1 /* Chains of recurrences.
2 Copyright (C) 2003, 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
3 Contributed by Sebastian Pop <pop@cri.ensmp.fr>
5 This file is part of GCC.
7 GCC is free software; you can redistribute it and/or modify it under
8 the terms of the GNU General Public License as published by the Free
9 Software Foundation; either version 3, or (at your option) any later
12 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
13 WARRANTY; without even the implied warranty of MERCHANTABILITY or
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
17 You should have received a copy of the GNU General Public License
18 along with GCC; see the file COPYING3. If not see
19 <http://www.gnu.org/licenses/>. */
21 /* This file implements operations on chains of recurrences. Chains
22 of recurrences are used for modeling evolution functions of scalar
28 #include "coretypes.h"
33 #include "diagnostic.h"
35 #include "tree-flow.h"
36 #include "tree-chrec.h"
37 #include "tree-pass.h"
39 #include "tree-scalar-evolution.h"
43 /* Extended folder for chrecs. */
45 /* Determines whether CST is not a constant evolution. */
48 is_not_constant_evolution (tree cst
)
50 return (TREE_CODE (cst
) == POLYNOMIAL_CHREC
);
53 /* Fold CODE for a polynomial function and a constant. */
56 chrec_fold_poly_cst (enum tree_code code
,
63 gcc_assert (TREE_CODE (poly
) == POLYNOMIAL_CHREC
);
64 gcc_assert (!is_not_constant_evolution (cst
));
65 gcc_assert (type
== chrec_type (poly
));
70 return build_polynomial_chrec
71 (CHREC_VARIABLE (poly
),
72 chrec_fold_plus (type
, CHREC_LEFT (poly
), cst
),
76 return build_polynomial_chrec
77 (CHREC_VARIABLE (poly
),
78 chrec_fold_minus (type
, CHREC_LEFT (poly
), cst
),
82 return build_polynomial_chrec
83 (CHREC_VARIABLE (poly
),
84 chrec_fold_multiply (type
, CHREC_LEFT (poly
), cst
),
85 chrec_fold_multiply (type
, CHREC_RIGHT (poly
), cst
));
88 return chrec_dont_know
;
92 /* Fold the addition of two polynomial functions. */
95 chrec_fold_plus_poly_poly (enum tree_code code
,
101 struct loop
*loop0
= get_chrec_loop (poly0
);
102 struct loop
*loop1
= get_chrec_loop (poly1
);
103 tree rtype
= code
== POINTER_PLUS_EXPR
? sizetype
: type
;
107 gcc_assert (TREE_CODE (poly0
) == POLYNOMIAL_CHREC
);
108 gcc_assert (TREE_CODE (poly1
) == POLYNOMIAL_CHREC
);
109 if (POINTER_TYPE_P (chrec_type (poly0
)))
110 gcc_assert (chrec_type (poly1
) == sizetype
);
112 gcc_assert (chrec_type (poly0
) == chrec_type (poly1
));
113 gcc_assert (type
== chrec_type (poly0
));
116 {a, +, b}_1 + {c, +, d}_2 -> {{a, +, b}_1 + c, +, d}_2,
117 {a, +, b}_2 + {c, +, d}_1 -> {{c, +, d}_1 + a, +, b}_2,
118 {a, +, b}_x + {c, +, d}_x -> {a+c, +, b+d}_x. */
119 if (flow_loop_nested_p (loop0
, loop1
))
121 if (code
== PLUS_EXPR
|| code
== POINTER_PLUS_EXPR
)
122 return build_polynomial_chrec
123 (CHREC_VARIABLE (poly1
),
124 chrec_fold_plus (type
, poly0
, CHREC_LEFT (poly1
)),
125 CHREC_RIGHT (poly1
));
127 return build_polynomial_chrec
128 (CHREC_VARIABLE (poly1
),
129 chrec_fold_minus (type
, poly0
, CHREC_LEFT (poly1
)),
130 chrec_fold_multiply (type
, CHREC_RIGHT (poly1
),
131 SCALAR_FLOAT_TYPE_P (type
)
132 ? build_real (type
, dconstm1
)
133 : build_int_cst_type (type
, -1)));
136 if (flow_loop_nested_p (loop1
, loop0
))
138 if (code
== PLUS_EXPR
|| code
== POINTER_PLUS_EXPR
)
139 return build_polynomial_chrec
140 (CHREC_VARIABLE (poly0
),
141 chrec_fold_plus (type
, CHREC_LEFT (poly0
), poly1
),
142 CHREC_RIGHT (poly0
));
144 return build_polynomial_chrec
145 (CHREC_VARIABLE (poly0
),
146 chrec_fold_minus (type
, CHREC_LEFT (poly0
), poly1
),
147 CHREC_RIGHT (poly0
));
150 /* This function should never be called for chrecs of loops that
151 do not belong to the same loop nest. */
152 gcc_assert (loop0
== loop1
);
154 if (code
== PLUS_EXPR
|| code
== POINTER_PLUS_EXPR
)
156 left
= chrec_fold_plus
157 (type
, CHREC_LEFT (poly0
), CHREC_LEFT (poly1
));
158 right
= chrec_fold_plus
159 (rtype
, CHREC_RIGHT (poly0
), CHREC_RIGHT (poly1
));
163 left
= chrec_fold_minus
164 (type
, CHREC_LEFT (poly0
), CHREC_LEFT (poly1
));
165 right
= chrec_fold_minus
166 (type
, CHREC_RIGHT (poly0
), CHREC_RIGHT (poly1
));
169 if (chrec_zerop (right
))
172 return build_polynomial_chrec
173 (CHREC_VARIABLE (poly0
), left
, right
);
178 /* Fold the multiplication of two polynomial functions. */
181 chrec_fold_multiply_poly_poly (tree type
,
187 struct loop
*loop0
= get_chrec_loop (poly0
);
188 struct loop
*loop1
= get_chrec_loop (poly1
);
192 gcc_assert (TREE_CODE (poly0
) == POLYNOMIAL_CHREC
);
193 gcc_assert (TREE_CODE (poly1
) == POLYNOMIAL_CHREC
);
194 gcc_assert (chrec_type (poly0
) == chrec_type (poly1
));
195 gcc_assert (type
== chrec_type (poly0
));
197 /* {a, +, b}_1 * {c, +, d}_2 -> {c*{a, +, b}_1, +, d}_2,
198 {a, +, b}_2 * {c, +, d}_1 -> {a*{c, +, d}_1, +, b}_2,
199 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */
200 if (flow_loop_nested_p (loop0
, loop1
))
201 /* poly0 is a constant wrt. poly1. */
202 return build_polynomial_chrec
203 (CHREC_VARIABLE (poly1
),
204 chrec_fold_multiply (type
, CHREC_LEFT (poly1
), poly0
),
205 CHREC_RIGHT (poly1
));
207 if (flow_loop_nested_p (loop1
, loop0
))
208 /* poly1 is a constant wrt. poly0. */
209 return build_polynomial_chrec
210 (CHREC_VARIABLE (poly0
),
211 chrec_fold_multiply (type
, CHREC_LEFT (poly0
), poly1
),
212 CHREC_RIGHT (poly0
));
214 gcc_assert (loop0
== loop1
);
216 /* poly0 and poly1 are two polynomials in the same variable,
217 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */
220 t0
= chrec_fold_multiply (type
, CHREC_LEFT (poly0
), CHREC_LEFT (poly1
));
222 /* "a*d + b*c + b*d". */
223 t1
= chrec_fold_multiply (type
, CHREC_LEFT (poly0
), CHREC_RIGHT (poly1
));
224 t1
= chrec_fold_plus (type
, t1
, chrec_fold_multiply (type
,
226 CHREC_LEFT (poly1
)));
227 t1
= chrec_fold_plus (type
, t1
, chrec_fold_multiply (type
,
229 CHREC_RIGHT (poly1
)));
231 t2
= chrec_fold_multiply (type
, CHREC_RIGHT (poly0
), CHREC_RIGHT (poly1
));
232 t2
= chrec_fold_multiply (type
, SCALAR_FLOAT_TYPE_P (type
)
233 ? build_real (type
, dconst2
)
234 : build_int_cst (type
, 2), t2
);
236 var
= CHREC_VARIABLE (poly0
);
237 return build_polynomial_chrec (var
, t0
,
238 build_polynomial_chrec (var
, t1
, t2
));
241 /* When the operands are automatically_generated_chrec_p, the fold has
242 to respect the semantics of the operands. */
245 chrec_fold_automatically_generated_operands (tree op0
,
248 if (op0
== chrec_dont_know
249 || op1
== chrec_dont_know
)
250 return chrec_dont_know
;
252 if (op0
== chrec_known
253 || op1
== chrec_known
)
256 if (op0
== chrec_not_analyzed_yet
257 || op1
== chrec_not_analyzed_yet
)
258 return chrec_not_analyzed_yet
;
260 /* The default case produces a safe result. */
261 return chrec_dont_know
;
264 /* Fold the addition of two chrecs. */
267 chrec_fold_plus_1 (enum tree_code code
, tree type
,
270 tree op1_type
= code
== POINTER_PLUS_EXPR
? sizetype
: type
;
272 if (automatically_generated_chrec_p (op0
)
273 || automatically_generated_chrec_p (op1
))
274 return chrec_fold_automatically_generated_operands (op0
, op1
);
276 switch (TREE_CODE (op0
))
278 case POLYNOMIAL_CHREC
:
279 switch (TREE_CODE (op1
))
281 case POLYNOMIAL_CHREC
:
282 return chrec_fold_plus_poly_poly (code
, type
, op0
, op1
);
285 if (code
== PLUS_EXPR
|| code
== POINTER_PLUS_EXPR
)
286 return build_polynomial_chrec
287 (CHREC_VARIABLE (op0
),
288 chrec_fold_plus (type
, CHREC_LEFT (op0
), op1
),
291 return build_polynomial_chrec
292 (CHREC_VARIABLE (op0
),
293 chrec_fold_minus (type
, CHREC_LEFT (op0
), op1
),
298 switch (TREE_CODE (op1
))
300 case POLYNOMIAL_CHREC
:
301 if (code
== PLUS_EXPR
|| code
== POINTER_PLUS_EXPR
)
302 return build_polynomial_chrec
303 (CHREC_VARIABLE (op1
),
304 chrec_fold_plus (type
, op0
, CHREC_LEFT (op1
)),
307 return build_polynomial_chrec
308 (CHREC_VARIABLE (op1
),
309 chrec_fold_minus (type
, op0
, CHREC_LEFT (op1
)),
310 chrec_fold_multiply (type
, CHREC_RIGHT (op1
),
311 SCALAR_FLOAT_TYPE_P (type
)
312 ? build_real (type
, dconstm1
)
313 : build_int_cst_type (type
, -1)));
318 if ((tree_contains_chrecs (op0
, &size
)
319 || tree_contains_chrecs (op1
, &size
))
320 && size
< PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE
))
321 return build2 (code
, type
, op0
, op1
);
322 else if (size
< PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE
))
323 return fold_build2 (code
, type
,
324 fold_convert (type
, op0
),
325 fold_convert (op1_type
, op1
));
327 return chrec_dont_know
;
333 /* Fold the addition of two chrecs. */
336 chrec_fold_plus (tree type
,
341 if (automatically_generated_chrec_p (op0
)
342 || automatically_generated_chrec_p (op1
))
343 return chrec_fold_automatically_generated_operands (op0
, op1
);
345 if (integer_zerop (op0
))
346 return chrec_convert (type
, op1
, NULL_TREE
);
347 if (integer_zerop (op1
))
348 return chrec_convert (type
, op0
, NULL_TREE
);
350 if (POINTER_TYPE_P (type
))
351 code
= POINTER_PLUS_EXPR
;
355 return chrec_fold_plus_1 (code
, type
, op0
, op1
);
358 /* Fold the subtraction of two chrecs. */
361 chrec_fold_minus (tree type
,
365 if (automatically_generated_chrec_p (op0
)
366 || automatically_generated_chrec_p (op1
))
367 return chrec_fold_automatically_generated_operands (op0
, op1
);
369 if (integer_zerop (op1
))
372 return chrec_fold_plus_1 (MINUS_EXPR
, type
, op0
, op1
);
375 /* Fold the multiplication of two chrecs. */
378 chrec_fold_multiply (tree type
,
382 if (automatically_generated_chrec_p (op0
)
383 || automatically_generated_chrec_p (op1
))
384 return chrec_fold_automatically_generated_operands (op0
, op1
);
386 switch (TREE_CODE (op0
))
388 case POLYNOMIAL_CHREC
:
389 switch (TREE_CODE (op1
))
391 case POLYNOMIAL_CHREC
:
392 return chrec_fold_multiply_poly_poly (type
, op0
, op1
);
395 if (integer_onep (op1
))
397 if (integer_zerop (op1
))
398 return build_int_cst (type
, 0);
400 return build_polynomial_chrec
401 (CHREC_VARIABLE (op0
),
402 chrec_fold_multiply (type
, CHREC_LEFT (op0
), op1
),
403 chrec_fold_multiply (type
, CHREC_RIGHT (op0
), op1
));
407 if (integer_onep (op0
))
410 if (integer_zerop (op0
))
411 return build_int_cst (type
, 0);
413 switch (TREE_CODE (op1
))
415 case POLYNOMIAL_CHREC
:
416 return build_polynomial_chrec
417 (CHREC_VARIABLE (op1
),
418 chrec_fold_multiply (type
, CHREC_LEFT (op1
), op0
),
419 chrec_fold_multiply (type
, CHREC_RIGHT (op1
), op0
));
422 if (integer_onep (op1
))
424 if (integer_zerop (op1
))
425 return build_int_cst (type
, 0);
426 return fold_build2 (MULT_EXPR
, type
, op0
, op1
);
435 /* Evaluate the binomial coefficient. Return NULL_TREE if the intermediate
436 calculation overflows, otherwise return C(n,k) with type TYPE. */
439 tree_fold_binomial (tree type
, tree n
, unsigned int k
)
441 unsigned HOST_WIDE_INT lidx
, lnum
, ldenom
, lres
, ldum
;
442 HOST_WIDE_INT hidx
, hnum
, hdenom
, hres
, hdum
;
446 /* Handle the most frequent cases. */
448 return build_int_cst (type
, 1);
450 return fold_convert (type
, n
);
452 /* Check that k <= n. */
453 if (TREE_INT_CST_HIGH (n
) == 0
454 && TREE_INT_CST_LOW (n
) < k
)
458 lnum
= TREE_INT_CST_LOW (n
);
459 hnum
= TREE_INT_CST_HIGH (n
);
461 /* Denominator = 2. */
465 /* Index = Numerator-1. */
469 lidx
= ~ (unsigned HOST_WIDE_INT
) 0;
477 /* Numerator = Numerator*Index = n*(n-1). */
478 if (mul_double (lnum
, hnum
, lidx
, hidx
, &lnum
, &hnum
))
481 for (i
= 3; i
<= k
; i
++)
487 lidx
= ~ (unsigned HOST_WIDE_INT
) 0;
492 /* Numerator *= Index. */
493 if (mul_double (lnum
, hnum
, lidx
, hidx
, &lnum
, &hnum
))
496 /* Denominator *= i. */
497 mul_double (ldenom
, hdenom
, i
, 0, &ldenom
, &hdenom
);
500 /* Result = Numerator / Denominator. */
501 div_and_round_double (EXACT_DIV_EXPR
, 1, lnum
, hnum
, ldenom
, hdenom
,
502 &lres
, &hres
, &ldum
, &hdum
);
504 res
= build_int_cst_wide (type
, lres
, hres
);
505 return int_fits_type_p (res
, type
) ? res
: NULL_TREE
;
508 /* Helper function. Use the Newton's interpolating formula for
509 evaluating the value of the evolution function. */
512 chrec_evaluate (unsigned var
, tree chrec
, tree n
, unsigned int k
)
514 tree arg0
, arg1
, binomial_n_k
;
515 tree type
= TREE_TYPE (chrec
);
516 struct loop
*var_loop
= get_loop (var
);
518 while (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
519 && flow_loop_nested_p (var_loop
, get_chrec_loop (chrec
)))
520 chrec
= CHREC_LEFT (chrec
);
522 if (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
523 && CHREC_VARIABLE (chrec
) == var
)
525 arg0
= chrec_evaluate (var
, CHREC_RIGHT (chrec
), n
, k
+ 1);
526 if (arg0
== chrec_dont_know
)
527 return chrec_dont_know
;
528 binomial_n_k
= tree_fold_binomial (type
, n
, k
);
530 return chrec_dont_know
;
531 arg1
= fold_build2 (MULT_EXPR
, type
,
532 CHREC_LEFT (chrec
), binomial_n_k
);
533 return chrec_fold_plus (type
, arg0
, arg1
);
536 binomial_n_k
= tree_fold_binomial (type
, n
, k
);
538 return chrec_dont_know
;
540 return fold_build2 (MULT_EXPR
, type
, chrec
, binomial_n_k
);
543 /* Evaluates "CHREC (X)" when the varying variable is VAR.
544 Example: Given the following parameters,
550 The result is given by the Newton's interpolating formula:
551 3 * \binom{10}{0} + 4 * \binom{10}{1}.
555 chrec_apply (unsigned var
,
559 tree type
= chrec_type (chrec
);
560 tree res
= chrec_dont_know
;
562 if (automatically_generated_chrec_p (chrec
)
563 || automatically_generated_chrec_p (x
)
565 /* When the symbols are defined in an outer loop, it is possible
566 to symbolically compute the apply, since the symbols are
567 constants with respect to the varying loop. */
568 || chrec_contains_symbols_defined_in_loop (chrec
, var
))
569 return chrec_dont_know
;
571 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
572 fprintf (dump_file
, "(chrec_apply \n");
574 if (TREE_CODE (x
) == INTEGER_CST
&& SCALAR_FLOAT_TYPE_P (type
))
575 x
= build_real_from_int_cst (type
, x
);
577 if (evolution_function_is_affine_p (chrec
))
579 /* "{a, +, b} (x)" -> "a + b*x". */
580 x
= chrec_convert_rhs (type
, x
, NULL_TREE
);
581 res
= chrec_fold_multiply (TREE_TYPE (x
), CHREC_RIGHT (chrec
), x
);
582 if (!integer_zerop (CHREC_LEFT (chrec
)))
583 res
= chrec_fold_plus (type
, CHREC_LEFT (chrec
), res
);
586 else if (TREE_CODE (chrec
) != POLYNOMIAL_CHREC
)
589 else if (TREE_CODE (x
) == INTEGER_CST
590 && tree_int_cst_sgn (x
) == 1)
591 /* testsuite/.../ssa-chrec-38.c. */
592 res
= chrec_evaluate (var
, chrec
, x
, 0);
594 res
= chrec_dont_know
;
596 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
598 fprintf (dump_file
, " (varying_loop = %d\n", var
);
599 fprintf (dump_file
, ")\n (chrec = ");
600 print_generic_expr (dump_file
, chrec
, 0);
601 fprintf (dump_file
, ")\n (x = ");
602 print_generic_expr (dump_file
, x
, 0);
603 fprintf (dump_file
, ")\n (res = ");
604 print_generic_expr (dump_file
, res
, 0);
605 fprintf (dump_file
, "))\n");
611 /* Replaces the initial condition in CHREC with INIT_COND. */
614 chrec_replace_initial_condition (tree chrec
,
617 if (automatically_generated_chrec_p (chrec
))
620 gcc_assert (chrec_type (chrec
) == chrec_type (init_cond
));
622 switch (TREE_CODE (chrec
))
624 case POLYNOMIAL_CHREC
:
625 return build_polynomial_chrec
626 (CHREC_VARIABLE (chrec
),
627 chrec_replace_initial_condition (CHREC_LEFT (chrec
), init_cond
),
628 CHREC_RIGHT (chrec
));
635 /* Returns the initial condition of a given CHREC. */
638 initial_condition (tree chrec
)
640 if (automatically_generated_chrec_p (chrec
))
643 if (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
)
644 return initial_condition (CHREC_LEFT (chrec
));
649 /* Returns a univariate function that represents the evolution in
650 LOOP_NUM. Mask the evolution of any other loop. */
653 hide_evolution_in_other_loops_than_loop (tree chrec
,
656 struct loop
*loop
= get_loop (loop_num
), *chloop
;
657 if (automatically_generated_chrec_p (chrec
))
660 switch (TREE_CODE (chrec
))
662 case POLYNOMIAL_CHREC
:
663 chloop
= get_chrec_loop (chrec
);
666 return build_polynomial_chrec
668 hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec
),
670 CHREC_RIGHT (chrec
));
672 else if (flow_loop_nested_p (chloop
, loop
))
673 /* There is no evolution in this loop. */
674 return initial_condition (chrec
);
678 gcc_assert (flow_loop_nested_p (loop
, chloop
));
679 return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec
),
688 /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is
689 true, otherwise returns the initial condition in LOOP_NUM. */
692 chrec_component_in_loop_num (tree chrec
,
697 struct loop
*loop
= get_loop (loop_num
), *chloop
;
699 if (automatically_generated_chrec_p (chrec
))
702 switch (TREE_CODE (chrec
))
704 case POLYNOMIAL_CHREC
:
705 chloop
= get_chrec_loop (chrec
);
710 component
= CHREC_RIGHT (chrec
);
712 component
= CHREC_LEFT (chrec
);
714 if (TREE_CODE (CHREC_LEFT (chrec
)) != POLYNOMIAL_CHREC
715 || CHREC_VARIABLE (CHREC_LEFT (chrec
)) != CHREC_VARIABLE (chrec
))
719 return build_polynomial_chrec
721 chrec_component_in_loop_num (CHREC_LEFT (chrec
),
727 else if (flow_loop_nested_p (chloop
, loop
))
728 /* There is no evolution part in this loop. */
733 gcc_assert (flow_loop_nested_p (loop
, chloop
));
734 return chrec_component_in_loop_num (CHREC_LEFT (chrec
),
747 /* Returns the evolution part in LOOP_NUM. Example: the call
748 evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns
752 evolution_part_in_loop_num (tree chrec
,
755 return chrec_component_in_loop_num (chrec
, loop_num
, true);
758 /* Returns the initial condition in LOOP_NUM. Example: the call
759 initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns
763 initial_condition_in_loop_num (tree chrec
,
766 return chrec_component_in_loop_num (chrec
, loop_num
, false);
769 /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM.
770 This function is essentially used for setting the evolution to
771 chrec_dont_know, for example after having determined that it is
772 impossible to say how many times a loop will execute. */
775 reset_evolution_in_loop (unsigned loop_num
,
779 struct loop
*loop
= get_loop (loop_num
);
781 if (POINTER_TYPE_P (chrec_type (chrec
)))
782 gcc_assert (sizetype
== chrec_type (new_evol
));
784 gcc_assert (chrec_type (chrec
) == chrec_type (new_evol
));
786 if (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
787 && flow_loop_nested_p (loop
, get_chrec_loop (chrec
)))
789 tree left
= reset_evolution_in_loop (loop_num
, CHREC_LEFT (chrec
),
791 tree right
= reset_evolution_in_loop (loop_num
, CHREC_RIGHT (chrec
),
793 return build3 (POLYNOMIAL_CHREC
, TREE_TYPE (left
),
794 build_int_cst (NULL_TREE
, CHREC_VARIABLE (chrec
)),
798 while (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
799 && CHREC_VARIABLE (chrec
) == loop_num
)
800 chrec
= CHREC_LEFT (chrec
);
802 return build_polynomial_chrec (loop_num
, chrec
, new_evol
);
805 /* Merges two evolution functions that were found by following two
806 alternate paths of a conditional expression. */
809 chrec_merge (tree chrec1
,
812 if (chrec1
== chrec_dont_know
813 || chrec2
== chrec_dont_know
)
814 return chrec_dont_know
;
816 if (chrec1
== chrec_known
817 || chrec2
== chrec_known
)
820 if (chrec1
== chrec_not_analyzed_yet
)
822 if (chrec2
== chrec_not_analyzed_yet
)
825 if (eq_evolutions_p (chrec1
, chrec2
))
828 return chrec_dont_know
;
835 /* Helper function for is_multivariate_chrec. */
838 is_multivariate_chrec_rec (tree chrec
, unsigned int rec_var
)
840 if (chrec
== NULL_TREE
)
843 if (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
)
845 if (CHREC_VARIABLE (chrec
) != rec_var
)
848 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec
), rec_var
)
849 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec
), rec_var
));
855 /* Determine whether the given chrec is multivariate or not. */
858 is_multivariate_chrec (tree chrec
)
860 if (chrec
== NULL_TREE
)
863 if (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
)
864 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec
),
865 CHREC_VARIABLE (chrec
))
866 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec
),
867 CHREC_VARIABLE (chrec
)));
872 /* Determines whether the chrec contains symbolic names or not. */
875 chrec_contains_symbols (tree chrec
)
879 if (chrec
== NULL_TREE
)
882 if (TREE_CODE (chrec
) == SSA_NAME
883 || TREE_CODE (chrec
) == VAR_DECL
884 || TREE_CODE (chrec
) == PARM_DECL
885 || TREE_CODE (chrec
) == FUNCTION_DECL
886 || TREE_CODE (chrec
) == LABEL_DECL
887 || TREE_CODE (chrec
) == RESULT_DECL
888 || TREE_CODE (chrec
) == FIELD_DECL
)
891 n
= TREE_OPERAND_LENGTH (chrec
);
892 for (i
= 0; i
< n
; i
++)
893 if (chrec_contains_symbols (TREE_OPERAND (chrec
, i
)))
898 /* Determines whether the chrec contains undetermined coefficients. */
901 chrec_contains_undetermined (tree chrec
)
905 if (chrec
== chrec_dont_know
)
908 if (chrec
== NULL_TREE
)
911 n
= TREE_OPERAND_LENGTH (chrec
);
912 for (i
= 0; i
< n
; i
++)
913 if (chrec_contains_undetermined (TREE_OPERAND (chrec
, i
)))
918 /* Determines whether the tree EXPR contains chrecs, and increment
919 SIZE if it is not a NULL pointer by an estimation of the depth of
923 tree_contains_chrecs (tree expr
, int *size
)
927 if (expr
== NULL_TREE
)
933 if (tree_is_chrec (expr
))
936 n
= TREE_OPERAND_LENGTH (expr
);
937 for (i
= 0; i
< n
; i
++)
938 if (tree_contains_chrecs (TREE_OPERAND (expr
, i
), size
))
943 /* Recursive helper function. */
946 evolution_function_is_invariant_rec_p (tree chrec
, int loopnum
)
948 if (evolution_function_is_constant_p (chrec
))
951 if (TREE_CODE (chrec
) == SSA_NAME
952 && expr_invariant_in_loop_p (get_loop (loopnum
), chrec
))
955 if (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
)
957 if (CHREC_VARIABLE (chrec
) == (unsigned) loopnum
958 || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec
),
960 || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec
),
966 switch (TREE_OPERAND_LENGTH (chrec
))
969 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec
, 1),
974 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec
, 0),
986 /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */
989 evolution_function_is_invariant_p (tree chrec
, int loopnum
)
991 return evolution_function_is_invariant_rec_p (chrec
, loopnum
);
994 /* Determine whether the given tree is an affine multivariate
998 evolution_function_is_affine_multivariate_p (tree chrec
, int loopnum
)
1000 if (chrec
== NULL_TREE
)
1003 switch (TREE_CODE (chrec
))
1005 case POLYNOMIAL_CHREC
:
1006 if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec
), loopnum
))
1008 if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec
), loopnum
))
1012 if (TREE_CODE (CHREC_RIGHT (chrec
)) == POLYNOMIAL_CHREC
1013 && CHREC_VARIABLE (CHREC_RIGHT (chrec
))
1014 != CHREC_VARIABLE (chrec
)
1015 && evolution_function_is_affine_multivariate_p
1016 (CHREC_RIGHT (chrec
), loopnum
))
1024 if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec
), loopnum
)
1025 && TREE_CODE (CHREC_LEFT (chrec
)) == POLYNOMIAL_CHREC
1026 && CHREC_VARIABLE (CHREC_LEFT (chrec
)) != CHREC_VARIABLE (chrec
)
1027 && evolution_function_is_affine_multivariate_p
1028 (CHREC_LEFT (chrec
), loopnum
))
1039 /* Determine whether the given tree is a function in zero or one
1043 evolution_function_is_univariate_p (tree chrec
)
1045 if (chrec
== NULL_TREE
)
1048 switch (TREE_CODE (chrec
))
1050 case POLYNOMIAL_CHREC
:
1051 switch (TREE_CODE (CHREC_LEFT (chrec
)))
1053 case POLYNOMIAL_CHREC
:
1054 if (CHREC_VARIABLE (chrec
) != CHREC_VARIABLE (CHREC_LEFT (chrec
)))
1056 if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec
)))
1064 switch (TREE_CODE (CHREC_RIGHT (chrec
)))
1066 case POLYNOMIAL_CHREC
:
1067 if (CHREC_VARIABLE (chrec
) != CHREC_VARIABLE (CHREC_RIGHT (chrec
)))
1069 if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec
)))
1082 /* Returns the number of variables of CHREC. Example: the call
1083 nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2. */
1086 nb_vars_in_chrec (tree chrec
)
1088 if (chrec
== NULL_TREE
)
1091 switch (TREE_CODE (chrec
))
1093 case POLYNOMIAL_CHREC
:
1094 return 1 + nb_vars_in_chrec
1095 (initial_condition_in_loop_num (chrec
, CHREC_VARIABLE (chrec
)));
1102 /* Returns true if TYPE is a type in that we cannot directly perform
1103 arithmetics, even though it is a scalar type. */
1106 avoid_arithmetics_in_type_p (tree type
)
1108 /* Ada frontend uses subtypes -- an arithmetic cannot be directly performed
1109 in the subtype, but a base type must be used, and the result then can
1110 be casted to the subtype. */
1111 if (TREE_CODE (type
) == INTEGER_TYPE
&& TREE_TYPE (type
) != NULL_TREE
)
1117 static tree
chrec_convert_1 (tree
, tree
, tree
, bool);
1119 /* Converts BASE and STEP of affine scev to TYPE. LOOP is the loop whose iv
1120 the scev corresponds to. AT_STMT is the statement at that the scev is
1121 evaluated. USE_OVERFLOW_SEMANTICS is true if this function should assume that
1122 the rules for overflow of the given language apply (e.g., that signed
1123 arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1124 tests, but also to enforce that the result follows them. Returns true if the
1125 conversion succeeded, false otherwise. */
1128 convert_affine_scev (struct loop
*loop
, tree type
,
1129 tree
*base
, tree
*step
, tree at_stmt
,
1130 bool use_overflow_semantics
)
1132 tree ct
= TREE_TYPE (*step
);
1133 bool enforce_overflow_semantics
;
1134 bool must_check_src_overflow
, must_check_rslt_overflow
;
1135 tree new_base
, new_step
;
1136 tree step_type
= POINTER_TYPE_P (type
) ? sizetype
: type
;
1138 /* If we cannot perform arithmetic in TYPE, avoid creating an scev. */
1139 if (avoid_arithmetics_in_type_p (type
))
1143 (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i,
1144 but we must check some assumptions.
1146 1) If [BASE, +, STEP] wraps, the equation is not valid when precision
1147 of CT is smaller than the precision of TYPE. For example, when we
1148 cast unsigned char [254, +, 1] to unsigned, the values on left side
1149 are 254, 255, 0, 1, ..., but those on the right side are
1150 254, 255, 256, 257, ...
1151 2) In case that we must also preserve the fact that signed ivs do not
1152 overflow, we must additionally check that the new iv does not wrap.
1153 For example, unsigned char [125, +, 1] casted to signed char could
1154 become a wrapping variable with values 125, 126, 127, -128, -127, ...,
1155 which would confuse optimizers that assume that this does not
1157 must_check_src_overflow
= TYPE_PRECISION (ct
) < TYPE_PRECISION (type
);
1159 enforce_overflow_semantics
= (use_overflow_semantics
1160 && nowrap_type_p (type
));
1161 if (enforce_overflow_semantics
)
1163 /* We can avoid checking whether the result overflows in the following
1166 -- must_check_src_overflow is true, and the range of TYPE is superset
1167 of the range of CT -- i.e., in all cases except if CT signed and
1169 -- both CT and TYPE have the same precision and signedness, and we
1170 verify instead that the source does not overflow (this may be
1171 easier than verifying it for the result, as we may use the
1172 information about the semantics of overflow in CT). */
1173 if (must_check_src_overflow
)
1175 if (TYPE_UNSIGNED (type
) && !TYPE_UNSIGNED (ct
))
1176 must_check_rslt_overflow
= true;
1178 must_check_rslt_overflow
= false;
1180 else if (TYPE_UNSIGNED (ct
) == TYPE_UNSIGNED (type
)
1181 && TYPE_PRECISION (ct
) == TYPE_PRECISION (type
))
1183 must_check_rslt_overflow
= false;
1184 must_check_src_overflow
= true;
1187 must_check_rslt_overflow
= true;
1190 must_check_rslt_overflow
= false;
1192 if (must_check_src_overflow
1193 && scev_probably_wraps_p (*base
, *step
, at_stmt
, loop
,
1194 use_overflow_semantics
))
1197 new_base
= chrec_convert_1 (type
, *base
, at_stmt
,
1198 use_overflow_semantics
);
1199 /* The step must be sign extended, regardless of the signedness
1200 of CT and TYPE. This only needs to be handled specially when
1201 CT is unsigned -- to avoid e.g. unsigned char [100, +, 255]
1202 (with values 100, 99, 98, ...) from becoming signed or unsigned
1203 [100, +, 255] with values 100, 355, ...; the sign-extension is
1204 performed by default when CT is signed. */
1206 if (TYPE_PRECISION (step_type
) > TYPE_PRECISION (ct
) && TYPE_UNSIGNED (ct
))
1207 new_step
= chrec_convert_1 (signed_type_for (ct
), new_step
, at_stmt
,
1208 use_overflow_semantics
);
1209 new_step
= chrec_convert_1 (step_type
, new_step
, at_stmt
, use_overflow_semantics
);
1211 if (automatically_generated_chrec_p (new_base
)
1212 || automatically_generated_chrec_p (new_step
))
1215 if (must_check_rslt_overflow
1216 /* Note that in this case we cannot use the fact that signed variables
1217 do not overflow, as this is what we are verifying for the new iv. */
1218 && scev_probably_wraps_p (new_base
, new_step
, at_stmt
, loop
, false))
1227 /* Convert CHREC for the right hand side of a CREC.
1228 The increment for a pointer type is always sizetype. */
1230 chrec_convert_rhs (tree type
, tree chrec
, tree at_stmt
)
1232 if (POINTER_TYPE_P (type
))
1234 return chrec_convert (type
, chrec
, at_stmt
);
1237 /* Convert CHREC to TYPE. When the analyzer knows the context in
1238 which the CHREC is built, it sets AT_STMT to the statement that
1239 contains the definition of the analyzed variable, otherwise the
1240 conversion is less accurate: the information is used for
1241 determining a more accurate estimation of the number of iterations.
1242 By default AT_STMT could be safely set to NULL_TREE.
1244 The following rule is always true: TREE_TYPE (chrec) ==
1245 TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)).
1246 An example of what could happen when adding two chrecs and the type
1247 of the CHREC_RIGHT is different than CHREC_LEFT is:
1249 {(uint) 0, +, (uchar) 10} +
1250 {(uint) 0, +, (uchar) 250}
1252 that would produce a wrong result if CHREC_RIGHT is not (uint):
1254 {(uint) 0, +, (uchar) 4}
1258 {(uint) 0, +, (uint) 260}
1262 chrec_convert (tree type
, tree chrec
, tree at_stmt
)
1264 return chrec_convert_1 (type
, chrec
, at_stmt
, true);
1267 /* Convert CHREC to TYPE. When the analyzer knows the context in
1268 which the CHREC is built, it sets AT_STMT to the statement that
1269 contains the definition of the analyzed variable, otherwise the
1270 conversion is less accurate: the information is used for
1271 determining a more accurate estimation of the number of iterations.
1272 By default AT_STMT could be safely set to NULL_TREE.
1274 USE_OVERFLOW_SEMANTICS is true if this function should assume that
1275 the rules for overflow of the given language apply (e.g., that signed
1276 arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1277 tests, but also to enforce that the result follows them. */
1280 chrec_convert_1 (tree type
, tree chrec
, tree at_stmt
,
1281 bool use_overflow_semantics
)
1287 if (automatically_generated_chrec_p (chrec
))
1290 ct
= chrec_type (chrec
);
1294 if (!evolution_function_is_affine_p (chrec
))
1297 loop
= get_chrec_loop (chrec
);
1298 base
= CHREC_LEFT (chrec
);
1299 step
= CHREC_RIGHT (chrec
);
1301 if (convert_affine_scev (loop
, type
, &base
, &step
, at_stmt
,
1302 use_overflow_semantics
))
1303 return build_polynomial_chrec (loop
->num
, base
, step
);
1305 /* If we cannot propagate the cast inside the chrec, just keep the cast. */
1307 res
= fold_convert (type
, chrec
);
1309 /* Don't propagate overflows. */
1310 if (CONSTANT_CLASS_P (res
))
1311 TREE_OVERFLOW (res
) = 0;
1313 /* But reject constants that don't fit in their type after conversion.
1314 This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the
1315 natural values associated with TYPE_PRECISION and TYPE_UNSIGNED,
1316 and can cause problems later when computing niters of loops. Note
1317 that we don't do the check before converting because we don't want
1318 to reject conversions of negative chrecs to unsigned types. */
1319 if (TREE_CODE (res
) == INTEGER_CST
1320 && TREE_CODE (type
) == INTEGER_TYPE
1321 && !int_fits_type_p (res
, type
))
1322 res
= chrec_dont_know
;
1327 /* Convert CHREC to TYPE, without regard to signed overflows. Returns the new
1328 chrec if something else than what chrec_convert would do happens, NULL_TREE
1332 chrec_convert_aggressive (tree type
, tree chrec
)
1334 tree inner_type
, left
, right
, lc
, rc
, rtype
;
1336 if (automatically_generated_chrec_p (chrec
)
1337 || TREE_CODE (chrec
) != POLYNOMIAL_CHREC
)
1340 inner_type
= TREE_TYPE (chrec
);
1341 if (TYPE_PRECISION (type
) > TYPE_PRECISION (inner_type
))
1344 /* If we cannot perform arithmetic in TYPE, avoid creating an scev. */
1345 if (avoid_arithmetics_in_type_p (type
))
1348 rtype
= POINTER_TYPE_P (type
) ? sizetype
: type
;
1350 left
= CHREC_LEFT (chrec
);
1351 right
= CHREC_RIGHT (chrec
);
1352 lc
= chrec_convert_aggressive (type
, left
);
1354 lc
= chrec_convert (type
, left
, NULL_TREE
);
1355 rc
= chrec_convert_aggressive (rtype
, right
);
1357 rc
= chrec_convert (rtype
, right
, NULL_TREE
);
1359 return build_polynomial_chrec (CHREC_VARIABLE (chrec
), lc
, rc
);
1362 /* Returns true when CHREC0 == CHREC1. */
1365 eq_evolutions_p (tree chrec0
,
1368 if (chrec0
== NULL_TREE
1369 || chrec1
== NULL_TREE
1370 || TREE_CODE (chrec0
) != TREE_CODE (chrec1
))
1373 if (chrec0
== chrec1
)
1376 switch (TREE_CODE (chrec0
))
1379 return operand_equal_p (chrec0
, chrec1
, 0);
1381 case POLYNOMIAL_CHREC
:
1382 return (CHREC_VARIABLE (chrec0
) == CHREC_VARIABLE (chrec1
)
1383 && eq_evolutions_p (CHREC_LEFT (chrec0
), CHREC_LEFT (chrec1
))
1384 && eq_evolutions_p (CHREC_RIGHT (chrec0
), CHREC_RIGHT (chrec1
)));
1390 /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow),
1391 EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine
1392 which of these cases happens. */
1395 scev_direction (tree chrec
)
1399 if (!evolution_function_is_affine_p (chrec
))
1400 return EV_DIR_UNKNOWN
;
1402 step
= CHREC_RIGHT (chrec
);
1403 if (TREE_CODE (step
) != INTEGER_CST
)
1404 return EV_DIR_UNKNOWN
;
1406 if (tree_int_cst_sign_bit (step
))
1407 return EV_DIR_DECREASES
;
1409 return EV_DIR_GROWS
;