GNU Compiler Collection (GCC) Internals: Dependency analysis

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### 15.8 Data Dependency Analysis

The code for the data dependence analysis can be found in `tree-data-ref.c` and its interface and data structures are described in `tree-data-ref.h`. The function that computes the data dependences for all the array and pointer references for a given loop is `compute_data_dependences_for_loop`. This function is currently used by the linear loop transform and the vectorization passes. Before calling this function, one has to allocate two vectors: a first vector will contain the set of data references that are contained in the analyzed loop body, and the second vector will contain the dependence relations between the data references. Thus if the vector of data references is of size `n`, the vector containing the dependence relations will contain `n*n` elements. However if the analyzed loop contains side effects, such as calls that potentially can interfere with the data references in the current analyzed loop, the analysis stops while scanning the loop body for data references, and inserts a single `chrec_dont_know` in the dependence relation array.

The data references are discovered in a particular order during the scanning of the loop body: the loop body is analyzed in execution order, and the data references of each statement are pushed at the end of the data reference array. Two data references syntactically occur in the program in the same order as in the array of data references. This syntactic order is important in some classical data dependence tests, and mapping this order to the elements of this array avoids costly queries to the loop body representation.

Three types of data references are currently handled: ARRAY_REF, INDIRECT_REF and COMPONENT_REF. The data structure for the data reference is `data_reference`, where `data_reference_p` is a name of a pointer to the data reference structure. The structure contains the following elements:

- `base_object_info`: Provides information about the base object of the data reference and its access functions. These access functions represent the evolution of the data reference in the loop relative to its base, in keeping with the classical meaning of the data reference access function for the support of arrays. For example, for a reference `a.b[i][j]`, the base object is `a.b` and the access functions, one for each array subscript, are: `{i_init, + i_step}_1, {j_init, +, j_step}_2`.
- `first_location_in_loop`: Provides information about the first location accessed by the data reference in the loop and about the access function used to represent evolution relative to this location. This data is used to support pointers, and is not used for arrays (for which we have base objects). Pointer accesses are represented as a one-dimensional access that starts from the first location accessed in the loop. For example:

            for1 i
               for2 j
                *((int *)p + i + j) = a[i][j];

  The access function of the pointer access is `{0, + 4B}_for2` relative to `p + i`. The access functions of the array are `{i_init, + i_step}_for1` and `{j_init, +, j_step}_for2` relative to `a`.

  Usually, the object the pointer refers to is either unknown, or we can’t prove that the access is confined to the boundaries of a certain object.

  Two data references can be compared only if at least one of these two representations has all its fields filled for both data references.

  The current strategy for data dependence tests is as follows: If both `a` and `b` are represented as arrays, compare `a.base_object` and `b.base_object`; if they are equal, apply dependence tests (use access functions based on base_objects). Else if both `a` and `b` are represented as pointers, compare `a.first_location` and `b.first_location`; if they are equal, apply dependence tests (use access functions based on first location). However, if `a` and `b` are represented differently, only try to prove that the bases are definitely different.

- Aliasing information.
- Alignment information.

The structure describing the relation between two data references is `data_dependence_relation` and the shorter name for a pointer to such a structure is `ddr_p`. This structure contains:

- a pointer to each data reference,
- a tree node `are_dependent` that is set to `chrec_known` if the analysis has proved that there is no dependence between these two data references, `chrec_dont_know` if the analysis was not able to determine any useful result and potentially there could exist a dependence between these data references, and `are_dependent` is set to `NULL_TREE` if there exist a dependence relation between the data references, and the description of this dependence relation is given in the `subscripts`, `dir_vects`, and `dist_vects` arrays,
- a boolean that determines whether the dependence relation can be represented by a classical distance vector,
- an array `subscripts` that contains a description of each subscript of the data references. Given two array accesses a subscript is the tuple composed of the access functions for a given dimension. For example, given `A[f1][f2][f3]` and `B[g1][g2][g3]`, there are three subscripts: `(f1, g1), (f2, g2), (f3, g3)`.
- two arrays `dir_vects` and `dist_vects` that contain classical representations of the data dependences under the form of direction and distance dependence vectors,
- an array of loops `loop_nest` that contains the loops to which the distance and direction vectors refer to.

Several functions for pretty printing the information extracted by the data dependence analysis are available: `dump_ddrs` prints with a maximum verbosity the details of a data dependence relations array, `dump_dist_dir_vectors` prints only the classical distance and direction vectors for a data dependence relations array, and `dump_data_references` prints the details of the data references contained in a data reference array.

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