/* Functions to determine/estimate number of iterations of a loop.
- Copyright (C) 2004, 2005 Free Software Foundation, Inc.
+ Copyright (C) 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
This file is part of GCC.
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. */
+Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
+02110-1301, USA. */
#include "config.h"
#include "system.h"
#include "basic-block.h"
#include "output.h"
#include "diagnostic.h"
+#include "intl.h"
#include "tree-flow.h"
#include "tree-dump.h"
#include "cfgloop.h"
#include "tree-data-ref.h"
#include "params.h"
#include "flags.h"
+#include "toplev.h"
#include "tree-inline.h"
+#include "gmp.h"
#define SWAP(X, Y) do { void *tmp = (X); (X) = (Y); (Y) = tmp; } while (0)
+/* The maximum number of dominator BBs we search for conditions
+ of loop header copies we use for simplifying a conditional
+ expression. */
+#define MAX_DOMINATORS_TO_WALK 8
/*
*/
-/* Returns true if ARG is either NULL_TREE or constant zero. Unlike
- integer_zerop, it does not care about overflow flags. */
+/* Bounds on some value, BELOW <= X <= UP. */
-bool
-zero_p (tree arg)
+typedef struct
{
- if (!arg)
- return true;
-
- if (TREE_CODE (arg) != INTEGER_CST)
- return false;
+ mpz_t below, up;
+} bounds;
- return (TREE_INT_CST_LOW (arg) == 0 && TREE_INT_CST_HIGH (arg) == 0);
-}
-
-/* Returns true if ARG a nonzero constant. Unlike integer_nonzerop, it does
- not care about overflow flags. */
+/* Sets RESULT to VAL, taken unsigned if UNS is true and as signed
+ otherwise. */
-static bool
-nonzero_p (tree arg)
+static void
+mpz_set_double_int (mpz_t result, double_int val, bool uns)
{
- if (!arg)
- return false;
+ bool negate = false;
+ unsigned HOST_WIDE_INT vp[2];
- if (TREE_CODE (arg) != INTEGER_CST)
- return false;
+ if (!uns && double_int_negative_p (val))
+ {
+ negate = true;
+ val = double_int_neg (val);
+ }
- return (TREE_INT_CST_LOW (arg) != 0 || TREE_INT_CST_HIGH (arg) != 0);
+ vp[0] = val.low;
+ vp[1] = (unsigned HOST_WIDE_INT) val.high;
+ mpz_import (result, 2, -1, sizeof (HOST_WIDE_INT), 0, 0, vp);
+
+ if (negate)
+ mpz_neg (result, result);
}
-/* Returns inverse of X modulo 2^s, where MASK = 2^s-1. */
+/* Stores bounds of TYPE to MIN and MAX. */
-static tree
-inverse (tree x, tree mask)
+static void
+get_type_bounds (tree type, mpz_t min, mpz_t max)
{
- tree type = TREE_TYPE (x);
- tree rslt;
- unsigned ctr = tree_floor_log2 (mask);
-
- if (TYPE_PRECISION (type) <= HOST_BITS_PER_WIDE_INT)
+ if (TYPE_UNSIGNED (type))
{
- unsigned HOST_WIDE_INT ix;
- unsigned HOST_WIDE_INT imask;
- unsigned HOST_WIDE_INT irslt = 1;
-
- gcc_assert (cst_and_fits_in_hwi (x));
- gcc_assert (cst_and_fits_in_hwi (mask));
-
- ix = int_cst_value (x);
- imask = int_cst_value (mask);
-
- for (; ctr; ctr--)
- {
- irslt *= ix;
- ix *= ix;
- }
- irslt &= imask;
-
- rslt = build_int_cst_type (type, irslt);
+ mpz_set_ui (min, 0);
+ mpz_set_double_int (max, double_int_mask (TYPE_PRECISION (type)), true);
}
else
{
- rslt = build_int_cst_type (type, 1);
- for (; ctr; ctr--)
- {
- rslt = fold_binary_to_constant (MULT_EXPR, type, rslt, x);
- x = fold_binary_to_constant (MULT_EXPR, type, x, x);
- }
- rslt = fold_binary_to_constant (BIT_AND_EXPR, type, rslt, mask);
+ double_int mx, mn;
+
+ mx = double_int_mask (TYPE_PRECISION (type) - 1);
+ mn = double_int_sext (double_int_add (mx, double_int_one),
+ TYPE_PRECISION (type));
+ mpz_set_double_int (max, mx, true);
+ mpz_set_double_int (min, mn, false);
}
+}
- return rslt;
+/* Returns VAL converted to TYPE. If VAL does not fit in TYPE,
+ the minimum or maximum value of the type is returned instead. */
+
+static double_int
+mpz_to_double_int (tree type, mpz_t val)
+{
+ mpz_t min, max;
+ unsigned HOST_WIDE_INT vp[2];
+ bool negate = false;
+ size_t count;
+ double_int res;
+
+ mpz_init (min);
+ mpz_init (max);
+ get_type_bounds (type, min, max);
+
+ if (mpz_cmp (val, min) < 0)
+ mpz_set (val, min);
+ else if (mpz_cmp (val, max) > 0)
+ mpz_set (val, max);
+
+ if (mpz_sgn (val) < 0)
+ negate = true;
+
+ vp[0] = 0;
+ vp[1] = 0;
+ mpz_export (vp, &count, -1, sizeof (HOST_WIDE_INT), 0, 0, val);
+ gcc_assert (count <= 2);
+
+ mpz_clear (min);
+ mpz_clear (max);
+
+ res.low = vp[0];
+ res.high = (HOST_WIDE_INT) vp[1];
+
+ res = double_int_ext (res, TYPE_PRECISION (type), TYPE_UNSIGNED (type));
+ if (negate)
+ res = double_int_neg (res);
+
+ return res;
}
-/* Determine the number of iterations according to condition (for staying
- inside loop) which compares two induction variables using comparison
- operator CODE. The induction variable on left side of the comparison
- has base BASE0 and step STEP0. the right-hand side one has base
- BASE1 and step STEP1. Both induction variables must have type TYPE,
- which must be an integer or pointer type. STEP0 and STEP1 must be
- constants (or NULL_TREE, which is interpreted as constant zero).
-
- The results (number of iterations and assumptions as described in
- comments at struct tree_niter_desc in tree-flow.h) are stored to NITER.
- In case we are unable to determine number of iterations, contents of
- this structure is unchanged. */
+/* Splits expression EXPR to a variable part VAR and constant OFFSET. */
static void
-number_of_iterations_cond (tree type, tree base0, tree step0,
- enum tree_code code, tree base1, tree step1,
- struct tree_niter_desc *niter)
+split_to_var_and_offset (tree expr, tree *var, mpz_t offset)
{
- tree step, delta, mmin, mmax;
- tree may_xform, bound, s, d, tmp;
- bool was_sharp = false;
- tree assumption;
- tree assumptions = boolean_true_node;
- tree noloop_assumptions = boolean_false_node;
- tree niter_type, signed_niter_type;
- tree bits;
+ tree type = TREE_TYPE (expr);
+ tree op0, op1;
+ double_int off;
+ bool negate = false;
- /* The meaning of these assumptions is this:
- if !assumptions
- then the rest of information does not have to be valid
- if noloop_assumptions then the loop does not have to roll
- (but it is only conservative approximation, i.e. it only says that
- if !noloop_assumptions, then the loop does not end before the computed
- number of iterations) */
+ *var = expr;
+ mpz_set_ui (offset, 0);
- /* Make < comparison from > ones. */
- if (code == GE_EXPR
- || code == GT_EXPR)
+ switch (TREE_CODE (expr))
{
- SWAP (base0, base1);
- SWAP (step0, step1);
- code = swap_tree_comparison (code);
- }
+ case MINUS_EXPR:
+ negate = true;
+ /* Fallthru. */
+
+ case PLUS_EXPR:
+ op0 = TREE_OPERAND (expr, 0);
+ op1 = TREE_OPERAND (expr, 1);
+
+ if (TREE_CODE (op1) != INTEGER_CST)
+ break;
+
+ *var = op0;
+ /* Always sign extend the offset. */
+ off = double_int_sext (tree_to_double_int (op1),
+ TYPE_PRECISION (type));
+ mpz_set_double_int (offset, off, false);
+ break;
- /* We can handle the case when neither of the sides of the comparison is
- invariant, provided that the test is NE_EXPR. This rarely occurs in
- practice, but it is simple enough to manage. */
- if (!zero_p (step0) && !zero_p (step1))
- {
- if (code != NE_EXPR)
- return;
+ case INTEGER_CST:
+ *var = build_int_cst_type (type, 0);
+ off = tree_to_double_int (expr);
+ mpz_set_double_int (offset, off, TYPE_UNSIGNED (type));
+ break;
- step0 = fold_binary_to_constant (MINUS_EXPR, type, step0, step1);
- step1 = NULL_TREE;
+ default:
+ break;
}
+}
- /* If the result is a constant, the loop is weird. More precise handling
- would be possible, but the situation is not common enough to waste time
- on it. */
- if (zero_p (step0) && zero_p (step1))
- return;
+/* Stores estimate on the minimum/maximum value of the expression VAR + OFF
+ in TYPE to MIN and MAX. */
- /* Ignore loops of while (i-- < 10) type. */
- if (code != NE_EXPR)
+static void
+determine_value_range (tree type, tree var, mpz_t off,
+ mpz_t min, mpz_t max)
+{
+ /* If the expression is a constant, we know its value exactly. */
+ if (integer_zerop (var))
{
- if (step0 && !tree_expr_nonnegative_p (step0))
- return;
-
- if (!zero_p (step1) && tree_expr_nonnegative_p (step1))
- return;
+ mpz_set (min, off);
+ mpz_set (max, off);
+ return;
}
- if (POINTER_TYPE_P (type))
- {
- /* We assume pointer arithmetic never overflows. */
- mmin = mmax = NULL_TREE;
- }
+ /* If the computation may wrap, we know nothing about the value, except for
+ the range of the type. */
+ get_type_bounds (type, min, max);
+ if (!nowrap_type_p (type))
+ return;
+
+ /* Since the addition of OFF does not wrap, if OFF is positive, then we may
+ add it to MIN, otherwise to MAX. */
+ if (mpz_sgn (off) < 0)
+ mpz_add (max, max, off);
else
+ mpz_add (min, min, off);
+}
+
+/* Stores the bounds on the difference of the values of the expressions
+ (var + X) and (var + Y), computed in TYPE, to BNDS. */
+
+static void
+bound_difference_of_offsetted_base (tree type, mpz_t x, mpz_t y,
+ bounds *bnds)
+{
+ int rel = mpz_cmp (x, y);
+ bool may_wrap = !nowrap_type_p (type);
+ mpz_t m;
+
+ /* If X == Y, then the expressions are always equal.
+ If X > Y, there are the following possibilities:
+ a) neither of var + X and var + Y overflow or underflow, or both of
+ them do. Then their difference is X - Y.
+ b) var + X overflows, and var + Y does not. Then the values of the
+ expressions are var + X - M and var + Y, where M is the range of
+ the type, and their difference is X - Y - M.
+ c) var + Y underflows and var + X does not. Their difference again
+ is M - X + Y.
+ Therefore, if the arithmetics in type does not overflow, then the
+ bounds are (X - Y, X - Y), otherwise they are (X - Y - M, X - Y)
+ Similarly, if X < Y, the bounds are either (X - Y, X - Y) or
+ (X - Y, X - Y + M). */
+
+ if (rel == 0)
{
- mmin = TYPE_MIN_VALUE (type);
- mmax = TYPE_MAX_VALUE (type);
+ mpz_set_ui (bnds->below, 0);
+ mpz_set_ui (bnds->up, 0);
+ return;
}
- /* Some more condition normalization. We must record some assumptions
- due to overflows. */
+ mpz_init (m);
+ mpz_set_double_int (m, double_int_mask (TYPE_PRECISION (type)), true);
+ mpz_add_ui (m, m, 1);
+ mpz_sub (bnds->up, x, y);
+ mpz_set (bnds->below, bnds->up);
- if (code == LT_EXPR)
+ if (may_wrap)
{
- /* We want to take care only of <=; this is easy,
- as in cases the overflow would make the transformation unsafe the loop
- does not roll. Seemingly it would make more sense to want to take
- care of <, as NE is more similar to it, but the problem is that here
- the transformation would be more difficult due to possibly infinite
- loops. */
- if (zero_p (step0))
- {
- if (mmax)
- assumption = fold_build2 (EQ_EXPR, boolean_type_node, base0, mmax);
- else
- assumption = boolean_false_node;
- if (nonzero_p (assumption))
- goto zero_iter;
- base0 = fold_build2 (PLUS_EXPR, type, base0,
- build_int_cst_type (type, 1));
- }
+ if (rel > 0)
+ mpz_sub (bnds->below, bnds->below, m);
else
- {
- if (mmin)
- assumption = fold_build2 (EQ_EXPR, boolean_type_node, base1, mmin);
- else
- assumption = boolean_false_node;
- if (nonzero_p (assumption))
- goto zero_iter;
- base1 = fold_build2 (MINUS_EXPR, type, base1,
- build_int_cst_type (type, 1));
- }
- noloop_assumptions = assumption;
- code = LE_EXPR;
-
- /* It will be useful to be able to tell the difference once more in
- <= -> != reduction. */
- was_sharp = true;
+ mpz_add (bnds->up, bnds->up, m);
}
- /* Take care of trivially infinite loops. */
- if (code != NE_EXPR)
+ mpz_clear (m);
+}
+
+/* From condition C0 CMP C1 derives information regarding the
+ difference of values of VARX + OFFX and VARY + OFFY, computed in TYPE,
+ and stores it to BNDS. */
+
+static void
+refine_bounds_using_guard (tree type, tree varx, mpz_t offx,
+ tree vary, mpz_t offy,
+ tree c0, enum tree_code cmp, tree c1,
+ bounds *bnds)
+{
+ tree varc0, varc1, tmp, ctype;
+ mpz_t offc0, offc1, loffx, loffy, bnd;
+ bool lbound = false;
+ bool no_wrap = nowrap_type_p (type);
+ bool x_ok, y_ok;
+
+ switch (cmp)
{
- if (zero_p (step0)
- && mmin
- && operand_equal_p (base0, mmin, 0))
+ case LT_EXPR:
+ case LE_EXPR:
+ case GT_EXPR:
+ case GE_EXPR:
+ STRIP_SIGN_NOPS (c0);
+ STRIP_SIGN_NOPS (c1);
+ ctype = TREE_TYPE (c0);
+ if (!tree_ssa_useless_type_conversion_1 (ctype, type))
return;
- if (zero_p (step1)
- && mmax
- && operand_equal_p (base1, mmax, 0))
+
+ break;
+
+ case EQ_EXPR:
+ /* We could derive quite precise information from EQ_EXPR, however, such
+ a guard is unlikely to appear, so we do not bother with handling
+ it. */
+ return;
+
+ case NE_EXPR:
+ /* NE_EXPR comparisons do not contain much of useful information, except for
+ special case of comparing with the bounds of the type. */
+ if (TREE_CODE (c1) != INTEGER_CST
+ || !INTEGRAL_TYPE_P (type))
return;
- }
- /* If we can we want to take care of NE conditions instead of size
- comparisons, as they are much more friendly (most importantly
- this takes care of special handling of loops with step 1). We can
- do it if we first check that upper bound is greater or equal to
- lower bound, their difference is constant c modulo step and that
- there is not an overflow. */
- if (code != NE_EXPR)
- {
- if (zero_p (step0))
- step = fold_unary_to_constant (NEGATE_EXPR, type, step1);
- else
- step = step0;
- delta = build2 (MINUS_EXPR, type, base1, base0);
- delta = fold_build2 (FLOOR_MOD_EXPR, type, delta, step);
- may_xform = boolean_false_node;
+ /* Ensure that the condition speaks about an expression in the same type
+ as X and Y. */
+ ctype = TREE_TYPE (c0);
+ if (TYPE_PRECISION (ctype) != TYPE_PRECISION (type))
+ return;
+ c0 = fold_convert (type, c0);
+ c1 = fold_convert (type, c1);
- if (TREE_CODE (delta) == INTEGER_CST)
+ if (TYPE_MIN_VALUE (type)
+ && operand_equal_p (c1, TYPE_MIN_VALUE (type), 0))
{
- tmp = fold_binary_to_constant (MINUS_EXPR, type, step,
- build_int_cst_type (type, 1));
- if (was_sharp
- && operand_equal_p (delta, tmp, 0))
- {
- /* A special case. We have transformed condition of type
- for (i = 0; i < 4; i += 4)
- into
- for (i = 0; i <= 3; i += 4)
- obviously if the test for overflow during that transformation
- passed, we cannot overflow here. Most importantly any
- loop with sharp end condition and step 1 falls into this
- category, so handling this case specially is definitely
- worth the troubles. */
- may_xform = boolean_true_node;
- }
- else if (zero_p (step0))
- {
- if (!mmin)
- may_xform = boolean_true_node;
- else
- {
- bound = fold_binary_to_constant (PLUS_EXPR, type,
- mmin, step);
- bound = fold_binary_to_constant (MINUS_EXPR, type,
- bound, delta);
- may_xform = fold_build2 (LE_EXPR, boolean_type_node,
- bound, base0);
- }
- }
- else
- {
- if (!mmax)
- may_xform = boolean_true_node;
- else
- {
- bound = fold_binary_to_constant (MINUS_EXPR, type,
- mmax, step);
- bound = fold_binary_to_constant (PLUS_EXPR, type,
- bound, delta);
- may_xform = fold_build2 (LE_EXPR, boolean_type_node,
- base1, bound);
- }
- }
+ cmp = GT_EXPR;
+ break;
}
-
- if (!zero_p (may_xform))
+ if (TYPE_MAX_VALUE (type)
+ && operand_equal_p (c1, TYPE_MAX_VALUE (type), 0))
{
- /* We perform the transformation always provided that it is not
- completely senseless. This is OK, as we would need this assumption
- to determine the number of iterations anyway. */
- if (!nonzero_p (may_xform))
- assumptions = may_xform;
+ cmp = LT_EXPR;
+ break;
+ }
- if (zero_p (step0))
- {
- base0 = fold_build2 (PLUS_EXPR, type, base0, delta);
- base0 = fold_build2 (MINUS_EXPR, type, base0, step);
- }
- else
- {
- base1 = fold_build2 (MINUS_EXPR, type, base1, delta);
- base1 = fold_build2 (PLUS_EXPR, type, base1, step);
- }
+ return;
+ default:
+ return;
+ }
- assumption = fold_build2 (GT_EXPR, boolean_type_node, base0, base1);
- noloop_assumptions = fold_build2 (TRUTH_OR_EXPR, boolean_type_node,
- noloop_assumptions, assumption);
- code = NE_EXPR;
- }
- }
+ mpz_init (offc0);
+ mpz_init (offc1);
+ split_to_var_and_offset (expand_simple_operations (c0), &varc0, offc0);
+ split_to_var_and_offset (expand_simple_operations (c1), &varc1, offc1);
- /* Count the number of iterations. */
- niter_type = unsigned_type_for (type);
- signed_niter_type = signed_type_for (type);
+ /* We are only interested in comparisons of expressions based on VARX and
+ VARY. TODO -- we might also be able to derive some bounds from
+ expressions containing just one of the variables. */
- if (code == NE_EXPR)
+ if (operand_equal_p (varx, varc1, 0))
{
- /* Everything we do here is just arithmetics modulo size of mode. This
- makes us able to do more involved computations of number of iterations
- than in other cases. First transform the condition into shape
- s * i <> c, with s positive. */
- base1 = fold_build2 (MINUS_EXPR, type, base1, base0);
- base0 = NULL_TREE;
- if (!zero_p (step1))
- step0 = fold_unary_to_constant (NEGATE_EXPR, type, step1);
- step1 = NULL_TREE;
- if (!tree_expr_nonnegative_p (fold_convert (signed_niter_type, step0)))
- {
- step0 = fold_unary_to_constant (NEGATE_EXPR, type, step0);
- base1 = fold_build1 (NEGATE_EXPR, type, base1);
- }
+ tmp = varc0; varc0 = varc1; varc1 = tmp;
+ mpz_swap (offc0, offc1);
+ cmp = swap_tree_comparison (cmp);
+ }
- base1 = fold_convert (niter_type, base1);
- step0 = fold_convert (niter_type, step0);
+ if (!operand_equal_p (varx, varc0, 0)
+ || !operand_equal_p (vary, varc1, 0))
+ goto end;
- /* Let nsd (step, size of mode) = d. If d does not divide c, the loop
- is infinite. Otherwise, the number of iterations is
- (inverse(s/d) * (c/d)) mod (size of mode/d). */
- bits = num_ending_zeros (step0);
- d = fold_binary_to_constant (LSHIFT_EXPR, niter_type,
- build_int_cst_type (niter_type, 1), bits);
- s = fold_binary_to_constant (RSHIFT_EXPR, niter_type, step0, bits);
+ mpz_init_set (loffx, offx);
+ mpz_init_set (loffy, offy);
- bound = build_low_bits_mask (niter_type,
- (TYPE_PRECISION (niter_type)
- - tree_low_cst (bits, 1)));
+ if (cmp == GT_EXPR || cmp == GE_EXPR)
+ {
+ tmp = varx; varx = vary; vary = tmp;
+ mpz_swap (offc0, offc1);
+ mpz_swap (loffx, loffy);
+ cmp = swap_tree_comparison (cmp);
+ lbound = true;
+ }
- assumption = fold_build2 (FLOOR_MOD_EXPR, niter_type, base1, d);
- assumption = fold_build2 (EQ_EXPR, boolean_type_node,
- assumption,
- build_int_cst (niter_type, 0));
- assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
- assumptions, assumption);
+ /* If there is no overflow, the condition implies that
+
+ (VARX + OFFX) cmp (VARY + OFFY) + (OFFX - OFFY + OFFC1 - OFFC0).
- tmp = fold_build2 (EXACT_DIV_EXPR, niter_type, base1, d);
- tmp = fold_build2 (MULT_EXPR, niter_type, tmp, inverse (s, bound));
- niter->niter = fold_build2 (BIT_AND_EXPR, niter_type, tmp, bound);
+ The overflows and underflows may complicate things a bit; each
+ overflow decreases the appropriate offset by M, and underflow
+ increases it by M. The above inequality would not necessarily be
+ true if
+
+ -- VARX + OFFX underflows and VARX + OFFC0 does not, or
+ VARX + OFFC0 overflows, but VARX + OFFX does not.
+ This may only happen if OFFX < OFFC0.
+ -- VARY + OFFY overflows and VARY + OFFC1 does not, or
+ VARY + OFFC1 underflows and VARY + OFFY does not.
+ This may only happen if OFFY > OFFC1. */
+
+ if (no_wrap)
+ {
+ x_ok = true;
+ y_ok = true;
}
else
{
- if (zero_p (step1))
- /* Condition in shape a + s * i <= b
- We must know that b + s does not overflow and a <= b + s and then we
- can compute number of iterations as (b + s - a) / s. (It might
- seem that we in fact could be more clever about testing the b + s
- overflow condition using some information about b - a mod s,
- but it was already taken into account during LE -> NE transform). */
- {
- if (mmax)
- {
- bound = fold_binary_to_constant (MINUS_EXPR, type, mmax, step0);
- assumption = fold_build2 (LE_EXPR, boolean_type_node,
- base1, bound);
- assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
- assumptions, assumption);
- }
+ x_ok = (integer_zerop (varx)
+ || mpz_cmp (loffx, offc0) >= 0);
+ y_ok = (integer_zerop (vary)
+ || mpz_cmp (loffy, offc1) <= 0);
+ }
+
+ if (x_ok && y_ok)
+ {
+ mpz_init (bnd);
+ mpz_sub (bnd, loffx, loffy);
+ mpz_add (bnd, bnd, offc1);
+ mpz_sub (bnd, bnd, offc0);
- step = step0;
- tmp = fold_build2 (PLUS_EXPR, type, base1, step0);
- assumption = fold_build2 (GT_EXPR, boolean_type_node, base0, tmp);
- delta = fold_build2 (PLUS_EXPR, type, base1, step);
- delta = fold_build2 (MINUS_EXPR, type, delta, base0);
- delta = fold_convert (niter_type, delta);
+ if (cmp == LT_EXPR)
+ mpz_sub_ui (bnd, bnd, 1);
+
+ if (lbound)
+ {
+ mpz_neg (bnd, bnd);
+ if (mpz_cmp (bnds->below, bnd) < 0)
+ mpz_set (bnds->below, bnd);
}
else
{
- /* Condition in shape a <= b - s * i
- We must know that a - s does not overflow and a - s <= b and then
- we can again compute number of iterations as (b - (a - s)) / s. */
- if (mmin)
- {
- bound = fold_binary_to_constant (MINUS_EXPR, type, mmin, step1);
- assumption = fold_build2 (LE_EXPR, boolean_type_node,
- bound, base0);
- assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
- assumptions, assumption);
- }
- step = fold_build1 (NEGATE_EXPR, type, step1);
- tmp = fold_build2 (PLUS_EXPR, type, base0, step1);
- assumption = fold_build2 (GT_EXPR, boolean_type_node, tmp, base1);
- delta = fold_build2 (MINUS_EXPR, type, base0, step);
- delta = fold_build2 (MINUS_EXPR, type, base1, delta);
- delta = fold_convert (niter_type, delta);
+ if (mpz_cmp (bnd, bnds->up) < 0)
+ mpz_set (bnds->up, bnd);
}
- noloop_assumptions = fold_build2 (TRUTH_OR_EXPR, boolean_type_node,
- noloop_assumptions, assumption);
- delta = fold_build2 (FLOOR_DIV_EXPR, niter_type, delta,
- fold_convert (niter_type, step));
- niter->niter = delta;
+ mpz_clear (bnd);
}
- niter->assumptions = assumptions;
- niter->may_be_zero = noloop_assumptions;
- return;
-
-zero_iter:
- niter->assumptions = boolean_true_node;
- niter->may_be_zero = boolean_true_node;
- niter->niter = build_int_cst_type (type, 0);
- return;
+ mpz_clear (loffx);
+ mpz_clear (loffy);
+end:
+ mpz_clear (offc0);
+ mpz_clear (offc1);
}
+/* Stores the bounds on the value of the expression X - Y in LOOP to BNDS.
+ The subtraction is considered to be performed in arbitrary precision,
+ without overflows.
+
+ We do not attempt to be too clever regarding the value ranges of X and
+ Y; most of the time, they are just integers or ssa names offsetted by
+ integer. However, we try to use the information contained in the
+ comparisons before the loop (usually created by loop header copying). */
-/* Similar to number_of_iterations_cond, but only handles the special
- case of loops with step 1 or -1. The meaning of the arguments
- is the same as in number_of_iterations_cond. The function
- returns true if the special case was recognized, false otherwise. */
-
-static bool
-number_of_iterations_special (tree type, tree base0, tree step0,
- enum tree_code code, tree base1, tree step1,
- struct tree_niter_desc *niter)
+static void
+bound_difference (struct loop *loop, tree x, tree y, bounds *bnds)
{
- tree niter_type = unsigned_type_for (type), mmax, mmin;
+ tree type = TREE_TYPE (x);
+ tree varx, vary;
+ mpz_t offx, offy;
+ mpz_t minx, maxx, miny, maxy;
+ int cnt = 0;
+ edge e;
+ basic_block bb;
+ tree cond, c0, c1;
+ enum tree_code cmp;
+
+ /* Get rid of unnecessary casts, but preserve the value of
+ the expressions. */
+ STRIP_SIGN_NOPS (x);
+ STRIP_SIGN_NOPS (y);
- /* Make < comparison from > ones. */
- if (code == GE_EXPR
- || code == GT_EXPR)
+ mpz_init (bnds->below);
+ mpz_init (bnds->up);
+ mpz_init (offx);
+ mpz_init (offy);
+ split_to_var_and_offset (x, &varx, offx);
+ split_to_var_and_offset (y, &vary, offy);
+
+ if (!integer_zerop (varx)
+ && operand_equal_p (varx, vary, 0))
{
- SWAP (base0, base1);
- SWAP (step0, step1);
- code = swap_tree_comparison (code);
+ /* Special case VARX == VARY -- we just need to compare the
+ offsets. The matters are a bit more complicated in the
+ case addition of offsets may wrap. */
+ bound_difference_of_offsetted_base (type, offx, offy, bnds);
}
-
- switch (code)
+ else
{
- case NE_EXPR:
- if (zero_p (step0))
- {
- if (zero_p (step1))
- return false;
- SWAP (base0, base1);
- SWAP (step0, step1);
- }
- else if (!zero_p (step1))
- return false;
-
- if (integer_onep (step0))
- {
- /* for (i = base0; i != base1; i++) */
- niter->assumptions = boolean_true_node;
- niter->may_be_zero = boolean_false_node;
- niter->niter = fold_build2 (MINUS_EXPR, type, base1, base0);
- niter->additional_info = boolean_true_node;
- }
- else if (integer_all_onesp (step0))
- {
- /* for (i = base0; i != base1; i--) */
- niter->assumptions = boolean_true_node;
- niter->may_be_zero = boolean_false_node;
- niter->niter = fold_build2 (MINUS_EXPR, type, base0, base1);
- }
- else
- return false;
-
- break;
-
- case LT_EXPR:
- if ((step0 && integer_onep (step0) && zero_p (step1))
- || (step1 && integer_all_onesp (step1) && zero_p (step0)))
- {
- /* for (i = base0; i < base1; i++)
-
- or
+ /* Otherwise, use the value ranges to determine the initial
+ estimates on below and up. */
+ mpz_init (minx);
+ mpz_init (maxx);
+ mpz_init (miny);
+ mpz_init (maxy);
+ determine_value_range (type, varx, offx, minx, maxx);
+ determine_value_range (type, vary, offy, miny, maxy);
+
+ mpz_sub (bnds->below, minx, maxy);
+ mpz_sub (bnds->up, maxx, miny);
+ mpz_clear (minx);
+ mpz_clear (maxx);
+ mpz_clear (miny);
+ mpz_clear (maxy);
+ }
- for (i = base1; i > base0; i--).
-
- In both cases # of iterations is base1 - base0. */
+ /* If both X and Y are constants, we cannot get any more precise. */
+ if (integer_zerop (varx) && integer_zerop (vary))
+ goto end;
- niter->assumptions = boolean_true_node;
- niter->may_be_zero = fold_build2 (GT_EXPR, boolean_type_node,
- base0, base1);
- niter->niter = fold_build2 (MINUS_EXPR, type, base1, base0);
- }
- else
- return false;
- break;
+ /* Now walk the dominators of the loop header and use the entry
+ guards to refine the estimates. */
+ for (bb = loop->header;
+ bb != ENTRY_BLOCK_PTR && cnt < MAX_DOMINATORS_TO_WALK;
+ bb = get_immediate_dominator (CDI_DOMINATORS, bb))
+ {
+ if (!single_pred_p (bb))
+ continue;
+ e = single_pred_edge (bb);
- case LE_EXPR:
- if (POINTER_TYPE_P (type))
- {
- /* We assume pointer arithmetic never overflows. */
- mmin = mmax = NULL_TREE;
- }
- else
- {
- mmin = TYPE_MIN_VALUE (type);
- mmax = TYPE_MAX_VALUE (type);
- }
+ if (!(e->flags & (EDGE_TRUE_VALUE | EDGE_FALSE_VALUE)))
+ continue;
- if (step0 && integer_onep (step0) && zero_p (step1))
- {
- /* for (i = base0; i <= base1; i++) */
- if (mmax)
- niter->assumptions = fold_build2 (NE_EXPR, boolean_type_node,
- base1, mmax);
- else
- niter->assumptions = boolean_true_node;
- base1 = fold_build2 (PLUS_EXPR, type, base1,
- build_int_cst_type (type, 1));
- }
- else if (step1 && integer_all_onesp (step1) && zero_p (step0))
- {
- /* for (i = base1; i >= base0; i--) */
- if (mmin)
- niter->assumptions = fold_build2 (NE_EXPR, boolean_type_node,
- base0, mmin);
- else
- niter->assumptions = boolean_true_node;
- base0 = fold_build2 (MINUS_EXPR, type, base0,
- build_int_cst_type (type, 1));
- }
- else
- return false;
+ cond = COND_EXPR_COND (last_stmt (e->src));
+ if (!COMPARISON_CLASS_P (cond))
+ continue;
+ c0 = TREE_OPERAND (cond, 0);
+ cmp = TREE_CODE (cond);
+ c1 = TREE_OPERAND (cond, 1);
- niter->may_be_zero = fold_build2 (GT_EXPR, boolean_type_node,
- base0, base1);
- niter->niter = fold_build2 (MINUS_EXPR, type, base1, base0);
- break;
+ if (e->flags & EDGE_FALSE_VALUE)
+ cmp = invert_tree_comparison (cmp, false);
- default:
- gcc_unreachable ();
+ refine_bounds_using_guard (type, varx, offx, vary, offy,
+ c0, cmp, c1, bnds);
+ ++cnt;
}
- niter->niter = fold_convert (niter_type, niter->niter);
- niter->additional_info = boolean_true_node;
- return true;
+end:
+ mpz_clear (offx);
+ mpz_clear (offy);
}
-/* Substitute NEW for OLD in EXPR and fold the result. */
+/* Update the bounds in BNDS that restrict the value of X to the bounds
+ that restrict the value of X + DELTA. X can be obtained as a
+ difference of two values in TYPE. */
-static tree
-simplify_replace_tree (tree expr, tree old, tree new)
+static void
+bounds_add (bounds *bnds, double_int delta, tree type)
{
- unsigned i, n;
- tree ret = NULL_TREE, e, se;
+ mpz_t mdelta, max;
- if (!expr)
- return NULL_TREE;
-
- if (expr == old
- || operand_equal_p (expr, old, 0))
- return unshare_expr (new);
+ mpz_init (mdelta);
+ mpz_set_double_int (mdelta, delta, false);
- if (!EXPR_P (expr))
- return expr;
+ mpz_init (max);
+ mpz_set_double_int (max, double_int_mask (TYPE_PRECISION (type)), true);
- n = TREE_CODE_LENGTH (TREE_CODE (expr));
- for (i = 0; i < n; i++)
- {
- e = TREE_OPERAND (expr, i);
- se = simplify_replace_tree (e, old, new);
- if (e == se)
- continue;
+ mpz_add (bnds->up, bnds->up, mdelta);
+ mpz_add (bnds->below, bnds->below, mdelta);
- if (!ret)
- ret = copy_node (expr);
+ if (mpz_cmp (bnds->up, max) > 0)
+ mpz_set (bnds->up, max);
- TREE_OPERAND (ret, i) = se;
- }
+ mpz_neg (max, max);
+ if (mpz_cmp (bnds->below, max) < 0)
+ mpz_set (bnds->below, max);
- return (ret ? fold (ret) : expr);
+ mpz_clear (mdelta);
+ mpz_clear (max);
}
-/* Expand definitions of ssa names in EXPR as long as they are simple
- enough, and return the new expression. */
+/* Update the bounds in BNDS that restrict the value of X to the bounds
+ that restrict the value of -X. */
-static tree
-expand_simple_operations (tree expr)
+static void
+bounds_negate (bounds *bnds)
{
- unsigned i, n;
- tree ret = NULL_TREE, e, ee, stmt;
- enum tree_code code = TREE_CODE (expr);
+ mpz_t tmp;
- if (is_gimple_min_invariant (expr))
- return expr;
+ mpz_init_set (tmp, bnds->up);
+ mpz_neg (bnds->up, bnds->below);
+ mpz_neg (bnds->below, tmp);
+ mpz_clear (tmp);
+}
- if (IS_EXPR_CODE_CLASS (TREE_CODE_CLASS (code)))
+/* Returns inverse of X modulo 2^s, where MASK = 2^s-1. */
+
+static tree
+inverse (tree x, tree mask)
+{
+ tree type = TREE_TYPE (x);
+ tree rslt;
+ unsigned ctr = tree_floor_log2 (mask);
+
+ if (TYPE_PRECISION (type) <= HOST_BITS_PER_WIDE_INT)
{
- n = TREE_CODE_LENGTH (code);
- for (i = 0; i < n; i++)
- {
- e = TREE_OPERAND (expr, i);
- ee = expand_simple_operations (e);
- if (e == ee)
- continue;
+ unsigned HOST_WIDE_INT ix;
+ unsigned HOST_WIDE_INT imask;
+ unsigned HOST_WIDE_INT irslt = 1;
- if (!ret)
- ret = copy_node (expr);
+ gcc_assert (cst_and_fits_in_hwi (x));
+ gcc_assert (cst_and_fits_in_hwi (mask));
- TREE_OPERAND (ret, i) = ee;
+ ix = int_cst_value (x);
+ imask = int_cst_value (mask);
+
+ for (; ctr; ctr--)
+ {
+ irslt *= ix;
+ ix *= ix;
}
+ irslt &= imask;
- return (ret ? fold (ret) : expr);
+ rslt = build_int_cst_type (type, irslt);
+ }
+ else
+ {
+ rslt = build_int_cst (type, 1);
+ for (; ctr; ctr--)
+ {
+ rslt = int_const_binop (MULT_EXPR, rslt, x, 0);
+ x = int_const_binop (MULT_EXPR, x, x, 0);
+ }
+ rslt = int_const_binop (BIT_AND_EXPR, rslt, mask, 0);
}
- if (TREE_CODE (expr) != SSA_NAME)
- return expr;
+ return rslt;
+}
- stmt = SSA_NAME_DEF_STMT (expr);
- if (TREE_CODE (stmt) != MODIFY_EXPR)
- return expr;
+/* Derives the upper bound BND on the number of executions of loop with exit
+ condition S * i <> C, assuming that the loop is not infinite. If
+ NO_OVERFLOW is true, then the control variable of the loop does not
+ overflow. If NO_OVERFLOW is true or BNDS.below >= 0, then BNDS.up
+ contains the upper bound on the value of C. */
- e = TREE_OPERAND (stmt, 1);
- if (/* Casts are simple. */
- TREE_CODE (e) != NOP_EXPR
- && TREE_CODE (e) != CONVERT_EXPR
- /* Copies are simple. */
- && TREE_CODE (e) != SSA_NAME
- /* Assignments of invariants are simple. */
- && !is_gimple_min_invariant (e)
- /* And increments and decrements by a constant are simple. */
- && !((TREE_CODE (e) == PLUS_EXPR
- || TREE_CODE (e) == MINUS_EXPR)
- && is_gimple_min_invariant (TREE_OPERAND (e, 1))))
- return expr;
+static void
+number_of_iterations_ne_max (mpz_t bnd, bool no_overflow, tree c, tree s,
+ bounds *bnds)
+{
+ double_int max;
+ mpz_t d;
- return expand_simple_operations (e);
+ /* If the control variable does not overflow, the number of iterations is
+ at most c / s. Otherwise it is at most the period of the control
+ variable. */
+ if (!no_overflow && !multiple_of_p (TREE_TYPE (c), c, s))
+ {
+ max = double_int_mask (TYPE_PRECISION (TREE_TYPE (c))
+ - tree_low_cst (num_ending_zeros (s), 1));
+ mpz_set_double_int (bnd, max, true);
+ return;
+ }
+
+ /* Determine the upper bound on C. */
+ if (no_overflow || mpz_sgn (bnds->below) >= 0)
+ mpz_set (bnd, bnds->up);
+ else if (TREE_CODE (c) == INTEGER_CST)
+ mpz_set_double_int (bnd, tree_to_double_int (c), true);
+ else
+ mpz_set_double_int (bnd, double_int_mask (TYPE_PRECISION (TREE_TYPE (c))),
+ true);
+
+ mpz_init (d);
+ mpz_set_double_int (d, tree_to_double_int (s), true);
+ mpz_fdiv_q (bnd, bnd, d);
+ mpz_clear (d);
}
-/* Tries to simplify EXPR using the condition COND. Returns the simplified
- expression (or EXPR unchanged, if no simplification was possible). */
+/* Determines number of iterations of loop whose ending condition
+ is IV <> FINAL. TYPE is the type of the iv. The number of
+ iterations is stored to NITER. NEVER_INFINITE is true if
+ we know that the exit must be taken eventually, i.e., that the IV
+ ever reaches the value FINAL (we derived this earlier, and possibly set
+ NITER->assumptions to make sure this is the case). BNDS contains the
+ bounds on the difference FINAL - IV->base. */
-static tree
-tree_simplify_using_condition_1 (tree cond, tree expr)
+static bool
+number_of_iterations_ne (tree type, affine_iv *iv, tree final,
+ struct tree_niter_desc *niter, bool never_infinite,
+ bounds *bnds)
{
- bool changed;
- tree e, te, e0, e1, e2, notcond;
- enum tree_code code = TREE_CODE (expr);
+ tree niter_type = unsigned_type_for (type);
+ tree s, c, d, bits, assumption, tmp, bound;
+ mpz_t max;
+
+ niter->control = *iv;
+ niter->bound = final;
+ niter->cmp = NE_EXPR;
+
+ /* Rearrange the terms so that we get inequality S * i <> C, with S
+ positive. Also cast everything to the unsigned type. If IV does
+ not overflow, BNDS bounds the value of C. Also, this is the
+ case if the computation |FINAL - IV->base| does not overflow, i.e.,
+ if BNDS->below in the result is nonnegative. */
+ if (tree_int_cst_sign_bit (iv->step))
+ {
+ s = fold_convert (niter_type,
+ fold_build1 (NEGATE_EXPR, type, iv->step));
+ c = fold_build2 (MINUS_EXPR, niter_type,
+ fold_convert (niter_type, iv->base),
+ fold_convert (niter_type, final));
+ bounds_negate (bnds);
+ }
+ else
+ {
+ s = fold_convert (niter_type, iv->step);
+ c = fold_build2 (MINUS_EXPR, niter_type,
+ fold_convert (niter_type, final),
+ fold_convert (niter_type, iv->base));
+ }
- if (code == INTEGER_CST)
- return expr;
+ mpz_init (max);
+ number_of_iterations_ne_max (max, iv->no_overflow, c, s, bnds);
+ niter->max = mpz_to_double_int (niter_type, max);
+ mpz_clear (max);
- if (code == TRUTH_OR_EXPR
- || code == TRUTH_AND_EXPR
- || code == COND_EXPR)
+ /* First the trivial cases -- when the step is 1. */
+ if (integer_onep (s))
{
- changed = false;
+ niter->niter = c;
+ return true;
+ }
- e0 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 0));
- if (TREE_OPERAND (expr, 0) != e0)
- changed = true;
+ /* Let nsd (step, size of mode) = d. If d does not divide c, the loop
+ is infinite. Otherwise, the number of iterations is
+ (inverse(s/d) * (c/d)) mod (size of mode/d). */
+ bits = num_ending_zeros (s);
+ bound = build_low_bits_mask (niter_type,
+ (TYPE_PRECISION (niter_type)
+ - tree_low_cst (bits, 1)));
- e1 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 1));
- if (TREE_OPERAND (expr, 1) != e1)
- changed = true;
+ d = fold_binary_to_constant (LSHIFT_EXPR, niter_type,
+ build_int_cst (niter_type, 1), bits);
+ s = fold_binary_to_constant (RSHIFT_EXPR, niter_type, s, bits);
- if (code == COND_EXPR)
+ if (!never_infinite)
+ {
+ /* If we cannot assume that the loop is not infinite, record the
+ assumptions for divisibility of c. */
+ assumption = fold_build2 (FLOOR_MOD_EXPR, niter_type, c, d);
+ assumption = fold_build2 (EQ_EXPR, boolean_type_node,
+ assumption, build_int_cst (niter_type, 0));
+ if (!integer_nonzerop (assumption))
+ niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
+ niter->assumptions, assumption);
+ }
+
+ c = fold_build2 (EXACT_DIV_EXPR, niter_type, c, d);
+ tmp = fold_build2 (MULT_EXPR, niter_type, c, inverse (s, bound));
+ niter->niter = fold_build2 (BIT_AND_EXPR, niter_type, tmp, bound);
+ return true;
+}
+
+/* Checks whether we can determine the final value of the control variable
+ of the loop with ending condition IV0 < IV1 (computed in TYPE).
+ DELTA is the difference IV1->base - IV0->base, STEP is the absolute value
+ of the step. The assumptions necessary to ensure that the computation
+ of the final value does not overflow are recorded in NITER. If we
+ find the final value, we adjust DELTA and return TRUE. Otherwise
+ we return false. BNDS bounds the value of IV1->base - IV0->base,
+ and will be updated by the same amount as DELTA. */
+
+static bool
+number_of_iterations_lt_to_ne (tree type, affine_iv *iv0, affine_iv *iv1,
+ struct tree_niter_desc *niter,
+ tree *delta, tree step,
+ bounds *bnds)
+{
+ tree niter_type = TREE_TYPE (step);
+ tree mod = fold_build2 (FLOOR_MOD_EXPR, niter_type, *delta, step);
+ tree tmod;
+ mpz_t mmod;
+ tree assumption = boolean_true_node, bound, noloop;
+ bool ret = false;
+
+ if (TREE_CODE (mod) != INTEGER_CST)
+ return false;
+ if (integer_nonzerop (mod))
+ mod = fold_build2 (MINUS_EXPR, niter_type, step, mod);
+ tmod = fold_convert (type, mod);
+
+ mpz_init (mmod);
+ mpz_set_double_int (mmod, tree_to_double_int (mod), true);
+ mpz_neg (mmod, mmod);
+
+ if (integer_nonzerop (iv0->step))
+ {
+ /* The final value of the iv is iv1->base + MOD, assuming that this
+ computation does not overflow, and that
+ iv0->base <= iv1->base + MOD. */
+ if (!iv1->no_overflow && !integer_zerop (mod))
{
- e2 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 2));
- if (TREE_OPERAND (expr, 2) != e2)
- changed = true;
+ bound = fold_build2 (MINUS_EXPR, type,
+ TYPE_MAX_VALUE (type), tmod);
+ assumption = fold_build2 (LE_EXPR, boolean_type_node,
+ iv1->base, bound);
+ if (integer_zerop (assumption))
+ goto end;
}
+ if (mpz_cmp (mmod, bnds->below) < 0)
+ noloop = boolean_false_node;
else
- e2 = NULL_TREE;
-
- if (changed)
+ noloop = fold_build2 (GT_EXPR, boolean_type_node,
+ iv0->base,
+ fold_build2 (PLUS_EXPR, type,
+ iv1->base, tmod));
+ }
+ else
+ {
+ /* The final value of the iv is iv0->base - MOD, assuming that this
+ computation does not overflow, and that
+ iv0->base - MOD <= iv1->base. */
+ if (!iv0->no_overflow && !integer_zerop (mod))
{
- if (code == COND_EXPR)
- expr = fold_build3 (code, boolean_type_node, e0, e1, e2);
- else
- expr = fold_build2 (code, boolean_type_node, e0, e1);
+ bound = fold_build2 (PLUS_EXPR, type,
+ TYPE_MIN_VALUE (type), tmod);
+ assumption = fold_build2 (GE_EXPR, boolean_type_node,
+ iv0->base, bound);
+ if (integer_zerop (assumption))
+ goto end;
}
-
- return expr;
+ if (mpz_cmp (mmod, bnds->below) < 0)
+ noloop = boolean_false_node;
+ else
+ noloop = fold_build2 (GT_EXPR, boolean_type_node,
+ fold_build2 (MINUS_EXPR, type,
+ iv0->base, tmod),
+ iv1->base);
}
- /* In case COND is equality, we may be able to simplify EXPR by copy/constant
- propagation, and vice versa. Fold does not handle this, since it is
- considered too expensive. */
- if (TREE_CODE (cond) == EQ_EXPR)
- {
- e0 = TREE_OPERAND (cond, 0);
- e1 = TREE_OPERAND (cond, 1);
+ if (!integer_nonzerop (assumption))
+ niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
+ niter->assumptions,
+ assumption);
+ if (!integer_zerop (noloop))
+ niter->may_be_zero = fold_build2 (TRUTH_OR_EXPR, boolean_type_node,
+ niter->may_be_zero,
+ noloop);
+ bounds_add (bnds, tree_to_double_int (mod), type);
+ *delta = fold_build2 (PLUS_EXPR, niter_type, *delta, mod);
+
+ ret = true;
+end:
+ mpz_clear (mmod);
+ return ret;
+}
- /* We know that e0 == e1. Check whether we cannot simplify expr
- using this fact. */
- e = simplify_replace_tree (expr, e0, e1);
- if (zero_p (e) || nonzero_p (e))
- return e;
+/* Add assertions to NITER that ensure that the control variable of the loop
+ with ending condition IV0 < IV1 does not overflow. Types of IV0 and IV1
+ are TYPE. Returns false if we can prove that there is an overflow, true
+ otherwise. STEP is the absolute value of the step. */
- e = simplify_replace_tree (expr, e1, e0);
- if (zero_p (e) || nonzero_p (e))
- return e;
- }
- if (TREE_CODE (expr) == EQ_EXPR)
+static bool
+assert_no_overflow_lt (tree type, affine_iv *iv0, affine_iv *iv1,
+ struct tree_niter_desc *niter, tree step)
+{
+ tree bound, d, assumption, diff;
+ tree niter_type = TREE_TYPE (step);
+
+ if (integer_nonzerop (iv0->step))
{
- e0 = TREE_OPERAND (expr, 0);
- e1 = TREE_OPERAND (expr, 1);
+ /* for (i = iv0->base; i < iv1->base; i += iv0->step) */
+ if (iv0->no_overflow)
+ return true;
- /* If e0 == e1 (EXPR) implies !COND, then EXPR cannot be true. */
- e = simplify_replace_tree (cond, e0, e1);
- if (zero_p (e))
- return e;
- e = simplify_replace_tree (cond, e1, e0);
- if (zero_p (e))
- return e;
+ /* If iv0->base is a constant, we can determine the last value before
+ overflow precisely; otherwise we conservatively assume
+ MAX - STEP + 1. */
+
+ if (TREE_CODE (iv0->base) == INTEGER_CST)
+ {
+ d = fold_build2 (MINUS_EXPR, niter_type,
+ fold_convert (niter_type, TYPE_MAX_VALUE (type)),
+ fold_convert (niter_type, iv0->base));
+ diff = fold_build2 (FLOOR_MOD_EXPR, niter_type, d, step);
+ }
+ else
+ diff = fold_build2 (MINUS_EXPR, niter_type, step,
+ build_int_cst (niter_type, 1));
+ bound = fold_build2 (MINUS_EXPR, type,
+ TYPE_MAX_VALUE (type), fold_convert (type, diff));
+ assumption = fold_build2 (LE_EXPR, boolean_type_node,
+ iv1->base, bound);
}
- if (TREE_CODE (expr) == NE_EXPR)
+ else
{
- e0 = TREE_OPERAND (expr, 0);
- e1 = TREE_OPERAND (expr, 1);
+ /* for (i = iv1->base; i > iv0->base; i += iv1->step) */
+ if (iv1->no_overflow)
+ return true;
- /* If e0 == e1 (!EXPR) implies !COND, then EXPR must be true. */
- e = simplify_replace_tree (cond, e0, e1);
- if (zero_p (e))
- return boolean_true_node;
- e = simplify_replace_tree (cond, e1, e0);
- if (zero_p (e))
- return boolean_true_node;
+ if (TREE_CODE (iv1->base) == INTEGER_CST)
+ {
+ d = fold_build2 (MINUS_EXPR, niter_type,
+ fold_convert (niter_type, iv1->base),
+ fold_convert (niter_type, TYPE_MIN_VALUE (type)));
+ diff = fold_build2 (FLOOR_MOD_EXPR, niter_type, d, step);
+ }
+ else
+ diff = fold_build2 (MINUS_EXPR, niter_type, step,
+ build_int_cst (niter_type, 1));
+ bound = fold_build2 (PLUS_EXPR, type,
+ TYPE_MIN_VALUE (type), fold_convert (type, diff));
+ assumption = fold_build2 (GE_EXPR, boolean_type_node,
+ iv0->base, bound);
}
- te = expand_simple_operations (expr);
-
- /* Check whether COND ==> EXPR. */
- notcond = invert_truthvalue (cond);
- e = fold_build2 (TRUTH_OR_EXPR, boolean_type_node, notcond, te);
- if (nonzero_p (e))
- return e;
-
- /* Check whether COND ==> not EXPR. */
- e = fold_build2 (TRUTH_AND_EXPR, boolean_type_node, cond, te);
- if (zero_p (e))
- return e;
-
- return expr;
+ if (integer_zerop (assumption))
+ return false;
+ if (!integer_nonzerop (assumption))
+ niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
+ niter->assumptions, assumption);
+
+ iv0->no_overflow = true;
+ iv1->no_overflow = true;
+ return true;
}
-/* Tries to simplify EXPR using the condition COND. Returns the simplified
- expression (or EXPR unchanged, if no simplification was possible).
- Wrapper around tree_simplify_using_condition_1 that ensures that chains
- of simple operations in definitions of ssa names in COND are expanded,
- so that things like casts or incrementing the value of the bound before
- the loop do not cause us to fail. */
+/* Add an assumption to NITER that a loop whose ending condition
+ is IV0 < IV1 rolls. TYPE is the type of the control iv. BNDS
+ bounds the value of IV1->base - IV0->base. */
-static tree
-tree_simplify_using_condition (tree cond, tree expr)
+static void
+assert_loop_rolls_lt (tree type, affine_iv *iv0, affine_iv *iv1,
+ struct tree_niter_desc *niter, bounds *bnds)
{
- cond = expand_simple_operations (cond);
-
- return tree_simplify_using_condition_1 (cond, expr);
-}
+ tree assumption = boolean_true_node, bound, diff;
+ tree mbz, mbzl, mbzr;
+ bool rolls_p, no_overflow_p;
+ double_int dstep;
+ mpz_t mstep, max;
+
+ /* We are going to compute the number of iterations as
+ (iv1->base - iv0->base + step - 1) / step, computed in the unsigned
+ variant of TYPE. This formula only works if
-/* Tries to simplify EXPR using the conditions on entry to LOOP.
- Record the conditions used for simplification to CONDS_USED.
- Returns the simplified expression (or EXPR unchanged, if no
- simplification was possible).*/
+ -step + 1 <= (iv1->base - iv0->base) <= MAX - step + 1
+
+ (where MAX is the maximum value of the unsigned variant of TYPE, and
+ the computations in this formula are performed in full precision
+ (without overflows).
+
+ Usually, for loops with exit condition iv0->base + step * i < iv1->base,
+ we have a condition of form iv0->base - step < iv1->base before the loop,
+ and for loops iv0->base < iv1->base - step * i the condition
+ iv0->base < iv1->base + step, due to loop header copying, which enable us
+ to prove the lower bound.
+
+ The upper bound is more complicated. Unless the expressions for initial
+ and final value themselves contain enough information, we usually cannot
+ derive it from the context. */
+
+ /* First check whether the answer does not follow from the bounds we gathered
+ before. */
+ if (integer_nonzerop (iv0->step))
+ dstep = tree_to_double_int (iv0->step);
+ else
+ {
+ dstep = double_int_sext (tree_to_double_int (iv1->step),
+ TYPE_PRECISION (type));
+ dstep = double_int_neg (dstep);
+ }
-static tree
-simplify_using_initial_conditions (struct loop *loop, tree expr,
- tree *conds_used)
-{
- edge e;
- basic_block bb;
- tree exp, cond;
+ mpz_init (mstep);
+ mpz_set_double_int (mstep, dstep, true);
+ mpz_neg (mstep, mstep);
+ mpz_add_ui (mstep, mstep, 1);
+
+ rolls_p = mpz_cmp (mstep, bnds->below) <= 0;
+
+ mpz_init (max);
+ mpz_set_double_int (max, double_int_mask (TYPE_PRECISION (type)), true);
+ mpz_add (max, max, mstep);
+ no_overflow_p = (mpz_cmp (bnds->up, max) <= 0
+ /* For pointers, only values lying inside a single object
+ can be compared or manipulated by pointer arithmetics.
+ Gcc in general does not allow or handle objects larger
+ than half of the address space, hence the upper bound
+ is satisfied for pointers. */
+ || POINTER_TYPE_P (type));
+ mpz_clear (mstep);
+ mpz_clear (max);
+
+ if (rolls_p && no_overflow_p)
+ return;
- if (TREE_CODE (expr) == INTEGER_CST)
- return expr;
+ /* Now the hard part; we must formulate the assumption(s) as expressions, and
+ we must be careful not to introduce overflow. */
- for (bb = loop->header;
- bb != ENTRY_BLOCK_PTR;
- bb = get_immediate_dominator (CDI_DOMINATORS, bb))
+ if (integer_nonzerop (iv0->step))
{
- if (!single_pred_p (bb))
- continue;
- e = single_pred_edge (bb);
+ diff = fold_build2 (MINUS_EXPR, type,
+ iv0->step, build_int_cst (type, 1));
- if (!(e->flags & (EDGE_TRUE_VALUE | EDGE_FALSE_VALUE)))
- continue;
+ /* We need to know that iv0->base >= MIN + iv0->step - 1. Since
+ 0 address never belongs to any object, we can assume this for
+ pointers. */
+ if (!POINTER_TYPE_P (type))
+ {
+ bound = fold_build2 (PLUS_EXPR, type,
+ TYPE_MIN_VALUE (type), diff);
+ assumption = fold_build2 (GE_EXPR, boolean_type_node,
+ iv0->base, bound);
+ }
- cond = COND_EXPR_COND (last_stmt (e->src));
- if (e->flags & EDGE_FALSE_VALUE)
- cond = invert_truthvalue (cond);
- exp = tree_simplify_using_condition (cond, expr);
+ /* And then we can compute iv0->base - diff, and compare it with
+ iv1->base. */
+ mbzl = fold_build2 (MINUS_EXPR, type, iv0->base, diff);
+ mbzr = iv1->base;
+ }
+ else
+ {
+ diff = fold_build2 (PLUS_EXPR, type,
+ iv1->step, build_int_cst (type, 1));
- if (exp != expr)
- *conds_used = fold_build2 (TRUTH_AND_EXPR,
- boolean_type_node,
- *conds_used,
- cond);
+ if (!POINTER_TYPE_P (type))
+ {
+ bound = fold_build2 (PLUS_EXPR, type,
+ TYPE_MAX_VALUE (type), diff);
+ assumption = fold_build2 (LE_EXPR, boolean_type_node,
+ iv1->base, bound);
+ }
- expr = exp;
+ mbzl = iv0->base;
+ mbzr = fold_build2 (MINUS_EXPR, type, iv1->base, diff);
}
- return expr;
+ if (!integer_nonzerop (assumption))
+ niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
+ niter->assumptions, assumption);
+ if (!rolls_p)
+ {
+ mbz = fold_build2 (GT_EXPR, boolean_type_node, mbzl, mbzr);
+ niter->may_be_zero = fold_build2 (TRUTH_OR_EXPR, boolean_type_node,
+ niter->may_be_zero, mbz);
+ }
}
-/* Tries to simplify EXPR using the evolutions of the loop invariants
- in the superloops of LOOP. Returns the simplified expression
- (or EXPR unchanged, if no simplification was possible). */
+/* Determines number of iterations of loop whose ending condition
+ is IV0 < IV1. TYPE is the type of the iv. The number of
+ iterations is stored to NITER. BNDS bounds the difference
+ IV1->base - IV0->base. */
-static tree
-simplify_using_outer_evolutions (struct loop *loop, tree expr)
+static bool
+number_of_iterations_lt (tree type, affine_iv *iv0, affine_iv *iv1,
+ struct tree_niter_desc *niter,
+ bool never_infinite ATTRIBUTE_UNUSED,
+ bounds *bnds)
{
- enum tree_code code = TREE_CODE (expr);
- bool changed;
- tree e, e0, e1, e2;
+ tree niter_type = unsigned_type_for (type);
+ tree delta, step, s;
+ mpz_t mstep, tmp;
- if (is_gimple_min_invariant (expr))
- return expr;
+ if (integer_nonzerop (iv0->step))
+ {
+ niter->control = *iv0;
+ niter->cmp = LT_EXPR;
+ niter->bound = iv1->base;
+ }
+ else
+ {
+ niter->control = *iv1;
+ niter->cmp = GT_EXPR;
+ niter->bound = iv0->base;
+ }
- if (code == TRUTH_OR_EXPR
- || code == TRUTH_AND_EXPR
- || code == COND_EXPR)
+ delta = fold_build2 (MINUS_EXPR, niter_type,
+ fold_convert (niter_type, iv1->base),
+ fold_convert (niter_type, iv0->base));
+
+ /* First handle the special case that the step is +-1. */
+ if ((integer_onep (iv0->step) && integer_zerop (iv1->step))
+ || (integer_all_onesp (iv1->step) && integer_zerop (iv0->step)))
{
- changed = false;
+ /* for (i = iv0->base; i < iv1->base; i++)
- e0 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 0));
+ or
+
+ for (i = iv1->base; i > iv0->base; i--).
+
+ In both cases # of iterations is iv1->base - iv0->base, assuming that
+ iv1->base >= iv0->base.
+
+ First try to derive a lower bound on the value of
+ iv1->base - iv0->base, computed in full precision. If the difference
+ is nonnegative, we are done, otherwise we must record the
+ condition. */
+
+ if (mpz_sgn (bnds->below) < 0)
+ niter->may_be_zero = fold_build2 (LT_EXPR, boolean_type_node,
+ iv1->base, iv0->base);
+ niter->niter = delta;
+ niter->max = mpz_to_double_int (niter_type, bnds->up);
+ return true;
+ }
+
+ if (integer_nonzerop (iv0->step))
+ step = fold_convert (niter_type, iv0->step);
+ else
+ step = fold_convert (niter_type,
+ fold_build1 (NEGATE_EXPR, type, iv1->step));
+
+ /* If we can determine the final value of the control iv exactly, we can
+ transform the condition to != comparison. In particular, this will be
+ the case if DELTA is constant. */
+ if (number_of_iterations_lt_to_ne (type, iv0, iv1, niter, &delta, step,
+ bnds))
+ {
+ affine_iv zps;
+
+ zps.base = build_int_cst (niter_type, 0);
+ zps.step = step;
+ /* number_of_iterations_lt_to_ne will add assumptions that ensure that
+ zps does not overflow. */
+ zps.no_overflow = true;
+
+ return number_of_iterations_ne (type, &zps, delta, niter, true, bnds);
+ }
+
+ /* Make sure that the control iv does not overflow. */
+ if (!assert_no_overflow_lt (type, iv0, iv1, niter, step))
+ return false;
+
+ /* We determine the number of iterations as (delta + step - 1) / step. For
+ this to work, we must know that iv1->base >= iv0->base - step + 1,
+ otherwise the loop does not roll. */
+ assert_loop_rolls_lt (type, iv0, iv1, niter, bnds);
+
+ s = fold_build2 (MINUS_EXPR, niter_type,
+ step, build_int_cst (niter_type, 1));
+ delta = fold_build2 (PLUS_EXPR, niter_type, delta, s);
+ niter->niter = fold_build2 (FLOOR_DIV_EXPR, niter_type, delta, step);
+
+ mpz_init (mstep);
+ mpz_init (tmp);
+ mpz_set_double_int (mstep, tree_to_double_int (step), true);
+ mpz_add (tmp, bnds->up, mstep);
+ mpz_sub_ui (tmp, tmp, 1);
+ mpz_fdiv_q (tmp, tmp, mstep);
+ niter->max = mpz_to_double_int (niter_type, tmp);
+ mpz_clear (mstep);
+ mpz_clear (tmp);
+
+ return true;
+}
+
+/* Determines number of iterations of loop whose ending condition
+ is IV0 <= IV1. TYPE is the type of the iv. The number of
+ iterations is stored to NITER. NEVER_INFINITE is true if
+ we know that this condition must eventually become false (we derived this
+ earlier, and possibly set NITER->assumptions to make sure this
+ is the case). BNDS bounds the difference IV1->base - IV0->base. */
+
+static bool
+number_of_iterations_le (tree type, affine_iv *iv0, affine_iv *iv1,
+ struct tree_niter_desc *niter, bool never_infinite,
+ bounds *bnds)
+{
+ tree assumption;
+
+ /* Say that IV0 is the control variable. Then IV0 <= IV1 iff
+ IV0 < IV1 + 1, assuming that IV1 is not equal to the greatest
+ value of the type. This we must know anyway, since if it is
+ equal to this value, the loop rolls forever. */
+
+ if (!never_infinite)
+ {
+ if (integer_nonzerop (iv0->step))
+ assumption = fold_build2 (NE_EXPR, boolean_type_node,
+ iv1->base, TYPE_MAX_VALUE (type));
+ else
+ assumption = fold_build2 (NE_EXPR, boolean_type_node,
+ iv0->base, TYPE_MIN_VALUE (type));
+
+ if (integer_zerop (assumption))
+ return false;
+ if (!integer_nonzerop (assumption))
+ niter->assumptions = fold_build2 (TRUTH_AND_EXPR, boolean_type_node,
+ niter->assumptions, assumption);
+ }
+
+ if (integer_nonzerop (iv0->step))
+ iv1->base = fold_build2 (PLUS_EXPR, type,
+ iv1->base, build_int_cst (type, 1));
+ else
+ iv0->base = fold_build2 (MINUS_EXPR, type,
+ iv0->base, build_int_cst (type, 1));
+
+ bounds_add (bnds, double_int_one, type);
+
+ return number_of_iterations_lt (type, iv0, iv1, niter, never_infinite, bnds);
+}
+
+/* Dumps description of affine induction variable IV to FILE. */
+
+static void
+dump_affine_iv (FILE *file, affine_iv *iv)
+{
+ if (!integer_zerop (iv->step))
+ fprintf (file, "[");
+
+ print_generic_expr (dump_file, iv->base, TDF_SLIM);
+
+ if (!integer_zerop (iv->step))
+ {
+ fprintf (file, ", + , ");
+ print_generic_expr (dump_file, iv->step, TDF_SLIM);
+ fprintf (file, "]%s", iv->no_overflow ? "(no_overflow)" : "");
+ }
+}
+
+/* Determine the number of iterations according to condition (for staying
+ inside loop) which compares two induction variables using comparison
+ operator CODE. The induction variable on left side of the comparison
+ is IV0, the right-hand side is IV1. Both induction variables must have
+ type TYPE, which must be an integer or pointer type. The steps of the
+ ivs must be constants (or NULL_TREE, which is interpreted as constant zero).
+
+ LOOP is the loop whose number of iterations we are determining.
+
+ ONLY_EXIT is true if we are sure this is the only way the loop could be
+ exited (including possibly non-returning function calls, exceptions, etc.)
+ -- in this case we can use the information whether the control induction
+ variables can overflow or not in a more efficient way.
+
+ The results (number of iterations and assumptions as described in
+ comments at struct tree_niter_desc in tree-flow.h) are stored to NITER.
+ Returns false if it fails to determine number of iterations, true if it
+ was determined (possibly with some assumptions). */
+
+static bool
+number_of_iterations_cond (struct loop *loop,
+ tree type, affine_iv *iv0, enum tree_code code,
+ affine_iv *iv1, struct tree_niter_desc *niter,
+ bool only_exit)
+{
+ bool never_infinite, ret;
+ bounds bnds;
+
+ /* The meaning of these assumptions is this:
+ if !assumptions
+ then the rest of information does not have to be valid
+ if may_be_zero then the loop does not roll, even if
+ niter != 0. */
+ niter->assumptions = boolean_true_node;
+ niter->may_be_zero = boolean_false_node;
+ niter->niter = NULL_TREE;
+ niter->max = double_int_zero;
+
+ niter->bound = NULL_TREE;
+ niter->cmp = ERROR_MARK;
+
+ /* Make < comparison from > ones, and for NE_EXPR comparisons, ensure that
+ the control variable is on lhs. */
+ if (code == GE_EXPR || code == GT_EXPR
+ || (code == NE_EXPR && integer_zerop (iv0->step)))
+ {
+ SWAP (iv0, iv1);
+ code = swap_tree_comparison (code);
+ }
+
+ if (!only_exit)
+ {
+ /* If this is not the only possible exit from the loop, the information
+ that the induction variables cannot overflow as derived from
+ signedness analysis cannot be relied upon. We use them e.g. in the
+ following way: given loop for (i = 0; i <= n; i++), if i is
+ signed, it cannot overflow, thus this loop is equivalent to
+ for (i = 0; i < n + 1; i++); however, if n == MAX, but the loop
+ is exited in some other way before i overflows, this transformation
+ is incorrect (the new loop exits immediately). */
+ iv0->no_overflow = false;
+ iv1->no_overflow = false;
+ }
+
+ if (POINTER_TYPE_P (type))
+ {
+ /* Comparison of pointers is undefined unless both iv0 and iv1 point
+ to the same object. If they do, the control variable cannot wrap
+ (as wrap around the bounds of memory will never return a pointer
+ that would be guaranteed to point to the same object, even if we
+ avoid undefined behavior by casting to size_t and back). The
+ restrictions on pointer arithmetics and comparisons of pointers
+ ensure that using the no-overflow assumptions is correct in this
+ case even if ONLY_EXIT is false. */
+ iv0->no_overflow = true;
+ iv1->no_overflow = true;
+ }
+
+ /* If the control induction variable does not overflow, the loop obviously
+ cannot be infinite. */
+ if (!integer_zerop (iv0->step) && iv0->no_overflow)
+ never_infinite = true;
+ else if (!integer_zerop (iv1->step) && iv1->no_overflow)
+ never_infinite = true;
+ else
+ never_infinite = false;
+
+ /* We can handle the case when neither of the sides of the comparison is
+ invariant, provided that the test is NE_EXPR. This rarely occurs in
+ practice, but it is simple enough to manage. */
+ if (!integer_zerop (iv0->step) && !integer_zerop (iv1->step))
+ {
+ if (code != NE_EXPR)
+ return false;
+
+ iv0->step = fold_binary_to_constant (MINUS_EXPR, type,
+ iv0->step, iv1->step);
+ iv0->no_overflow = false;
+ iv1->step = build_int_cst (type, 0);
+ iv1->no_overflow = true;
+ }
+
+ /* If the result of the comparison is a constant, the loop is weird. More
+ precise handling would be possible, but the situation is not common enough
+ to waste time on it. */
+ if (integer_zerop (iv0->step) && integer_zerop (iv1->step))
+ return false;
+
+ /* Ignore loops of while (i-- < 10) type. */
+ if (code != NE_EXPR)
+ {
+ if (iv0->step && tree_int_cst_sign_bit (iv0->step))
+ return false;
+
+ if (!integer_zerop (iv1->step) && !tree_int_cst_sign_bit (iv1->step))
+ return false;
+ }
+
+ /* If the loop exits immediately, there is nothing to do. */
+ if (integer_zerop (fold_build2 (code, boolean_type_node, iv0->base, iv1->base)))
+ {
+ niter->niter = build_int_cst (unsigned_type_for (type), 0);
+ niter->max = double_int_zero;
+ return true;
+ }
+
+ /* OK, now we know we have a senseful loop. Handle several cases, depending
+ on what comparison operator is used. */
+ bound_difference (loop, iv1->base, iv0->base, &bnds);
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file,
+ "Analysing # of iterations of loop %d\n", loop->num);
+
+ fprintf (dump_file, " exit condition ");
+ dump_affine_iv (dump_file, iv0);
+ fprintf (dump_file, " %s ",
+ code == NE_EXPR ? "!="
+ : code == LT_EXPR ? "<"
+ : "<=");
+ dump_affine_iv (dump_file, iv1);
+ fprintf (dump_file, "\n");
+
+ fprintf (dump_file, " bounds on difference of bases: ");
+ mpz_out_str (dump_file, 10, bnds.below);
+ fprintf (dump_file, " ... ");
+ mpz_out_str (dump_file, 10, bnds.up);
+ fprintf (dump_file, "\n");
+ }
+
+ switch (code)
+ {
+ case NE_EXPR:
+ gcc_assert (integer_zerop (iv1->step));
+ ret = number_of_iterations_ne (type, iv0, iv1->base, niter,
+ never_infinite, &bnds);
+ break;
+
+ case LT_EXPR:
+ ret = number_of_iterations_lt (type, iv0, iv1, niter, never_infinite,
+ &bnds);
+ break;
+
+ case LE_EXPR:
+ ret = number_of_iterations_le (type, iv0, iv1, niter, never_infinite,
+ &bnds);
+ break;
+
+ default:
+ gcc_unreachable ();
+ }
+
+ mpz_clear (bnds.up);
+ mpz_clear (bnds.below);
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ if (ret)
+ {
+ fprintf (dump_file, " result:\n");
+ if (!integer_nonzerop (niter->assumptions))
+ {
+ fprintf (dump_file, " under assumptions ");
+ print_generic_expr (dump_file, niter->assumptions, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+
+ if (!integer_zerop (niter->may_be_zero))
+ {
+ fprintf (dump_file, " zero if ");
+ print_generic_expr (dump_file, niter->may_be_zero, TDF_SLIM);
+ fprintf (dump_file, "\n");
+ }
+
+ fprintf (dump_file, " # of iterations ");
+ print_generic_expr (dump_file, niter->niter, TDF_SLIM);
+ fprintf (dump_file, ", bounded by ");
+ dump_double_int (dump_file, niter->max, true);
+ fprintf (dump_file, "\n");
+ }
+ else
+ fprintf (dump_file, " failed\n\n");
+ }
+ return ret;
+}
+
+/* Substitute NEW for OLD in EXPR and fold the result. */
+
+static tree
+simplify_replace_tree (tree expr, tree old, tree new)
+{
+ unsigned i, n;
+ tree ret = NULL_TREE, e, se;
+
+ if (!expr)
+ return NULL_TREE;
+
+ if (expr == old
+ || operand_equal_p (expr, old, 0))
+ return unshare_expr (new);
+
+ if (!EXPR_P (expr) && !GIMPLE_STMT_P (expr))
+ return expr;
+
+ n = TREE_OPERAND_LENGTH (expr);
+ for (i = 0; i < n; i++)
+ {
+ e = TREE_OPERAND (expr, i);
+ se = simplify_replace_tree (e, old, new);
+ if (e == se)
+ continue;
+
+ if (!ret)
+ ret = copy_node (expr);
+
+ TREE_OPERAND (ret, i) = se;
+ }
+
+ return (ret ? fold (ret) : expr);
+}
+
+/* Expand definitions of ssa names in EXPR as long as they are simple
+ enough, and return the new expression. */
+
+tree
+expand_simple_operations (tree expr)
+{
+ unsigned i, n;
+ tree ret = NULL_TREE, e, ee, stmt;
+ enum tree_code code;
+
+ if (expr == NULL_TREE)
+ return expr;
+
+ if (is_gimple_min_invariant (expr))
+ return expr;
+
+ code = TREE_CODE (expr);
+ if (IS_EXPR_CODE_CLASS (TREE_CODE_CLASS (code)))
+ {
+ n = TREE_OPERAND_LENGTH (expr);
+ for (i = 0; i < n; i++)
+ {
+ e = TREE_OPERAND (expr, i);
+ ee = expand_simple_operations (e);
+ if (e == ee)
+ continue;
+
+ if (!ret)
+ ret = copy_node (expr);
+
+ TREE_OPERAND (ret, i) = ee;
+ }
+
+ if (!ret)
+ return expr;
+
+ fold_defer_overflow_warnings ();
+ ret = fold (ret);
+ fold_undefer_and_ignore_overflow_warnings ();
+ return ret;
+ }
+
+ if (TREE_CODE (expr) != SSA_NAME)
+ return expr;
+
+ stmt = SSA_NAME_DEF_STMT (expr);
+ if (TREE_CODE (stmt) == PHI_NODE)
+ {
+ basic_block src, dest;
+
+ if (PHI_NUM_ARGS (stmt) != 1)
+ return expr;
+ e = PHI_ARG_DEF (stmt, 0);
+
+ /* Avoid propagating through loop exit phi nodes, which
+ could break loop-closed SSA form restrictions. */
+ dest = bb_for_stmt (stmt);
+ src = single_pred (dest);
+ if (TREE_CODE (e) == SSA_NAME
+ && src->loop_father != dest->loop_father)
+ return expr;
+
+ return expand_simple_operations (e);
+ }
+ if (TREE_CODE (stmt) != GIMPLE_MODIFY_STMT)
+ return expr;
+
+ e = GIMPLE_STMT_OPERAND (stmt, 1);
+ if (/* Casts are simple. */
+ TREE_CODE (e) != NOP_EXPR
+ && TREE_CODE (e) != CONVERT_EXPR
+ /* Copies are simple. */
+ && TREE_CODE (e) != SSA_NAME
+ /* Assignments of invariants are simple. */
+ && !is_gimple_min_invariant (e)
+ /* And increments and decrements by a constant are simple. */
+ && !((TREE_CODE (e) == PLUS_EXPR
+ || TREE_CODE (e) == MINUS_EXPR)
+ && is_gimple_min_invariant (TREE_OPERAND (e, 1))))
+ return expr;
+
+ return expand_simple_operations (e);
+}
+
+/* Tries to simplify EXPR using the condition COND. Returns the simplified
+ expression (or EXPR unchanged, if no simplification was possible). */
+
+static tree
+tree_simplify_using_condition_1 (tree cond, tree expr)
+{
+ bool changed;
+ tree e, te, e0, e1, e2, notcond;
+ enum tree_code code = TREE_CODE (expr);
+
+ if (code == INTEGER_CST)
+ return expr;
+
+ if (code == TRUTH_OR_EXPR
+ || code == TRUTH_AND_EXPR
+ || code == COND_EXPR)
+ {
+ changed = false;
+
+ e0 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 0));
if (TREE_OPERAND (expr, 0) != e0)
changed = true;
- e1 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 1));
+ e1 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 1));
if (TREE_OPERAND (expr, 1) != e1)
changed = true;
if (code == COND_EXPR)
{
- e2 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 2));
+ e2 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 2));
if (TREE_OPERAND (expr, 2) != e2)
changed = true;
}
return expr;
}
- e = instantiate_parameters (loop, expr);
- if (is_gimple_min_invariant (e))
- return e;
-
+ /* In case COND is equality, we may be able to simplify EXPR by copy/constant
+ propagation, and vice versa. Fold does not handle this, since it is
+ considered too expensive. */
+ if (TREE_CODE (cond) == EQ_EXPR)
+ {
+ e0 = TREE_OPERAND (cond, 0);
+ e1 = TREE_OPERAND (cond, 1);
+
+ /* We know that e0 == e1. Check whether we cannot simplify expr
+ using this fact. */
+ e = simplify_replace_tree (expr, e0, e1);
+ if (integer_zerop (e) || integer_nonzerop (e))
+ return e;
+
+ e = simplify_replace_tree (expr, e1, e0);
+ if (integer_zerop (e) || integer_nonzerop (e))
+ return e;
+ }
+ if (TREE_CODE (expr) == EQ_EXPR)
+ {
+ e0 = TREE_OPERAND (expr, 0);
+ e1 = TREE_OPERAND (expr, 1);
+
+ /* If e0 == e1 (EXPR) implies !COND, then EXPR cannot be true. */
+ e = simplify_replace_tree (cond, e0, e1);
+ if (integer_zerop (e))
+ return e;
+ e = simplify_replace_tree (cond, e1, e0);
+ if (integer_zerop (e))
+ return e;
+ }
+ if (TREE_CODE (expr) == NE_EXPR)
+ {
+ e0 = TREE_OPERAND (expr, 0);
+ e1 = TREE_OPERAND (expr, 1);
+
+ /* If e0 == e1 (!EXPR) implies !COND, then EXPR must be true. */
+ e = simplify_replace_tree (cond, e0, e1);
+ if (integer_zerop (e))
+ return boolean_true_node;
+ e = simplify_replace_tree (cond, e1, e0);
+ if (integer_zerop (e))
+ return boolean_true_node;
+ }
+
+ te = expand_simple_operations (expr);
+
+ /* Check whether COND ==> EXPR. */
+ notcond = invert_truthvalue (cond);
+ e = fold_binary (TRUTH_OR_EXPR, boolean_type_node, notcond, te);
+ if (e && integer_nonzerop (e))
+ return e;
+
+ /* Check whether COND ==> not EXPR. */
+ e = fold_binary (TRUTH_AND_EXPR, boolean_type_node, cond, te);
+ if (e && integer_zerop (e))
+ return e;
+
+ return expr;
+}
+
+/* Tries to simplify EXPR using the condition COND. Returns the simplified
+ expression (or EXPR unchanged, if no simplification was possible).
+ Wrapper around tree_simplify_using_condition_1 that ensures that chains
+ of simple operations in definitions of ssa names in COND are expanded,
+ so that things like casts or incrementing the value of the bound before
+ the loop do not cause us to fail. */
+
+static tree
+tree_simplify_using_condition (tree cond, tree expr)
+{
+ cond = expand_simple_operations (cond);
+
+ return tree_simplify_using_condition_1 (cond, expr);
+}
+
+/* Tries to simplify EXPR using the conditions on entry to LOOP.
+ Returns the simplified expression (or EXPR unchanged, if no
+ simplification was possible).*/
+
+static tree
+simplify_using_initial_conditions (struct loop *loop, tree expr)
+{
+ edge e;
+ basic_block bb;
+ tree cond;
+ int cnt = 0;
+
+ if (TREE_CODE (expr) == INTEGER_CST)
+ return expr;
+
+ /* Limit walking the dominators to avoid quadraticness in
+ the number of BBs times the number of loops in degenerate
+ cases. */
+ for (bb = loop->header;
+ bb != ENTRY_BLOCK_PTR && cnt < MAX_DOMINATORS_TO_WALK;
+ bb = get_immediate_dominator (CDI_DOMINATORS, bb))
+ {
+ if (!single_pred_p (bb))
+ continue;
+ e = single_pred_edge (bb);
+
+ if (!(e->flags & (EDGE_TRUE_VALUE | EDGE_FALSE_VALUE)))
+ continue;
+
+ cond = COND_EXPR_COND (last_stmt (e->src));
+ if (e->flags & EDGE_FALSE_VALUE)
+ cond = invert_truthvalue (cond);
+ expr = tree_simplify_using_condition (cond, expr);
+ ++cnt;
+ }
+
+ return expr;
+}
+
+/* Tries to simplify EXPR using the evolutions of the loop invariants
+ in the superloops of LOOP. Returns the simplified expression
+ (or EXPR unchanged, if no simplification was possible). */
+
+static tree
+simplify_using_outer_evolutions (struct loop *loop, tree expr)
+{
+ enum tree_code code = TREE_CODE (expr);
+ bool changed;
+ tree e, e0, e1, e2;
+
+ if (is_gimple_min_invariant (expr))
+ return expr;
+
+ if (code == TRUTH_OR_EXPR
+ || code == TRUTH_AND_EXPR
+ || code == COND_EXPR)
+ {
+ changed = false;
+
+ e0 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 0));
+ if (TREE_OPERAND (expr, 0) != e0)
+ changed = true;
+
+ e1 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 1));
+ if (TREE_OPERAND (expr, 1) != e1)
+ changed = true;
+
+ if (code == COND_EXPR)
+ {
+ e2 = simplify_using_outer_evolutions (loop, TREE_OPERAND (expr, 2));
+ if (TREE_OPERAND (expr, 2) != e2)
+ changed = true;
+ }
+ else
+ e2 = NULL_TREE;
+
+ if (changed)
+ {
+ if (code == COND_EXPR)
+ expr = fold_build3 (code, boolean_type_node, e0, e1, e2);
+ else
+ expr = fold_build2 (code, boolean_type_node, e0, e1);
+ }
+
+ return expr;
+ }
+
+ e = instantiate_parameters (loop, expr);
+ if (is_gimple_min_invariant (e))
+ return e;
+
return expr;
}
+/* Returns true if EXIT is the only possible exit from LOOP. */
+
+static bool
+loop_only_exit_p (struct loop *loop, edge exit)
+{
+ basic_block *body;
+ block_stmt_iterator bsi;
+ unsigned i;
+ tree call;
+
+ if (exit != single_exit (loop))
+ return false;
+
+ body = get_loop_body (loop);
+ for (i = 0; i < loop->num_nodes; i++)
+ {
+ for (bsi = bsi_start (body[0]); !bsi_end_p (bsi); bsi_next (&bsi))
+ {
+ call = get_call_expr_in (bsi_stmt (bsi));
+ if (call && TREE_SIDE_EFFECTS (call))
+ {
+ free (body);
+ return false;
+ }
+ }
+ }
+
+ free (body);
+ return true;
+}
+
/* Stores description of number of iterations of LOOP derived from
EXIT (an exit edge of the LOOP) in NITER. Returns true if some
useful information could be derived (and fields of NITER has
meaning described in comments at struct tree_niter_desc
- declaration), false otherwise. */
+ declaration), false otherwise. If WARN is true and
+ -Wunsafe-loop-optimizations was given, warn if the optimizer is going to use
+ potentially unsafe assumptions. */
bool
number_of_iterations_exit (struct loop *loop, edge exit,
- struct tree_niter_desc *niter)
+ struct tree_niter_desc *niter,
+ bool warn)
{
tree stmt, cond, type;
- tree op0, base0, step0;
- tree op1, base1, step1;
+ tree op0, op1;
enum tree_code code;
+ affine_iv iv0, iv1;
if (!dominated_by_p (CDI_DOMINATORS, loop->latch, exit->src))
return false;
- niter->assumptions = boolean_false_node;
- stmt = last_stmt (exit->src);
- if (!stmt || TREE_CODE (stmt) != COND_EXPR)
- return false;
+ niter->assumptions = boolean_false_node;
+ stmt = last_stmt (exit->src);
+ if (!stmt || TREE_CODE (stmt) != COND_EXPR)
+ return false;
+
+ /* We want the condition for staying inside loop. */
+ cond = COND_EXPR_COND (stmt);
+ if (exit->flags & EDGE_TRUE_VALUE)
+ cond = invert_truthvalue (cond);
+
+ code = TREE_CODE (cond);
+ switch (code)
+ {
+ case GT_EXPR:
+ case GE_EXPR:
+ case NE_EXPR:
+ case LT_EXPR:
+ case LE_EXPR:
+ break;
+
+ default:
+ return false;
+ }
+
+ op0 = TREE_OPERAND (cond, 0);
+ op1 = TREE_OPERAND (cond, 1);
+ type = TREE_TYPE (op0);
+
+ if (TREE_CODE (type) != INTEGER_TYPE
+ && !POINTER_TYPE_P (type))
+ return false;
+
+ if (!simple_iv (loop, stmt, op0, &iv0, false))
+ return false;
+ if (!simple_iv (loop, stmt, op1, &iv1, false))
+ return false;
+
+ /* We don't want to see undefined signed overflow warnings while
+ computing the number of iterations. */
+ fold_defer_overflow_warnings ();
+
+ iv0.base = expand_simple_operations (iv0.base);
+ iv1.base = expand_simple_operations (iv1.base);
+ if (!number_of_iterations_cond (loop, type, &iv0, code, &iv1, niter,
+ loop_only_exit_p (loop, exit)))
+ {
+ fold_undefer_and_ignore_overflow_warnings ();
+ return false;
+ }
+
+ if (optimize >= 3)
+ {
+ niter->assumptions = simplify_using_outer_evolutions (loop,
+ niter->assumptions);
+ niter->may_be_zero = simplify_using_outer_evolutions (loop,
+ niter->may_be_zero);
+ niter->niter = simplify_using_outer_evolutions (loop, niter->niter);
+ }
+
+ niter->assumptions
+ = simplify_using_initial_conditions (loop,
+ niter->assumptions);
+ niter->may_be_zero
+ = simplify_using_initial_conditions (loop,
+ niter->may_be_zero);
+
+ fold_undefer_and_ignore_overflow_warnings ();
+
+ if (integer_onep (niter->assumptions))
+ return true;
+
+ /* With -funsafe-loop-optimizations we assume that nothing bad can happen.
+ But if we can prove that there is overflow or some other source of weird
+ behavior, ignore the loop even with -funsafe-loop-optimizations. */
+ if (integer_zerop (niter->assumptions))
+ return false;
+
+ if (flag_unsafe_loop_optimizations)
+ niter->assumptions = boolean_true_node;
+
+ if (warn)
+ {
+ const char *wording;
+ location_t loc = EXPR_LOCATION (stmt);
+
+ /* We can provide a more specific warning if one of the operator is
+ constant and the other advances by +1 or -1. */
+ if (!integer_zerop (iv1.step)
+ ? (integer_zerop (iv0.step)
+ && (integer_onep (iv1.step) || integer_all_onesp (iv1.step)))
+ : (integer_onep (iv0.step) || integer_all_onesp (iv0.step)))
+ wording =
+ flag_unsafe_loop_optimizations
+ ? N_("assuming that the loop is not infinite")
+ : N_("cannot optimize possibly infinite loops");
+ else
+ wording =
+ flag_unsafe_loop_optimizations
+ ? N_("assuming that the loop counter does not overflow")
+ : N_("cannot optimize loop, the loop counter may overflow");
+
+ if (LOCATION_LINE (loc) > 0)
+ warning (OPT_Wunsafe_loop_optimizations, "%H%s", &loc, gettext (wording));
+ else
+ warning (OPT_Wunsafe_loop_optimizations, "%s", gettext (wording));
+ }
+
+ return flag_unsafe_loop_optimizations;
+}
+
+/* Try to determine the number of iterations of LOOP. If we succeed,
+ expression giving number of iterations is returned and *EXIT is
+ set to the edge from that the information is obtained. Otherwise
+ chrec_dont_know is returned. */
+
+tree
+find_loop_niter (struct loop *loop, edge *exit)
+{
+ unsigned i;
+ VEC (edge, heap) *exits = get_loop_exit_edges (loop);
+ edge ex;
+ tree niter = NULL_TREE, aniter;
+ struct tree_niter_desc desc;
+
+ *exit = NULL;
+ for (i = 0; VEC_iterate (edge, exits, i, ex); i++)
+ {
+ if (!just_once_each_iteration_p (loop, ex->src))
+ continue;
+
+ if (!number_of_iterations_exit (loop, ex, &desc, false))
+ continue;
+
+ if (integer_nonzerop (desc.may_be_zero))
+ {
+ /* We exit in the first iteration through this exit.
+ We won't find anything better. */
+ niter = build_int_cst (unsigned_type_node, 0);
+ *exit = ex;
+ break;
+ }
+
+ if (!integer_zerop (desc.may_be_zero))
+ continue;
+
+ aniter = desc.niter;
+
+ if (!niter)
+ {
+ /* Nothing recorded yet. */
+ niter = aniter;
+ *exit = ex;
+ continue;
+ }
+
+ /* Prefer constants, the lower the better. */
+ if (TREE_CODE (aniter) != INTEGER_CST)
+ continue;
+
+ if (TREE_CODE (niter) != INTEGER_CST)
+ {
+ niter = aniter;
+ *exit = ex;
+ continue;
+ }
+
+ if (tree_int_cst_lt (aniter, niter))
+ {
+ niter = aniter;
+ *exit = ex;
+ continue;
+ }
+ }
+ VEC_free (edge, heap, exits);
+
+ return niter ? niter : chrec_dont_know;
+}
+
+/*
+
+ Analysis of a number of iterations of a loop by a brute-force evaluation.
+
+*/
+
+/* Bound on the number of iterations we try to evaluate. */
+
+#define MAX_ITERATIONS_TO_TRACK \
+ ((unsigned) PARAM_VALUE (PARAM_MAX_ITERATIONS_TO_TRACK))
+
+/* Returns the loop phi node of LOOP such that ssa name X is derived from its
+ result by a chain of operations such that all but exactly one of their
+ operands are constants. */
+
+static tree
+chain_of_csts_start (struct loop *loop, tree x)
+{
+ tree stmt = SSA_NAME_DEF_STMT (x);
+ tree use;
+ basic_block bb = bb_for_stmt (stmt);
+
+ if (!bb
+ || !flow_bb_inside_loop_p (loop, bb))
+ return NULL_TREE;
+
+ if (TREE_CODE (stmt) == PHI_NODE)
+ {
+ if (bb == loop->header)
+ return stmt;
+
+ return NULL_TREE;
+ }
+
+ if (TREE_CODE (stmt) != GIMPLE_MODIFY_STMT)
+ return NULL_TREE;
+
+ if (!ZERO_SSA_OPERANDS (stmt, SSA_OP_ALL_VIRTUALS))
+ return NULL_TREE;
+ if (SINGLE_SSA_DEF_OPERAND (stmt, SSA_OP_DEF) == NULL_DEF_OPERAND_P)
+ return NULL_TREE;
+
+ use = SINGLE_SSA_TREE_OPERAND (stmt, SSA_OP_USE);
+ if (use == NULL_USE_OPERAND_P)
+ return NULL_TREE;
+
+ return chain_of_csts_start (loop, use);
+}
+
+/* Determines whether the expression X is derived from a result of a phi node
+ in header of LOOP such that
+
+ * the derivation of X consists only from operations with constants
+ * the initial value of the phi node is constant
+ * the value of the phi node in the next iteration can be derived from the
+ value in the current iteration by a chain of operations with constants.
+
+ If such phi node exists, it is returned. If X is a constant, X is returned
+ unchanged. Otherwise NULL_TREE is returned. */
+
+static tree
+get_base_for (struct loop *loop, tree x)
+{
+ tree phi, init, next;
+
+ if (is_gimple_min_invariant (x))
+ return x;
+
+ phi = chain_of_csts_start (loop, x);
+ if (!phi)
+ return NULL_TREE;
+
+ init = PHI_ARG_DEF_FROM_EDGE (phi, loop_preheader_edge (loop));
+ next = PHI_ARG_DEF_FROM_EDGE (phi, loop_latch_edge (loop));
+
+ if (TREE_CODE (next) != SSA_NAME)
+ return NULL_TREE;
+
+ if (!is_gimple_min_invariant (init))
+ return NULL_TREE;
+
+ if (chain_of_csts_start (loop, next) != phi)
+ return NULL_TREE;
+
+ return phi;
+}
+
+/* Given an expression X, then
+
+ * if X is NULL_TREE, we return the constant BASE.
+ * otherwise X is a SSA name, whose value in the considered loop is derived
+ by a chain of operations with constant from a result of a phi node in
+ the header of the loop. Then we return value of X when the value of the
+ result of this phi node is given by the constant BASE. */
+
+static tree
+get_val_for (tree x, tree base)
+{
+ tree stmt, nx, val;
+ use_operand_p op;
+ ssa_op_iter iter;
+
+ gcc_assert (is_gimple_min_invariant (base));
+
+ if (!x)
+ return base;
+
+ stmt = SSA_NAME_DEF_STMT (x);
+ if (TREE_CODE (stmt) == PHI_NODE)
+ return base;
+
+ FOR_EACH_SSA_USE_OPERAND (op, stmt, iter, SSA_OP_USE)
+ {
+ nx = USE_FROM_PTR (op);
+ val = get_val_for (nx, base);
+ SET_USE (op, val);
+ val = fold (GIMPLE_STMT_OPERAND (stmt, 1));
+ SET_USE (op, nx);
+ /* only iterate loop once. */
+ return val;
+ }
+
+ /* Should never reach here. */
+ gcc_unreachable ();
+}
+
+/* Tries to count the number of iterations of LOOP till it exits by EXIT
+ by brute force -- i.e. by determining the value of the operands of the
+ condition at EXIT in first few iterations of the loop (assuming that
+ these values are constant) and determining the first one in that the
+ condition is not satisfied. Returns the constant giving the number
+ of the iterations of LOOP if successful, chrec_dont_know otherwise. */
+
+tree
+loop_niter_by_eval (struct loop *loop, edge exit)
+{
+ tree cond, cnd, acnd;
+ tree op[2], val[2], next[2], aval[2], phi[2];
+ unsigned i, j;
+ enum tree_code cmp;
+
+ cond = last_stmt (exit->src);
+ if (!cond || TREE_CODE (cond) != COND_EXPR)
+ return chrec_dont_know;
- /* We want the condition for staying inside loop. */
- cond = COND_EXPR_COND (stmt);
+ cnd = COND_EXPR_COND (cond);
if (exit->flags & EDGE_TRUE_VALUE)
- cond = invert_truthvalue (cond);
+ cnd = invert_truthvalue (cnd);
- code = TREE_CODE (cond);
- switch (code)
+ cmp = TREE_CODE (cnd);
+ switch (cmp)
{
+ case EQ_EXPR:
+ case NE_EXPR:
case GT_EXPR:
case GE_EXPR:
- case NE_EXPR:
case LT_EXPR:
case LE_EXPR:
+ for (j = 0; j < 2; j++)
+ op[j] = TREE_OPERAND (cnd, j);
break;
default:
- return false;
+ return chrec_dont_know;
}
-
- op0 = TREE_OPERAND (cond, 0);
- op1 = TREE_OPERAND (cond, 1);
- type = TREE_TYPE (op0);
- if (TREE_CODE (type) != INTEGER_TYPE
- && !POINTER_TYPE_P (type))
- return false;
-
- if (!simple_iv (loop, stmt, op0, &base0, &step0, false))
- return false;
- if (!simple_iv (loop, stmt, op1, &base1, &step1, false))
- return false;
+ for (j = 0; j < 2; j++)
+ {
+ phi[j] = get_base_for (loop, op[j]);
+ if (!phi[j])
+ return chrec_dont_know;
+ }
- niter->niter = NULL_TREE;
+ for (j = 0; j < 2; j++)
+ {
+ if (TREE_CODE (phi[j]) == PHI_NODE)
+ {
+ val[j] = PHI_ARG_DEF_FROM_EDGE (phi[j], loop_preheader_edge (loop));
+ next[j] = PHI_ARG_DEF_FROM_EDGE (phi[j], loop_latch_edge (loop));
+ }
+ else
+ {
+ val[j] = phi[j];
+ next[j] = NULL_TREE;
+ op[j] = NULL_TREE;
+ }
+ }
+
+ /* Don't issue signed overflow warnings. */
+ fold_defer_overflow_warnings ();
- /* Handle common special cases first, so that we do not need to use
- generic (and slow) analysis very often. */
- if (!number_of_iterations_special (type, base0, step0, code, base1, step1,
- niter))
+ for (i = 0; i < MAX_ITERATIONS_TO_TRACK; i++)
{
+ for (j = 0; j < 2; j++)
+ aval[j] = get_val_for (op[j], val[j]);
- number_of_iterations_cond (type, base0, step0, code, base1, step1,
- niter);
+ acnd = fold_binary (cmp, boolean_type_node, aval[0], aval[1]);
+ if (acnd && integer_zerop (acnd))
+ {
+ fold_undefer_and_ignore_overflow_warnings ();
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ fprintf (dump_file,
+ "Proved that loop %d iterates %d times using brute force.\n",
+ loop->num, i);
+ return build_int_cst (unsigned_type_node, i);
+ }
- if (!niter->niter)
- return false;
+ for (j = 0; j < 2; j++)
+ {
+ val[j] = get_val_for (next[j], val[j]);
+ if (!is_gimple_min_invariant (val[j]))
+ {
+ fold_undefer_and_ignore_overflow_warnings ();
+ return chrec_dont_know;
+ }
+ }
}
- if (optimize >= 3)
- {
- niter->assumptions = simplify_using_outer_evolutions (loop,
- niter->assumptions);
- niter->may_be_zero = simplify_using_outer_evolutions (loop,
- niter->may_be_zero);
- niter->niter = simplify_using_outer_evolutions (loop, niter->niter);
- }
+ fold_undefer_and_ignore_overflow_warnings ();
- niter->additional_info = boolean_true_node;
- niter->assumptions
- = simplify_using_initial_conditions (loop,
- niter->assumptions,
- &niter->additional_info);
- niter->may_be_zero
- = simplify_using_initial_conditions (loop,
- niter->may_be_zero,
- &niter->additional_info);
- return integer_onep (niter->assumptions);
+ return chrec_dont_know;
}
-/* Try to determine the number of iterations of LOOP. If we succeed,
- expression giving number of iterations is returned and *EXIT is
- set to the edge from that the information is obtained. Otherwise
- chrec_dont_know is returned. */
+/* Finds the exit of the LOOP by that the loop exits after a constant
+ number of iterations and stores the exit edge to *EXIT. The constant
+ giving the number of iterations of LOOP is returned. The number of
+ iterations is determined using loop_niter_by_eval (i.e. by brute force
+ evaluation). If we are unable to find the exit for that loop_niter_by_eval
+ determines the number of iterations, chrec_dont_know is returned. */
tree
-find_loop_niter (struct loop *loop, edge *exit)
+find_loop_niter_by_eval (struct loop *loop, edge *exit)
{
- unsigned n_exits, i;
- edge *exits = get_loop_exit_edges (loop, &n_exits);
+ unsigned i;
+ VEC (edge, heap) *exits = get_loop_exit_edges (loop);
edge ex;
tree niter = NULL_TREE, aniter;
- struct tree_niter_desc desc;
*exit = NULL;
- for (i = 0; i < n_exits; i++)
+ for (i = 0; VEC_iterate (edge, exits, i, ex); i++)
{
- ex = exits[i];
if (!just_once_each_iteration_p (loop, ex->src))
continue;
- if (!number_of_iterations_exit (loop, ex, &desc))
+ aniter = loop_niter_by_eval (loop, ex);
+ if (chrec_contains_undetermined (aniter))
continue;
- if (nonzero_p (desc.may_be_zero))
- {
- /* We exit in the first iteration through this exit.
- We won't find anything better. */
- niter = build_int_cst_type (unsigned_type_node, 0);
- *exit = ex;
- break;
- }
-
- if (!zero_p (desc.may_be_zero))
+ if (niter
+ && !tree_int_cst_lt (aniter, niter))
continue;
- aniter = desc.niter;
+ niter = aniter;
+ *exit = ex;
+ }
+ VEC_free (edge, heap, exits);
- if (!niter)
- {
- /* Nothing recorded yet. */
- niter = aniter;
- *exit = ex;
- continue;
- }
+ return niter ? niter : chrec_dont_know;
+}
- /* Prefer constants, the lower the better. */
- if (TREE_CODE (aniter) != INTEGER_CST)
- continue;
+/*
- if (TREE_CODE (niter) != INTEGER_CST)
+ Analysis of upper bounds on number of iterations of a loop.
+
+*/
+
+/* Returns a constant upper bound on the value of expression VAL. VAL
+ is considered to be unsigned. If its type is signed, its value must
+ be nonnegative. */
+
+static double_int
+derive_constant_upper_bound (tree val)
+{
+ tree type = TREE_TYPE (val);
+ tree op0, op1, subtype, maxt;
+ double_int bnd, max, mmax, cst;
+ tree stmt;
+
+ if (INTEGRAL_TYPE_P (type))
+ maxt = TYPE_MAX_VALUE (type);
+ else
+ maxt = upper_bound_in_type (type, type);
+
+ max = tree_to_double_int (maxt);
+
+ switch (TREE_CODE (val))
+ {
+ case INTEGER_CST:
+ return tree_to_double_int (val);
+
+ case NOP_EXPR:
+ case CONVERT_EXPR:
+ op0 = TREE_OPERAND (val, 0);
+ subtype = TREE_TYPE (op0);
+ if (!TYPE_UNSIGNED (subtype)
+ /* If TYPE is also signed, the fact that VAL is nonnegative implies
+ that OP0 is nonnegative. */
+ && TYPE_UNSIGNED (type)
+ && !tree_expr_nonnegative_p (op0))
{
- niter = aniter;
- *exit = ex;
- continue;
+ /* If we cannot prove that the casted expression is nonnegative,
+ we cannot establish more useful upper bound than the precision
+ of the type gives us. */
+ return max;
}
- if (tree_int_cst_lt (aniter, niter))
+ /* We now know that op0 is an nonnegative value. Try deriving an upper
+ bound for it. */
+ bnd = derive_constant_upper_bound (op0);
+
+ /* If the bound does not fit in TYPE, max. value of TYPE could be
+ attained. */
+ if (double_int_ucmp (max, bnd) < 0)
+ return max;
+
+ return bnd;
+
+ case PLUS_EXPR:
+ case MINUS_EXPR:
+ op0 = TREE_OPERAND (val, 0);
+ op1 = TREE_OPERAND (val, 1);
+
+ if (TREE_CODE (op1) != INTEGER_CST
+ || !tree_expr_nonnegative_p (op0))
+ return max;
+
+ /* Canonicalize to OP0 - CST. Consider CST to be signed, in order to
+ choose the most logical way how to treat this constant regardless
+ of the signedness of the type. */
+ cst = tree_to_double_int (op1);
+ cst = double_int_sext (cst, TYPE_PRECISION (type));
+ if (TREE_CODE (val) == PLUS_EXPR)
+ cst = double_int_neg (cst);
+
+ bnd = derive_constant_upper_bound (op0);
+
+ if (double_int_negative_p (cst))
{
- niter = aniter;
- *exit = ex;
- continue;
+ cst = double_int_neg (cst);
+ /* Avoid CST == 0x80000... */
+ if (double_int_negative_p (cst))
+ return max;;
+
+ /* OP0 + CST. We need to check that
+ BND <= MAX (type) - CST. */
+
+ mmax = double_int_add (max, double_int_neg (cst));
+ if (double_int_ucmp (bnd, mmax) > 0)
+ return max;
+
+ return double_int_add (bnd, cst);
}
- }
- free (exits);
+ else
+ {
+ /* OP0 - CST, where CST >= 0.
- return niter ? niter : chrec_dont_know;
-}
+ If TYPE is signed, we have already verified that OP0 >= 0, and we
+ know that the result is nonnegative. This implies that
+ VAL <= BND - CST.
-/*
+ If TYPE is unsigned, we must additionally know that OP0 >= CST,
+ otherwise the operation underflows.
+ */
- Analysis of a number of iterations of a loop by a brute-force evaluation.
+ /* This should only happen if the type is unsigned; however, for
+ buggy programs that use overflowing signed arithmetics even with
+ -fno-wrapv, this condition may also be true for signed values. */
+ if (double_int_ucmp (bnd, cst) < 0)
+ return max;
-*/
+ if (TYPE_UNSIGNED (type))
+ {
+ tree tem = fold_binary (GE_EXPR, boolean_type_node, op0,
+ double_int_to_tree (type, cst));
+ if (!tem || integer_nonzerop (tem))
+ return max;
+ }
-/* Bound on the number of iterations we try to evaluate. */
+ bnd = double_int_add (bnd, double_int_neg (cst));
+ }
-#define MAX_ITERATIONS_TO_TRACK \
- ((unsigned) PARAM_VALUE (PARAM_MAX_ITERATIONS_TO_TRACK))
+ return bnd;
+
+ case FLOOR_DIV_EXPR:
+ case EXACT_DIV_EXPR:
+ op0 = TREE_OPERAND (val, 0);
+ op1 = TREE_OPERAND (val, 1);
+ if (TREE_CODE (op1) != INTEGER_CST
+ || tree_int_cst_sign_bit (op1))
+ return max;
+
+ bnd = derive_constant_upper_bound (op0);
+ return double_int_udiv (bnd, tree_to_double_int (op1), FLOOR_DIV_EXPR);
+
+ case BIT_AND_EXPR:
+ op1 = TREE_OPERAND (val, 1);
+ if (TREE_CODE (op1) != INTEGER_CST
+ || tree_int_cst_sign_bit (op1))
+ return max;
+ return tree_to_double_int (op1);
+
+ case SSA_NAME:
+ stmt = SSA_NAME_DEF_STMT (val);
+ if (TREE_CODE (stmt) != GIMPLE_MODIFY_STMT
+ || GIMPLE_STMT_OPERAND (stmt, 0) != val)
+ return max;
+ return derive_constant_upper_bound (GIMPLE_STMT_OPERAND (stmt, 1));
+
+ default:
+ return max;
+ }
+}
-/* Returns the loop phi node of LOOP such that ssa name X is derived from its
- result by a chain of operations such that all but exactly one of their
- operands are constants. */
+/* Records that every statement in LOOP is executed I_BOUND times.
+ REALISTIC is true if I_BOUND is expected to be close the the real number
+ of iterations. UPPER is true if we are sure the loop iterates at most
+ I_BOUND times. */
-static tree
-chain_of_csts_start (struct loop *loop, tree x)
+static void
+record_niter_bound (struct loop *loop, double_int i_bound, bool realistic,
+ bool upper)
{
- tree stmt = SSA_NAME_DEF_STMT (x);
- basic_block bb = bb_for_stmt (stmt);
- use_optype uses;
+ /* Update the bounds only when there is no previous estimation, or when the current
+ estimation is smaller. */
+ if (upper
+ && (!loop->any_upper_bound
+ || double_int_ucmp (i_bound, loop->nb_iterations_upper_bound) < 0))
+ {
+ loop->any_upper_bound = true;
+ loop->nb_iterations_upper_bound = i_bound;
+ }
+ if (realistic
+ && (!loop->any_estimate
+ || double_int_ucmp (i_bound, loop->nb_iterations_estimate) < 0))
+ {
+ loop->any_estimate = true;
+ loop->nb_iterations_estimate = i_bound;
+ }
+}
- if (!bb
- || !flow_bb_inside_loop_p (loop, bb))
- return NULL_TREE;
-
- if (TREE_CODE (stmt) == PHI_NODE)
+/* Records that AT_STMT is executed at most BOUND + 1 times in LOOP. IS_EXIT
+ is true if the loop is exited immediately after STMT, and this exit
+ is taken at last when the STMT is executed BOUND + 1 times.
+ REALISTIC is true if BOUND is expected to be close the the real number
+ of iterations. UPPER is true if we are sure the loop iterates at most
+ BOUND times. I_BOUND is an unsigned double_int upper estimate on BOUND. */
+
+static void
+record_estimate (struct loop *loop, tree bound, double_int i_bound,
+ tree at_stmt, bool is_exit, bool realistic, bool upper)
+{
+ double_int delta;
+ edge exit;
+
+ if (dump_file && (dump_flags & TDF_DETAILS))
{
- if (bb == loop->header)
- return stmt;
+ fprintf (dump_file, "Statement %s", is_exit ? "(exit)" : "");
+ print_generic_expr (dump_file, at_stmt, TDF_SLIM);
+ fprintf (dump_file, " is %sexecuted at most ",
+ upper ? "" : "probably ");
+ print_generic_expr (dump_file, bound, TDF_SLIM);
+ fprintf (dump_file, " (bounded by ");
+ dump_double_int (dump_file, i_bound, true);
+ fprintf (dump_file, ") + 1 times in loop %d.\n", loop->num);
+ }
- return NULL_TREE;
+ /* If the I_BOUND is just an estimate of BOUND, it rarely is close to the
+ real number of iterations. */
+ if (TREE_CODE (bound) != INTEGER_CST)
+ realistic = false;
+ if (!upper && !realistic)
+ return;
+
+ /* If we have a guaranteed upper bound, record it in the appropriate
+ list. */
+ if (upper)
+ {
+ struct nb_iter_bound *elt = XNEW (struct nb_iter_bound);
+
+ elt->bound = i_bound;
+ elt->stmt = at_stmt;
+ elt->is_exit = is_exit;
+ elt->next = loop->bounds;
+ loop->bounds = elt;
}
- if (TREE_CODE (stmt) != MODIFY_EXPR)
- return NULL_TREE;
+ /* Update the number of iteration estimates according to the bound.
+ If at_stmt is an exit, then every statement in the loop is
+ executed at most BOUND + 1 times. If it is not an exit, then
+ some of the statements before it could be executed BOUND + 2
+ times, if an exit of LOOP is before stmt. */
+ exit = single_exit (loop);
+ if (is_exit
+ || (exit != NULL
+ && dominated_by_p (CDI_DOMINATORS,
+ exit->src, bb_for_stmt (at_stmt))))
+ delta = double_int_one;
+ else
+ delta = double_int_two;
+ i_bound = double_int_add (i_bound, delta);
- if (NUM_VUSES (STMT_VUSE_OPS (stmt)) > 0)
- return NULL_TREE;
- if (NUM_V_MAY_DEFS (STMT_V_MAY_DEF_OPS (stmt)) > 0)
- return NULL_TREE;
- if (NUM_V_MUST_DEFS (STMT_V_MUST_DEF_OPS (stmt)) > 0)
- return NULL_TREE;
- if (NUM_DEFS (STMT_DEF_OPS (stmt)) > 1)
- return NULL_TREE;
- uses = STMT_USE_OPS (stmt);
- if (NUM_USES (uses) != 1)
- return NULL_TREE;
+ /* If an overflow occured, ignore the result. */
+ if (double_int_ucmp (i_bound, delta) < 0)
+ return;
- return chain_of_csts_start (loop, USE_OP (uses, 0));
+ record_niter_bound (loop, i_bound, realistic, upper);
}
-/* Determines whether the expression X is derived from a result of a phi node
- in header of LOOP such that
-
- * the derivation of X consists only from operations with constants
- * the initial value of the phi node is constant
- * the value of the phi node in the next iteration can be derived from the
- value in the current iteration by a chain of operations with constants.
-
- If such phi node exists, it is returned. If X is a constant, X is returned
- unchanged. Otherwise NULL_TREE is returned. */
+/* Record the estimate on number of iterations of LOOP based on the fact that
+ the induction variable BASE + STEP * i evaluated in STMT does not wrap and
+ its values belong to the range <LOW, HIGH>. REALISTIC is true if the
+ estimated number of iterations is expected to be close to the real one.
+ UPPER is true if we are sure the induction variable does not wrap. */
-static tree
-get_base_for (struct loop *loop, tree x)
+static void
+record_nonwrapping_iv (struct loop *loop, tree base, tree step, tree stmt,
+ tree low, tree high, bool realistic, bool upper)
{
- tree phi, init, next;
+ tree niter_bound, extreme, delta;
+ tree type = TREE_TYPE (base), unsigned_type;
+ double_int max;
- if (is_gimple_min_invariant (x))
- return x;
+ if (TREE_CODE (step) != INTEGER_CST || integer_zerop (step))
+ return;
- phi = chain_of_csts_start (loop, x);
- if (!phi)
- return NULL_TREE;
+ if (dump_file && (dump_flags & TDF_DETAILS))
+ {
+ fprintf (dump_file, "Induction variable (");
+ print_generic_expr (dump_file, TREE_TYPE (base), TDF_SLIM);
+ fprintf (dump_file, ") ");
+ print_generic_expr (dump_file, base, TDF_SLIM);
+ fprintf (dump_file, " + ");
+ print_generic_expr (dump_file, step, TDF_SLIM);
+ fprintf (dump_file, " * iteration does not wrap in statement ");
+ print_generic_expr (dump_file, stmt, TDF_SLIM);
+ fprintf (dump_file, " in loop %d.\n", loop->num);
+ }
- init = PHI_ARG_DEF_FROM_EDGE (phi, loop_preheader_edge (loop));
- next = PHI_ARG_DEF_FROM_EDGE (phi, loop_latch_edge (loop));
+ unsigned_type = unsigned_type_for (type);
+ base = fold_convert (unsigned_type, base);
+ step = fold_convert (unsigned_type, step);
+
+ if (tree_int_cst_sign_bit (step))
+ {
+ extreme = fold_convert (unsigned_type, low);
+ if (TREE_CODE (base) != INTEGER_CST)
+ base = fold_convert (unsigned_type, high);
+ delta = fold_build2 (MINUS_EXPR, unsigned_type, base, extreme);
+ step = fold_build1 (NEGATE_EXPR, unsigned_type, step);
+ }
+ else
+ {
+ extreme = fold_convert (unsigned_type, high);
+ if (TREE_CODE (base) != INTEGER_CST)
+ base = fold_convert (unsigned_type, low);
+ delta = fold_build2 (MINUS_EXPR, unsigned_type, extreme, base);
+ }
+
+ /* STMT is executed at most NITER_BOUND + 1 times, since otherwise the value
+ would get out of the range. */
+ niter_bound = fold_build2 (FLOOR_DIV_EXPR, unsigned_type, delta, step);
+ max = derive_constant_upper_bound (niter_bound);
+ record_estimate (loop, niter_bound, max, stmt, false, realistic, upper);
+}
+
+/* Returns true if REF is a reference to an array at the end of a dynamically
+ allocated structure. If this is the case, the array may be allocated larger
+ than its upper bound implies. */
+
+static bool
+array_at_struct_end_p (tree ref)
+{
+ tree base = get_base_address (ref);
+ tree parent, field;
+
+ /* Unless the reference is through a pointer, the size of the array matches
+ its declaration. */
+ if (!base || !INDIRECT_REF_P (base))
+ return false;
+
+ for (;handled_component_p (ref); ref = parent)
+ {
+ parent = TREE_OPERAND (ref, 0);
- if (TREE_CODE (next) != SSA_NAME)
- return NULL_TREE;
+ if (TREE_CODE (ref) == COMPONENT_REF)
+ {
+ /* All fields of a union are at its end. */
+ if (TREE_CODE (TREE_TYPE (parent)) == UNION_TYPE)
+ continue;
- if (!is_gimple_min_invariant (init))
- return NULL_TREE;
+ /* Unless the field is at the end of the struct, we are done. */
+ field = TREE_OPERAND (ref, 1);
+ if (TREE_CHAIN (field))
+ return false;
+ }
- if (chain_of_csts_start (loop, next) != phi)
- return NULL_TREE;
+ /* The other options are ARRAY_REF, ARRAY_RANGE_REF, VIEW_CONVERT_EXPR.
+ In all these cases, we might be accessing the last element, and
+ although in practice this will probably never happen, it is legal for
+ the indices of this last element to exceed the bounds of the array.
+ Therefore, continue checking. */
+ }
- return phi;
+ gcc_assert (INDIRECT_REF_P (ref));
+ return true;
}
-/* Given an expression X, then
-
- * if BASE is NULL_TREE, X must be a constant and we return X.
- * otherwise X is a SSA name, whose value in the considered loop is derived
- by a chain of operations with constant from a result of a phi node in
- the header of the loop. Then we return value of X when the value of the
- result of this phi node is given by the constant BASE. */
+/* Determine information about number of iterations a LOOP from the index
+ IDX of a data reference accessed in STMT. Callback for for_each_index. */
-static tree
-get_val_for (tree x, tree base)
+struct ilb_data
{
- tree stmt, nx, val;
- use_optype uses;
- use_operand_p op;
+ struct loop *loop;
+ tree stmt;
+};
- if (!x)
- return base;
+static bool
+idx_infer_loop_bounds (tree base, tree *idx, void *dta)
+{
+ struct ilb_data *data = dta;
+ tree ev, init, step;
+ tree low, high, type, next;
+ bool sign, upper = true;
+ struct loop *loop = data->loop;
- stmt = SSA_NAME_DEF_STMT (x);
- if (TREE_CODE (stmt) == PHI_NODE)
- return base;
+ if (TREE_CODE (base) != ARRAY_REF)
+ return true;
+
+ /* For arrays at the end of the structure, we are not guaranteed that they
+ do not really extend over their declared size. However, for arrays of
+ size greater than one, this is unlikely to be intended. */
+ if (array_at_struct_end_p (base))
+ upper = false;
+
+ ev = instantiate_parameters (loop, analyze_scalar_evolution (loop, *idx));
+ init = initial_condition (ev);
+ step = evolution_part_in_loop_num (ev, loop->num);
+
+ if (!init
+ || !step
+ || TREE_CODE (step) != INTEGER_CST
+ || integer_zerop (step)
+ || tree_contains_chrecs (init, NULL)
+ || chrec_contains_symbols_defined_in_loop (init, loop->num))
+ return true;
+
+ low = array_ref_low_bound (base);
+ high = array_ref_up_bound (base);
+
+ /* The case of nonconstant bounds could be handled, but it would be
+ complicated. */
+ if (TREE_CODE (low) != INTEGER_CST
+ || !high
+ || TREE_CODE (high) != INTEGER_CST)
+ return true;
+ sign = tree_int_cst_sign_bit (step);
+ type = TREE_TYPE (step);
- uses = STMT_USE_OPS (stmt);
- op = USE_OP_PTR (uses, 0);
+ /* The array of length 1 at the end of a structure most likely extends
+ beyond its bounds. */
+ if (!upper
+ && operand_equal_p (low, high, 0))
+ return true;
+
+ /* In case the relevant bound of the array does not fit in type, or
+ it does, but bound + step (in type) still belongs into the range of the
+ array, the index may wrap and still stay within the range of the array
+ (consider e.g. if the array is indexed by the full range of
+ unsigned char).
+
+ To make things simpler, we require both bounds to fit into type, although
+ there are cases where this would not be strictly necessary. */
+ if (!int_fits_type_p (high, type)
+ || !int_fits_type_p (low, type))
+ return true;
+ low = fold_convert (type, low);
+ high = fold_convert (type, high);
- nx = USE_FROM_PTR (op);
- val = get_val_for (nx, base);
- SET_USE (op, val);
- val = fold (TREE_OPERAND (stmt, 1));
- SET_USE (op, nx);
+ if (sign)
+ next = fold_binary (PLUS_EXPR, type, low, step);
+ else
+ next = fold_binary (PLUS_EXPR, type, high, step);
+
+ if (tree_int_cst_compare (low, next) <= 0
+ && tree_int_cst_compare (next, high) <= 0)
+ return true;
- return val;
+ record_nonwrapping_iv (loop, init, step, data->stmt, low, high, true, upper);
+ return true;
}
-/* Tries to count the number of iterations of LOOP till it exits by EXIT
- by brute force -- i.e. by determining the value of the operands of the
- condition at EXIT in first few iterations of the loop (assuming that
- these values are constant) and determining the first one in that the
- condition is not satisfied. Returns the constant giving the number
- of the iterations of LOOP if successful, chrec_dont_know otherwise. */
+/* Determine information about number of iterations a LOOP from the bounds
+ of arrays in the data reference REF accessed in STMT. */
-tree
-loop_niter_by_eval (struct loop *loop, edge exit)
+static void
+infer_loop_bounds_from_ref (struct loop *loop, tree stmt, tree ref)
{
- tree cond, cnd, acnd;
- tree op[2], val[2], next[2], aval[2], phi[2];
- unsigned i, j;
- enum tree_code cmp;
+ struct ilb_data data;
- cond = last_stmt (exit->src);
- if (!cond || TREE_CODE (cond) != COND_EXPR)
- return chrec_dont_know;
+ data.loop = loop;
+ data.stmt = stmt;
+ for_each_index (&ref, idx_infer_loop_bounds, &data);
+}
- cnd = COND_EXPR_COND (cond);
- if (exit->flags & EDGE_TRUE_VALUE)
- cnd = invert_truthvalue (cnd);
+/* Determine information about number of iterations of a LOOP from the way
+ arrays are used in STMT. */
- cmp = TREE_CODE (cnd);
- switch (cmp)
+static void
+infer_loop_bounds_from_array (struct loop *loop, tree stmt)
+{
+ tree call;
+
+ if (TREE_CODE (stmt) == GIMPLE_MODIFY_STMT)
{
- case EQ_EXPR:
- case NE_EXPR:
- case GT_EXPR:
- case GE_EXPR:
- case LT_EXPR:
- case LE_EXPR:
- for (j = 0; j < 2; j++)
- op[j] = TREE_OPERAND (cnd, j);
- break;
+ tree op0 = GIMPLE_STMT_OPERAND (stmt, 0);
+ tree op1 = GIMPLE_STMT_OPERAND (stmt, 1);
- default:
- return chrec_dont_know;
- }
+ /* For each memory access, analyze its access function
+ and record a bound on the loop iteration domain. */
+ if (REFERENCE_CLASS_P (op0))
+ infer_loop_bounds_from_ref (loop, stmt, op0);
- for (j = 0; j < 2; j++)
- {
- phi[j] = get_base_for (loop, op[j]);
- if (!phi[j])
- return chrec_dont_know;
+ if (REFERENCE_CLASS_P (op1))
+ infer_loop_bounds_from_ref (loop, stmt, op1);
}
-
- for (j = 0; j < 2; j++)
+
+
+ call = get_call_expr_in (stmt);
+ if (call)
{
- if (TREE_CODE (phi[j]) == PHI_NODE)
- {
- val[j] = PHI_ARG_DEF_FROM_EDGE (phi[j], loop_preheader_edge (loop));
- next[j] = PHI_ARG_DEF_FROM_EDGE (phi[j], loop_latch_edge (loop));
- }
- else
- {
- val[j] = phi[j];
- next[j] = NULL_TREE;
- op[j] = NULL_TREE;
- }
+ tree arg;
+ call_expr_arg_iterator iter;
+
+ FOR_EACH_CALL_EXPR_ARG (arg, iter, call)
+ if (REFERENCE_CLASS_P (arg))
+ infer_loop_bounds_from_ref (loop, stmt, arg);
}
+}
- for (i = 0; i < MAX_ITERATIONS_TO_TRACK; i++)
- {
- for (j = 0; j < 2; j++)
- aval[j] = get_val_for (op[j], val[j]);
+/* Determine information about number of iterations of a LOOP from the fact
+ that signed arithmetics in STMT does not overflow. */
- acnd = fold_build2 (cmp, boolean_type_node, aval[0], aval[1]);
- if (zero_p (acnd))
- {
- if (dump_file && (dump_flags & TDF_DETAILS))
- fprintf (dump_file,
- "Proved that loop %d iterates %d times using brute force.\n",
- loop->num, i);
- return build_int_cst (unsigned_type_node, i);
- }
+static void
+infer_loop_bounds_from_signedness (struct loop *loop, tree stmt)
+{
+ tree def, base, step, scev, type, low, high;
- for (j = 0; j < 2; j++)
- val[j] = get_val_for (next[j], val[j]);
- }
+ if (TREE_CODE (stmt) != GIMPLE_MODIFY_STMT)
+ return;
- return chrec_dont_know;
-}
+ def = GIMPLE_STMT_OPERAND (stmt, 0);
-/* Finds the exit of the LOOP by that the loop exits after a constant
- number of iterations and stores the exit edge to *EXIT. The constant
- giving the number of iterations of LOOP is returned. The number of
- iterations is determined using loop_niter_by_eval (i.e. by brute force
- evaluation). If we are unable to find the exit for that loop_niter_by_eval
- determines the number of iterations, chrec_dont_know is returned. */
+ if (TREE_CODE (def) != SSA_NAME)
+ return;
-tree
-find_loop_niter_by_eval (struct loop *loop, edge *exit)
-{
- unsigned n_exits, i;
- edge *exits = get_loop_exit_edges (loop, &n_exits);
- edge ex;
- tree niter = NULL_TREE, aniter;
+ type = TREE_TYPE (def);
+ if (!INTEGRAL_TYPE_P (type)
+ || !TYPE_OVERFLOW_UNDEFINED (type))
+ return;
- *exit = NULL;
- for (i = 0; i < n_exits; i++)
- {
- ex = exits[i];
- if (!just_once_each_iteration_p (loop, ex->src))
- continue;
+ scev = instantiate_parameters (loop, analyze_scalar_evolution (loop, def));
+ if (chrec_contains_undetermined (scev))
+ return;
- aniter = loop_niter_by_eval (loop, ex);
- if (chrec_contains_undetermined (aniter))
- continue;
+ base = initial_condition_in_loop_num (scev, loop->num);
+ step = evolution_part_in_loop_num (scev, loop->num);
- if (niter
- && !tree_int_cst_lt (aniter, niter))
- continue;
+ if (!base || !step
+ || TREE_CODE (step) != INTEGER_CST
+ || tree_contains_chrecs (base, NULL)
+ || chrec_contains_symbols_defined_in_loop (base, loop->num))
+ return;
- niter = aniter;
- *exit = ex;
- }
- free (exits);
+ low = lower_bound_in_type (type, type);
+ high = upper_bound_in_type (type, type);
- return niter ? niter : chrec_dont_know;
+ record_nonwrapping_iv (loop, base, step, stmt, low, high, false, true);
}
-/*
+/* The following analyzers are extracting informations on the bounds
+ of LOOP from the following undefined behaviors:
- Analysis of upper bounds on number of iterations of a loop.
+ - data references should not access elements over the statically
+ allocated size,
+ - signed variables should not overflow when flag_wrapv is not set.
*/
-/* Records that AT_STMT is executed at most BOUND times in LOOP. The
- additional condition ADDITIONAL is recorded with the bound. */
-
-void
-record_estimate (struct loop *loop, tree bound, tree additional, tree at_stmt)
+static void
+infer_loop_bounds_from_undefined (struct loop *loop)
{
- struct nb_iter_bound *elt = xmalloc (sizeof (struct nb_iter_bound));
+ unsigned i;
+ basic_block *bbs;
+ block_stmt_iterator bsi;
+ basic_block bb;
+
+ bbs = get_loop_body (loop);
- if (dump_file && (dump_flags & TDF_DETAILS))
+ for (i = 0; i < loop->num_nodes; i++)
{
- fprintf (dump_file, "Statements after ");
- print_generic_expr (dump_file, at_stmt, TDF_SLIM);
- fprintf (dump_file, " are executed at most ");
- print_generic_expr (dump_file, bound, TDF_SLIM);
- fprintf (dump_file, " times in loop %d.\n", loop->num);
+ bb = bbs[i];
+
+ /* If BB is not executed in each iteration of the loop, we cannot
+ use it to infer any information about # of iterations of the loop. */
+ if (!dominated_by_p (CDI_DOMINATORS, loop->latch, bb))
+ continue;
+
+ for (bsi = bsi_start (bb); !bsi_end_p (bsi); bsi_next (&bsi))
+ {
+ tree stmt = bsi_stmt (bsi);
+
+ infer_loop_bounds_from_array (loop, stmt);
+ infer_loop_bounds_from_signedness (loop, stmt);
+ }
+
}
- elt->bound = bound;
- elt->at_stmt = at_stmt;
- elt->additional = additional;
- elt->next = loop->bounds;
- loop->bounds = elt;
+ free (bbs);
}
/* Records estimates on numbers of iterations of LOOP. */
-static void
+void
estimate_numbers_of_iterations_loop (struct loop *loop)
{
- edge *exits;
+ VEC (edge, heap) *exits;
tree niter, type;
- unsigned i, n_exits;
+ unsigned i;
struct tree_niter_desc niter_desc;
+ edge ex;
+ double_int bound;
+
+ /* Give up if we already have tried to compute an estimation. */
+ if (loop->estimate_state != EST_NOT_COMPUTED)
+ return;
+ loop->estimate_state = EST_AVAILABLE;
+ loop->any_upper_bound = false;
+ loop->any_estimate = false;
- exits = get_loop_exit_edges (loop, &n_exits);
- for (i = 0; i < n_exits; i++)
+ exits = get_loop_exit_edges (loop);
+ for (i = 0; VEC_iterate (edge, exits, i, ex); i++)
{
- if (!number_of_iterations_exit (loop, exits[i], &niter_desc))
+ if (!number_of_iterations_exit (loop, ex, &niter_desc, false))
continue;
niter = niter_desc.niter;
type = TREE_TYPE (niter);
- if (!zero_p (niter_desc.may_be_zero)
- && !nonzero_p (niter_desc.may_be_zero))
+ if (TREE_CODE (niter_desc.may_be_zero) != INTEGER_CST)
niter = build3 (COND_EXPR, type, niter_desc.may_be_zero,
- build_int_cst_type (type, 0),
+ build_int_cst (type, 0),
niter);
- record_estimate (loop, niter,
- niter_desc.additional_info,
- last_stmt (exits[i]->src));
+ record_estimate (loop, niter, niter_desc.max,
+ last_stmt (ex->src),
+ true, true, true);
}
- free (exits);
+ VEC_free (edge, heap, exits);
- /* Analyzes the bounds of arrays accessed in the loop. */
- if (loop->estimated_nb_iterations == NULL_TREE)
+ infer_loop_bounds_from_undefined (loop);
+
+ /* If we have a measured profile, use it to estimate the number of
+ iterations. */
+ if (loop->header->count != 0)
{
- varray_type datarefs;
- VARRAY_GENERIC_PTR_INIT (datarefs, 3, "datarefs");
- find_data_references_in_loop (loop, &datarefs);
- free_data_refs (datarefs);
+ bound = uhwi_to_double_int (expected_loop_iterations (loop) + 1);
+ record_niter_bound (loop, bound, true, false);
}
+
+ /* If an upper bound is smaller than the realistic estimate of the
+ number of iterations, use the upper bound instead. */
+ if (loop->any_upper_bound
+ && loop->any_estimate
+ && double_int_ucmp (loop->nb_iterations_upper_bound,
+ loop->nb_iterations_estimate) < 0)
+ loop->nb_iterations_estimate = loop->nb_iterations_upper_bound;
}
-/* Records estimates on numbers of iterations of LOOPS. */
+/* Records estimates on numbers of iterations of loops. */
void
-estimate_numbers_of_iterations (struct loops *loops)
+estimate_numbers_of_iterations (void)
{
- unsigned i;
+ loop_iterator li;
struct loop *loop;
- for (i = 1; i < loops->num; i++)
+ /* We don't want to issue signed overflow warnings while getting
+ loop iteration estimates. */
+ fold_defer_overflow_warnings ();
+
+ FOR_EACH_LOOP (li, loop, 0)
{
- loop = loops->parray[i];
- if (loop)
- estimate_numbers_of_iterations_loop (loop);
+ estimate_numbers_of_iterations_loop (loop);
}
-}
-
-/* If A > B, returns -1. If A == B, returns 0. If A < B, returns 1.
- If neither of these relations can be proved, returns 2. */
-
-static int
-compare_trees (tree a, tree b)
-{
- tree typea = TREE_TYPE (a), typeb = TREE_TYPE (b);
- tree type;
-
- if (TYPE_PRECISION (typea) > TYPE_PRECISION (typeb))
- type = typea;
- else
- type = typeb;
-
- a = fold_convert (type, a);
- b = fold_convert (type, b);
- if (nonzero_p (fold_build2 (EQ_EXPR, boolean_type_node, a, b)))
- return 0;
- if (nonzero_p (fold_build2 (LT_EXPR, boolean_type_node, a, b)))
- return 1;
- if (nonzero_p (fold_build2 (GT_EXPR, boolean_type_node, a, b)))
- return -1;
-
- return 2;
+ fold_undefer_and_ignore_overflow_warnings ();
}
/* Returns true if statement S1 dominates statement S2. */
return dominated_by_p (CDI_DOMINATORS, bb2, bb1);
}
-/* Checks whether it is correct to count the induction variable BASE + STEP * I
- at AT_STMT in wider TYPE, using the fact that statement OF is executed at
- most BOUND times in the loop. If it is possible, return the value of step
- of the induction variable in the TYPE, otherwise return NULL_TREE.
-
- ADDITIONAL is the additional condition recorded for operands of the bound.
- This is useful in the following case, created by loop header copying:
-
- i = 0;
- if (n > 0)
- do
- {
- something;
- } while (++i < n)
-
- If the n > 0 condition is taken into account, the number of iterations of the
- loop can be expressed as n - 1. If the type of n is signed, the ADDITIONAL
- assumption "n > 0" says us that the value of the number of iterations is at
- most MAX_TYPE - 1 (without this assumption, it might overflow). */
+/* Returns true when we can prove that the number of executions of
+ STMT in the loop is at most NITER, according to the bound on
+ the number of executions of the statement NITER_BOUND->stmt recorded in
+ NITER_BOUND. If STMT is NULL, we must prove this bound for all
+ statements in the loop. */
-static tree
-can_count_iv_in_wider_type_bound (tree type, tree base, tree step,
- tree at_stmt,
- tree bound,
- tree additional,
- tree of)
+static bool
+n_of_executions_at_most (tree stmt,
+ struct nb_iter_bound *niter_bound,
+ tree niter)
{
- tree inner_type = TREE_TYPE (base), b, bplusstep, new_step, new_step_abs;
- tree valid_niter, extreme, unsigned_type, delta, bound_type;
- tree cond;
-
- b = fold_convert (type, base);
- bplusstep = fold_convert (type,
- fold_build2 (PLUS_EXPR, inner_type, base, step));
- new_step = fold_build2 (MINUS_EXPR, type, bplusstep, b);
- if (TREE_CODE (new_step) != INTEGER_CST)
- return NULL_TREE;
-
- switch (compare_trees (bplusstep, b))
- {
- case -1:
- extreme = upper_bound_in_type (type, inner_type);
- delta = fold_build2 (MINUS_EXPR, type, extreme, b);
- new_step_abs = new_step;
- break;
-
- case 1:
- extreme = lower_bound_in_type (type, inner_type);
- new_step_abs = fold_build1 (NEGATE_EXPR, type, new_step);
- delta = fold_build2 (MINUS_EXPR, type, b, extreme);
- break;
+ double_int bound = niter_bound->bound;
+ tree nit_type = TREE_TYPE (niter), e;
+ enum tree_code cmp;
- case 0:
- return new_step;
+ gcc_assert (TYPE_UNSIGNED (nit_type));
- default:
- return NULL_TREE;
- }
+ /* If the bound does not even fit into NIT_TYPE, it cannot tell us that
+ the number of iterations is small. */
+ if (!double_int_fits_to_tree_p (nit_type, bound))
+ return false;
- unsigned_type = unsigned_type_for (type);
- delta = fold_convert (unsigned_type, delta);
- new_step_abs = fold_convert (unsigned_type, new_step_abs);
- valid_niter = fold_build2 (FLOOR_DIV_EXPR, unsigned_type,
- delta, new_step_abs);
-
- bound_type = TREE_TYPE (bound);
- if (TYPE_PRECISION (type) > TYPE_PRECISION (bound_type))
- bound = fold_convert (unsigned_type, bound);
- else
- valid_niter = fold_convert (bound_type, valid_niter);
-
- if (at_stmt && stmt_dominates_stmt_p (of, at_stmt))
+ /* We know that NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
+ times. This means that:
+
+ -- if NITER_BOUND->is_exit is true, then everything before
+ NITER_BOUND->stmt is executed at most NITER_BOUND->bound + 1
+ times, and everything after it at most NITER_BOUND->bound times.
+
+ -- If NITER_BOUND->is_exit is false, then if we can prove that when STMT
+ is executed, then NITER_BOUND->stmt is executed as well in the same
+ iteration (we conclude that if both statements belong to the same
+ basic block, or if STMT is after NITER_BOUND->stmt), then STMT
+ is executed at most NITER_BOUND->bound + 1 times. Otherwise STMT is
+ executed at most NITER_BOUND->bound + 2 times. */
+
+ if (niter_bound->is_exit)
{
- /* After the statement OF we know that anything is executed at most
- BOUND times. */
- cond = fold_build2 (GE_EXPR, boolean_type_node, valid_niter, bound);
+ if (stmt
+ && stmt != niter_bound->stmt
+ && stmt_dominates_stmt_p (niter_bound->stmt, stmt))
+ cmp = GE_EXPR;
+ else
+ cmp = GT_EXPR;
}
else
{
- /* Before the statement OF we know that anything is executed at most
- BOUND + 1 times. */
- cond = fold_build2 (GT_EXPR, boolean_type_node, valid_niter, bound);
+ if (!stmt
+ || (bb_for_stmt (stmt) != bb_for_stmt (niter_bound->stmt)
+ && !stmt_dominates_stmt_p (niter_bound->stmt, stmt)))
+ {
+ bound = double_int_add (bound, double_int_one);
+ if (double_int_zero_p (bound)
+ || !double_int_fits_to_tree_p (nit_type, bound))
+ return false;
+ }
+ cmp = GT_EXPR;
}
- if (nonzero_p (cond))
- return new_step;
+ e = fold_binary (cmp, boolean_type_node,
+ niter, double_int_to_tree (nit_type, bound));
+ return e && integer_nonzerop (e);
+}
+
+/* Returns true if the arithmetics in TYPE can be assumed not to wrap. */
+
+bool
+nowrap_type_p (tree type)
+{
+ if (INTEGRAL_TYPE_P (type)
+ && TYPE_OVERFLOW_UNDEFINED (type))
+ return true;
- /* Try taking additional conditions into account. */
- cond = fold_build2 (TRUTH_OR_EXPR, boolean_type_node,
- invert_truthvalue (additional),
- cond);
- if (nonzero_p (cond))
- return new_step;
+ if (POINTER_TYPE_P (type))
+ return true;
- return NULL_TREE;
+ return false;
}
-/* Checks whether it is correct to count the induction variable BASE + STEP * I
- at AT_STMT in wider TYPE, using the bounds on numbers of iterations of a
- LOOP. If it is possible, return the value of step of the induction variable
- in the TYPE, otherwise return NULL_TREE. */
+/* Return false only when the induction variable BASE + STEP * I is
+ known to not overflow: i.e. when the number of iterations is small
+ enough with respect to the step and initial condition in order to
+ keep the evolution confined in TYPEs bounds. Return true when the
+ iv is known to overflow or when the property is not computable.
+
+ USE_OVERFLOW_SEMANTICS is true if this function should assume that
+ the rules for overflow of the given language apply (e.g., that signed
+ arithmetics in C does not overflow). */
-tree
-can_count_iv_in_wider_type (struct loop *loop, tree type, tree base, tree step,
- tree at_stmt)
+bool
+scev_probably_wraps_p (tree base, tree step,
+ tree at_stmt, struct loop *loop,
+ bool use_overflow_semantics)
{
struct nb_iter_bound *bound;
- tree new_step;
+ tree delta, step_abs;
+ tree unsigned_type, valid_niter;
+ tree type = TREE_TYPE (step);
+
+ /* FIXME: We really need something like
+ http://gcc.gnu.org/ml/gcc-patches/2005-06/msg02025.html.
+
+ We used to test for the following situation that frequently appears
+ during address arithmetics:
+
+ D.1621_13 = (long unsigned intD.4) D.1620_12;
+ D.1622_14 = D.1621_13 * 8;
+ D.1623_15 = (doubleD.29 *) D.1622_14;
+
+ And derived that the sequence corresponding to D_14
+ can be proved to not wrap because it is used for computing a
+ memory access; however, this is not really the case -- for example,
+ if D_12 = (unsigned char) [254,+,1], then D_14 has values
+ 2032, 2040, 0, 8, ..., but the code is still legal. */
+
+ if (chrec_contains_undetermined (base)
+ || chrec_contains_undetermined (step)
+ || TREE_CODE (step) != INTEGER_CST)
+ return true;
- for (bound = loop->bounds; bound; bound = bound->next)
+ if (integer_zerop (step))
+ return false;
+
+ /* If we can use the fact that signed and pointer arithmetics does not
+ wrap, we are done. */
+ if (use_overflow_semantics && nowrap_type_p (type))
+ return false;
+
+ /* Don't issue signed overflow warnings. */
+ fold_defer_overflow_warnings ();
+
+ /* Otherwise, compute the number of iterations before we reach the
+ bound of the type, and verify that the loop is exited before this
+ occurs. */
+ unsigned_type = unsigned_type_for (type);
+ base = fold_convert (unsigned_type, base);
+
+ if (tree_int_cst_sign_bit (step))
+ {
+ tree extreme = fold_convert (unsigned_type,
+ lower_bound_in_type (type, type));
+ delta = fold_build2 (MINUS_EXPR, unsigned_type, base, extreme);
+ step_abs = fold_build1 (NEGATE_EXPR, unsigned_type,
+ fold_convert (unsigned_type, step));
+ }
+ else
{
- new_step = can_count_iv_in_wider_type_bound (type, base, step,
- at_stmt,
- bound->bound,
- bound->additional,
- bound->at_stmt);
+ tree extreme = fold_convert (unsigned_type,
+ upper_bound_in_type (type, type));
+ delta = fold_build2 (MINUS_EXPR, unsigned_type, extreme, base);
+ step_abs = fold_convert (unsigned_type, step);
+ }
+
+ valid_niter = fold_build2 (FLOOR_DIV_EXPR, unsigned_type, delta, step_abs);
- if (new_step)
- return new_step;
+ estimate_numbers_of_iterations_loop (loop);
+ for (bound = loop->bounds; bound; bound = bound->next)
+ {
+ if (n_of_executions_at_most (at_stmt, bound, valid_niter))
+ {
+ fold_undefer_and_ignore_overflow_warnings ();
+ return false;
+ }
}
- return NULL_TREE;
+ fold_undefer_and_ignore_overflow_warnings ();
+
+ /* At this point we still don't have a proof that the iv does not
+ overflow: give up. */
+ return true;
}
/* Frees the information on upper bounds on numbers of iterations of LOOP. */
-static void
+void
free_numbers_of_iterations_estimates_loop (struct loop *loop)
{
struct nb_iter_bound *bound, *next;
-
+
+ loop->nb_iterations = NULL;
+ loop->estimate_state = EST_NOT_COMPUTED;
for (bound = loop->bounds; bound; bound = next)
{
next = bound->next;
loop->bounds = NULL;
}
-/* Frees the information on upper bounds on numbers of iterations of LOOPS. */
+/* Frees the information on upper bounds on numbers of iterations of loops. */
void
-free_numbers_of_iterations_estimates (struct loops *loops)
+free_numbers_of_iterations_estimates (void)
{
- unsigned i;
+ loop_iterator li;
struct loop *loop;
- for (i = 1; i < loops->num; i++)
+ FOR_EACH_LOOP (li, loop, 0)
{
- loop = loops->parray[i];
- if (loop)
- free_numbers_of_iterations_estimates_loop (loop);
+ free_numbers_of_iterations_estimates_loop (loop);
}
}
+
+/* Substitute value VAL for ssa name NAME inside expressions held
+ at LOOP. */
+
+void
+substitute_in_loop_info (struct loop *loop, tree name, tree val)
+{
+ loop->nb_iterations = simplify_replace_tree (loop->nb_iterations, name, val);
+}
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