return (abs (a) * abs (b) / gcd (a, b));
}
+/* Perform Fourier-Motzkin elimination to calculate the bounds of the
+ auxillary nest.
+ Fourier-Motzkin is a way of reducing systems of linear inequality so that
+ it is easy to calculate the answer and bounds.
+ A sketch of how it works:
+ Given a system of linear inequalities, ai * xj >= bk, you can always
+ rewrite the constraints so they are all of the form
+ a <= x, or x <= b, or x >= constant for some x in x1 ... xj (and some b
+ in b1 ... bk, and some a in a1...ai)
+ You can then eliminate this x from the non-constant inequalities by
+ rewriting these as a <= b, x >= constant, and delete the x variable.
+ You can then repeat this for any remaining x variables, and then we have
+ an easy to use variable <= constant (or no variables at all) form that we
+ can construct our bounds from.
+
+ In our case, each time we eliminate, we construct part of the bound from
+ the ith variable, then delete the ith variable.
+
+ Remember the constant are in our vector a, our coefficient matrix is A,
+ and our invariant coefficient matrix is B.
+
+ SIZE is the size of the matrices being passed.
+ DEPTH is the loop nest depth.
+ INVARIANTS is the number of loop invariants.
+ A, B, and a are the coefficient matrix, invariant coefficient, and a
+ vector of constants, respectively. */
+
+static lambda_loopnest
+compute_nest_using_fourier_motzkin (int size,
+ int depth,
+ int invariants,
+ lambda_matrix A,
+ lambda_matrix B,
+ lambda_vector a)
+{
+
+ int multiple, f1, f2;
+ int i, j, k;
+ lambda_linear_expression expression;
+ lambda_loop loop;
+ lambda_loopnest auxillary_nest;
+ lambda_matrix swapmatrix, A1, B1;
+ lambda_vector swapvector, a1;
+ int newsize;
+
+ A1 = lambda_matrix_new (128, depth);
+ B1 = lambda_matrix_new (128, invariants);
+ a1 = lambda_vector_new (128);
+
+ auxillary_nest = lambda_loopnest_new (depth, invariants);
+
+ for (i = depth - 1; i >= 0; i--)
+ {
+ loop = lambda_loop_new ();
+ LN_LOOPS (auxillary_nest)[i] = loop;
+ LL_STEP (loop) = 1;
+
+ for (j = 0; j < size; j++)
+ {
+ if (A[j][i] < 0)
+ {
+ /* Any linear expression in the matrix with a coefficient less
+ than 0 becomes part of the new lower bound. */
+ expression = lambda_linear_expression_new (depth, invariants);
+
+ for (k = 0; k < i; k++)
+ LLE_COEFFICIENTS (expression)[k] = A[j][k];
+
+ for (k = 0; k < invariants; k++)
+ LLE_INVARIANT_COEFFICIENTS (expression)[k] = -1 * B[j][k];
+
+ LLE_DENOMINATOR (expression) = -1 * A[j][i];
+ LLE_CONSTANT (expression) = -1 * a[j];
+
+ /* Ignore if identical to the existing lower bound. */
+ if (!lle_equal (LL_LOWER_BOUND (loop),
+ expression, depth, invariants))
+ {
+ LLE_NEXT (expression) = LL_LOWER_BOUND (loop);
+ LL_LOWER_BOUND (loop) = expression;
+ }
+
+ }
+ else if (A[j][i] > 0)
+ {
+ /* Any linear expression with a coefficient greater than 0
+ becomes part of the new upper bound. */
+ expression = lambda_linear_expression_new (depth, invariants);
+ for (k = 0; k < i; k++)
+ LLE_COEFFICIENTS (expression)[k] = -1 * A[j][k];
+
+ for (k = 0; k < invariants; k++)
+ LLE_INVARIANT_COEFFICIENTS (expression)[k] = B[j][k];
+
+ LLE_DENOMINATOR (expression) = A[j][i];
+ LLE_CONSTANT (expression) = a[j];
+
+ /* Ignore if identical to the existing upper bound. */
+ if (!lle_equal (LL_UPPER_BOUND (loop),
+ expression, depth, invariants))
+ {
+ LLE_NEXT (expression) = LL_UPPER_BOUND (loop);
+ LL_UPPER_BOUND (loop) = expression;
+ }
+
+ }
+ }
+
+ /* This portion creates a new system of linear inequalities by deleting
+ the i'th variable, reducing the system by one variable. */
+ newsize = 0;
+ for (j = 0; j < size; j++)
+ {
+ /* If the coefficient for the i'th variable is 0, then we can just
+ eliminate the variable straightaway. Otherwise, we have to
+ multiply through by the coefficients we are eliminating. */
+ if (A[j][i] == 0)
+ {
+ lambda_vector_copy (A[j], A1[newsize], depth);
+ lambda_vector_copy (B[j], B1[newsize], invariants);
+ a1[newsize] = a[j];
+ newsize++;
+ }
+ else if (A[j][i] > 0)
+ {
+ for (k = 0; k < size; k++)
+ {
+ if (A[k][i] < 0)
+ {
+ multiple = lcm (A[j][i], A[k][i]);
+ f1 = multiple / A[j][i];
+ f2 = -1 * multiple / A[k][i];
+
+ lambda_vector_add_mc (A[j], f1, A[k], f2,
+ A1[newsize], depth);
+ lambda_vector_add_mc (B[j], f1, B[k], f2,
+ B1[newsize], invariants);
+ a1[newsize] = f1 * a[j] + f2 * a[k];
+ newsize++;
+ }
+ }
+ }
+ }
+
+ swapmatrix = A;
+ A = A1;
+ A1 = swapmatrix;
+
+ swapmatrix = B;
+ B = B1;
+ B1 = swapmatrix;
+
+ swapvector = a;
+ a = a1;
+ a1 = swapvector;
+
+ size = newsize;
+ }
+
+ return auxillary_nest;
+}
+
/* Compute the loop bounds for the auxiliary space NEST.
Input system used is Ax <= b. TRANS is the unimodular transformation. */
lambda_compute_auxillary_space (lambda_loopnest nest,
lambda_trans_matrix trans)
{
- lambda_matrix A, B, A1, B1, temp0;
- lambda_vector a, a1, temp1;
+ lambda_matrix A, B, A1, B1;
+ lambda_vector a, a1;
lambda_matrix invertedtrans;
- int determinant, depth, invariants, size, newsize;
- int i, j, k;
- lambda_loopnest auxillary_nest;
+ int determinant, depth, invariants, size;
+ int i, j;
lambda_loop loop;
lambda_linear_expression expression;
lambda_lattice lattice;
- int multiple, f1, f2;
-
depth = LN_DEPTH (nest);
invariants = LN_INVARIANTS (nest);
/* A = A1 inv(U). */
lambda_matrix_mult (A1, invertedtrans, A, size, depth, depth);
- /* Perform Fourier-Motzkin elimination to calculate the bounds of the
- auxillary nest.
- Fourier-Motzkin is a way of reducing systems of linear inequality so that
- it is easy to calculate the answer and bounds.
- A sketch of how it works:
- Given a system of linear inequalities, ai * xj >= bk, you can always
- rewrite the constraints so they are all of the form
- a <= x, or x <= b, or x >= constant for some x in x1 ... xj (and some b
- in b1 ... bk, and some a in a1...ai)
- You can then eliminate this x from the non-constant inequalities by
- rewriting these as a <= b, x >= constant, and delete the x variable.
- You can then repeat this for any remaining x variables, and then we have
- an easy to use variable <= constant (or no variables at all) form that we
- can construct our bounds from.
-
- In our case, each time we eliminate, we construct part of the bound from
- the ith variable, then delete the ith variable.
-
- Remember the constant are in our vector a, our coefficient matrix is A,
- and our invariant coefficient matrix is B */
-
- /* Swap B and B1, and a1 and a. */
- temp0 = B1;
- B1 = B;
- B = temp0;
-
- temp1 = a1;
- a1 = a;
- a = temp1;
-
- auxillary_nest = lambda_loopnest_new (depth, invariants);
-
- for (i = depth - 1; i >= 0; i--)
- {
- loop = lambda_loop_new ();
- LN_LOOPS (auxillary_nest)[i] = loop;
- LL_STEP (loop) = 1;
-
- for (j = 0; j < size; j++)
- {
- if (A[j][i] < 0)
- {
- /* Lower bound. */
- expression = lambda_linear_expression_new (depth, invariants);
-
- for (k = 0; k < i; k++)
- LLE_COEFFICIENTS (expression)[k] = A[j][k];
- for (k = 0; k < invariants; k++)
- LLE_INVARIANT_COEFFICIENTS (expression)[k] = -1 * B[j][k];
- LLE_DENOMINATOR (expression) = -1 * A[j][i];
- LLE_CONSTANT (expression) = -1 * a[j];
- /* Ignore if identical to the existing lower bound. */
- if (!lle_equal (LL_LOWER_BOUND (loop),
- expression, depth, invariants))
- {
- LLE_NEXT (expression) = LL_LOWER_BOUND (loop);
- LL_LOWER_BOUND (loop) = expression;
- }
-
- }
- else if (A[j][i] > 0)
- {
- /* Upper bound. */
- expression = lambda_linear_expression_new (depth, invariants);
- for (k = 0; k < i; k++)
- LLE_COEFFICIENTS (expression)[k] = -1 * A[j][k];
- LLE_CONSTANT (expression) = a[j];
-
- for (k = 0; k < invariants; k++)
- LLE_INVARIANT_COEFFICIENTS (expression)[k] = B[j][k];
-
- LLE_DENOMINATOR (expression) = A[j][i];
- /* Ignore if identical to the existing upper bound. */
- if (!lle_equal (LL_UPPER_BOUND (loop),
- expression, depth, invariants))
- {
- LLE_NEXT (expression) = LL_UPPER_BOUND (loop);
- LL_UPPER_BOUND (loop) = expression;
- }
-
- }
- }
- /* creates a new system by deleting the i'th variable. */
- newsize = 0;
- for (j = 0; j < size; j++)
- {
- if (A[j][i] == 0)
- {
- lambda_vector_copy (A[j], A1[newsize], depth);
- lambda_vector_copy (B[j], B1[newsize], invariants);
- a1[newsize] = a[j];
- newsize++;
- }
- else if (A[j][i] > 0)
- {
- for (k = 0; k < size; k++)
- {
- if (A[k][i] < 0)
- {
- multiple = lcm (A[j][i], A[k][i]);
- f1 = multiple / A[j][i];
- f2 = -1 * multiple / A[k][i];
-
- lambda_vector_add_mc (A[j], f1, A[k], f2,
- A1[newsize], depth);
- lambda_vector_add_mc (B[j], f1, B[k], f2,
- B1[newsize], invariants);
- a1[newsize] = f1 * a[j] + f2 * a[k];
- newsize++;
- }
- }
- }
- }
-
- temp0 = A;
- A = A1;
- A1 = temp0;
-
- temp0 = B;
- B = B1;
- B1 = temp0;
-
- temp1 = a;
- a = a1;
- a1 = temp1;
-
- size = newsize;
- }
-
- return auxillary_nest;
+ return compute_nest_using_fourier_motzkin (size, depth, invariants,
+ A, B1, a1);
}
/* Compute the loop bounds for the target space, using the bounds of
/* Return true if OP is invariant in LOOP and all outer loops. */
static bool
-invariant_in_loop (struct loop *loop, tree op)
+invariant_in_loop_and_outer_loops (struct loop *loop, tree op)
{
if (is_gimple_min_invariant (op))
return true;
if (loop->depth == 0)
return true;
- if (TREE_CODE (op) == SSA_NAME)
- {
- tree def;
- def = SSA_NAME_DEF_STMT (op);
- if (TREE_CODE (SSA_NAME_VAR (op)) == PARM_DECL
- && IS_EMPTY_STMT (def))
- return true;
- if (IS_EMPTY_STMT (def))
- return false;
- if (loop->outer
- && !invariant_in_loop (loop->outer, op))
- return false;
- return !flow_bb_inside_loop_p (loop, bb_for_stmt (def));
- }
- return false;
+ if (!expr_invariant_in_loop_p (loop, op))
+ return false;
+ if (loop->outer
+ && !invariant_in_loop_and_outer_loops (loop->outer, op))
+ return false;
+ return true;
}
/* Generate a lambda loop from a gcc loop LOOP. Return the new lambda loop,
}
/* One part of the test may be a loop invariant tree. */
if (TREE_CODE (TREE_OPERAND (test, 1)) == SSA_NAME
- && invariant_in_loop (loop, TREE_OPERAND (test, 1)))
+ && invariant_in_loop_and_outer_loops (loop, TREE_OPERAND (test, 1)))
VEC_safe_push (tree, *invariants, TREE_OPERAND (test, 1));
else if (TREE_CODE (TREE_OPERAND (test, 0)) == SSA_NAME
- && invariant_in_loop (loop, TREE_OPERAND (test, 0)))
+ && invariant_in_loop_and_outer_loops (loop, TREE_OPERAND (test, 0)))
VEC_safe_push (tree, *invariants, TREE_OPERAND (test, 0));
/* The non-induction variable part of the test is the upper bound variable.
case LE_EXPR:
case NE_EXPR:
ivarop = TREE_OPERAND (test, 0);
- break;
+ break;
case GT_EXPR:
case GE_EXPR:
+ case EQ_EXPR:
ivarop = TREE_OPERAND (test, 1);
break;
default:
dataflow_t imm = get_immediate_uses (SSA_NAME_DEF_STMT (oldiv));
for (j = 0; j < num_immediate_uses (imm); j++)
{
- size_t k;
tree stmt = immediate_use (imm, j);
- use_optype uses;
- get_stmt_operands (stmt);
- uses = STMT_USE_OPS (stmt);
- for (k = 0; k < NUM_USES (uses); k++)
+ use_operand_p use_p;
+ ssa_op_iter iter;
+ FOR_EACH_SSA_USE_OPERAND (use_p, stmt, iter, SSA_OP_USE)
{
- use_operand_p use = USE_OP_PTR (uses, k);
- if (USE_FROM_PTR (use) == oldiv)
+ if (USE_FROM_PTR (use_p) == oldiv)
{
tree newiv, stmts;
lambda_body_vector lbv;
/* Insert the statements to build that
expression. */
bsi_insert_before (&bsi, stmts, BSI_SAME_STMT);
- SET_USE (use, newiv);
+ propagate_value (use_p, newiv);
modify_stmt (stmt);
}
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