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/* Functions to determine/estimate number of iterations of a loop.
Copyright (C) 2004, 2005, 2006, 2007, 2008, 2009, 2010
Free Software Foundation, Inc.
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 3, or (at your option) any
later version.
GCC is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING3. If not see
<http://www.gnu.org/licenses/>. */
#include "config.h"
#include "system.h"
#include "coretypes.h"
#include "tm.h"
#include "tree.h"
#include "tm_p.h"
#include "basic-block.h"
#include "output.h"
#include "tree-pretty-print.h"
#include "gimple-pretty-print.h"
#include "intl.h"
#include "tree-flow.h"
#include "tree-dump.h"
#include "cfgloop.h"
#include "tree-pass.h"
#include "ggc.h"
#include "tree-chrec.h"
#include "tree-scalar-evolution.h"
#include "tree-data-ref.h"
#include "params.h"
#include "flags.h"
#include "diagnostic-core.h"
#include "tree-inline.h"
#include "gmp.h"
#define SWAP(X, Y) do { affine_iv *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
/*
Analysis of number of iterations of an affine exit test.
*/
/* Bounds on some value, BELOW <= X <= UP. */
typedef struct
{
mpz_t below, up;
} bounds;
/* Splits expression EXPR to a variable part VAR and constant OFFSET. */
static void
split_to_var_and_offset (tree expr, tree *var, mpz_t offset)
{
tree type = TREE_TYPE (expr);
tree op0, op1;
double_int off;
bool negate = false;
*var = expr;
mpz_set_ui (offset, 0);
switch (TREE_CODE (expr))
{
case MINUS_EXPR:
negate = true;
/* Fallthru. */
case PLUS_EXPR:
case POINTER_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 = tree_to_double_int (op1);
off = double_int_sext (off, TYPE_PRECISION (type));
mpz_set_double_int (offset, off, false);
if (negate)
mpz_neg (offset, offset);
break;
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;
default:
break;
}
}
/* Stores estimate on the minimum/maximum value of the expression VAR + OFF
in TYPE to MIN and MAX. */
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))
{
mpz_set (min, off);
mpz_set (max, off);
return;
}
/* If the computation may wrap, we know nothing about the value, except for
the range of the type. */
get_type_static_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)
{
mpz_set_ui (bnds->below, 0);
mpz_set_ui (bnds->up, 0);
return;
}
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 (may_wrap)
{
if (rel > 0)
mpz_sub (bnds->below, bnds->below, m);
else
mpz_add (bnds->up, bnds->up, m);
}
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)
{
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 (!useless_type_conversion_p (ctype, type))
return;
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;
/* 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 (TYPE_MIN_VALUE (type)
&& operand_equal_p (c1, TYPE_MIN_VALUE (type), 0))
{
cmp = GT_EXPR;
break;
}
if (TYPE_MAX_VALUE (type)
&& operand_equal_p (c1, TYPE_MAX_VALUE (type), 0))
{
cmp = LT_EXPR;
break;
}
return;
default:
return;
}
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);
/* 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 (operand_equal_p (varx, varc1, 0))
{
tmp = varc0; varc0 = varc1; varc1 = tmp;
mpz_swap (offc0, offc1);
cmp = swap_tree_comparison (cmp);
}
if (!operand_equal_p (varx, varc0, 0)
|| !operand_equal_p (vary, varc1, 0))
goto end;
mpz_init_set (loffx, offx);
mpz_init_set (loffy, offy);
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;
}
/* If there is no overflow, the condition implies that
(VARX + OFFX) cmp (VARY + OFFY) + (OFFX - OFFY + OFFC1 - OFFC0).
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
{
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);
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
{
if (mpz_cmp (bnd, bnds->up) < 0)
mpz_set (bnds->up, bnd);
}
mpz_clear (bnd);
}
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). */
static void
bound_difference (struct loop *loop, tree x, tree y, bounds *bnds)
{
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 c0, c1;
gimple cond;
enum tree_code cmp;
/* Get rid of unnecessary casts, but preserve the value of
the expressions. */
STRIP_SIGN_NOPS (x);
STRIP_SIGN_NOPS (y);
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))
{
/* 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);
}
else
{
/* 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);
}
/* If both X and Y are constants, we cannot get any more precise. */
if (integer_zerop (varx) && integer_zerop (vary))
goto end;
/* 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);
if (!(e->flags & (EDGE_TRUE_VALUE | EDGE_FALSE_VALUE)))
continue;
cond = last_stmt (e->src);
c0 = gimple_cond_lhs (cond);
cmp = gimple_cond_code (cond);
c1 = gimple_cond_rhs (cond);
if (e->flags & EDGE_FALSE_VALUE)
cmp = invert_tree_comparison (cmp, false);
refine_bounds_using_guard (type, varx, offx, vary, offy,
c0, cmp, c1, bnds);
++cnt;
}
end:
mpz_clear (offx);
mpz_clear (offy);
}
/* 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 void
bounds_add (bounds *bnds, double_int delta, tree type)
{
mpz_t mdelta, max;
mpz_init (mdelta);
mpz_set_double_int (mdelta, delta, false);
mpz_init (max);
mpz_set_double_int (max, double_int_mask (TYPE_PRECISION (type)), true);
mpz_add (bnds->up, bnds->up, mdelta);
mpz_add (bnds->below, bnds->below, mdelta);
if (mpz_cmp (bnds->up, max) > 0)
mpz_set (bnds->up, max);
mpz_neg (max, max);
if (mpz_cmp (bnds->below, max) < 0)
mpz_set (bnds->below, max);
mpz_clear (mdelta);
mpz_clear (max);
}
/* Update the bounds in BNDS that restrict the value of X to the bounds
that restrict the value of -X. */
static void
bounds_negate (bounds *bnds)
{
mpz_t tmp;
mpz_init_set (tmp, bnds->up);
mpz_neg (bnds->up, bnds->below);
mpz_neg (bnds->below, tmp);
mpz_clear (tmp);
}
/* 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)
{
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);
}
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);
}
return rslt;
}
/* Derives the upper bound BND on the number of executions of loop with exit
condition S * i <> C. If NO_OVERFLOW is true, then the control variable of
the loop does not overflow. EXIT_MUST_BE_TAKEN is true if we are guaranteed
that the loop ends through this exit, i.e., the induction variable ever
reaches the value of C.
The value C is equal to final - base, where final and base are the final and
initial value of the actual induction variable in the analysed loop. BNDS
bounds the value of this difference when computed in signed type with
unbounded range, while the computation of C is performed in an unsigned
type with the range matching the range of the type of the induction variable.
In particular, BNDS.up contains an upper bound on C in the following cases:
-- if the iv must reach its final value without overflow, i.e., if
NO_OVERFLOW && EXIT_MUST_BE_TAKEN is true, or
-- if final >= base, which we know to hold when BNDS.below >= 0. */
static void
number_of_iterations_ne_max (mpz_t bnd, bool no_overflow, tree c, tree s,
bounds *bnds, bool exit_must_be_taken)
{
double_int max;
mpz_t d;
bool bnds_u_valid = ((no_overflow && exit_must_be_taken)
|| mpz_sgn (bnds->below) >= 0);
if (multiple_of_p (TREE_TYPE (c), c, s))
{
/* If C is an exact multiple of S, then its value will be reached before
the induction variable overflows (unless the loop is exited in some
other way before). Note that the actual induction variable in the
loop (which ranges from base to final instead of from 0 to C) may
overflow, in which case BNDS.up will not be giving a correct upper
bound on C; thus, BNDS_U_VALID had to be computed in advance. */
no_overflow = true;
exit_must_be_taken = true;
}
/* If the induction variable can overflow, the number of iterations is at
most the period of the control variable (or infinite, but in that case
the whole # of iterations analysis will fail). */
if (!no_overflow)
{
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;
}
/* Now we know that the induction variable does not overflow, so the loop
iterates at most (range of type / S) times. */
mpz_set_double_int (bnd, double_int_mask (TYPE_PRECISION (TREE_TYPE (c))),
true);
/* If the induction variable is guaranteed to reach the value of C before
overflow, ... */
if (exit_must_be_taken)
{
/* ... then we can strenghten this to C / S, and possibly we can use
the upper bound on C given by BNDS. */
if (TREE_CODE (c) == INTEGER_CST)
mpz_set_double_int (bnd, tree_to_double_int (c), true);
else if (bnds_u_valid)
mpz_set (bnd, bnds->up);
}
mpz_init (d);
mpz_set_double_int (d, tree_to_double_int (s), true);
mpz_fdiv_q (bnd, bnd, d);
mpz_clear (d);
}
/* 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. EXIT_MUST_BE_TAKEN 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 bool
number_of_iterations_ne (tree type, affine_iv *iv, tree final,
struct tree_niter_desc *niter, bool exit_must_be_taken,
bounds *bnds)
{
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));
}
mpz_init (max);
number_of_iterations_ne_max (max, iv->no_overflow, c, s, bnds,
exit_must_be_taken);
niter->max = mpz_get_double_int (niter_type, max, false);
mpz_clear (max);
/* First the trivial cases -- when the step is 1. */
if (integer_onep (s))
{
niter->niter = c;
return 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)));
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 (!exit_must_be_taken)
{
/* If we cannot assume that the exit is taken eventually, 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. EXIT_MUST_BE_TAKEN is
true if we know that the exit must be taken eventually. */
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,
bool exit_must_be_taken, 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, fv_comp_no_overflow;
tree type1 = type;
if (POINTER_TYPE_P (type))
type1 = sizetype;
if (TREE_CODE (mod) != INTEGER_CST)
return false;
if (integer_nonzerop (mod))
mod = fold_build2 (MINUS_EXPR, niter_type, step, mod);
tmod = fold_convert (type1, mod);
mpz_init (mmod);
mpz_set_double_int (mmod, tree_to_double_int (mod), true);
mpz_neg (mmod, mmod);
/* If the induction variable does not overflow and the exit is taken,
then the computation of the final value does not overflow. This is
also obviously the case if the new final value is equal to the
current one. Finally, we postulate this for pointer type variables,
as the code cannot rely on the object to that the pointer points being
placed at the end of the address space (and more pragmatically,
TYPE_{MIN,MAX}_VALUE is not defined for pointers). */
if (integer_zerop (mod) || POINTER_TYPE_P (type))
fv_comp_no_overflow = true;
else if (!exit_must_be_taken)
fv_comp_no_overflow = false;
else
fv_comp_no_overflow =
(iv0->no_overflow && integer_nonzerop (iv0->step))
|| (iv1->no_overflow && integer_nonzerop (iv1->step));
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 (!fv_comp_no_overflow)
{
bound = fold_build2 (MINUS_EXPR, type1,
TYPE_MAX_VALUE (type1), 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 if (POINTER_TYPE_P (type))
noloop = fold_build2 (GT_EXPR, boolean_type_node,
iv0->base,
fold_build2 (POINTER_PLUS_EXPR, type,
iv1->base, tmod));
else
noloop = fold_build2 (GT_EXPR, boolean_type_node,
iv0->base,
fold_build2 (PLUS_EXPR, type1,
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 (!fv_comp_no_overflow)
{
bound = fold_build2 (PLUS_EXPR, type1,
TYPE_MIN_VALUE (type1), tmod);
assumption = fold_build2 (GE_EXPR, boolean_type_node,
iv0->base, bound);
if (integer_zerop (assumption))
goto end;
}
if (mpz_cmp (mmod, bnds->below) < 0)
noloop = boolean_false_node;
else if (POINTER_TYPE_P (type))
noloop = fold_build2 (GT_EXPR, boolean_type_node,
fold_build2 (POINTER_PLUS_EXPR, type,
iv0->base,
fold_build1 (NEGATE_EXPR,
type1, tmod)),
iv1->base);
else
noloop = fold_build2 (GT_EXPR, boolean_type_node,
fold_build2 (MINUS_EXPR, type1,
iv0->base, tmod),
iv1->base);
}
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;
}
/* 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. */
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))
{
/* for (i = iv0->base; i < iv1->base; i += iv0->step) */
if (iv0->no_overflow)
return true;
/* 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);
}
else
{
/* for (i = iv1->base; i > iv0->base; i += iv1->step) */
if (iv1->no_overflow)
return true;
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);
}
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;
}
/* 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 void
assert_loop_rolls_lt (tree type, affine_iv *iv0, affine_iv *iv1,
struct tree_niter_desc *niter, bounds *bnds)
{
tree assumption = boolean_true_node, bound, diff;
tree mbz, mbzl, mbzr, type1;
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
-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,
i.e., without overflows).
Usually, for loops with exit condition iv0->base + step * i < iv1->base,
we have a condition of the 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);
}
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;
type1 = type;
if (POINTER_TYPE_P (type))
type1 = sizetype;
/* Now the hard part; we must formulate the assumption(s) as expressions, and
we must be careful not to introduce overflow. */
if (integer_nonzerop (iv0->step))
{
diff = fold_build2 (MINUS_EXPR, type1,
iv0->step, build_int_cst (type1, 1));
/* 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, type1,
TYPE_MIN_VALUE (type), diff);
assumption = fold_build2 (GE_EXPR, boolean_type_node,
iv0->base, bound);
}
/* And then we can compute iv0->base - diff, and compare it with
iv1->base. */
mbzl = fold_build2 (MINUS_EXPR, type1,
fold_convert (type1, iv0->base), diff);
mbzr = fold_convert (type1, iv1->base);
}
else
{
diff = fold_build2 (PLUS_EXPR, type1,
iv1->step, build_int_cst (type1, 1));
if (!POINTER_TYPE_P (type))
{
bound = fold_build2 (PLUS_EXPR, type1,
TYPE_MAX_VALUE (type), diff);
assumption = fold_build2 (LE_EXPR, boolean_type_node,
iv1->base, bound);
}
mbzl = fold_convert (type1, iv0->base);
mbzr = fold_build2 (MINUS_EXPR, type1,
fold_convert (type1, iv1->base), diff);
}
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);
}
}
/* 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. EXIT_MUST_BE_TAKEN is true if we know
that the exit must be taken eventually. */
static bool
number_of_iterations_lt (tree type, affine_iv *iv0, affine_iv *iv1,
struct tree_niter_desc *niter,
bool exit_must_be_taken, bounds *bnds)
{
tree niter_type = unsigned_type_for (type);
tree delta, step, s;
mpz_t mstep, tmp;
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;
}
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)))
{
/* for (i = iv0->base; i < iv1->base; i++)
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_get_double_int (niter_type, bnds->up, false);
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,
exit_must_be_taken, 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_get_double_int (niter_type, tmp, false);
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. EXIT_MUST_BE_TAKEN 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 exit_must_be_taken,
bounds *bnds)
{
tree assumption;
tree type1 = type;
if (POINTER_TYPE_P (type))
type1 = sizetype;
/* 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. We do not check
this condition for pointer type ivs, as the code cannot rely on
the object to that the pointer points being placed at the end of
the address space (and more pragmatically, TYPE_{MIN,MAX}_VALUE is
not defined for pointers). */
if (!exit_must_be_taken && !POINTER_TYPE_P (type))
{
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))
{
if (POINTER_TYPE_P (type))
iv1->base = fold_build2 (POINTER_PLUS_EXPR, type, iv1->base,
build_int_cst (type1, 1));
else
iv1->base = fold_build2 (PLUS_EXPR, type1, iv1->base,
build_int_cst (type1, 1));
}
else if (POINTER_TYPE_P (type))
iv0->base = fold_build2 (POINTER_PLUS_EXPR, type, iv0->base,
fold_build1 (NEGATE_EXPR, type1,
build_int_cst (type1, 1)));
else
iv0->base = fold_build2 (MINUS_EXPR, type1,
iv0->base, build_int_cst (type1, 1));
bounds_add (bnds, double_int_one, type1);
return number_of_iterations_lt (type, iv0, iv1, niter, exit_must_be_taken,
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 exit_must_be_taken = false, 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 (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). */
iv0->no_overflow = true;
iv1->no_overflow = true;
}
/* If the control induction variable does not overflow and the only exit
from the loop is the one that we analyze, we know it must be taken
eventually. */
if (only_exit)
{
if (!integer_zerop (iv0->step) && iv0->no_overflow)
exit_must_be_taken = true;
else if (!integer_zerop (iv1->step) && iv1->no_overflow)
exit_must_be_taken = true;
}
/* 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,
"Analyzing # 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,
exit_must_be_taken, &bnds);
break;
case LT_EXPR:
ret = number_of_iterations_lt (type, iv0, iv1, niter, exit_must_be_taken,
&bnds);
break;
case LE_EXPR:
ret = number_of_iterations_le (type, iv0, iv1, niter, exit_must_be_taken,
&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_tree)
{
unsigned i, n;
tree ret = NULL_TREE, e, se;
if (!expr)
return NULL_TREE;
/* Do not bother to replace constants. */
if (CONSTANT_CLASS_P (old))
return expr;
if (expr == old
|| operand_equal_p (expr, old, 0))
return unshare_expr (new_tree);
if (!EXPR_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_tree);
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, e1;
enum tree_code code;
gimple stmt;
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 (gimple_code (stmt) == GIMPLE_PHI)
{
basic_block src, dest;
if (gimple_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 = gimple_bb (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 (gimple_code (stmt) != GIMPLE_ASSIGN)
return expr;
e = gimple_assign_rhs1 (stmt);
code = gimple_assign_rhs_code (stmt);
if (get_gimple_rhs_class (code) == GIMPLE_SINGLE_RHS)
{
if (is_gimple_min_invariant (e))
return e;
if (code == SSA_NAME)
return expand_simple_operations (e);
return expr;
}
switch (code)
{
CASE_CONVERT:
/* Casts are simple. */
ee = expand_simple_operations (e);
return fold_build1 (code, TREE_TYPE (expr), ee);
case PLUS_EXPR:
case MINUS_EXPR:
case POINTER_PLUS_EXPR:
/* And increments and decrements by a constant are simple. */
e1 = gimple_assign_rhs2 (stmt);
if (!is_gimple_min_invariant (e1))
return expr;
ee = expand_simple_operations (e);
return fold_build2 (code, TREE_TYPE (expr), ee, e1);
default:
return expr;
}
}
/* 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 = tree_simplify_using_condition_1 (cond, TREE_OPERAND (expr, 1));
if (TREE_OPERAND (expr, 1) != e1)
changed = true;
if (code == COND_EXPR)
{
e2 = tree_simplify_using_condition_1 (cond, 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;
}
/* 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;
gimple stmt;
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;
stmt = last_stmt (e->src);
cond = fold_build2 (gimple_cond_code (stmt),
boolean_type_node,
gimple_cond_lhs (stmt),
gimple_cond_rhs (stmt));
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. */
bool
loop_only_exit_p (const struct loop *loop, const_edge exit)
{
basic_block *body;
gimple_stmt_iterator bsi;
unsigned i;
gimple call;
if (exit != single_exit (loop))
return false;
body = get_loop_body (loop);
for (i = 0; i < loop->num_nodes; i++)
{
for (bsi = gsi_start_bb (body[i]); !gsi_end_p (bsi); gsi_next (&bsi))
{
call = gsi_stmt (bsi);
if (gimple_code (call) != GIMPLE_CALL)
continue;
if (gimple_has_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. 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,
bool warn)
{
gimple stmt;
tree type;
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 || gimple_code (stmt) != GIMPLE_COND)
return false;
/* We want the condition for staying inside loop. */
code = gimple_cond_code (stmt);
if (exit->flags & EDGE_TRUE_VALUE)
code = invert_tree_comparison (code, false);
switch (code)
{
case GT_EXPR:
case GE_EXPR:
case NE_EXPR:
case LT_EXPR:
case LE_EXPR:
break;
default:
return false;
}
op0 = gimple_cond_lhs (stmt);
op1 = gimple_cond_rhs (stmt);
type = TREE_TYPE (op0);
if (TREE_CODE (type) != INTEGER_TYPE
&& !POINTER_TYPE_P (type))
return false;
if (!simple_iv (loop, loop_containing_stmt (stmt), op0, &iv0, false))
return false;
if (!simple_iv (loop, loop_containing_stmt (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) || !single_exit (loop))
return false;
if (flag_unsafe_loop_optimizations)
niter->assumptions = boolean_true_node;
if (warn)
{
const char *wording;
location_t loc = gimple_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");
warning_at ((LOCATION_LINE (loc) > 0) ? loc : input_location,
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_EACH_VEC_ELT (edge, exits, i, ex)
{
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;
}
/* Return true if loop is known to have bounded number of iterations. */
bool
finite_loop_p (struct loop *loop)
{
unsigned i;
VEC (edge, heap) *exits;
edge ex;
struct tree_niter_desc desc;
bool finite = false;
int flags;
if (flag_unsafe_loop_optimizations)
return true;
flags = flags_from_decl_or_type (current_function_decl);
if ((flags & (ECF_CONST|ECF_PURE)) && !(flags & ECF_LOOPING_CONST_OR_PURE))
{
if (dump_file && (dump_flags & TDF_DETAILS))
fprintf (dump_file, "Found loop %i to be finite: it is within pure or const function.\n",
loop->num);
return true;
}
exits = get_loop_exit_edges (loop);
FOR_EACH_VEC_ELT (edge, exits, i, ex)
{
if (!just_once_each_iteration_p (loop, ex->src))
continue;
if (number_of_iterations_exit (loop, ex, &desc, false))
{
if (dump_file && (dump_flags & TDF_DETAILS))
{
fprintf (dump_file, "Found loop %i to be finite: iterating ", loop->num);
print_generic_expr (dump_file, desc.niter, TDF_SLIM);
fprintf (dump_file, " times\n");
}
finite = true;
break;
}
}
VEC_free (edge, heap, exits);
return finite;
}
/*
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 gimple
chain_of_csts_start (struct loop *loop, tree x)
{
gimple stmt = SSA_NAME_DEF_STMT (x);
tree use;
basic_block bb = gimple_bb (stmt);
enum tree_code code;
if (!bb
|| !flow_bb_inside_loop_p (loop, bb))
return NULL;
if (gimple_code (stmt) == GIMPLE_PHI)
{
if (bb == loop->header)
return stmt;
return NULL;
}
if (gimple_code (stmt) != GIMPLE_ASSIGN)
return NULL;
code = gimple_assign_rhs_code (stmt);
if (gimple_references_memory_p (stmt)
|| TREE_CODE_CLASS (code) == tcc_reference
|| (code == ADDR_EXPR
&& !is_gimple_min_invariant (gimple_assign_rhs1 (stmt))))
return NULL;
use = SINGLE_SSA_TREE_OPERAND (stmt, SSA_OP_USE);
if (use == NULL_TREE)
return NULL;
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, otherwise NULL is returned. */
static gimple
get_base_for (struct loop *loop, tree x)
{
gimple phi;
tree init, next;
if (is_gimple_min_invariant (x))
return NULL;
phi = chain_of_csts_start (loop, x);
if (!phi)
return NULL;
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;
if (!is_gimple_min_invariant (init))
return NULL;
if (chain_of_csts_start (loop, next) != phi)
return NULL;
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)
{
gimple stmt;
gcc_assert (is_gimple_min_invariant (base));
if (!x)
return base;
stmt = SSA_NAME_DEF_STMT (x);
if (gimple_code (stmt) == GIMPLE_PHI)
return base;
gcc_assert (is_gimple_assign (stmt));
/* STMT must be either an assignment of a single SSA name or an
expression involving an SSA name and a constant. Try to fold that
expression using the value for the SSA name. */
if (gimple_assign_ssa_name_copy_p (stmt))
return get_val_for (gimple_assign_rhs1 (stmt), base);
else if (gimple_assign_rhs_class (stmt) == GIMPLE_UNARY_RHS
&& TREE_CODE (gimple_assign_rhs1 (stmt)) == SSA_NAME)
{
return fold_build1 (gimple_assign_rhs_code (stmt),
gimple_expr_type (stmt),
get_val_for (gimple_assign_rhs1 (stmt), base));
}
else if (gimple_assign_rhs_class (stmt) == GIMPLE_BINARY_RHS)
{
tree rhs1 = gimple_assign_rhs1 (stmt);
tree rhs2 = gimple_assign_rhs2 (stmt);
if (TREE_CODE (rhs1) == SSA_NAME)
rhs1 = get_val_for (rhs1, base);
else if (TREE_CODE (rhs2) == SSA_NAME)
rhs2 = get_val_for (rhs2, base);
else
gcc_unreachable ();
return fold_build2 (gimple_assign_rhs_code (stmt),
gimple_expr_type (stmt), rhs1, rhs2);
}
else
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 acnd;
tree op[2], val[2], next[2], aval[2];
gimple phi, cond;
unsigned i, j;
enum tree_code cmp;
cond = last_stmt (exit->src);
if (!cond || gimple_code (cond) != GIMPLE_COND)
return chrec_dont_know;
cmp = gimple_cond_code (cond);
if (exit->flags & EDGE_TRUE_VALUE)
cmp = invert_tree_comparison (cmp, false);
switch (cmp)
{
case EQ_EXPR:
case NE_EXPR:
case GT_EXPR:
case GE_EXPR:
case LT_EXPR:
case LE_EXPR:
op[0] = gimple_cond_lhs (cond);
op[1] = gimple_cond_rhs (cond);
break;
default:
return chrec_dont_know;
}
for (j = 0; j < 2; j++)
{
if (is_gimple_min_invariant (op[j]))
{
val[j] = op[j];
next[j] = NULL_TREE;
op[j] = NULL_TREE;
}
else
{
phi = get_base_for (loop, op[j]);
if (!phi)
return chrec_dont_know;
val[j] = PHI_ARG_DEF_FROM_EDGE (phi, loop_preheader_edge (loop));
next[j] = PHI_ARG_DEF_FROM_EDGE (phi, loop_latch_edge (loop));
}
}
/* Don't issue signed overflow warnings. */
fold_defer_overflow_warnings ();
for (i = 0; i < MAX_ITERATIONS_TO_TRACK; i++)
{
for (j = 0; j < 2; j++)
aval[j] = get_val_for (op[j], val[j]);
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);
}
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;
}
}
}
fold_undefer_and_ignore_overflow_warnings ();
return chrec_dont_know;
}
/* 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_by_eval (struct loop *loop, edge *exit)
{
unsigned i;
VEC (edge, heap) *exits = get_loop_exit_edges (loop);
edge ex;
tree niter = NULL_TREE, aniter;
*exit = NULL;
/* Loops with multiple exits are expensive to handle and less important. */
if (!flag_expensive_optimizations
&& VEC_length (edge, exits) > 1)
return chrec_dont_know;
FOR_EACH_VEC_ELT (edge, exits, i, ex)
{
if (!just_once_each_iteration_p (loop, ex->src))
continue;
aniter = loop_niter_by_eval (loop, ex);
if (chrec_contains_undetermined (aniter))
continue;
if (niter
&& !tree_int_cst_lt (aniter, niter))
continue;
niter = aniter;
*exit = ex;
}
VEC_free (edge, heap, exits);
return niter ? niter : chrec_dont_know;
}
/*
Analysis of upper bounds on number of iterations of a loop.
*/
static double_int derive_constant_upper_bound_ops (tree, tree,
enum tree_code, tree);
/* Returns a constant upper bound on the value of the right-hand side of
an assignment statement STMT. */
static double_int
derive_constant_upper_bound_assign (gimple stmt)
{
enum tree_code code = gimple_assign_rhs_code (stmt);
tree op0 = gimple_assign_rhs1 (stmt);
tree op1 = gimple_assign_rhs2 (stmt);
return derive_constant_upper_bound_ops (TREE_TYPE (gimple_assign_lhs (stmt)),
op0, code, op1);
}
/* 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)
{
enum tree_code code;
tree op0, op1;
extract_ops_from_tree (val, &code, &op0, &op1);
return derive_constant_upper_bound_ops (TREE_TYPE (val), op0, code, op1);
}
/* Returns a constant upper bound on the value of expression OP0 CODE OP1,
whose type is TYPE. The expression is considered to be unsigned. If
its type is signed, its value must be nonnegative. */
static double_int
derive_constant_upper_bound_ops (tree type, tree op0,
enum tree_code code, tree op1)
{
tree subtype, maxt;
double_int bnd, max, mmax, cst;
gimple 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 (code)
{
case INTEGER_CST:
return tree_to_double_int (op0);
CASE_CONVERT:
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))
{
/* 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;
}
/* 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 POINTER_PLUS_EXPR:
case MINUS_EXPR:
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 (code != MINUS_EXPR)
cst = double_int_neg (cst);
bnd = derive_constant_upper_bound (op0);
if (double_int_negative_p (cst))
{
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_sub (max, cst);
if (double_int_ucmp (bnd, mmax) > 0)
return max;
return double_int_add (bnd, cst);
}
else
{
/* OP0 - CST, where CST >= 0.
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.
*/
/* 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;
}
bnd = double_int_sub (bnd, cst);
}
return bnd;
case FLOOR_DIV_EXPR:
case EXACT_DIV_EXPR:
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:
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 (op0);
if (gimple_code (stmt) != GIMPLE_ASSIGN
|| gimple_assign_lhs (stmt) != op0)
return max;
return derive_constant_upper_bound_assign (stmt);
default:
return max;
}
}
/* Records that every statement in LOOP is executed I_BOUND times.
REALISTIC is true if I_BOUND is expected to be close to the real number
of iterations. UPPER is true if we are sure the loop iterates at most
I_BOUND times. */
static void
record_niter_bound (struct loop *loop, double_int i_bound, bool realistic,
bool upper)
{
/* 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;
}
}
/* 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 to 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,
gimple at_stmt, bool is_exit, bool realistic, bool upper)
{
double_int delta;
edge exit;
if (dump_file && (dump_flags & TDF_DETAILS))
{
fprintf (dump_file, "Statement %s", is_exit ? "(exit)" : "");
print_gimple_stmt (dump_file, at_stmt, 0, 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);
}
/* 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 = ggc_alloc_nb_iter_bound ();
elt->bound = i_bound;
elt->stmt = at_stmt;
elt->is_exit = is_exit;
elt->next = loop->bounds;
loop->bounds = elt;
}
/* 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, gimple_bb (at_stmt))))
delta = double_int_one;
else
delta = double_int_two;
i_bound = double_int_add (i_bound, delta);
/* If an overflow occurred, ignore the result. */
if (double_int_ucmp (i_bound, delta) < 0)
return;
record_niter_bound (loop, i_bound, realistic, upper);
}
/* 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 void
record_nonwrapping_iv (struct loop *loop, tree base, tree step, gimple stmt,
tree low, tree high, bool realistic, bool upper)
{
tree niter_bound, extreme, delta;
tree type = TREE_TYPE (base), unsigned_type;
double_int max;
if (TREE_CODE (step) != INTEGER_CST || integer_zerop (step))
return;
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_gimple_stmt (dump_file, stmt, 0, TDF_SLIM);
fprintf (dump_file, " in loop %d.\n", loop->num);
}
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. */
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) && TREE_CODE (base) != MEM_REF))
return false;
for (;handled_component_p (ref); ref = parent)
{
parent = TREE_OPERAND (ref, 0);
if (TREE_CODE (ref) == COMPONENT_REF)
{
/* All fields of a union are at its end. */
if (TREE_CODE (TREE_TYPE (parent)) == UNION_TYPE)
continue;
/* Unless the field is at the end of the struct, we are done. */
field = TREE_OPERAND (ref, 1);
if (DECL_CHAIN (field))
return false;
}
/* 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 true;
}
/* Determine information about number of iterations a LOOP from the index
IDX of a data reference accessed in STMT. RELIABLE is true if STMT is
guaranteed to be executed in every iteration of LOOP. Callback for
for_each_index. */
struct ilb_data
{
struct loop *loop;
gimple stmt;
bool reliable;
};
static bool
idx_infer_loop_bounds (tree base, tree *idx, void *dta)
{
struct ilb_data *data = (struct ilb_data *) dta;
tree ev, init, step;
tree low, high, type, next;
bool sign, upper = data->reliable, at_end = false;
struct loop *loop = data->loop;
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))
{
at_end = true;
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);
/* The array of length 1 at the end of a structure most likely extends
beyond its bounds. */
if (at_end
&& 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);
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;
record_nonwrapping_iv (loop, init, step, data->stmt, low, high, true, upper);
return true;
}
/* Determine information about number of iterations a LOOP from the bounds
of arrays in the data reference REF accessed in STMT. RELIABLE is true if
STMT is guaranteed to be executed in every iteration of LOOP.*/
static void
infer_loop_bounds_from_ref (struct loop *loop, gimple stmt, tree ref,
bool reliable)
{
struct ilb_data data;
data.loop = loop;
data.stmt = stmt;
data.reliable = reliable;
for_each_index (&ref, idx_infer_loop_bounds, &data);
}
/* Determine information about number of iterations of a LOOP from the way
arrays are used in STMT. RELIABLE is true if STMT is guaranteed to be
executed in every iteration of LOOP. */
static void
infer_loop_bounds_from_array (struct loop *loop, gimple stmt, bool reliable)
{
if (is_gimple_assign (stmt))
{
tree op0 = gimple_assign_lhs (stmt);
tree op1 = gimple_assign_rhs1 (stmt);
/* 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, reliable);
if (REFERENCE_CLASS_P (op1))
infer_loop_bounds_from_ref (loop, stmt, op1, reliable);
}
else if (is_gimple_call (stmt))
{
tree arg, lhs;
unsigned i, n = gimple_call_num_args (stmt);
lhs = gimple_call_lhs (stmt);
if (lhs && REFERENCE_CLASS_P (lhs))
infer_loop_bounds_from_ref (loop, stmt, lhs, reliable);
for (i = 0; i < n; i++)
{
arg = gimple_call_arg (stmt, i);
if (REFERENCE_CLASS_P (arg))
infer_loop_bounds_from_ref (loop, stmt, arg, reliable);
}
}
}
/* Determine information about number of iterations of a LOOP from the fact
that signed arithmetics in STMT does not overflow. */
static void
infer_loop_bounds_from_signedness (struct loop *loop, gimple stmt)
{
tree def, base, step, scev, type, low, high;
if (gimple_code (stmt) != GIMPLE_ASSIGN)
return;
def = gimple_assign_lhs (stmt);
if (TREE_CODE (def) != SSA_NAME)
return;
type = TREE_TYPE (def);
if (!INTEGRAL_TYPE_P (type)
|| !TYPE_OVERFLOW_UNDEFINED (type))
return;
scev = instantiate_parameters (loop, analyze_scalar_evolution (loop, def));
if (chrec_contains_undetermined (scev))
return;
base = initial_condition_in_loop_num (scev, loop->num);
step = evolution_part_in_loop_num (scev, loop->num);
if (!base || !step
|| TREE_CODE (step) != INTEGER_CST
|| tree_contains_chrecs (base, NULL)
|| chrec_contains_symbols_defined_in_loop (base, loop->num))
return;
low = lower_bound_in_type (type, type);
high = upper_bound_in_type (type, type);
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:
- data references should not access elements over the statically
allocated size,
- signed variables should not overflow when flag_wrapv is not set.
*/
static void
infer_loop_bounds_from_undefined (struct loop *loop)
{
unsigned i;
basic_block *bbs;
gimple_stmt_iterator bsi;
basic_block bb;
bool reliable;
bbs = get_loop_body (loop);
for (i = 0; i < loop->num_nodes; i++)
{
bb = bbs[i];
/* If BB is not executed in each iteration of the loop, we cannot
use the operations in it to infer reliable upper bound on the
# of iterations of the loop. However, we can use it as a guess. */
reliable = dominated_by_p (CDI_DOMINATORS, loop->latch, bb);
for (bsi = gsi_start_bb (bb); !gsi_end_p (bsi); gsi_next (&bsi))
{
gimple stmt = gsi_stmt (bsi);
infer_loop_bounds_from_array (loop, stmt, reliable);
if (reliable)
infer_loop_bounds_from_signedness (loop, stmt);
}
}
free (bbs);
}
/* Converts VAL to double_int. */
static double_int
gcov_type_to_double_int (gcov_type val)
{
double_int ret;
ret.low = (unsigned HOST_WIDE_INT) val;
/* If HOST_BITS_PER_WIDE_INT == HOST_BITS_PER_WIDEST_INT, avoid shifting by
the size of type. */
val >>= HOST_BITS_PER_WIDE_INT - 1;
val >>= 1;
ret.high = (unsigned HOST_WIDE_INT) val;
return ret;
}
/* Records estimates on numbers of iterations of LOOP. If USE_UNDEFINED_P
is true also use estimates derived from undefined behavior. */
void
estimate_numbers_of_iterations_loop (struct loop *loop, bool use_undefined_p)
{
VEC (edge, heap) *exits;
tree niter, type;
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);
FOR_EACH_VEC_ELT (edge, exits, i, ex)
{
if (!number_of_iterations_exit (loop, ex, &niter_desc, false))
continue;
niter = niter_desc.niter;
type = TREE_TYPE (niter);
if (TREE_CODE (niter_desc.may_be_zero) != INTEGER_CST)
niter = build3 (COND_EXPR, type, niter_desc.may_be_zero,
build_int_cst (type, 0),
niter);
record_estimate (loop, niter, niter_desc.max,
last_stmt (ex->src),
true, true, true);
}
VEC_free (edge, heap, exits);
if (use_undefined_p)
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)
{
gcov_type nit = expected_loop_iterations_unbounded (loop) + 1;
bound = gcov_type_to_double_int (nit);
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. */
void
estimate_numbers_of_iterations (bool use_undefined_p)
{
loop_iterator li;
struct loop *loop;
/* We don't want to issue signed overflow warnings while getting
loop iteration estimates. */
fold_defer_overflow_warnings ();
FOR_EACH_LOOP (li, loop, 0)
{
estimate_numbers_of_iterations_loop (loop, use_undefined_p);
}
fold_undefer_and_ignore_overflow_warnings ();
}
/* Returns true if statement S1 dominates statement S2. */
bool
stmt_dominates_stmt_p (gimple s1, gimple s2)
{
basic_block bb1 = gimple_bb (s1), bb2 = gimple_bb (s2);
if (!bb1
|| s1 == s2)
return true;
if (bb1 == bb2)
{
gimple_stmt_iterator bsi;
if (gimple_code (s2) == GIMPLE_PHI)
return false;
if (gimple_code (s1) == GIMPLE_PHI)
return true;
for (bsi = gsi_start_bb (bb1); gsi_stmt (bsi) != s2; gsi_next (&bsi))
if (gsi_stmt (bsi) == s1)
return true;
return false;
}
return dominated_by_p (CDI_DOMINATORS, bb2, bb1);
}
/* 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 bool
n_of_executions_at_most (gimple stmt,
struct nb_iter_bound *niter_bound,
tree niter)
{
double_int bound = niter_bound->bound;
tree nit_type = TREE_TYPE (niter), e;
enum tree_code cmp;
gcc_assert (TYPE_UNSIGNED (nit_type));
/* 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;
/* 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)
{
if (stmt
&& stmt != niter_bound->stmt
&& stmt_dominates_stmt_p (niter_bound->stmt, stmt))
cmp = GE_EXPR;
else
cmp = GT_EXPR;
}
else
{
if (!stmt
|| (gimple_bb (stmt) != gimple_bb (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;
}
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;
if (POINTER_TYPE_P (type))
return true;
return false;
}
/* 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). */
bool
scev_probably_wraps_p (tree base, tree step,
gimple at_stmt, struct loop *loop,
bool use_overflow_semantics)
{
struct nb_iter_bound *bound;
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))
return true;
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 (TREE_TYPE (base)))
return false;
/* To be able to use estimates on number of iterations of the loop,
we must have an upper bound on the absolute value of the step. */
if (TREE_CODE (step) != INTEGER_CST)
return true;
/* 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
{
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);
estimate_numbers_of_iterations_loop (loop, true);
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;
}
}
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. */
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;
ggc_free (bound);
}
loop->bounds = NULL;
}
/* Frees the information on upper bounds on numbers of iterations of loops. */
void
free_numbers_of_iterations_estimates (void)
{
loop_iterator li;
struct loop *loop;
FOR_EACH_LOOP (li, loop, 0)
{
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);
}