result

 	prog *ssa.Program

 	worklist []*ssa.Function // list of functions to visit

 	// addrTakenFuncsBySig contains all address-taken *Functions, grouped by signature.
 	// Keys are *types.Signature, values are map[*ssa.Function]bool sets.
 	addrTakenFuncsBySig typeutil.Map

 	// dynCallSites contains all dynamic "call"-mode call sites, grouped by signature.
 	// Keys are *types.Signature, values are unordered []ssa.CallInstruction.
 	dynCallSites typeutil.Map

 	// invokeSites contains all "invoke"-mode call sites, grouped by interface.
 	// Keys are *types.Interface (never *types.Named),
 	// Values are unordered []ssa.CallInstruction sets.
 	invokeSites typeutil.Map

 	// The following two maps together define the subset of the
 	// m:n "implements" relation needed by the algorithm.

 	// concreteTypes maps each concrete type to the set of interfaces that it implements.
 	// Keys are types.Type, values are unordered []*types.Interface.
 	// Only concrete types used as MakeInterface operands are included.
 	concreteTypes typeutil.Map

 	// interfaceTypes maps each interface type to
 	// the set of concrete types that implement it.
 	// Keys are *types.Interface, values are unordered []types.Type.
 	// Only interfaces used in "invoke"-mode CallInstructions are included.
 	interfaceTypes typeutil.Map
 }

 // addReachable marks a function as potentially callable at run-time,
 // and ensures that it gets processed.
 func (r *rta) addReachable(f *ssa.Function, addrTaken bool) {
 	reachable := r.result.Reachable
 	n := len(reachable)
 	v := reachable[f]
 	if addrTaken {
 		v.AddrTaken = true
 	}
 	reachable[f] = v
 	if len(reachable) > n {
 		// First time seeing f.  Add it to the worklist.
 		r.worklist = append(r.worklist, f)
 	}
 }

 // addEdge adds the specified call graph edge, and marks it reachable.
 // addrTaken indicates whether to mark the callee as "address-taken".
 func (r *rta) addEdge(site ssa.CallInstruction, callee *ssa.Function, addrTaken bool) {
 	r.addReachable(callee, addrTaken)

 	if g := r.result.CallGraph; g != nil {
 		if site.Parent() == nil {
 			panic(site)
 		}
 		from := g.CreateNode(site.Parent())
 		to := g.CreateNode(callee)
 		callgraph.AddEdge(from, site, to)
 	}
 }

 // ---------- addrTakenFuncs × dynCallSites ----------

 // visitAddrTakenFunc is called each time we encounter an address-taken function f.
 func (r *rta) visitAddrTakenFunc(f *ssa.Function) {
 	// Create two-level map (Signature -> Function -> bool).
 	S := f.Signature
 	funcs, _ := r.addrTakenFuncsBySig.At(S).(map[*ssa.Function]bool)
 	if funcs == nil {
 		funcs = make(map[*ssa.Function]bool)
 		r.addrTakenFuncsBySig.Set(S, funcs)
 	}
 	if !funcs[f] {
 		// First time seeing f.
 		funcs[f] = true

 		// If we've seen any dyncalls of this type, mark it reachable,
 		// and add call graph edges.
 		sites, _ := r.dynCallSites.At(S).([]ssa.CallInstruction)
 		for _, site := range sites {
 			r.addEdge(site, f, true)
 		}
 	}
 }

 // visitDynCall is called each time we encounter a dynamic "call"-mode call.
 func (r *rta) visitDynCall(site ssa.CallInstruction) {
 	S := site.Common().Signature()

 	// Record the call site.
 	sites, _ := r.dynCallSites.At(S).([]ssa.CallInstruction)
 	r.dynCallSites.Set(S, append(sites, site))

 	// For each function of signature S that we know is address-taken,
 	// add an edge and mark it reachable.
 	funcs, _ := r.addrTakenFuncsBySig.At(S).(map[*ssa.Function]bool)
 	for g := range funcs {
 		r.addEdge(site, g, true)
 	}
 }

 // ---------- concrete types × invoke sites ----------

 // addInvokeEdge is called for each new pair (site, C) in the matrix.
 func (r *rta) addInvokeEdge(site ssa.CallInstruction, C types.Type) {
 	// Ascertain the concrete method of C to be called.
 	imethod := site.Common().Method
 	cmethod := r.prog.MethodValue(r.prog.MethodSets.MethodSet(C).Lookup(imethod.Pkg(), imethod.Name()))
 	r.addEdge(site, cmethod, true)
 }

 // visitInvoke is called each time the algorithm encounters an "invoke"-mode call.
 func (r *rta) visitInvoke(site ssa.CallInstruction) {
 	I := site.Common().Value.Type().Underlying().(*types.Interface)

 	// Record the invoke site.
 	sites, _ := r.invokeSites.At(I).([]ssa.CallInstruction)
 	r.invokeSites.Set(I, append(sites, site))

 	// Add callgraph edge for each existing
 	// address-taken concrete type implementing I.
 	for _, C := range r.implementations(I) {
 		r.addInvokeEdge(site, C)
 	}
 }

 // ---------- main algorithm ----------

 // visitFunc processes function f.
 func (r *rta) visitFunc(f *ssa.Function) {
 	var space [32]*ssa.Value // preallocate space for common case

 	for _, b := range f.Blocks {
 		for _, instr := range b.Instrs {
 			rands := instr.Operands(space[:0])

 			switch instr := instr.(type) {
 			case ssa.CallInstruction:
 				call := instr.Common()
 				if call.IsInvoke() {
 					r.visitInvoke(instr)
 				} else if g := call.StaticCallee(); g != nil {
 					r.addEdge(instr, g, false)
 				} else if _, ok := call.Value.(*ssa.Builtin); !ok {
 					r.visitDynCall(instr)
 				}

 				// Ignore the call-position operand when
 				// looking for address-taken Functions.
 				// Hack: assume this is rands[0].
 				rands = rands[1:]

 			case *ssa.MakeInterface:
 				r.addRuntimeType(instr.X.Type(), false)
 			}

 			// Process all address-taken functions.
 			for _, op := range rands {
 				if g, ok := (*op).(*ssa.Function); ok {
 					r.visitAddrTakenFunc(g)
 				}
 			}
 		}
 	}
 }

 // Analyze performs Rapid Type Analysis, starting at the specified root
 // functions.  It returns nil if no roots were specified.
 //
 // If buildCallGraph is true, Result.CallGraph will contain a call
 // graph; otherwise, only the other fields (reachable functions) are
 // populated.
 //
 func Analyze(roots []*ssa.Function, buildCallGraph bool) *Result {
 	if len(roots) == 0 {
 		return nil
 	}

 	r := &rta{
 		result: &Result{Reachable: make(map[*ssa.Function]struct{ AddrTaken bool })},
 		prog:   roots[0].Prog,
 	}

 	if buildCallGraph {
 		// TODO(adonovan): change callgraph API to eliminate the
 		// notion of a distinguished root node.  Some callgraphs
 		// have many roots, or none.
 		r.result.CallGraph = callgraph.New(roots[0])
 	}

 	hasher := typeutil.MakeHasher()
 	r.result.RuntimeTypes.SetHasher(hasher)
 	r.addrTakenFuncsBySig.SetHasher(hasher)
 	r.dynCallSites.SetHasher(hasher)
 	r.invokeSites.SetHasher(hasher)
 	r.concreteTypes.SetHasher(hasher)
 	r.interfaceTypes.SetHasher(hasher)

 	// Visit functions, processing their instructions, and adding
 	// new functions to the worklist, until a fixed point is
 	// reached.
 	var shadow []*ssa.Function // for efficiency, we double-buffer the worklist
 	r.worklist = append(r.worklist, roots...)
 	for len(r.worklist) > 0 {
 		shadow, r.worklist = r.worklist, shadow[:0]
 		for _, f := range shadow {
 			r.visitFunc(f)
 		}
 	}
 	return r.result
 }

 // interfaces(C) returns all currently known interfaces implemented by C.
 func (r *rta) interfaces(C types.Type) []*types.Interface {
 	// Ascertain set of interfaces C implements
 	// and update 'implements' relation.
 	var ifaces []*types.Interface
 	r.interfaceTypes.Iterate(func(I types.Type, concs interface{}) {
 		if I := I.(*types.Interface); types.Implements(C, I) {
 			concs, _ := concs.([]types.Type)
 			r.interfaceTypes.Set(I, append(concs, C))
 			ifaces = append(ifaces, I)
 		}
 	})
 	r.concreteTypes.Set(C, ifaces)
 	return ifaces
 }

 // implementations(I) returns all currently known concrete types that implement I.
 func (r *rta) implementations(I *types.Interface) []types.Type {
 	var concs []types.Type
 	if v := r.interfaceTypes.At(I); v != nil {
 		concs = v.([]types.Type)
 	} else {
 		// First time seeing this interface.
 		// Update the 'implements' relation.
 		r.concreteTypes.Iterate(func(C types.Type, ifaces interface{}) {
 			if types.Implements(C, I) {
 				ifaces, _ := ifaces.([]*types.Interface)
 				r.concreteTypes.Set(C, append(ifaces, I))
 				concs = append(concs, C)
 			}
 		})
 		r.interfaceTypes.Set(I, concs)
 	}
 	return concs
 }

 // addRuntimeType is called for each concrete type that can be the
 // dynamic type of some interface or reflect.Value.
 // Adapted from needMethods in go/ssa/builder.go
 //
 func (r *rta) addRuntimeType(T types.Type, skip bool) {
 	if prev, ok := r.result.RuntimeTypes.At(T).(bool); ok {
 		if skip && !prev {
 			r.result.RuntimeTypes.Set(T, skip)
 		}
 		return
 	}
 	r.result.RuntimeTypes.Set(T, skip)

 	mset := r.prog.MethodSets.MethodSet(T)

 	if _, ok := T.Underlying().(*types.Interface); !ok {
 		// T is a new concrete type.
 		for i, n := 0, mset.Len(); i < n; i++ {
 			sel := mset.At(i)
 			m := sel.Obj()

 			if m.Exported() {
 				// Exported methods are always potentially callable via reflection.
 				r.addReachable(r.prog.MethodValue(sel), true)
 			}
 		}

 		// Add callgraph edge for each existing dynamic
 		// "invoke"-mode call via that interface.
 		for _, I := range r.interfaces(T) {
 			sites, _ := r.invokeSites.At(I).([]ssa.CallInstruction)
 			for _, site := range sites {
 				r.addInvokeEdge(site, T)
 			}
 		}
 	}

 	// Precondition: T is not a method signature (*Signature with Recv()!=nil).
 	// Recursive case: skip => don't call makeMethods(T).
 	// Each package maintains its own set of types it has visited.

 	var n *types.Named
 	switch T := T.(type) {
 	case *types.Named:
 		n = T
 	case *types.Pointer:
 		n, _ = T.Elem().(*types.Named)
 	}
 	if n != nil {
 		owner := n.Obj().Pkg()
 		if owner == nil {
 			return // built-in error type
 		}
 	}

 	// Recursion over signatures of each exported method.
 	for i := 0; i < mset.Len(); i++ {
 		if mset.At(i).Obj().Exported() {
 			sig := mset.At(i).Type().(*types.Signature)
 			r.addRuntimeType(sig.Params(), true)  // skip the Tuple itself
 			r.addRuntimeType(sig.Results(), true) // skip the Tuple itself
 		}
 	}

 	switch t := T.(type) {
 	case *types.Basic:
 		// nop

 	case *types.Interface:
 		// nop---handled by recursion over method set.

 	case *types.Pointer:
 		r.addRuntimeType(t.Elem(), false)

 	case *types.Slice:
 		r.addRuntimeType(t.Elem(), false)

 	case *types.Chan:
 		r.addRuntimeType(t.Elem(), false)

 	case *types.Map:
 		r.addRuntimeType(t.Key(), false)
 		r.addRuntimeType(t.Elem(), false)

 	case *types.Signature:
 		if t.Recv() != nil {
 			panic(fmt.Sprintf("Signature %s has Recv %s", t, t.Recv()))
 		}
 		r.addRuntimeType(t.Params(), true)  // skip the Tuple itself
 		r.addRuntimeType(t.Results(), true) // skip the Tuple itself

 	case *types.Named:
 		// A pointer-to-named type can be derived from a named
 		// type via reflection.  It may have methods too.
 		r.addRuntimeType(types.NewPointer(T), false)

 		// Consider 'type T struct{S}' where S has methods.
 		// Reflection provides no way to get from T to struct{S},
 		// only to S, so the method set of struct{S} is unwanted,
 		// so set 'skip' flag during recursion.
 		r.addRuntimeType(t.Underlying(), true)

 	case *types.Array:
 		r.addRuntimeType(t.Elem(), false)

 	case *types.Struct:
 		for i, n := 0, t.NumFields(); i < n; i++ {
 			r.addRuntimeType(t.Field(i).Type(), false)
 		}

 	case *types.Tuple:
 		for i, n := 0, t.Len(); i < n; i++ {
 			r.addRuntimeType(t.At(i).Type(), false)
 		}

 	default:
 		panic(T)
 	}
 }
	// Copyright 2013 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.

	// This package provides Rapid Type Analysis (RTA) for Go, a fast
	// algorithm for call graph construction and discovery of reachable code
	// (and hence dead code) and runtime types. The algorithm was first
	// described in:
	//
	// David F. Bacon and Peter F. Sweeney. 1996.
	// Fast static analysis of C++ virtual function calls. (OOPSLA '96)
	// http://doi.acm.org/10.1145/236337.236371
	//
	// The algorithm uses dynamic programming to tabulate the cross-product
	// of the set of known "address taken" functions with the set of known
	// dynamic calls of the same type. As each new address-taken function
	// is discovered, call graph edges are added from each known callsite,
	// and as each new call site is discovered, call graph edges are added
	// from it to each known address-taken function.
	//
	// A similar approach is used for dynamic calls via interfaces: it
	// tabulates the cross-product of the set of known "runtime types",
	// i.e. types that may appear in an interface value, or be derived from
	// one via reflection, with the set of known "invoke"-mode dynamic
	// calls. As each new "runtime type" is discovered, call edges are
	// added from the known call sites, and as each new call site is
	// discovered, call graph edges are added to each compatible
	// method.
	//
	// In addition, we must consider all exported methods of any runtime type
	// as reachable, since they may be called via reflection.
	//
	// Each time a newly added call edge causes a new function to become
	// reachable, the code of that function is analyzed for more call sites,
	// address-taken functions, and runtime types. The process continues
	// until a fixed point is achieved.
	//
	// The resulting call graph is less precise than one produced by pointer
	// analysis, but the algorithm is much faster. For example, running the
	// cmd/callgraph tool on its own source takes ~2.1s for RTA and ~5.4s
	// for points-to analysis.
	//
	package rta // import "golang.org/x/tools/go/callgraph/rta"

	// TODO(adonovan): test it by connecting it to the interpreter and
	// replacing all "unreachable" functions by a special intrinsic, and
	// ensure that that intrinsic is never called.

	import (
	"fmt"
	"go/types"

	"golang.org/x/tools/go/callgraph"
	"golang.org/x/tools/go/ssa"
	"golang.org/x/tools/go/types/typeutil"
	)

	// A Result holds the results of Rapid Type Analysis, which includes the
	// set of reachable functions/methods, runtime types, and the call graph.
	//
	type Result struct {
	// CallGraph is the discovered callgraph.
	// It does not include edges for calls made via reflection.
	CallGraph *callgraph.Graph

	// Reachable contains the set of reachable functions and methods.
	// This includes exported methods of runtime types, since
	// they may be accessed via reflection.
	// The value indicates whether the function is address-taken.
	//
	// (We wrap the bool in a struct to avoid inadvertent use of
	// "if Reachable[f] {" to test for set membership.)
	Reachable map[*ssa.Function]struct{ AddrTaken bool }

	// RuntimeTypes contains the set of types that are needed at
	// runtime, for interfaces or reflection.
	//
	// The value indicates whether the type is inaccessible to reflection.
	// Consider:
	// type A struct{B}
	// fmt.Println(new(A))
	// Types *A, A and B are accessible to reflection, but the unnamed
	// type struct{B} is not.
	RuntimeTypes typeutil.Map
	}

	// Working state of the RTA algorithm.
	type rta struct {
	result *Result

	prog *ssa.Program

	worklist []*ssa.Function // list of functions to visit

	// addrTakenFuncsBySig contains all address-taken *Functions, grouped by signature.
	// Keys are types.Signature, values are map[ssa.Function]bool sets.
	addrTakenFuncsBySig typeutil.Map

	// dynCallSites contains all dynamic "call"-mode call sites, grouped by signature.
	// Keys are *types.Signature, values are unordered []ssa.CallInstruction.
	dynCallSites typeutil.Map

	// invokeSites contains all "invoke"-mode call sites, grouped by interface.
	// Keys are types.Interface (never types.Named),
	// Values are unordered []ssa.CallInstruction sets.
	invokeSites typeutil.Map

	// The following two maps together define the subset of the
	// m:n "implements" relation needed by the algorithm.

	// concreteTypes maps each concrete type to the set of interfaces that it implements.
	// Keys are types.Type, values are unordered []*types.Interface.
	// Only concrete types used as MakeInterface operands are included.
	concreteTypes typeutil.Map

	// interfaceTypes maps each interface type to
	// the set of concrete types that implement it.
	// Keys are *types.Interface, values are unordered []types.Type.
	// Only interfaces used in "invoke"-mode CallInstructions are included.
	interfaceTypes typeutil.Map
	}

	// addReachable marks a function as potentially callable at run-time,
	// and ensures that it gets processed.
	func (r rta) addReachable(f ssa.Function, addrTaken bool) {
	reachable := r.result.Reachable
	n := len(reachable)
	v := reachable[f]
	if addrTaken {
	v.AddrTaken = true
	}
	reachable[f] = v
	if len(reachable) > n {
	// First time seeing f. Add it to the worklist.
	r.worklist = append(r.worklist, f)
	}
	}

	// addEdge adds the specified call graph edge, and marks it reachable.
	// addrTaken indicates whether to mark the callee as "address-taken".
	func (r rta) addEdge(site ssa.CallInstruction, callee ssa.Function, addrTaken bool) {
	r.addReachable(callee, addrTaken)

	if g := r.result.CallGraph; g != nil {
	if site.Parent() == nil {
	panic(site)
	}
	from := g.CreateNode(site.Parent())
	to := g.CreateNode(callee)
	callgraph.AddEdge(from, site, to)
	}
	}

	// ---------- addrTakenFuncs × dynCallSites ----------

	// visitAddrTakenFunc is called each time we encounter an address-taken function f.
	func (r rta) visitAddrTakenFunc(f ssa.Function) {
	// Create two-level map (Signature -> Function -> bool).
	S := f.Signature
	funcs, _ := r.addrTakenFuncsBySig.At(S).(map[*ssa.Function]bool)
	if funcs == nil {
	funcs = make(map[*ssa.Function]bool)
	r.addrTakenFuncsBySig.Set(S, funcs)
	}
	if !funcs[f] {
	// First time seeing f.
	funcs[f] = true

	// If we've seen any dyncalls of this type, mark it reachable,
	// and add call graph edges.
	sites, _ := r.dynCallSites.At(S).([]ssa.CallInstruction)
	for _, site := range sites {
	r.addEdge(site, f, true)
	}
	}
	}

	// visitDynCall is called each time we encounter a dynamic "call"-mode call.
	func (r *rta) visitDynCall(site ssa.CallInstruction) {
	S := site.Common().Signature()

	// Record the call site.
	sites, _ := r.dynCallSites.At(S).([]ssa.CallInstruction)
	r.dynCallSites.Set(S, append(sites, site))

	// For each function of signature S that we know is address-taken,
	// add an edge and mark it reachable.
	funcs, _ := r.addrTakenFuncsBySig.At(S).(map[*ssa.Function]bool)
	for g := range funcs {
	r.addEdge(site, g, true)
	}
	}

	// ---------- concrete types × invoke sites ----------

	// addInvokeEdge is called for each new pair (site, C) in the matrix.
	func (r *rta) addInvokeEdge(site ssa.CallInstruction, C types.Type) {
	// Ascertain the concrete method of C to be called.
	imethod := site.Common().Method
	cmethod := r.prog.MethodValue(r.prog.MethodSets.MethodSet(C).Lookup(imethod.Pkg(), imethod.Name()))
	r.addEdge(site, cmethod, true)
	}

	// visitInvoke is called each time the algorithm encounters an "invoke"-mode call.
	func (r *rta) visitInvoke(site ssa.CallInstruction) {
	I := site.Common().Value.Type().Underlying().(*types.Interface)

	// Record the invoke site.
	sites, _ := r.invokeSites.At(I).([]ssa.CallInstruction)
	r.invokeSites.Set(I, append(sites, site))

	// Add callgraph edge for each existing
	// address-taken concrete type implementing I.
	for _, C := range r.implementations(I) {
	r.addInvokeEdge(site, C)
	}
	}

	// ---------- main algorithm ----------

	// visitFunc processes function f.
	func (r rta) visitFunc(f ssa.Function) {
	var space [32]*ssa.Value // preallocate space for common case

	for _, b := range f.Blocks {
	for _, instr := range b.Instrs {
	rands := instr.Operands(space[:0])

	switch instr := instr.(type) {
	case ssa.CallInstruction:
	call := instr.Common()
	if call.IsInvoke() {
	r.visitInvoke(instr)
	} else if g := call.StaticCallee(); g != nil {
	r.addEdge(instr, g, false)
	} else if _, ok := call.Value.(*ssa.Builtin); !ok {
	r.visitDynCall(instr)
	}

	// Ignore the call-position operand when
	// looking for address-taken Functions.
	// Hack: assume this is rands[0].
	rands = rands[1:]

	case *ssa.MakeInterface:
	r.addRuntimeType(instr.X.Type(), false)
	}

	// Process all address-taken functions.
	for _, op := range rands {
	if g, ok := (op).(ssa.Function); ok {
	r.visitAddrTakenFunc(g)
	}
	}
	}
	}
	}

	// Analyze performs Rapid Type Analysis, starting at the specified root
	// functions. It returns nil if no roots were specified.
	//
	// If buildCallGraph is true, Result.CallGraph will contain a call
	// graph; otherwise, only the other fields (reachable functions) are
	// populated.
	//
	func Analyze(roots []ssa.Function, buildCallGraph bool) Result {
	if len(roots) == 0 {
	return nil
	}

	r := &rta{
	result: &Result{Reachable: make(map[*ssa.Function]struct{ AddrTaken bool })},
	prog: roots[0].Prog,
	}

	if buildCallGraph {
	// TODO(adonovan): change callgraph API to eliminate the
	// notion of a distinguished root node. Some callgraphs
	// have many roots, or none.
	r.result.CallGraph = callgraph.New(roots[0])
	}

	hasher := typeutil.MakeHasher()
	r.result.RuntimeTypes.SetHasher(hasher)
	r.addrTakenFuncsBySig.SetHasher(hasher)
	r.dynCallSites.SetHasher(hasher)
	r.invokeSites.SetHasher(hasher)
	r.concreteTypes.SetHasher(hasher)
	r.interfaceTypes.SetHasher(hasher)

	// Visit functions, processing their instructions, and adding
	// new functions to the worklist, until a fixed point is
	// reached.
	var shadow []*ssa.Function // for efficiency, we double-buffer the worklist
	r.worklist = append(r.worklist, roots...)
	for len(r.worklist) > 0 {
	shadow, r.worklist = r.worklist, shadow[:0]
	for _, f := range shadow {
	r.visitFunc(f)
	}
	}
	return r.result
	}

	// interfaces(C) returns all currently known interfaces implemented by C.
	func (r rta) interfaces(C types.Type) []types.Interface {
	// Ascertain set of interfaces C implements
	// and update 'implements' relation.
	var ifaces []*types.Interface
	r.interfaceTypes.Iterate(func(I types.Type, concs interface{}) {
	if I := I.(*types.Interface); types.Implements(C, I) {
	concs, _ := concs.([]types.Type)
	r.interfaceTypes.Set(I, append(concs, C))
	ifaces = append(ifaces, I)
	}
	})
	r.concreteTypes.Set(C, ifaces)
	return ifaces
	}

	// implementations(I) returns all currently known concrete types that implement I.
	func (r rta) implementations(I types.Interface) []types.Type {
	var concs []types.Type
	if v := r.interfaceTypes.At(I); v != nil {
	concs = v.([]types.Type)
	} else {
	// First time seeing this interface.
	// Update the 'implements' relation.
	r.concreteTypes.Iterate(func(C types.Type, ifaces interface{}) {
	if types.Implements(C, I) {
	ifaces, _ := ifaces.([]*types.Interface)
	r.concreteTypes.Set(C, append(ifaces, I))
	concs = append(concs, C)
	}
	})
	r.interfaceTypes.Set(I, concs)
	}
	return concs
	}

	// addRuntimeType is called for each concrete type that can be the
	// dynamic type of some interface or reflect.Value.
	// Adapted from needMethods in go/ssa/builder.go
	//
	func (r *rta) addRuntimeType(T types.Type, skip bool) {
	if prev, ok := r.result.RuntimeTypes.At(T).(bool); ok {
	if skip && !prev {
	r.result.RuntimeTypes.Set(T, skip)
	}
	return
	}
	r.result.RuntimeTypes.Set(T, skip)

	mset := r.prog.MethodSets.MethodSet(T)

	if _, ok := T.Underlying().(*types.Interface); !ok {
	// T is a new concrete type.
	for i, n := 0, mset.Len(); i < n; i++ {
	sel := mset.At(i)
	m := sel.Obj()

	if m.Exported() {
	// Exported methods are always potentially callable via reflection.
	r.addReachable(r.prog.MethodValue(sel), true)
	}
	}

	// Add callgraph edge for each existing dynamic
	// "invoke"-mode call via that interface.
	for _, I := range r.interfaces(T) {
	sites, _ := r.invokeSites.At(I).([]ssa.CallInstruction)
	for _, site := range sites {
	r.addInvokeEdge(site, T)
	}
	}
	}

	// Precondition: T is not a method signature (*Signature with Recv()!=nil).
	// Recursive case: skip => don't call makeMethods(T).
	// Each package maintains its own set of types it has visited.

	var n *types.Named
	switch T := T.(type) {
	case *types.Named:
	n = T
	case *types.Pointer:
	n, _ = T.Elem().(*types.Named)
	}
	if n != nil {
	owner := n.Obj().Pkg()
	if owner == nil {
	return // built-in error type
	}
	}

	// Recursion over signatures of each exported method.
	for i := 0; i < mset.Len(); i++ {
	if mset.At(i).Obj().Exported() {
	sig := mset.At(i).Type().(*types.Signature)
	r.addRuntimeType(sig.Params(), true) // skip the Tuple itself
	r.addRuntimeType(sig.Results(), true) // skip the Tuple itself
	}
	}

	switch t := T.(type) {
	case *types.Basic:
	// nop

	case *types.Interface:
	// nop---handled by recursion over method set.

	case *types.Pointer:
	r.addRuntimeType(t.Elem(), false)

	case *types.Slice:
	r.addRuntimeType(t.Elem(), false)

	case *types.Chan:
	r.addRuntimeType(t.Elem(), false)

	case *types.Map:
	r.addRuntimeType(t.Key(), false)
	r.addRuntimeType(t.Elem(), false)

	case *types.Signature:
	if t.Recv() != nil {
	panic(fmt.Sprintf("Signature %s has Recv %s", t, t.Recv()))
	}
	r.addRuntimeType(t.Params(), true) // skip the Tuple itself
	r.addRuntimeType(t.Results(), true) // skip the Tuple itself

	case *types.Named:
	// A pointer-to-named type can be derived from a named
	// type via reflection. It may have methods too.
	r.addRuntimeType(types.NewPointer(T), false)

	// Consider 'type T struct{S}' where S has methods.
	// Reflection provides no way to get from T to struct{S},
	// only to S, so the method set of struct{S} is unwanted,
	// so set 'skip' flag during recursion.
	r.addRuntimeType(t.Underlying(), true)

	case *types.Array:
	r.addRuntimeType(t.Elem(), false)

	case *types.Struct:
	for i, n := 0, t.NumFields(); i < n; i++ {
	r.addRuntimeType(t.Field(i).Type(), false)
	}

	case *types.Tuple:
	for i, n := 0, t.Len(); i < n; i++ {
	r.addRuntimeType(t.At(i).Type(), false)
	}

	default:
	panic(T)
	}
	}