GCC Middle and Back End API Reference

Functions  
static isl_constraint *  build_linearized_memory_access () 
static void  pdr_stride_in_loop () 
static void  memory_strides_in_loop_1 () 
static void  memory_strides_in_loop () 
static bool  lst_interchange_profitable_p () 
static void  pbb_interchange_loop_depths (graphite_dim_t depth1, graphite_dim_t depth2, poly_bb_p pbb) 
static void  lst_apply_interchange () 
static bool  lst_perfectly_nested_p () 
static void  lst_perfect_nestify (lst_p loop1, lst_p loop2, lst_p *before, lst_p *nest, lst_p *after) 
static bool  lst_try_interchange_loops () 
static bool  lst_interchange_select_inner (scop_p scop, lst_p outer_father, int outer, lst_p inner_father) 
static int  lst_interchange_select_outer () 
int  scop_do_interchange () 

static 
@verbatim
Interchange heuristics and transform for loop interchange on polyhedral representation.
Copyright (C) 20092013 Free Software Foundation, Inc. Contributed by Sebastian Pop sebas and Harsha Jagasia tian .pop@ amd. comharsh. a.ja gasia @amd .com
This file is part of GCC.
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XXX isl rewrite following comment
Builds a linear expression, of dimension DIM, representing PDR's memory access: L = r_{n}*r_{n1}*...*r_{1}*s_{0} + ... + r_{n}*s_{n1} + s_{n}. For an array A[10][20] with two subscript locations s0 and s1, the linear memory access is 20 * s0 + s1: a stride of 1 in subscript s0 corresponds to a memory stride of 20. OFFSET is a number of dimensions to prepend before the subscript dimensions: s_0, s_1, ..., s_n. Thus, the final linear expression has the following format: 0 .. 0_{offset}  0 .. 0_{nit}  0 .. 0_{gd}  0  c_0 c_1 ... c_n where the expression itself is: c_0 * s_0 + c_1 * s_1 + ... c_n * s_n.
1 for the already included L dimension.
Go through all subscripts from last to first. First dimension is the alias set, ignore it.

static 
Apply the interchange of loops at depths DEPTH1 and DEPTH2 to all the statements below LST.
Referenced by pbb_interchange_loop_depths().

static 
Return true when the interchange of loops LOOP1 and LOOP2 is profitable. Example:  int a[100][100];   int  foo (int N)  {  int j;  int i;   for (i = 0; i < N; i++)  for (j = 0; j < N; j++)  a[j][2 * i] += 1;   return a[N][12];  } The data access A[j][i] is described like this:  i j N a s0 s1 1  0 0 0 1 0 0 5 = 0  0 1 0 0 1 0 0 = 0 2 0 0 0 0 1 0 = 0  0 0 0 0 1 0 0 >= 0  0 0 0 0 0 1 0 >= 0  0 0 0 0 1 0 100 >= 0  0 0 0 0 0 1 100 >= 0 The linearized memory access L to A[100][100] is:  i j N a s0 s1 1  0 0 0 0 100 1 0 TODO: the shown format is not valid as it does not show the fact that the iteration domain "i j" is transformed using the scattering. Next, to measure the impact of iterating once in loop "i", we build a maximization problem: first, we add to DR accesses the dimensions k, s2, s3, L1 = 100 * s0 + s1, L2, and D1: this is the polyhedron P1. L1 and L2 are the linearized memory access functions.  i j N a s0 s1 k s2 s3 L1 L2 D1 1  0 0 0 1 0 0 0 0 0 0 0 0 5 = 0 alias = 5  0 1 0 0 1 0 0 0 0 0 0 0 0 = 0 s0 = j 2 0 0 0 0 1 0 0 0 0 0 0 0 = 0 s1 = 2 * i  0 0 0 0 1 0 0 0 0 0 0 0 0 >= 0  0 0 0 0 0 1 0 0 0 0 0 0 0 >= 0  0 0 0 0 1 0 0 0 0 0 0 0 100 >= 0  0 0 0 0 0 1 0 0 0 0 0 0 100 >= 0  0 0 0 0 100 1 0 0 0 1 0 0 0 = 0 L1 = 100 * s0 + s1 Then, we generate the polyhedron P2 by interchanging the dimensions (s0, s2), (s1, s3), (L1, L2), (k, i)  i j N a s0 s1 k s2 s3 L1 L2 D1 1  0 0 0 1 0 0 0 0 0 0 0 0 5 = 0 alias = 5  0 1 0 0 0 0 0 1 0 0 0 0 0 = 0 s2 = j  0 0 0 0 0 0 2 0 1 0 0 0 0 = 0 s3 = 2 * k  0 0 0 0 0 0 0 1 0 0 0 0 0 >= 0  0 0 0 0 0 0 0 0 1 0 0 0 0 >= 0  0 0 0 0 0 0 0 1 0 0 0 0 100 >= 0  0 0 0 0 0 0 0 0 1 0 0 0 100 >= 0  0 0 0 0 0 0 0 100 1 0 1 0 0 = 0 L2 = 100 * s2 + s3 then we add to P2 the equality k = i + 1: 1 0 0 0 0 0 1 0 0 0 0 0 1 = 0 k = i + 1 and finally we maximize the expression "D1 = max (P1 inter P2, L2  L1)". Similarly, to determine the impact of one iteration on loop "j", we interchange (k, j), we add "k = j + 1", and we compute D2 the maximal value of the difference. Finally, the profitability test is D1 < D2: if in the outer loop the strides are smaller than in the inner loop, then it is profitable to interchange the loops at DEPTH1 and DEPTH2.
References d1, d2, psct_dynamic_dim(), and poly_bb::transformed.

static 
Selects the inner loop in LST_SEQ (INNER_FATHER) to be interchanged with the loop OUTER in LST_SEQ (OUTER_FATHER).

static 
Interchanges all the loops of LOOP and the loops of its body that are considered profitable to interchange. Return the number of interchanged loops. OUTER is the index in LST_SEQ (LOOP) that points to the next outer loop to be considered for interchange.

static 
Transform the loop nest between LOOP1 and LOOP2 into a perfect nest. To continue the naming tradition, this function is called after perfect_nestify. NEST is set to the perfectly nested loop that is created. BEFORE/AFTER are set to the loops distributed before/after the loop NEST.
References free_lst().

static 
Return true when the nest starting at LOOP1 and ending on LOOP2 is perfect: i.e. there are no sequence of statements.

static 
Try to interchange LOOP1 with LOOP2 for all the statements of the body of LOOP2. LOOP1 contains LOOP2. Return true if it did the interchange.
Sync the transformed LST information and the PBB scatterings before using the scatterings in the data dependence analysis.
Transform the SCOP_TRANSFORMED_SCHEDULE of the SCOP.
Undo the transform.

static 

static 
Sets STRIDES to the sum of all the strides of the data references accessed in LOOP at DEPTH.

static 
Interchanges the loops at DEPTH1 and DEPTH2 of the original scattering and assigns the resulting polyhedron to the transformed scattering.
References lst_apply_interchange().

static 
Set STRIDE to the stride of PDR in memory by advancing by one in the loop at DEPTH.
XXX isl rewrite following comments.
Builds a partial difference equations and inserts them into pointset powerset polyhedron P. Polyhedron is assumed to have the format: TIT'I'GSS'l1l2. TIME_DEPTH is the time dimension w.r.t. which we are differentiating. OFFSET represents the number of dimensions between columns t_{time_depth} and t'_{time_depth}. DIM_SCTR is the number of scattering dimensions. It is essentially the dimensionality of the T vector. The following equations are inserted into the polyhedron P:  t_1 = t_1'  ...  t_{time_depth1} = t'_{time_depth1}  t_{time_depth} = t'_{time_depth} + 1  t_{time_depth+1} = t'_{time_depth + 1}  ...  t_{dim_sctr} = t'_{dim_sctr}.
Add the equality: t_{time_depth} = t'_{time_depth} + 1. This is the core part of this alogrithm, since this constraint asks for the memory access stride (difference) between two consecutive points in time dimensions.
Add equalities:  t1 = t1'  ...  t_{time_depth1} = t'_{time_depth1}  t_{time_depth+1} = t'_{time_depth+1}  ...  t_{dim_sctr} = t'_{dim_sctr} This means that all the time dimensions are equal except for time_depth, where the constraint is t_{depth} = t'_{depth} + 1 step. More to this: we should be careful not to add equalities to the 'coupled' dimensions, which happens when the one dimension is stripmined dimension, and the other dimension corresponds to the point loop inside stripmined dimension.
pdr>accesses: [P1..nb_param,I1..nb_domain]>[a,S1..nb_subscript] ??? [P] not used for PDRs? pdr>extent: [a,S1..nb_subscript] pbb>domain: [P1..nb_param,I1..nb_domain] pbb>transformed: [P1..nb_param,I1..nb_domain]>[T1..Tnb_sctr] [T] includes local vars (currently unused) First we create [P,I] > [T,a,S].
Add a dimension for L: [P,I] > [T,a,S,L].
Build a constraint for "lma[S]  L == 0", effectively calculating L in terms of subscripts.
And add it to the map, so we now have: [P,I] > [T,a,S,L] : lma([S]) == L.
Then we create [P,I,P',I'] > [T,a,S,L,T',a',S',L'].
Now add the equality T[time_depth] == T'[time_depth]+1. This will force L' to be the linear address at T[time_depth] + 1.
Length of [a,S] plus [L] ...
... plus [T].
Now we equate most of the T/T' elements (making PITaSL nearly the same is (PITaSL)', except for one dimension, namely for 'depth' (an index into [I]), after translating to index into [T]. Take care to not produce an empty map, which indicates we wanted to equate two dimensions that are already coupled via the above time_depth dimension. Happens with strip mining where several scatter dimension are interdependend.
Length of [T].
Now maximize the expression L'  L.
int scop_do_interchange  (  ) 
Interchanges all the loop depths that are considered profitable for SCOP. Return the number of interchanged loops.