github.com/pankona/gometalinter@v2.0.11+incompatible/_linters/src/golang.org/x/tools/go/pointer/doc.go (about)

     1  // Copyright 2013 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  /*
     6  
     7  Package pointer implements Andersen's analysis, an inclusion-based
     8  pointer analysis algorithm first described in (Andersen, 1994).
     9  
    10  A pointer analysis relates every pointer expression in a whole program
    11  to the set of memory locations to which it might point.  This
    12  information can be used to construct a call graph of the program that
    13  precisely represents the destinations of dynamic function and method
    14  calls.  It can also be used to determine, for example, which pairs of
    15  channel operations operate on the same channel.
    16  
    17  The package allows the client to request a set of expressions of
    18  interest for which the points-to information will be returned once the
    19  analysis is complete.  In addition, the client may request that a
    20  callgraph is constructed.  The example program in example_test.go
    21  demonstrates both of these features.  Clients should not request more
    22  information than they need since it may increase the cost of the
    23  analysis significantly.
    24  
    25  
    26  CLASSIFICATION
    27  
    28  Our algorithm is INCLUSION-BASED: the points-to sets for x and y will
    29  be related by pts(y) ⊇ pts(x) if the program contains the statement
    30  y = x.
    31  
    32  It is FLOW-INSENSITIVE: it ignores all control flow constructs and the
    33  order of statements in a program.  It is therefore a "MAY ALIAS"
    34  analysis: its facts are of the form "P may/may not point to L",
    35  not "P must point to L".
    36  
    37  It is FIELD-SENSITIVE: it builds separate points-to sets for distinct
    38  fields, such as x and y in struct { x, y *int }.
    39  
    40  It is mostly CONTEXT-INSENSITIVE: most functions are analyzed once,
    41  so values can flow in at one call to the function and return out at
    42  another.  Only some smaller functions are analyzed with consideration
    43  of their calling context.
    44  
    45  It has a CONTEXT-SENSITIVE HEAP: objects are named by both allocation
    46  site and context, so the objects returned by two distinct calls to f:
    47     func f() *T { return new(T) }
    48  are distinguished up to the limits of the calling context.
    49  
    50  It is a WHOLE PROGRAM analysis: it requires SSA-form IR for the
    51  complete Go program and summaries for native code.
    52  
    53  See the (Hind, PASTE'01) survey paper for an explanation of these terms.
    54  
    55  
    56  SOUNDNESS
    57  
    58  The analysis is fully sound when invoked on pure Go programs that do not
    59  use reflection or unsafe.Pointer conversions.  In other words, if there
    60  is any possible execution of the program in which pointer P may point to
    61  object O, the analysis will report that fact.
    62  
    63  
    64  REFLECTION
    65  
    66  By default, the "reflect" library is ignored by the analysis, as if all
    67  its functions were no-ops, but if the client enables the Reflection flag,
    68  the analysis will make a reasonable attempt to model the effects of
    69  calls into this library.  However, this comes at a significant
    70  performance cost, and not all features of that library are yet
    71  implemented.  In addition, some simplifying approximations must be made
    72  to ensure that the analysis terminates; for example, reflection can be
    73  used to construct an infinite set of types and values of those types,
    74  but the analysis arbitrarily bounds the depth of such types.
    75  
    76  Most but not all reflection operations are supported.
    77  In particular, addressable reflect.Values are not yet implemented, so
    78  operations such as (reflect.Value).Set have no analytic effect.
    79  
    80  
    81  UNSAFE POINTER CONVERSIONS
    82  
    83  The pointer analysis makes no attempt to understand aliasing between the
    84  operand x and result y of an unsafe.Pointer conversion:
    85     y = (*T)(unsafe.Pointer(x))
    86  It is as if the conversion allocated an entirely new object:
    87     y = new(T)
    88  
    89  
    90  NATIVE CODE
    91  
    92  The analysis cannot model the aliasing effects of functions written in
    93  languages other than Go, such as runtime intrinsics in C or assembly, or
    94  code accessed via cgo.  The result is as if such functions are no-ops.
    95  However, various important intrinsics are understood by the analysis,
    96  along with built-ins such as append.
    97  
    98  The analysis currently provides no way for users to specify the aliasing
    99  effects of native code.
   100  
   101  ------------------------------------------------------------------------
   102  
   103  IMPLEMENTATION
   104  
   105  The remaining documentation is intended for package maintainers and
   106  pointer analysis specialists.  Maintainers should have a solid
   107  understanding of the referenced papers (especially those by H&L and PKH)
   108  before making making significant changes.
   109  
   110  The implementation is similar to that described in (Pearce et al,
   111  PASTE'04).  Unlike many algorithms which interleave constraint
   112  generation and solving, constructing the callgraph as they go, this
   113  implementation for the most part observes a phase ordering (generation
   114  before solving), with only simple (copy) constraints being generated
   115  during solving.  (The exception is reflection, which creates various
   116  constraints during solving as new types flow to reflect.Value
   117  operations.)  This improves the traction of presolver optimisations,
   118  but imposes certain restrictions, e.g. potential context sensitivity
   119  is limited since all variants must be created a priori.
   120  
   121  
   122  TERMINOLOGY
   123  
   124  A type is said to be "pointer-like" if it is a reference to an object.
   125  Pointer-like types include pointers and also interfaces, maps, channels,
   126  functions and slices.
   127  
   128  We occasionally use C's x->f notation to distinguish the case where x
   129  is a struct pointer from x.f where is a struct value.
   130  
   131  Pointer analysis literature (and our comments) often uses the notation
   132  dst=*src+offset to mean something different than what it means in Go.
   133  It means: for each node index p in pts(src), the node index p+offset is
   134  in pts(dst).  Similarly *dst+offset=src is used for store constraints
   135  and dst=src+offset for offset-address constraints.
   136  
   137  
   138  NODES
   139  
   140  Nodes are the key datastructure of the analysis, and have a dual role:
   141  they represent both constraint variables (equivalence classes of
   142  pointers) and members of points-to sets (things that can be pointed
   143  at, i.e. "labels").
   144  
   145  Nodes are naturally numbered.  The numbering enables compact
   146  representations of sets of nodes such as bitvectors (or BDDs); and the
   147  ordering enables a very cheap way to group related nodes together.  For
   148  example, passing n parameters consists of generating n parallel
   149  constraints from caller+i to callee+i for 0<=i<n.
   150  
   151  The zero nodeid means "not a pointer".  For simplicity, we generate flow
   152  constraints even for non-pointer types such as int.  The pointer
   153  equivalence (PE) presolver optimization detects which variables cannot
   154  point to anything; this includes not only all variables of non-pointer
   155  types (such as int) but also variables of pointer-like types if they are
   156  always nil, or are parameters to a function that is never called.
   157  
   158  Each node represents a scalar part of a value or object.
   159  Aggregate types (structs, tuples, arrays) are recursively flattened
   160  out into a sequential list of scalar component types, and all the
   161  elements of an array are represented by a single node.  (The
   162  flattening of a basic type is a list containing a single node.)
   163  
   164  Nodes are connected into a graph with various kinds of labelled edges:
   165  simple edges (or copy constraints) represent value flow.  Complex
   166  edges (load, store, etc) trigger the creation of new simple edges
   167  during the solving phase.
   168  
   169  
   170  OBJECTS
   171  
   172  Conceptually, an "object" is a contiguous sequence of nodes denoting
   173  an addressable location: something that a pointer can point to.  The
   174  first node of an object has a non-nil obj field containing information
   175  about the allocation: its size, context, and ssa.Value.
   176  
   177  Objects include:
   178     - functions and globals;
   179     - variable allocations in the stack frame or heap;
   180     - maps, channels and slices created by calls to make();
   181     - allocations to construct an interface;
   182     - allocations caused by conversions, e.g. []byte(str).
   183     - arrays allocated by calls to append();
   184  
   185  Many objects have no Go types.  For example, the func, map and chan type
   186  kinds in Go are all varieties of pointers, but their respective objects
   187  are actual functions (executable code), maps (hash tables), and channels
   188  (synchronized queues).  Given the way we model interfaces, they too are
   189  pointers to "tagged" objects with no Go type.  And an *ssa.Global denotes
   190  the address of a global variable, but the object for a Global is the
   191  actual data.  So, the types of an ssa.Value that creates an object is
   192  "off by one indirection": a pointer to the object.
   193  
   194  The individual nodes of an object are sometimes referred to as "labels".
   195  
   196  For uniformity, all objects have a non-zero number of fields, even those
   197  of the empty type struct{}.  (All arrays are treated as if of length 1,
   198  so there are no empty arrays.  The empty tuple is never address-taken,
   199  so is never an object.)
   200  
   201  
   202  TAGGED OBJECTS
   203  
   204  An tagged object has the following layout:
   205  
   206      T          -- obj.flags ⊇ {otTagged}
   207      v
   208      ...
   209  
   210  The T node's typ field is the dynamic type of the "payload": the value
   211  v which follows, flattened out.  The T node's obj has the otTagged
   212  flag.
   213  
   214  Tagged objects are needed when generalizing across types: interfaces,
   215  reflect.Values, reflect.Types.  Each of these three types is modelled
   216  as a pointer that exclusively points to tagged objects.
   217  
   218  Tagged objects may be indirect (obj.flags ⊇ {otIndirect}) meaning that
   219  the value v is not of type T but *T; this is used only for
   220  reflect.Values that represent lvalues.  (These are not implemented yet.)
   221  
   222  
   223  ANALYSIS ABSTRACTION OF EACH TYPE
   224  
   225  Variables of the following "scalar" types may be represented by a
   226  single node: basic types, pointers, channels, maps, slices, 'func'
   227  pointers, interfaces.
   228  
   229  Pointers
   230    Nothing to say here, oddly.
   231  
   232  Basic types (bool, string, numbers, unsafe.Pointer)
   233    Currently all fields in the flattening of a type, including
   234    non-pointer basic types such as int, are represented in objects and
   235    values.  Though non-pointer nodes within values are uninteresting,
   236    non-pointer nodes in objects may be useful (if address-taken)
   237    because they permit the analysis to deduce, in this example,
   238  
   239       var s struct{ ...; x int; ... }
   240       p := &s.x
   241  
   242    that p points to s.x.  If we ignored such object fields, we could only
   243    say that p points somewhere within s.
   244  
   245    All other basic types are ignored.  Expressions of these types have
   246    zero nodeid, and fields of these types within aggregate other types
   247    are omitted.
   248  
   249    unsafe.Pointers are not modelled as pointers, so a conversion of an
   250    unsafe.Pointer to *T is (unsoundly) treated equivalent to new(T).
   251  
   252  Channels
   253    An expression of type 'chan T' is a kind of pointer that points
   254    exclusively to channel objects, i.e. objects created by MakeChan (or
   255    reflection).
   256  
   257    'chan T' is treated like *T.
   258    *ssa.MakeChan is treated as equivalent to new(T).
   259    *ssa.Send and receive (*ssa.UnOp(ARROW)) and are equivalent to store
   260     and load.
   261  
   262  Maps
   263    An expression of type 'map[K]V' is a kind of pointer that points
   264    exclusively to map objects, i.e. objects created by MakeMap (or
   265    reflection).
   266  
   267    map K[V] is treated like *M where M = struct{k K; v V}.
   268    *ssa.MakeMap is equivalent to new(M).
   269    *ssa.MapUpdate is equivalent to *y=x where *y and x have type M.
   270    *ssa.Lookup is equivalent to y=x.v where x has type *M.
   271  
   272  Slices
   273    A slice []T, which dynamically resembles a struct{array *T, len, cap int},
   274    is treated as if it were just a *T pointer; the len and cap fields are
   275    ignored.
   276  
   277    *ssa.MakeSlice is treated like new([1]T): an allocation of a
   278     singleton array.
   279    *ssa.Index on a slice is equivalent to a load.
   280    *ssa.IndexAddr on a slice returns the address of the sole element of the
   281    slice, i.e. the same address.
   282    *ssa.Slice is treated as a simple copy.
   283  
   284  Functions
   285    An expression of type 'func...' is a kind of pointer that points
   286    exclusively to function objects.
   287  
   288    A function object has the following layout:
   289  
   290       identity         -- typ:*types.Signature; obj.flags ⊇ {otFunction}
   291       params_0         -- (the receiver, if a method)
   292       ...
   293       params_n-1
   294       results_0
   295       ...
   296       results_m-1
   297  
   298    There may be multiple function objects for the same *ssa.Function
   299    due to context-sensitive treatment of some functions.
   300  
   301    The first node is the function's identity node.
   302    Associated with every callsite is a special "targets" variable,
   303    whose pts() contains the identity node of each function to which
   304    the call may dispatch.  Identity words are not otherwise used during
   305    the analysis, but we construct the call graph from the pts()
   306    solution for such nodes.
   307  
   308    The following block of contiguous nodes represents the flattened-out
   309    types of the parameters ("P-block") and results ("R-block") of the
   310    function object.
   311  
   312    The treatment of free variables of closures (*ssa.FreeVar) is like
   313    that of global variables; it is not context-sensitive.
   314    *ssa.MakeClosure instructions create copy edges to Captures.
   315  
   316    A Go value of type 'func' (i.e. a pointer to one or more functions)
   317    is a pointer whose pts() contains function objects.  The valueNode()
   318    for an *ssa.Function returns a singleton for that function.
   319  
   320  Interfaces
   321    An expression of type 'interface{...}' is a kind of pointer that
   322    points exclusively to tagged objects.  All tagged objects pointed to
   323    by an interface are direct (the otIndirect flag is clear) and
   324    concrete (the tag type T is not itself an interface type).  The
   325    associated ssa.Value for an interface's tagged objects may be an
   326    *ssa.MakeInterface instruction, or nil if the tagged object was
   327    created by an instrinsic (e.g. reflection).
   328  
   329    Constructing an interface value causes generation of constraints for
   330    all of the concrete type's methods; we can't tell a priori which
   331    ones may be called.
   332  
   333    TypeAssert y = x.(T) is implemented by a dynamic constraint
   334    triggered by each tagged object O added to pts(x): a typeFilter
   335    constraint if T is an interface type, or an untag constraint if T is
   336    a concrete type.  A typeFilter tests whether O.typ implements T; if
   337    so, O is added to pts(y).  An untagFilter tests whether O.typ is
   338    assignable to T,and if so, a copy edge O.v -> y is added.
   339  
   340    ChangeInterface is a simple copy because the representation of
   341    tagged objects is independent of the interface type (in contrast
   342    to the "method tables" approach used by the gc runtime).
   343  
   344    y := Invoke x.m(...) is implemented by allocating contiguous P/R
   345    blocks for the callsite and adding a dynamic rule triggered by each
   346    tagged object added to pts(x).  The rule adds param/results copy
   347    edges to/from each discovered concrete method.
   348  
   349    (Q. Why do we model an interface as a pointer to a pair of type and
   350    value, rather than as a pair of a pointer to type and a pointer to
   351    value?
   352    A. Control-flow joins would merge interfaces ({T1}, {V1}) and ({T2},
   353    {V2}) to make ({T1,T2}, {V1,V2}), leading to the infeasible and
   354    type-unsafe combination (T1,V2).  Treating the value and its concrete
   355    type as inseparable makes the analysis type-safe.)
   356  
   357  reflect.Value
   358    A reflect.Value is modelled very similar to an interface{}, i.e. as
   359    a pointer exclusively to tagged objects, but with two generalizations.
   360  
   361    1) a reflect.Value that represents an lvalue points to an indirect
   362       (obj.flags ⊇ {otIndirect}) tagged object, which has a similar
   363       layout to an tagged object except that the value is a pointer to
   364       the dynamic type.  Indirect tagged objects preserve the correct
   365       aliasing so that mutations made by (reflect.Value).Set can be
   366       observed.
   367  
   368       Indirect objects only arise when an lvalue is derived from an
   369       rvalue by indirection, e.g. the following code:
   370  
   371          type S struct { X T }
   372          var s S
   373          var i interface{} = &s    // i points to a *S-tagged object (from MakeInterface)
   374          v1 := reflect.ValueOf(i)  // v1 points to same *S-tagged object as i
   375          v2 := v1.Elem()           // v2 points to an indirect S-tagged object, pointing to s
   376          v3 := v2.FieldByName("X") // v3 points to an indirect int-tagged object, pointing to s.X
   377          v3.Set(y)                 // pts(s.X) ⊇ pts(y)
   378  
   379       Whether indirect or not, the concrete type of the tagged object
   380       corresponds to the user-visible dynamic type, and the existence
   381       of a pointer is an implementation detail.
   382  
   383       (NB: indirect tagged objects are not yet implemented)
   384  
   385    2) The dynamic type tag of a tagged object pointed to by a
   386       reflect.Value may be an interface type; it need not be concrete.
   387  
   388       This arises in code such as this:
   389          tEface := reflect.TypeOf(new(interface{}).Elem() // interface{}
   390          eface := reflect.Zero(tEface)
   391       pts(eface) is a singleton containing an interface{}-tagged
   392       object.  That tagged object's payload is an interface{} value,
   393       i.e. the pts of the payload contains only concrete-tagged
   394       objects, although in this example it's the zero interface{} value,
   395       so its pts is empty.
   396  
   397  reflect.Type
   398    Just as in the real "reflect" library, we represent a reflect.Type
   399    as an interface whose sole implementation is the concrete type,
   400    *reflect.rtype.  (This choice is forced on us by go/types: clients
   401    cannot fabricate types with arbitrary method sets.)
   402  
   403    rtype instances are canonical: there is at most one per dynamic
   404    type.  (rtypes are in fact large structs but since identity is all
   405    that matters, we represent them by a single node.)
   406  
   407    The payload of each *rtype-tagged object is an *rtype pointer that
   408    points to exactly one such canonical rtype object.  We exploit this
   409    by setting the node.typ of the payload to the dynamic type, not
   410    '*rtype'.  This saves us an indirection in each resolution rule.  As
   411    an optimisation, *rtype-tagged objects are canonicalized too.
   412  
   413  
   414  Aggregate types:
   415  
   416  Aggregate types are treated as if all directly contained
   417  aggregates are recursively flattened out.
   418  
   419  Structs
   420    *ssa.Field y = x.f creates a simple edge to y from x's node at f's offset.
   421  
   422    *ssa.FieldAddr y = &x->f requires a dynamic closure rule to create
   423     simple edges for each struct discovered in pts(x).
   424  
   425    The nodes of a struct consist of a special 'identity' node (whose
   426    type is that of the struct itself), followed by the nodes for all
   427    the struct's fields, recursively flattened out.  A pointer to the
   428    struct is a pointer to its identity node.  That node allows us to
   429    distinguish a pointer to a struct from a pointer to its first field.
   430  
   431    Field offsets are logical field offsets (plus one for the identity
   432    node), so the sizes of the fields can be ignored by the analysis.
   433  
   434    (The identity node is non-traditional but enables the distiction
   435    described above, which is valuable for code comprehension tools.
   436    Typical pointer analyses for C, whose purpose is compiler
   437    optimization, must soundly model unsafe.Pointer (void*) conversions,
   438    and this requires fidelity to the actual memory layout using physical
   439    field offsets.)
   440  
   441    *ssa.Field y = x.f creates a simple edge to y from x's node at f's offset.
   442  
   443    *ssa.FieldAddr y = &x->f requires a dynamic closure rule to create
   444     simple edges for each struct discovered in pts(x).
   445  
   446  Arrays
   447    We model an array by an identity node (whose type is that of the
   448    array itself) followed by a node representing all the elements of
   449    the array; the analysis does not distinguish elements with different
   450    indices.  Effectively, an array is treated like struct{elem T}, a
   451    load y=x[i] like y=x.elem, and a store x[i]=y like x.elem=y; the
   452    index i is ignored.
   453  
   454    A pointer to an array is pointer to its identity node.  (A slice is
   455    also a pointer to an array's identity node.)  The identity node
   456    allows us to distinguish a pointer to an array from a pointer to one
   457    of its elements, but it is rather costly because it introduces more
   458    offset constraints into the system.  Furthermore, sound treatment of
   459    unsafe.Pointer would require us to dispense with this node.
   460  
   461    Arrays may be allocated by Alloc, by make([]T), by calls to append,
   462    and via reflection.
   463  
   464  Tuples (T, ...)
   465    Tuples are treated like structs with naturally numbered fields.
   466    *ssa.Extract is analogous to *ssa.Field.
   467  
   468    However, tuples have no identity field since by construction, they
   469    cannot be address-taken.
   470  
   471  
   472  FUNCTION CALLS
   473  
   474    There are three kinds of function call:
   475    (1) static "call"-mode calls of functions.
   476    (2) dynamic "call"-mode calls of functions.
   477    (3) dynamic "invoke"-mode calls of interface methods.
   478    Cases 1 and 2 apply equally to methods and standalone functions.
   479  
   480    Static calls.
   481      A static call consists three steps:
   482      - finding the function object of the callee;
   483      - creating copy edges from the actual parameter value nodes to the
   484        P-block in the function object (this includes the receiver if
   485        the callee is a method);
   486      - creating copy edges from the R-block in the function object to
   487        the value nodes for the result of the call.
   488  
   489      A static function call is little more than two struct value copies
   490      between the P/R blocks of caller and callee:
   491  
   492         callee.P = caller.P
   493         caller.R = callee.R
   494  
   495      Context sensitivity
   496  
   497        Static calls (alone) may be treated context sensitively,
   498        i.e. each callsite may cause a distinct re-analysis of the
   499        callee, improving precision.  Our current context-sensitivity
   500        policy treats all intrinsics and getter/setter methods in this
   501        manner since such functions are small and seem like an obvious
   502        source of spurious confluences, though this has not yet been
   503        evaluated.
   504  
   505    Dynamic function calls
   506  
   507      Dynamic calls work in a similar manner except that the creation of
   508      copy edges occurs dynamically, in a similar fashion to a pair of
   509      struct copies in which the callee is indirect:
   510  
   511         callee->P = caller.P
   512         caller.R = callee->R
   513  
   514      (Recall that the function object's P- and R-blocks are contiguous.)
   515  
   516    Interface method invocation
   517  
   518      For invoke-mode calls, we create a params/results block for the
   519      callsite and attach a dynamic closure rule to the interface.  For
   520      each new tagged object that flows to the interface, we look up
   521      the concrete method, find its function object, and connect its P/R
   522      blocks to the callsite's P/R blocks, adding copy edges to the graph
   523      during solving.
   524  
   525    Recording call targets
   526  
   527      The analysis notifies its clients of each callsite it encounters,
   528      passing a CallSite interface.  Among other things, the CallSite
   529      contains a synthetic constraint variable ("targets") whose
   530      points-to solution includes the set of all function objects to
   531      which the call may dispatch.
   532  
   533      It is via this mechanism that the callgraph is made available.
   534      Clients may also elect to be notified of callgraph edges directly;
   535      internally this just iterates all "targets" variables' pts(·)s.
   536  
   537  
   538  PRESOLVER
   539  
   540  We implement Hash-Value Numbering (HVN), a pre-solver constraint
   541  optimization described in Hardekopf & Lin, SAS'07.  This is documented
   542  in more detail in hvn.go.  We intend to add its cousins HR and HU in
   543  future.
   544  
   545  
   546  SOLVER
   547  
   548  The solver is currently a naive Andersen-style implementation; it does
   549  not perform online cycle detection, though we plan to add solver
   550  optimisations such as Hybrid- and Lazy- Cycle Detection from (Hardekopf
   551  & Lin, PLDI'07).
   552  
   553  It uses difference propagation (Pearce et al, SQC'04) to avoid
   554  redundant re-triggering of closure rules for values already seen.
   555  
   556  Points-to sets are represented using sparse bit vectors (similar to
   557  those used in LLVM and gcc), which are more space- and time-efficient
   558  than sets based on Go's built-in map type or dense bit vectors.
   559  
   560  Nodes are permuted prior to solving so that object nodes (which may
   561  appear in points-to sets) are lower numbered than non-object (var)
   562  nodes.  This improves the density of the set over which the PTSs
   563  range, and thus the efficiency of the representation.
   564  
   565  Partly thanks to avoiding map iteration, the execution of the solver is
   566  100% deterministic, a great help during debugging.
   567  
   568  
   569  FURTHER READING
   570  
   571  Andersen, L. O. 1994. Program analysis and specialization for the C
   572  programming language. Ph.D. dissertation. DIKU, University of
   573  Copenhagen.
   574  
   575  David J. Pearce, Paul H. J. Kelly, and Chris Hankin. 2004.  Efficient
   576  field-sensitive pointer analysis for C. In Proceedings of the 5th ACM
   577  SIGPLAN-SIGSOFT workshop on Program analysis for software tools and
   578  engineering (PASTE '04). ACM, New York, NY, USA, 37-42.
   579  http://doi.acm.org/10.1145/996821.996835
   580  
   581  David J. Pearce, Paul H. J. Kelly, and Chris Hankin. 2004. Online
   582  Cycle Detection and Difference Propagation: Applications to Pointer
   583  Analysis. Software Quality Control 12, 4 (December 2004), 311-337.
   584  http://dx.doi.org/10.1023/B:SQJO.0000039791.93071.a2
   585  
   586  David Grove and Craig Chambers. 2001. A framework for call graph
   587  construction algorithms. ACM Trans. Program. Lang. Syst. 23, 6
   588  (November 2001), 685-746.
   589  http://doi.acm.org/10.1145/506315.506316
   590  
   591  Ben Hardekopf and Calvin Lin. 2007. The ant and the grasshopper: fast
   592  and accurate pointer analysis for millions of lines of code. In
   593  Proceedings of the 2007 ACM SIGPLAN conference on Programming language
   594  design and implementation (PLDI '07). ACM, New York, NY, USA, 290-299.
   595  http://doi.acm.org/10.1145/1250734.1250767
   596  
   597  Ben Hardekopf and Calvin Lin. 2007. Exploiting pointer and location
   598  equivalence to optimize pointer analysis. In Proceedings of the 14th
   599  international conference on Static Analysis (SAS'07), Hanne Riis
   600  Nielson and Gilberto Filé (Eds.). Springer-Verlag, Berlin, Heidelberg,
   601  265-280.
   602  
   603  Atanas Rountev and Satish Chandra. 2000. Off-line variable substitution
   604  for scaling points-to analysis. In Proceedings of the ACM SIGPLAN 2000
   605  conference on Programming language design and implementation (PLDI '00).
   606  ACM, New York, NY, USA, 47-56. DOI=10.1145/349299.349310
   607  http://doi.acm.org/10.1145/349299.349310
   608  
   609  */
   610  package pointer // import "golang.org/x/tools/go/pointer"