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tree-ssa-loop-niter.c
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tree-ssa-loop-niter.c
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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 "toplev.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);
if (negate)
off = double_int_neg (off);
off = double_int_sext (off, TYPE_PRECISION (type));
mpz_set_double_int (offset, off, false);
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, assuming that this exit is taken. 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. */
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;
/* 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);
}
/* 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);
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;