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diff --git a/gcc/lambda-code.c b/gcc/lambda-code.c new file mode 100644 index 00000000000..664092797ea --- /dev/null +++ b/gcc/lambda-code.c @@ -0,0 +1,1972 @@ +/* Loop transformation code generation + Copyright (C) 2003, 2004 Free Software Foundation, Inc. + Contributed by Daniel Berlin <dberlin@dberlin.org> + + This file is part of GCC. + + GCC is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation; either version 2, or (at your option) any later + version. + + GCC is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or + FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License + along with GCC; see the file COPYING. If not, write to the Free + Software Foundation, 59 Temple Place - Suite 330, Boston, MA + 02111-1307, USA. */ + +#include "config.h" +#include "system.h" +#include "coretypes.h" +#include "tm.h" +#include "errors.h" +#include "ggc.h" +#include "tree.h" +#include "target.h" +#include "rtl.h" +#include "basic-block.h" +#include "diagnostic.h" +#include "tree-flow.h" +#include "tree-dump.h" +#include "timevar.h" +#include "cfgloop.h" +#include "expr.h" +#include "optabs.h" +#include "tree-chrec.h" +#include "tree-data-ref.h" +#include "tree-pass.h" +#include "tree-scalar-evolution.h" +#include "vec.h" +#include "lambda.h" + +/* This loop nest code generation is based on non-singular matrix + math. + + A little terminology and a general sketch of the algorithm. See "A singular + loop transformatrion framework based on non-singular matrices" by Wei Li and + Keshav Pingali for formal proofs that the various statements below are + correct. + + A loop iteration space are the points traversed by the loop. A point in the + iteration space can be represented by a vector of size <loop depth>. You can + therefore represent the iteration space as a integral combinations of a set + of basis vectors. + + A loop iteration space is dense if every integer point between the loop + bounds is a point in the iteration space. Every loop with a step of 1 + therefore has a dense iteration space. + + for i = 1 to 3, step 1 is a dense iteration space. + + A loop iteration space is sparse if it is not dense. That is, the iteration + space skips integer points that are within the loop bounds. + + for i = 1 to 3, step 2 is a sparse iteration space, because the integer point + 2 is skipped. + + Dense source spaces are easy to transform, because they don't skip any + points to begin with. Thus we can compute the exact bounds of the target + space using min/max and floor/ceil. + + For a dense source space, we take the transformation matrix, decompose it + into a lower triangular part (H) and a unimodular part (U). + We then compute the auxillary space from the unimodular part (source loop + nest . U = auxillary space) , which has two important properties: + 1. It traverses the iterations in the same lexicographic order as the source + space. + 2. It is a dense space when the source is a dense space (even if the target + space is going to be sparse). + + Given the auxillary space, we use the lower triangular part to compute the + bounds in the target space by simple matrix multiplication. + The gaps in the target space (IE the new loop step sizes) will be the + diagonals of the H matrix. + + Sparse source spaces require another step, because you can't directly compute + the exact bounds of the auxillary and target space from the sparse space. + Rather than try to come up with a separate algorithm to handle sparse source + spaces directly, we just find a legal transformation matrix that gives you + the sparse source space, from a dense space, and then transform the dense + space. + + For a regular sparse space, you can represent the source space as an integer + lattice, and the base space of that lattice will always be dense. Thus, we + effectively use the lattice to figure out the transformation from the lattice + base space, to the sparse iteration space (IE what transform was applied to + the dense space to make it sparse). We then compose this transform with the + transformation matrix specified by the user (since our matrix transformations + are closed under composition, this is okay). We can then use the base space + (which is dense) plus the composed transformation matrix, to compute the rest + of the transform using the dense space algorithm above. + + In other words, our sparse source space (B) is decomposed into a dense base + space (A), and a matrix (L) that transforms A into B, such that A.L = B. + We then compute the composition of L and the user transformation matrix (T), + so that T is now a transform from A to the result, instead of from B to the + result. + IE A.(LT) = result instead of B.T = result + Since A is now a dense source space, we can use the dense source space + algorithm above to compute the result of applying transform (LT) to A. + + Fourier-Motzkin elimination is used to compute the bounds of the base space + of the lattice. */ + +/* Lattice stuff that is internal to the code generation algorithm. */ + +typedef struct +{ + /* Lattice base matrix. */ + lambda_matrix base; + /* Lattice dimension. */ + int dimension; + /* Origin vector for the coefficients. */ + lambda_vector origin; + /* Origin matrix for the invariants. */ + lambda_matrix origin_invariants; + /* Number of invariants. */ + int invariants; +} *lambda_lattice; + +#define LATTICE_BASE(T) ((T)->base) +#define LATTICE_DIMENSION(T) ((T)->dimension) +#define LATTICE_ORIGIN(T) ((T)->origin) +#define LATTICE_ORIGIN_INVARIANTS(T) ((T)->origin_invariants) +#define LATTICE_INVARIANTS(T) ((T)->invariants) + +static bool lle_equal (lambda_linear_expression, lambda_linear_expression, + int, int); +static lambda_lattice lambda_lattice_new (int, int); +static lambda_lattice lambda_lattice_compute_base (lambda_loopnest); + +static tree find_induction_var_from_exit_cond (struct loop *); + +/* Create a new lambda body vector. */ + +lambda_body_vector +lambda_body_vector_new (int size) +{ + lambda_body_vector ret; + + ret = ggc_alloc (sizeof (*ret)); + LBV_COEFFICIENTS (ret) = lambda_vector_new (size); + LBV_SIZE (ret) = size; + LBV_DENOMINATOR (ret) = 1; + return ret; +} + +/* Compute the new coefficients for the vector based on the + *inverse* of the transformation matrix. */ + +lambda_body_vector +lambda_body_vector_compute_new (lambda_trans_matrix transform, + lambda_body_vector vect) +{ + lambda_body_vector temp; + int depth; + + /* Make sure the matrix is square. */ + if (LTM_ROWSIZE (transform) != LTM_COLSIZE (transform)) + abort (); + + depth = LTM_ROWSIZE (transform); + + temp = lambda_body_vector_new (depth); + LBV_DENOMINATOR (temp) = + LBV_DENOMINATOR (vect) * LTM_DENOMINATOR (transform); + lambda_vector_matrix_mult (LBV_COEFFICIENTS (vect), depth, + LTM_MATRIX (transform), depth, + LBV_COEFFICIENTS (temp)); + LBV_SIZE (temp) = LBV_SIZE (vect); + return temp; +} + +/* Print out a lambda body vector. */ + +void +print_lambda_body_vector (FILE * outfile, lambda_body_vector body) +{ + print_lambda_vector (outfile, LBV_COEFFICIENTS (body), LBV_SIZE (body)); +} + +/* Return TRUE if two linear expressions are equal. */ + +static bool +lle_equal (lambda_linear_expression lle1, lambda_linear_expression lle2, + int depth, int invariants) +{ + int i; + + if (lle1 == NULL || lle2 == NULL) + return false; + if (LLE_CONSTANT (lle1) != LLE_CONSTANT (lle2)) + return false; + if (LLE_DENOMINATOR (lle1) != LLE_DENOMINATOR (lle2)) + return false; + for (i = 0; i < depth; i++) + if (LLE_COEFFICIENTS (lle1)[i] != LLE_COEFFICIENTS (lle2)[i]) + return false; + for (i = 0; i < invariants; i++) + if (LLE_INVARIANT_COEFFICIENTS (lle1)[i] != + LLE_INVARIANT_COEFFICIENTS (lle2)[i]) + return false; + return true; +} + +/* Create a new linear expression with dimension DIM, and total number + of invariants INVARIANTS. */ + +lambda_linear_expression +lambda_linear_expression_new (int dim, int invariants) +{ + lambda_linear_expression ret; + + ret = ggc_alloc_cleared (sizeof (*ret)); + + LLE_COEFFICIENTS (ret) = lambda_vector_new (dim); + LLE_CONSTANT (ret) = 0; + LLE_INVARIANT_COEFFICIENTS (ret) = lambda_vector_new (invariants); + LLE_DENOMINATOR (ret) = 1; + LLE_NEXT (ret) = NULL; + + return ret; +} + +/* Print out a linear expression EXPR, with SIZE coefficients, to OUTFILE. + The starting letter used for variable names is START. */ + +static void +print_linear_expression (FILE * outfile, lambda_vector expr, int size, + char start) +{ + int i; + bool first = true; + for (i = 0; i < size; i++) + { + if (expr[i] != 0) + { + if (first) + { + if (expr[i] < 0) + fprintf (outfile, "-"); + first = false; + } + else if (expr[i] > 0) + fprintf (outfile, " + "); + else + fprintf (outfile, " - "); + if (abs (expr[i]) == 1) + fprintf (outfile, "%c", start + i); + else + fprintf (outfile, "%d%c", abs (expr[i]), start + i); + } + } +} + +/* Print out a lambda linear expression structure, EXPR, to OUTFILE. The + depth/number of coefficients is given by DEPTH, the number of invariants is + given by INVARIANTS, and the character to start variable names with is given + by START. */ + +void +print_lambda_linear_expression (FILE * outfile, + lambda_linear_expression expr, + int depth, int invariants, char start) +{ + fprintf (outfile, "\tLinear expression: "); + print_linear_expression (outfile, LLE_COEFFICIENTS (expr), depth, start); + fprintf (outfile, " constant: %d ", LLE_CONSTANT (expr)); + fprintf (outfile, " invariants: "); + print_linear_expression (outfile, LLE_INVARIANT_COEFFICIENTS (expr), + invariants, 'A'); + fprintf (outfile, " denominator: %d\n", LLE_DENOMINATOR (expr)); +} + +/* Print a lambda loop structure LOOP to OUTFILE. The depth/number of + coefficients is given by DEPTH, the number of invariants is + given by INVARIANTS, and the character to start variable names with is given + by START. */ + +void +print_lambda_loop (FILE * outfile, lambda_loop loop, int depth, + int invariants, char start) +{ + int step; + lambda_linear_expression expr; + + if (!loop) + abort (); + + expr = LL_LINEAR_OFFSET (loop); + step = LL_STEP (loop); + fprintf (outfile, " step size = %d \n", step); + + if (expr) + { + fprintf (outfile, " linear offset: \n"); + print_lambda_linear_expression (outfile, expr, depth, invariants, + start); + } + + fprintf (outfile, " lower bound: \n"); + for (expr = LL_LOWER_BOUND (loop); expr != NULL; expr = LLE_NEXT (expr)) + print_lambda_linear_expression (outfile, expr, depth, invariants, start); + fprintf (outfile, " upper bound: \n"); + for (expr = LL_UPPER_BOUND (loop); expr != NULL; expr = LLE_NEXT (expr)) + print_lambda_linear_expression (outfile, expr, depth, invariants, start); +} + +/* Create a new loop nest structure with DEPTH loops, and INVARIANTS as the + number of invariants. */ + +lambda_loopnest +lambda_loopnest_new (int depth, int invariants) +{ + lambda_loopnest ret; + ret = ggc_alloc (sizeof (*ret)); + + LN_LOOPS (ret) = ggc_alloc_cleared (depth * sizeof (lambda_loop)); + LN_DEPTH (ret) = depth; + LN_INVARIANTS (ret) = invariants; + + return ret; +} + +/* Print a lambda loopnest structure, NEST, to OUTFILE. The starting + character to use for loop names is given by START. */ + +void +print_lambda_loopnest (FILE * outfile, lambda_loopnest nest, char start) +{ + int i; + for (i = 0; i < LN_DEPTH (nest); i++) + { + fprintf (outfile, "Loop %c\n", start + i); + print_lambda_loop (outfile, LN_LOOPS (nest)[i], LN_DEPTH (nest), + LN_INVARIANTS (nest), 'i'); + fprintf (outfile, "\n"); + } +} + +/* Allocate a new lattice structure of DEPTH x DEPTH, with INVARIANTS number + of invariants. */ + +static lambda_lattice +lambda_lattice_new (int depth, int invariants) +{ + lambda_lattice ret; + ret = ggc_alloc (sizeof (*ret)); + LATTICE_BASE (ret) = lambda_matrix_new (depth, depth); + LATTICE_ORIGIN (ret) = lambda_vector_new (depth); + LATTICE_ORIGIN_INVARIANTS (ret) = lambda_matrix_new (depth, invariants); + LATTICE_DIMENSION (ret) = depth; + LATTICE_INVARIANTS (ret) = invariants; + return ret; +} + +/* Compute the lattice base for NEST. The lattice base is essentially a + non-singular transform from a dense base space to a sparse iteration space. + We use it so that we don't have to specially handle the case of a sparse + iteration space in other parts of the algorithm. As a result, this routine + only does something interesting (IE produce a matrix that isn't the + identity matrix) if NEST is a sparse space. */ + +static lambda_lattice +lambda_lattice_compute_base (lambda_loopnest nest) +{ + lambda_lattice ret; + int depth, invariants; + lambda_matrix base; + + int i, j, step; + lambda_loop loop; + lambda_linear_expression expression; + + depth = LN_DEPTH (nest); + invariants = LN_INVARIANTS (nest); + + ret = lambda_lattice_new (depth, invariants); + base = LATTICE_BASE (ret); + for (i = 0; i < depth; i++) + { + loop = LN_LOOPS (nest)[i]; + if (!loop) + abort (); + step = LL_STEP (loop); + /* If we have a step of 1, then the base is one, and the + origin and invariant coefficients are 0. */ + if (step == 1) + { + for (j = 0; j < depth; j++) + base[i][j] = 0; + base[i][i] = 1; + LATTICE_ORIGIN (ret)[i] = 0; + for (j = 0; j < invariants; j++) + LATTICE_ORIGIN_INVARIANTS (ret)[i][j] = 0; + } + else + { + /* Otherwise, we need the lower bound expression (which must + be an affine function) to determine the base. */ + expression = LL_LOWER_BOUND (loop); + if (!expression + || LLE_NEXT (expression) || LLE_DENOMINATOR (expression) != 1) + abort (); + + /* The lower triangular portion of the base is going to be the + coefficient times the step */ + for (j = 0; j < i; j++) + base[i][j] = LLE_COEFFICIENTS (expression)[j] + * LL_STEP (LN_LOOPS (nest)[j]); + base[i][i] = step; + for (j = i + 1; j < depth; j++) + base[i][j] = 0; + + /* Origin for this loop is the constant of the lower bound + expression. */ + LATTICE_ORIGIN (ret)[i] = LLE_CONSTANT (expression); + + /* Coefficient for the invariants are equal to the invariant + coefficients in the expression. */ + for (j = 0; j < invariants; j++) + LATTICE_ORIGIN_INVARIANTS (ret)[i][j] = + LLE_INVARIANT_COEFFICIENTS (expression)[j]; + } + } + return ret; +} + +/* Compute the greatest common denominator of two numbers (A and B) using + Euclid's algorithm. */ + +static int +gcd (int a, int b) +{ + + int x, y, z; + + x = abs (a); + y = abs (b); + + while (x > 0) + { + z = y % x; + y = x; + x = z; + } + + return (y); +} + +/* Compute the greatest common denominator of a VECTOR of SIZE numbers. */ + +static int +gcd_vector (lambda_vector vector, int size) +{ + int i; + int gcd1 = 0; + + if (size > 0) + { + gcd1 = vector[0]; + for (i = 1; i < size; i++) + gcd1 = gcd (gcd1, vector[i]); + } + return gcd1; +} + +/* Compute the least common multiple of two numbers A and B . */ + +static int +lcm (int a, int b) +{ + return (abs (a) * abs (b) / gcd (a, b)); +} + +/* Compute the loop bounds for the auxiliary space NEST. + Input system used is Ax <= b. TRANS is the unimodular transformation. */ + +static lambda_loopnest +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 invertedtrans; + int determinant, depth, invariants, size, newsize; + int i, j, k; + lambda_loopnest auxillary_nest; + lambda_loop loop; + lambda_linear_expression expression; + lambda_lattice lattice; + + int multiple, f1, f2; + + depth = LN_DEPTH (nest); + invariants = LN_INVARIANTS (nest); + + /* Unfortunately, we can't know the number of constraints we'll have + ahead of time, but this should be enough even in ridiculous loop nest + cases. We abort if we go over this limit. */ + A = lambda_matrix_new (128, depth); + B = lambda_matrix_new (128, invariants); + a = lambda_vector_new (128); + + A1 = lambda_matrix_new (128, depth); + B1 = lambda_matrix_new (128, invariants); + a1 = lambda_vector_new (128); + + /* Store the bounds in the equation matrix A, constant vector a, and + invariant matrix B, so that we have Ax <= a + B. + This requires a little equation rearranging so that everything is on the + correct side of the inequality. */ + size = 0; + for (i = 0; i < depth; i++) + { + loop = LN_LOOPS (nest)[i]; + + /* First we do the lower bound. */ + if (LL_STEP (loop) > 0) + expression = LL_LOWER_BOUND (loop); + else + expression = LL_UPPER_BOUND (loop); + + for (; expression != NULL; expression = LLE_NEXT (expression)) + { + /* Fill in the coefficient. */ + for (j = 0; j < i; j++) + A[size][j] = LLE_COEFFICIENTS (expression)[j]; + + /* And the invariant coefficient. */ + for (j = 0; j < invariants; j++) + B[size][j] = LLE_INVARIANT_COEFFICIENTS (expression)[j]; + + /* And the constant. */ + a[size] = LLE_CONSTANT (expression); + + /* Convert (2x+3y+2+b)/4 <= z to 2x+3y-4z <= -2-b. IE put all + constants and single variables on */ + A[size][i] = -1 * LLE_DENOMINATOR (expression); + a[size] *= -1; + for (j = 0; j < invariants; j++) + B[size][j] *= -1; + + size++; + /* Need to increase matrix sizes above. */ + if (size > 127) + abort (); + } + + /* Then do the exact same thing for the upper bounds. */ + if (LL_STEP (loop) > 0) + expression = LL_UPPER_BOUND (loop); + else + expression = LL_LOWER_BOUND (loop); + + for (; expression != NULL; expression = LLE_NEXT (expression)) + { + /* Fill in the coefficient. */ + for (j = 0; j < i; j++) + A[size][j] = LLE_COEFFICIENTS (expression)[j]; + + /* And the invariant coefficient. */ + for (j = 0; j < invariants; j++) + B[size][j] = LLE_INVARIANT_COEFFICIENTS (expression)[j]; + + /* And the constant. */ + a[size] = LLE_CONSTANT (expression); + + /* Convert z <= (2x+3y+2+b)/4 to -2x-3y+4z <= 2+b. */ + for (j = 0; j < i; j++) + A[size][j] *= -1; + A[size][i] = LLE_DENOMINATOR (expression); + size++; + /* Need to increase matrix sizes above. */ + if (size > 127) + abort (); + } + } + + /* Compute the lattice base x = base * y + origin, where y is the + base space. */ + lattice = lambda_lattice_compute_base (nest); + + /* Ax <= a + B then becomes ALy <= a+B - A*origin. L is the lattice base */ + + /* A1 = A * L */ + lambda_matrix_mult (A, LATTICE_BASE (lattice), A1, size, depth, depth); + + /* a1 = a - A * origin constant. */ + lambda_matrix_vector_mult (A, size, depth, LATTICE_ORIGIN (lattice), a1); + lambda_vector_add_mc (a, 1, a1, -1, a1, size); + + /* B1 = B - A * origin invariant. */ + lambda_matrix_mult (A, LATTICE_ORIGIN_INVARIANTS (lattice), B1, size, depth, + invariants); + lambda_matrix_add_mc (B, 1, B1, -1, B1, size, invariants); + + /* Now compute the auxiliary space bounds by first inverting U, multiplying + it by A1, then performing fourier motzkin. */ + + invertedtrans = lambda_matrix_new (depth, depth); + + /* Compute the inverse of U. */ + determinant = lambda_matrix_inverse (LTM_MATRIX (trans), + invertedtrans, depth); + + /* 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; +} + +/* Compute the loop bounds for the target space, using the bounds of + the auxillary nest AUXILLARY_NEST, and the triangular matrix H. This is + done by matrix multiplication and then transformation of the new matrix + back into linear expression form. + Return the target loopnest. */ + +static lambda_loopnest +lambda_compute_target_space (lambda_loopnest auxillary_nest, + lambda_trans_matrix H, lambda_vector stepsigns) +{ + lambda_matrix inverse, H1; + int determinant, i, j; + int gcd1, gcd2; + int factor; + + lambda_loopnest target_nest; + int depth, invariants; + lambda_matrix target; + + lambda_loop auxillary_loop, target_loop; + lambda_linear_expression expression, auxillary_expr, target_expr, tmp_expr; + + depth = LN_DEPTH (auxillary_nest); + invariants = LN_INVARIANTS (auxillary_nest); + + inverse = lambda_matrix_new (depth, depth); + determinant = lambda_matrix_inverse (LTM_MATRIX (H), inverse, depth); + + /* H1 is H excluding its diagonal. */ + H1 = lambda_matrix_new (depth, depth); + lambda_matrix_copy (LTM_MATRIX (H), H1, depth, depth); + + for (i = 0; i < depth; i++) + H1[i][i] = 0; + + /* Computes the linear offsets of the loop bounds. */ + target = lambda_matrix_new (depth, depth); + lambda_matrix_mult (H1, inverse, target, depth, depth, depth); + + target_nest = lambda_loopnest_new (depth, invariants); + + for (i = 0; i < depth; i++) + { + + /* Get a new loop structure. */ + target_loop = lambda_loop_new (); + LN_LOOPS (target_nest)[i] = target_loop; + + /* Computes the gcd of the coefficients of the linear part. */ + gcd1 = gcd_vector (target[i], i); + + /* Include the denominator in the GCD */ + gcd1 = gcd (gcd1, determinant); + + /* Now divide through by the gcd */ + for (j = 0; j < i; j++) + target[i][j] = target[i][j] / gcd1; + + expression = lambda_linear_expression_new (depth, invariants); + lambda_vector_copy (target[i], LLE_COEFFICIENTS (expression), depth); + LLE_DENOMINATOR (expression) = determinant / gcd1; + LLE_CONSTANT (expression) = 0; + lambda_vector_clear (LLE_INVARIANT_COEFFICIENTS (expression), + invariants); + LL_LINEAR_OFFSET (target_loop) = expression; + } + + /* For each loop, compute the new bounds from H */ + for (i = 0; i < depth; i++) + { + auxillary_loop = LN_LOOPS (auxillary_nest)[i]; + target_loop = LN_LOOPS (target_nest)[i]; + LL_STEP (target_loop) = LTM_MATRIX (H)[i][i]; + factor = LTM_MATRIX (H)[i][i]; + + /* First we do the lower bound. */ + auxillary_expr = LL_LOWER_BOUND (auxillary_loop); + + for (; auxillary_expr != NULL; + auxillary_expr = LLE_NEXT (auxillary_expr)) + { + target_expr = lambda_linear_expression_new (depth, invariants); + lambda_vector_matrix_mult (LLE_COEFFICIENTS (auxillary_expr), + depth, inverse, depth, + LLE_COEFFICIENTS (target_expr)); + lambda_vector_mult_const (LLE_COEFFICIENTS (target_expr), + LLE_COEFFICIENTS (target_expr), depth, + factor); + + LLE_CONSTANT (target_expr) = LLE_CONSTANT (auxillary_expr) * factor; + lambda_vector_copy (LLE_INVARIANT_COEFFICIENTS (auxillary_expr), + LLE_INVARIANT_COEFFICIENTS (target_expr), + invariants); + lambda_vector_mult_const (LLE_INVARIANT_COEFFICIENTS (target_expr), + LLE_INVARIANT_COEFFICIENTS (target_expr), + invariants, factor); + LLE_DENOMINATOR (target_expr) = LLE_DENOMINATOR (auxillary_expr); + + if (!lambda_vector_zerop (LLE_COEFFICIENTS (target_expr), depth)) + { + LLE_CONSTANT (target_expr) = LLE_CONSTANT (target_expr) + * determinant; + lambda_vector_mult_const (LLE_INVARIANT_COEFFICIENTS + (target_expr), + LLE_INVARIANT_COEFFICIENTS + (target_expr), invariants, + determinant); + LLE_DENOMINATOR (target_expr) = + LLE_DENOMINATOR (target_expr) * determinant; + } + /* Find the gcd and divide by it here, rather than doing it + at the tree level. */ + gcd1 = gcd_vector (LLE_COEFFICIENTS (target_expr), depth); + gcd2 = gcd_vector (LLE_INVARIANT_COEFFICIENTS (target_expr), + invariants); + gcd1 = gcd (gcd1, gcd2); + gcd1 = gcd (gcd1, LLE_CONSTANT (target_expr)); + gcd1 = gcd (gcd1, LLE_DENOMINATOR (target_expr)); + for (j = 0; j < depth; j++) + LLE_COEFFICIENTS (target_expr)[j] /= gcd1; + for (j = 0; j < invariants; j++) + LLE_INVARIANT_COEFFICIENTS (target_expr)[j] /= gcd1; + LLE_CONSTANT (target_expr) /= gcd1; + LLE_DENOMINATOR (target_expr) /= gcd1; + /* Ignore if identical to existing bound. */ + if (!lle_equal (LL_LOWER_BOUND (target_loop), target_expr, depth, + invariants)) + { + LLE_NEXT (target_expr) = LL_LOWER_BOUND (target_loop); + LL_LOWER_BOUND (target_loop) = target_expr; + } + } + /* Now do the upper bound. */ + auxillary_expr = LL_UPPER_BOUND (auxillary_loop); + + for (; auxillary_expr != NULL; + auxillary_expr = LLE_NEXT (auxillary_expr)) + { + target_expr = lambda_linear_expression_new (depth, invariants); + lambda_vector_matrix_mult (LLE_COEFFICIENTS (auxillary_expr), + depth, inverse, depth, + LLE_COEFFICIENTS (target_expr)); + lambda_vector_mult_const (LLE_COEFFICIENTS (target_expr), + LLE_COEFFICIENTS (target_expr), depth, + factor); + LLE_CONSTANT (target_expr) = LLE_CONSTANT (auxillary_expr) * factor; + lambda_vector_copy (LLE_INVARIANT_COEFFICIENTS (auxillary_expr), + LLE_INVARIANT_COEFFICIENTS (target_expr), + invariants); + lambda_vector_mult_const (LLE_INVARIANT_COEFFICIENTS (target_expr), + LLE_INVARIANT_COEFFICIENTS (target_expr), + invariants, factor); + LLE_DENOMINATOR (target_expr) = LLE_DENOMINATOR (auxillary_expr); + + if (!lambda_vector_zerop (LLE_COEFFICIENTS (target_expr), depth)) + { + LLE_CONSTANT (target_expr) = LLE_CONSTANT (target_expr) + * determinant; + lambda_vector_mult_const (LLE_INVARIANT_COEFFICIENTS + (target_expr), + LLE_INVARIANT_COEFFICIENTS + (target_expr), invariants, + determinant); + LLE_DENOMINATOR (target_expr) = + LLE_DENOMINATOR (target_expr) * determinant; + } + /* Find the gcd and divide by it here, instead of at the + tree level. */ + gcd1 = gcd_vector (LLE_COEFFICIENTS (target_expr), depth); + gcd2 = gcd_vector (LLE_INVARIANT_COEFFICIENTS (target_expr), + invariants); + gcd1 = gcd (gcd1, gcd2); + gcd1 = gcd (gcd1, LLE_CONSTANT (target_expr)); + gcd1 = gcd (gcd1, LLE_DENOMINATOR (target_expr)); + for (j = 0; j < depth; j++) + LLE_COEFFICIENTS (target_expr)[j] /= gcd1; + for (j = 0; j < invariants; j++) + LLE_INVARIANT_COEFFICIENTS (target_expr)[j] /= gcd1; + LLE_CONSTANT (target_expr) /= gcd1; + LLE_DENOMINATOR (target_expr) /= gcd1; + /* Ignore if equal to existing bound. */ + if (!lle_equal (LL_UPPER_BOUND (target_loop), target_expr, depth, + invariants)) + { + LLE_NEXT (target_expr) = LL_UPPER_BOUND (target_loop); + LL_UPPER_BOUND (target_loop) = target_expr; + } + } + } + for (i = 0; i < depth; i++) + { + target_loop = LN_LOOPS (target_nest)[i]; + /* If necessary, exchange the upper and lower bounds and negate + the step size. */ + if (stepsigns[i] < 0) + { + LL_STEP (target_loop) *= -1; + tmp_expr = LL_LOWER_BOUND (target_loop); + LL_LOWER_BOUND (target_loop) = LL_UPPER_BOUND (target_loop); + LL_UPPER_BOUND (target_loop) = tmp_expr; + } + } + return target_nest; +} + +/* Compute the step signs of TRANS, using TRANS and stepsigns. Return the new + result. */ + +static lambda_vector +lambda_compute_step_signs (lambda_trans_matrix trans, lambda_vector stepsigns) +{ + lambda_matrix matrix, H; + int size; + lambda_vector newsteps; + int i, j, factor, minimum_column; + int temp; + + matrix = LTM_MATRIX (trans); + size = LTM_ROWSIZE (trans); + H = lambda_matrix_new (size, size); + + newsteps = lambda_vector_new (size); + lambda_vector_copy (stepsigns, newsteps, size); + + lambda_matrix_copy (matrix, H, size, size); + + for (j = 0; j < size; j++) + { + lambda_vector row; + row = H[j]; + for (i = j; i < size; i++) + if (row[i] < 0) + lambda_matrix_col_negate (H, size, i); + while (lambda_vector_first_nz (row, size, j + 1) < size) + { + minimum_column = lambda_vector_min_nz (row, size, j); + lambda_matrix_col_exchange (H, size, j, minimum_column); + + temp = newsteps[j]; + newsteps[j] = newsteps[minimum_column]; + newsteps[minimum_column] = temp; + + for (i = j + 1; i < size; i++) + { + factor = row[i] / row[j]; + lambda_matrix_col_add (H, size, j, i, -1 * factor); + } + } + } + return newsteps; +} + +/* Transform NEST according to TRANS, and return the new loopnest. + This involves + 1. Computing a lattice base for the transformation + 2. Composing the dense base with the specified transformation (TRANS) + 3. Decomposing the combined transformation into a lower triangular portion, + and a unimodular portion. + 4. Computing the auxillary nest using the unimodular portion. + 5. Computing the target nest using the auxillary nest and the lower + triangular portion. */ + +lambda_loopnest +lambda_loopnest_transform (lambda_loopnest nest, lambda_trans_matrix trans) +{ + lambda_loopnest auxillary_nest, target_nest; + + int depth, invariants; + int i, j; + lambda_lattice lattice; + lambda_trans_matrix trans1, H, U; + lambda_loop loop; + lambda_linear_expression expression; + lambda_vector origin; + lambda_matrix origin_invariants; + lambda_vector stepsigns; + int f; + + depth = LN_DEPTH (nest); + invariants = LN_INVARIANTS (nest); + + /* Keep track of the signs of the loop steps. */ + stepsigns = lambda_vector_new (depth); + for (i = 0; i < depth; i++) + { + if (LL_STEP (LN_LOOPS (nest)[i]) > 0) + stepsigns[i] = 1; + else + stepsigns[i] = -1; + } + + /* Compute the lattice base. */ + lattice = lambda_lattice_compute_base (nest); + trans1 = lambda_trans_matrix_new (depth, depth); + + /* Multiply the transformation matrix by the lattice base. */ + + lambda_matrix_mult (LTM_MATRIX (trans), LATTICE_BASE (lattice), + LTM_MATRIX (trans1), depth, depth, depth); + + /* Compute the Hermite normal form for the new transformation matrix. */ + H = lambda_trans_matrix_new (depth, depth); + U = lambda_trans_matrix_new (depth, depth); + lambda_matrix_hermite (LTM_MATRIX (trans1), depth, LTM_MATRIX (H), + LTM_MATRIX (U)); + + /* Compute the auxiliary loop nest's space from the unimodular + portion. */ + auxillary_nest = lambda_compute_auxillary_space (nest, U); + + /* Compute the loop step signs from the old step signs and the + transformation matrix. */ + stepsigns = lambda_compute_step_signs (trans1, stepsigns); + + /* Compute the target loop nest space from the auxiliary nest and + the lower triangular matrix H. */ + target_nest = lambda_compute_target_space (auxillary_nest, H, stepsigns); + origin = lambda_vector_new (depth); + origin_invariants = lambda_matrix_new (depth, invariants); + lambda_matrix_vector_mult (LTM_MATRIX (trans), depth, depth, + LATTICE_ORIGIN (lattice), origin); + lambda_matrix_mult (LTM_MATRIX (trans), LATTICE_ORIGIN_INVARIANTS (lattice), + origin_invariants, depth, depth, invariants); + + for (i = 0; i < depth; i++) + { + loop = LN_LOOPS (target_nest)[i]; + expression = LL_LINEAR_OFFSET (loop); + if (lambda_vector_zerop (LLE_COEFFICIENTS (expression), depth)) + f = 1; + else + f = LLE_DENOMINATOR (expression); + + LLE_CONSTANT (expression) += f * origin[i]; + + for (j = 0; j < invariants; j++) + LLE_INVARIANT_COEFFICIENTS (expression)[j] += + f * origin_invariants[i][j]; + } + + return target_nest; + +} + +/* Convert a gcc tree expression EXPR to a lambda linear expression, and + return the new expression. DEPTH is the depth of the loopnest. + OUTERINDUCTIONVARS is an array of the induction variables for outer loops + in this nest. INVARIANTS is the array of invariants for the loop. EXTRA + is the amount we have to add/subtract from the expression because of the + type of comparison it is used in. */ + +static lambda_linear_expression +gcc_tree_to_linear_expression (int depth, tree expr, + VEC(tree) *outerinductionvars, + VEC(tree) *invariants, int extra) +{ + lambda_linear_expression lle = NULL; + switch (TREE_CODE (expr)) + { + case INTEGER_CST: + { + lle = lambda_linear_expression_new (depth, 2 * depth); + LLE_CONSTANT (lle) = TREE_INT_CST_LOW (expr); + if (extra != 0) + LLE_CONSTANT (lle) = extra; + + LLE_DENOMINATOR (lle) = 1; + } + break; + case SSA_NAME: + { + tree iv, invar; + size_t i; + for (i = 0; VEC_iterate (tree, outerinductionvars, i, iv); i++) + if (iv != NULL) + { + if (SSA_NAME_VAR (iv) == SSA_NAME_VAR (expr)) + { + lle = lambda_linear_expression_new (depth, 2 * depth); + LLE_COEFFICIENTS (lle)[i] = 1; + if (extra != 0) + LLE_CONSTANT (lle) = extra; + + LLE_DENOMINATOR (lle) = 1; + } + } + for (i = 0; VEC_iterate (tree, invariants, i, invar); i++) + if (invar != NULL) + { + if (SSA_NAME_VAR (invar) == SSA_NAME_VAR (expr)) + { + lle = lambda_linear_expression_new (depth, 2 * depth); + LLE_INVARIANT_COEFFICIENTS (lle)[i] = 1; + if (extra != 0) + LLE_CONSTANT (lle) = extra; + LLE_DENOMINATOR (lle) = 1; + } + } + } + break; + default: + return NULL; + } + + return lle; +} + +/* Return true if OP is invariant in LOOP and all outer loops. */ + +static bool +invariant_in_loop (struct loop *loop, tree op) +{ + if (loop->depth == 0) + return true; + if (TREE_CODE (op) == SSA_NAME) + { + if (TREE_CODE (SSA_NAME_VAR (op)) == PARM_DECL + && IS_EMPTY_STMT (SSA_NAME_DEF_STMT (op))) + return true; + if (IS_EMPTY_STMT (SSA_NAME_DEF_STMT (op))) + return false; + if (loop->outer) + if (!invariant_in_loop (loop->outer, op)) + return false; + return !flow_bb_inside_loop_p (loop, + bb_for_stmt (SSA_NAME_DEF_STMT (op))); + } + return false; +} + +/* Generate a lambda loop from a gcc loop LOOP. Return the new lambda loop, + or NULL if it could not be converted. + DEPTH is the depth of the loop. + INVARIANTS is a pointer to the array of loop invariants. + The induction variable for this loop should be stored in the parameter + OURINDUCTIONVAR. + OUTERINDUCTIONVARS is an array of induction variables for outer loops. */ + +static lambda_loop +gcc_loop_to_lambda_loop (struct loop *loop, int depth, + VEC (tree) ** invariants, + tree * ourinductionvar, + VEC (tree) * outerinductionvars) +{ + tree phi; + tree exit_cond; + tree access_fn, inductionvar; + tree step; + lambda_loop lloop = NULL; + lambda_linear_expression lbound, ubound; + tree test; + int stepint; + int extra = 0; + + use_optype uses; + + /* Find out induction var and set the pointer so that the caller can + append it to the outerinductionvars array later. */ + + inductionvar = find_induction_var_from_exit_cond (loop); + *ourinductionvar = inductionvar; + + exit_cond = get_loop_exit_condition (loop); + + if (inductionvar == NULL || exit_cond == NULL) + { + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, + "Unable to convert loop: Cannot determine exit condition or induction variable for loop.\n"); + return NULL; + } + + test = TREE_OPERAND (exit_cond, 0); + if (TREE_CODE (test) != LE_EXPR + && TREE_CODE (test) != LT_EXPR && TREE_CODE (test) != NE_EXPR) + { + + if (dump_file && (dump_flags & TDF_DETAILS)) + { + fprintf (dump_file, + "Unable to convert loop: Loop exit test uses unhandled test condition:"); + print_generic_stmt (dump_file, test, 0); + fprintf (dump_file, "\n"); + } + return NULL; + } + if (SSA_NAME_DEF_STMT (inductionvar) == NULL_TREE) + { + + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, + "Unable to convert loop: Cannot find PHI node for induction variable\n"); + + return NULL; + } + + phi = SSA_NAME_DEF_STMT (inductionvar); + if (TREE_CODE (phi) != PHI_NODE) + { + get_stmt_operands (phi); + uses = STMT_USE_OPS (phi); + + if (!uses) + { + + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, + "Unable to convert loop: Cannot find PHI node for induction variable\n"); + + return NULL; + } + + phi = USE_OP (uses, 0); + phi = SSA_NAME_DEF_STMT (phi); + if (TREE_CODE (phi) != PHI_NODE) + { + + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, + "Unable to convert loop: Cannot find PHI node for induction variable\n"); + return NULL; + } + + } + + access_fn = instantiate_parameters + (loop, analyze_scalar_evolution (loop, PHI_RESULT (phi))); + if (!access_fn) + { + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, + "Unable to convert loop: Access function for induction variable phi is NULL\n"); + + return NULL; + } + + step = evolution_part_in_loop_num (access_fn, loop->num); + if (!step || step == chrec_dont_know) + { + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, + "Unable to convert loop: Cannot determine step of loop.\n"); + + return NULL; + } + if (TREE_CODE (step) != INTEGER_CST) + { + + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, + "Unable to convert loop: Step of loop is not integer.\n"); + return NULL; + } + + stepint = TREE_INT_CST_LOW (step); + + /* Only want phis for induction vars, which will have two + arguments. */ + if (PHI_NUM_ARGS (phi) != 2) + { + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, + "Unable to convert loop: PHI node for induction variable has >2 arguments\n"); + return NULL; + } + + /* Another induction variable check. One argument's source should be + in the loop, one outside the loop. */ + if (flow_bb_inside_loop_p (loop, PHI_ARG_EDGE (phi, 0)->src) + && flow_bb_inside_loop_p (loop, PHI_ARG_EDGE (phi, 1)->src)) + { + + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, + "Unable to convert loop: PHI edges both inside loop, or both outside loop.\n"); + + return NULL; + } + + if (flow_bb_inside_loop_p (loop, PHI_ARG_EDGE (phi, 0)->src)) + + lbound = gcc_tree_to_linear_expression (depth, PHI_ARG_DEF (phi, 1), + outerinductionvars, *invariants, + 0); + else + lbound = gcc_tree_to_linear_expression (depth, PHI_ARG_DEF (phi, 0), + outerinductionvars, *invariants, + 0); + if (!lbound) + { + + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, + "Unable to convert loop: Cannot convert lower bound to linear expression\n"); + + return NULL; + } + if (TREE_CODE (TREE_OPERAND (test, 1)) == SSA_NAME) + if (invariant_in_loop (loop, TREE_OPERAND (test, 1))) + VEC_safe_push (tree, *invariants, TREE_OPERAND (test, 1)); + + /* We only size the vectors assuming we have, at max, 2 times as many + invariants as we do loops (one for each bound). + This is just an arbitrary number, but it has to be matched against the + code below. */ + if (VEC_length (tree, *invariants) > (unsigned int) (2 * depth)) + abort (); + + /* We might have some leftover. */ + if (TREE_CODE (test) == LT_EXPR) + extra = -1 * stepint; + else if (TREE_CODE (test) == NE_EXPR) + extra = -1 * stepint; + + ubound = gcc_tree_to_linear_expression (depth, + TREE_OPERAND (test, 1), + outerinductionvars, + *invariants, extra); + if (!ubound) + { + + if (dump_file && (dump_flags & TDF_DETAILS)) + fprintf (dump_file, + "Unable to convert loop: Cannot convert upper bound to linear expression\n"); + return NULL; + } + + lloop = lambda_loop_new (); + LL_STEP (lloop) = stepint; + LL_LOWER_BOUND (lloop) = lbound; + LL_UPPER_BOUND (lloop) = ubound; + return lloop; +} + +/* Given a LOOP, find the induction variable it is testing against in the exit + condition. Return the induction variable if found, NULL otherwise. */ + +static tree +find_induction_var_from_exit_cond (struct loop *loop) +{ + tree expr = get_loop_exit_condition (loop); + tree test; + if (expr == NULL_TREE) + return NULL_TREE; + if (TREE_CODE (expr) != COND_EXPR) + return NULL_TREE; + test = TREE_OPERAND (expr, 0); + if (TREE_CODE_CLASS (TREE_CODE (test)) != '<') + return NULL_TREE; + if (TREE_CODE (TREE_OPERAND (test, 0)) != SSA_NAME) + return NULL_TREE; + return TREE_OPERAND (test, 0); +} + +DEF_VEC_P(lambda_loop); +/* Generate a lambda loopnest from a gcc loopnest LOOP_NEST. + Return the new loop nest. + INDUCTIONVARS is a pointer to an array of induction variables for the + loopnest that will be filled in during this process. + INVARIANTS is a pointer to an array of invariants that will be filled in + during this process. */ + +lambda_loopnest +gcc_loopnest_to_lambda_loopnest (struct loop * loop_nest, + VEC (tree) **inductionvars, + VEC (tree) **invariants) +{ + lambda_loopnest ret; + struct loop *temp; + int depth = 0; + size_t i; + VEC (lambda_loop) *loops; + lambda_loop newloop; + tree inductionvar = NULL; + + temp = loop_nest; + while (temp) + { + depth++; + temp = temp->inner; + } + loops = VEC_alloc (lambda_loop, 1); + *inductionvars = VEC_alloc (tree, 1); + *invariants = VEC_alloc (tree, 1); + temp = loop_nest; + while (temp) + { + newloop = gcc_loop_to_lambda_loop (temp, depth, invariants, + &inductionvar, *inductionvars); + if (!newloop) + return NULL; + VEC_safe_push (tree, *inductionvars, inductionvar); + VEC_safe_push (lambda_loop, loops, newloop); + temp = temp->inner; + } + + ret = lambda_loopnest_new (depth, 2 * depth); + for (i = 0; VEC_iterate (lambda_loop, loops, i, newloop); i++) + LN_LOOPS (ret)[i] = newloop; + + return ret; + +} + +/* Convert a lambda body vector LBV to a gcc tree, and return the new tree. + STMTS_TO_INSERT is a pointer to a tree where the statements we need to be + inserted for us are stored. INDUCTION_VARS is the array of induction + variables for the loop this LBV is from. */ + +static tree +lbv_to_gcc_expression (lambda_body_vector lbv, + VEC (tree) *induction_vars, tree * stmts_to_insert) +{ + tree stmts, stmt, resvar, name; + size_t i; + tree_stmt_iterator tsi; + + /* Create a statement list and a linear expression temporary. */ + stmts = alloc_stmt_list (); + resvar = create_tmp_var (integer_type_node, "lletmp"); + add_referenced_tmp_var (resvar); + + /* Start at 0. */ + stmt = build (MODIFY_EXPR, void_type_node, resvar, integer_zero_node); + name = make_ssa_name (resvar, stmt); + TREE_OPERAND (stmt, 0) = name; + tsi = tsi_last (stmts); + tsi_link_after (&tsi, stmt, TSI_CONTINUE_LINKING); + + for (i = 0; i < VEC_length (tree ,induction_vars) ; i++) + { + if (LBV_COEFFICIENTS (lbv)[i] != 0) + { + tree newname; + + /* newname = coefficient * induction_variable */ + stmt = build (MODIFY_EXPR, void_type_node, resvar, + fold (build (MULT_EXPR, integer_type_node, + VEC_index (tree, induction_vars, i), + build_int_cst (integer_type_node, + LBV_COEFFICIENTS (lbv)[i])))); + newname = make_ssa_name (resvar, stmt); + TREE_OPERAND (stmt, 0) = newname; + tsi = tsi_last (stmts); + tsi_link_after (&tsi, stmt, TSI_CONTINUE_LINKING); + /* name = name + newname */ + stmt = build (MODIFY_EXPR, void_type_node, resvar, + build (PLUS_EXPR, integer_type_node, name, newname)); + name = make_ssa_name (resvar, stmt); + TREE_OPERAND (stmt, 0) = name; + tsi = tsi_last (stmts); + tsi_link_after (&tsi, stmt, TSI_CONTINUE_LINKING); + } + } + + /* Handle any denominator that occurs. */ + if (LBV_DENOMINATOR (lbv) != 1) + { + stmt = build (MODIFY_EXPR, void_type_node, resvar, + build (CEIL_DIV_EXPR, integer_type_node, + name, build_int_cst (integer_type_node, + LBV_DENOMINATOR (lbv)))); + name = make_ssa_name (resvar, stmt); + TREE_OPERAND (stmt, 0) = name; + tsi = tsi_last (stmts); + tsi_link_after (&tsi, stmt, TSI_CONTINUE_LINKING); + } + *stmts_to_insert = stmts; + return name; +} + +/* Convert a linear expression from coefficient and constant form to a + gcc tree. + Return the tree that represents the final value of the expression. + LLE is the linear expression to convert. + OFFSET is the linear offset to apply to the expression. + INDUCTION_VARS is a vector of induction variables for the loops. + INVARIANTS is a vector of the loop nest invariants. + WRAP specifies what tree code to wrap the results in, if there is more than + one (it is either MAX_EXPR, or MIN_EXPR). + STMTS_TO_INSERT Is a pointer to the statement list we fill in with + statements that need to be inserted for the linear expression. */ + +static tree +lle_to_gcc_expression (lambda_linear_expression lle, + lambda_linear_expression offset, + VEC(tree) *induction_vars, + VEC(tree) *invariants, + enum tree_code wrap, tree * stmts_to_insert) +{ + tree stmts, stmt, resvar, name; + size_t i; + tree_stmt_iterator tsi; + VEC(tree) *results; + + name = NULL_TREE; + /* Create a statement list and a linear expression temporary. */ + stmts = alloc_stmt_list (); + resvar = create_tmp_var (integer_type_node, "lletmp"); + add_referenced_tmp_var (resvar); + results = VEC_alloc (tree, 1); + + /* Build up the linear expressions, and put the variable representing the + result in the results array. */ + for (; lle != NULL; lle = LLE_NEXT (lle)) + { + /* Start at name = 0. */ + stmt = build (MODIFY_EXPR, void_type_node, resvar, integer_zero_node); + name = make_ssa_name (resvar, stmt); + TREE_OPERAND (stmt, 0) = name; + tsi = tsi_last (stmts); + tsi_link_after (&tsi, stmt, TSI_CONTINUE_LINKING); + + /* First do the induction variables. + at the end, name = name + all the induction variables added + together. */ + for (i = 0; i < VEC_length (tree ,induction_vars); i++) + { + if (LLE_COEFFICIENTS (lle)[i] != 0) + { + tree newname; + tree mult; + tree coeff; + + /* mult = induction variable * coefficient. */ + if (LLE_COEFFICIENTS (lle)[i] == 1) + { + mult = VEC_index (tree, induction_vars, i); + } + else + { + coeff = build_int_cst (integer_type_node, + LLE_COEFFICIENTS (lle)[i]); + mult = fold (build (MULT_EXPR, integer_type_node, + VEC_index (tree, induction_vars, i), + coeff)); + } + + /* newname = mult */ + stmt = build (MODIFY_EXPR, void_type_node, resvar, mult); + newname = make_ssa_name (resvar, stmt); + TREE_OPERAND (stmt, 0) = newname; + tsi = tsi_last (stmts); + tsi_link_after (&tsi, stmt, TSI_CONTINUE_LINKING); + + /* name = name + newname */ + stmt = build (MODIFY_EXPR, void_type_node, resvar, + build (PLUS_EXPR, integer_type_node, + name, newname)); + name = make_ssa_name (resvar, stmt); + TREE_OPERAND (stmt, 0) = name; + tsi = tsi_last (stmts); + tsi_link_after (&tsi, stmt, TSI_CONTINUE_LINKING); + } + } + + /* Handle our invariants. + At the end, we have name = name + result of adding all multiplied + invariants. */ + for (i = 0; i < VEC_length (tree, invariants); i++) + { + if (LLE_INVARIANT_COEFFICIENTS (lle)[i] != 0) + { + tree newname; + tree mult; + tree coeff; + + /* mult = invariant * coefficient */ + if (LLE_INVARIANT_COEFFICIENTS (lle)[i] == 1) + { + mult = VEC_index (tree, invariants, i); + } + else + { + coeff = build_int_cst (integer_type_node, + LLE_INVARIANT_COEFFICIENTS (lle)[i]); + mult = fold (build (MULT_EXPR, integer_type_node, + VEC_index (tree, invariants, i), + coeff)); + } + + /* newname = mult */ + stmt = build (MODIFY_EXPR, void_type_node, resvar, mult); + newname = make_ssa_name (resvar, stmt); + TREE_OPERAND (stmt, 0) = newname; + tsi = tsi_last (stmts); + tsi_link_after (&tsi, stmt, TSI_CONTINUE_LINKING); + + /* name = name + newname */ + stmt = build (MODIFY_EXPR, void_type_node, resvar, + build (PLUS_EXPR, integer_type_node, + name, newname)); + name = make_ssa_name (resvar, stmt); + TREE_OPERAND (stmt, 0) = name; + tsi = tsi_last (stmts); + tsi_link_after (&tsi, stmt, TSI_CONTINUE_LINKING); + } + } + + /* Now handle the constant. + name = name + constant. */ + if (LLE_CONSTANT (lle) != 0) + { + stmt = build (MODIFY_EXPR, void_type_node, resvar, + build (PLUS_EXPR, integer_type_node, + name, build_int_cst (integer_type_node, + LLE_CONSTANT (lle)))); + name = make_ssa_name (resvar, stmt); + TREE_OPERAND (stmt, 0) = name; + tsi = tsi_last (stmts); + tsi_link_after (&tsi, stmt, TSI_CONTINUE_LINKING); + } + + /* Now handle the offset. + name = name + linear offset. */ + if (LLE_CONSTANT (offset) != 0) + { + stmt = build (MODIFY_EXPR, void_type_node, resvar, + build (PLUS_EXPR, integer_type_node, + name, build_int_cst (integer_type_node, + LLE_CONSTANT (offset)))); + name = make_ssa_name (resvar, stmt); + TREE_OPERAND (stmt, 0) = name; + tsi = tsi_last (stmts); + tsi_link_after (&tsi, stmt, TSI_CONTINUE_LINKING); + } + + /* Handle any denominator that occurs. */ + if (LLE_DENOMINATOR (lle) != 1) + { + if (wrap == MAX_EXPR) + stmt = build (MODIFY_EXPR, void_type_node, resvar, + build (CEIL_DIV_EXPR, integer_type_node, + name, build_int_cst (integer_type_node, + LLE_DENOMINATOR (lle)))); + else if (wrap == MIN_EXPR) + stmt = build (MODIFY_EXPR, void_type_node, resvar, + build (FLOOR_DIV_EXPR, integer_type_node, + name, build_int_cst (integer_type_node, + LLE_DENOMINATOR (lle)))); + else + abort (); + + /* name = {ceil, floor}(name/denominator) */ + name = make_ssa_name (resvar, stmt); + TREE_OPERAND (stmt, 0) = name; + tsi = tsi_last (stmts); + tsi_link_after (&tsi, stmt, TSI_CONTINUE_LINKING); + } + VEC_safe_push (tree, results, name); + } + + /* Again, out of laziness, we don't handle this case yet. It's not + hard, it just hasn't occurred. */ + if (VEC_length (tree, results) > 2) + abort (); + + /* We may need to wrap the results in a MAX_EXPR or MIN_EXPR. */ + if (VEC_length (tree, results) > 1) + { + tree op1 = VEC_index (tree, results, 0); + tree op2 = VEC_index (tree, results, 1); + stmt = build (MODIFY_EXPR, void_type_node, resvar, + build (wrap, integer_type_node, op1, op2)); + name = make_ssa_name (resvar, stmt); + TREE_OPERAND (stmt, 0) = name; + tsi = tsi_last (stmts); + tsi_link_after (&tsi, stmt, TSI_CONTINUE_LINKING); + } + + *stmts_to_insert = stmts; + return name; +} + +/* Transform a lambda loopnest NEW_LOOPNEST, which had TRANSFORM applied to + it, back into gcc code. This changes the + loops, their induction variables, and their bodies, so that they + match the transformed loopnest. + OLD_LOOPNEST is the loopnest before we've replaced it with the new + loopnest. + OLD_IVS is a vector of induction variables from the old loopnest. + INVARIANTS is a vector of loop invariants from the old loopnest. + NEW_LOOPNEST is the new lambda loopnest to replace OLD_LOOPNEST with. + TRANSFORM is the matrix transform that was applied to OLD_LOOPNEST to get + NEW_LOOPNEST. */ +void +lambda_loopnest_to_gcc_loopnest (struct loop *old_loopnest, + VEC(tree) *old_ivs, + VEC(tree) *invariants, + lambda_loopnest new_loopnest, + lambda_trans_matrix transform) +{ + + struct loop *temp; + size_t i = 0; + size_t depth = 0; + VEC(tree) *new_ivs; + block_stmt_iterator bsi; + basic_block *bbs; + + if (dump_file) + { + transform = lambda_trans_matrix_inverse (transform); + fprintf (dump_file, "Inverse of transformation matrix:\n"); + print_lambda_trans_matrix (dump_file, transform); + } + temp = old_loopnest; + new_ivs = VEC_alloc (tree, 1); + while (temp) + { + temp = temp->inner; + depth++; + } + temp = old_loopnest; + + while (temp) + { + lambda_loop newloop; + basic_block bb; + tree ivvar, ivvarinced, exitcond, stmts; + enum tree_code testtype; + tree newupperbound, newlowerbound; + lambda_linear_expression offset; + /* First, build the new induction variable temporary */ + + ivvar = create_tmp_var (integer_type_node, "lnivtmp"); + add_referenced_tmp_var (ivvar); + + VEC_safe_push (tree, new_ivs, ivvar); + + newloop = LN_LOOPS (new_loopnest)[i]; + + /* Linear offset is a bit tricky to handle. Punt on the unhandled + cases for now. */ + offset = LL_LINEAR_OFFSET (newloop); + + if (LLE_DENOMINATOR (offset) != 1 + || !lambda_vector_zerop (LLE_COEFFICIENTS (offset), depth)) + abort (); + + /* Now build the new lower bounds, and insert the statements + necessary to generate it on the loop preheader. */ + newlowerbound = lle_to_gcc_expression (LL_LOWER_BOUND (newloop), + LL_LINEAR_OFFSET (newloop), + new_ivs, + invariants, MAX_EXPR, &stmts); + bsi_insert_on_edge (loop_preheader_edge (temp), stmts); + bsi_commit_edge_inserts (NULL); + /* Build the new upper bound and insert its statements in the + basic block of the exit condition */ + newupperbound = lle_to_gcc_expression (LL_UPPER_BOUND (newloop), + LL_LINEAR_OFFSET (newloop), + new_ivs, + invariants, MIN_EXPR, &stmts); + exitcond = get_loop_exit_condition (temp); + bb = bb_for_stmt (exitcond); + bsi = bsi_start (bb); + bsi_insert_after (&bsi, stmts, BSI_NEW_STMT); + + /* Create the new iv, and insert it's increment on the latch + block. */ + + bb = temp->latch->pred->src; + bsi = bsi_last (bb); + create_iv (newlowerbound, + build_int_cst (integer_type_node, LL_STEP (newloop)), + ivvar, temp, &bsi, false, &ivvar, + &ivvarinced); + + /* Replace the exit condition with the new upper bound + comparison. */ + testtype = LL_STEP (newloop) >= 0 ? LE_EXPR : GE_EXPR; + COND_EXPR_COND (exitcond) = build (testtype, + boolean_type_node, + ivvarinced, newupperbound); + modify_stmt (exitcond); + VEC_replace (tree, new_ivs, i, ivvar); + + i++; + temp = temp->inner; + } + + /* Go through the loop and make iv replacements. */ + bbs = get_loop_body (old_loopnest); + for (i = 0; i < old_loopnest->num_nodes; i++) + for (bsi = bsi_start (bbs[i]); !bsi_end_p (bsi); bsi_next (&bsi)) + { + tree stmt = bsi_stmt (bsi); + use_optype uses; + size_t j; + + get_stmt_operands (stmt); + uses = STMT_USE_OPS (stmt); + for (j = 0; j < NUM_USES (uses); j++) + { + size_t k; + use_operand_p use = USE_OP_PTR (uses, j); + for (k = 0; k < VEC_length (tree, old_ivs); k++) + { + tree oldiv = VEC_index (tree, old_ivs, k); + if (USE_FROM_PTR (use) == oldiv) + { + tree newiv, stmts; + lambda_body_vector lbv; + + /* Compute the new expression for the induction + variable. */ + depth = VEC_length (tree, new_ivs); + lbv = lambda_body_vector_new (depth); + LBV_COEFFICIENTS (lbv)[k] = 1; + lbv = lambda_body_vector_compute_new (transform, lbv); + newiv = lbv_to_gcc_expression (lbv, new_ivs, &stmts); + + /* Insert the statements to build that + expression. */ + bsi_insert_before (&bsi, stmts, BSI_SAME_STMT); + + /* Replace the use with the result of that + expression. */ + if (dump_file) + { + fprintf (dump_file, + "Replacing induction variable use of "); + print_generic_stmt (dump_file, USE_FROM_PTR (use), 0); + fprintf (dump_file, " with "); + print_generic_stmt (dump_file, newiv, 0); + fprintf (dump_file, "\n"); + } + SET_USE (use, newiv); + } + } + + } + } +} + +/* Returns true when the vector V is lexicographically positive, in + other words, when the first non zero element is positive. */ + +static bool +lambda_vector_lexico_pos (lambda_vector v, unsigned n) +{ + unsigned i; + for (i = 0; i < n; i++) + { + if (v[i] == 0) + continue; + if (v[i] < 0) + return false; + if (v[i] > 0) + return true; + } + return true; +} + +/* Return true if TRANS is a legal transformation matrix that respects + the dependence vectors in DISTS and DIRS. The conservative answer + is false. + + "Wolfe proves that a unimodular transformation represented by the + matrix T is legal when applied to a loop nest with a set of + lexicographically non-negative distance vectors RDG if and only if + for each vector d in RDG, (T.d >= 0) is lexicographically positive. + ie.: if and only if it transforms the lexicographically positive + distance vectors to lexicographically positive vectors. Note that + a unimodular matrix must transform the zero vector (and only it) to + the zero vector." S.Muchnick. */ + +bool +lambda_transform_legal_p (lambda_trans_matrix trans, + int nb_loops, varray_type dependence_relations) +{ + unsigned int i; + lambda_vector distres; + struct data_dependence_relation *ddr; + +#if defined ENABLE_CHECKING + if (LTM_COLSIZE (trans) != nb_loops || LTM_ROWSIZE (trans) != nb_loops) + abort (); +#endif + + /* When there is an unknown relation in the dependence_relations, we + know that it is no worth looking at this loop nest: give up. */ + ddr = (struct data_dependence_relation *) + VARRAY_GENERIC_PTR (dependence_relations, 0); + if (ddr == NULL) + return true; + if (DDR_ARE_DEPENDENT (ddr) == chrec_dont_know) + return false; + + distres = lambda_vector_new (nb_loops); + + /* For each distance vector in the dependence graph. */ + for (i = 0; i < VARRAY_ACTIVE_SIZE (dependence_relations); i++) + { + ddr = (struct data_dependence_relation *) + VARRAY_GENERIC_PTR (dependence_relations, i); + + /* Don't care about relations for which we know that there is no + dependence, nor about read-read (aka. output-dependences): + these data accesses can happen in any order. */ + if (DDR_ARE_DEPENDENT (ddr) == chrec_known + || (DR_IS_READ (DDR_A (ddr)) && DR_IS_READ (DDR_B (ddr)))) + continue; + /* Conservatively answer: "this transformation is not valid". */ + if (DDR_ARE_DEPENDENT (ddr) == chrec_dont_know) + return false; + + /* Compute trans.dist_vect */ + lambda_matrix_vector_mult (LTM_MATRIX (trans), nb_loops, nb_loops, + DDR_DIST_VECT (ddr), distres); + + if (!lambda_vector_lexico_pos (distres, nb_loops)) + return false; + } + + return true; +} |