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 2, 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 COPYING. If not, write to the Free
19 Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA
22 /* This file implements operations on chains of recurrences. Chains
23 of recurrences are used for modeling evolution functions of scalar
29 #include "coretypes.h"
34 #include "diagnostic.h"
36 #include "tree-flow.h"
37 #include "tree-chrec.h"
38 #include "tree-pass.h"
40 #include "tree-scalar-evolution.h"
44 /* Extended folder for chrecs. */
46 /* Determines whether CST is not a constant evolution. */
49 is_not_constant_evolution (tree cst
)
51 return (TREE_CODE (cst
) == POLYNOMIAL_CHREC
);
54 /* Fold CODE for a polynomial function and a constant. */
57 chrec_fold_poly_cst (enum tree_code code
,
64 gcc_assert (TREE_CODE (poly
) == POLYNOMIAL_CHREC
);
65 gcc_assert (!is_not_constant_evolution (cst
));
66 gcc_assert (type
== chrec_type (poly
));
71 return build_polynomial_chrec
72 (CHREC_VARIABLE (poly
),
73 chrec_fold_plus (type
, CHREC_LEFT (poly
), cst
),
77 return build_polynomial_chrec
78 (CHREC_VARIABLE (poly
),
79 chrec_fold_minus (type
, CHREC_LEFT (poly
), cst
),
83 return build_polynomial_chrec
84 (CHREC_VARIABLE (poly
),
85 chrec_fold_multiply (type
, CHREC_LEFT (poly
), cst
),
86 chrec_fold_multiply (type
, CHREC_RIGHT (poly
), cst
));
89 return chrec_dont_know
;
93 /* Fold the addition of two polynomial functions. */
96 chrec_fold_plus_poly_poly (enum tree_code code
,
102 struct loop
*loop0
= get_chrec_loop (poly0
);
103 struct loop
*loop1
= get_chrec_loop (poly1
);
107 gcc_assert (TREE_CODE (poly0
) == POLYNOMIAL_CHREC
);
108 gcc_assert (TREE_CODE (poly1
) == POLYNOMIAL_CHREC
);
109 gcc_assert (chrec_type (poly0
) == chrec_type (poly1
));
110 gcc_assert (type
== chrec_type (poly0
));
113 {a, +, b}_1 + {c, +, d}_2 -> {{a, +, b}_1 + c, +, d}_2,
114 {a, +, b}_2 + {c, +, d}_1 -> {{c, +, d}_1 + a, +, b}_2,
115 {a, +, b}_x + {c, +, d}_x -> {a+c, +, b+d}_x. */
116 if (flow_loop_nested_p (loop0
, loop1
))
118 if (code
== PLUS_EXPR
)
119 return build_polynomial_chrec
120 (CHREC_VARIABLE (poly1
),
121 chrec_fold_plus (type
, poly0
, CHREC_LEFT (poly1
)),
122 CHREC_RIGHT (poly1
));
124 return build_polynomial_chrec
125 (CHREC_VARIABLE (poly1
),
126 chrec_fold_minus (type
, poly0
, CHREC_LEFT (poly1
)),
127 chrec_fold_multiply (type
, CHREC_RIGHT (poly1
),
128 SCALAR_FLOAT_TYPE_P (type
)
129 ? build_real (type
, dconstm1
)
130 : build_int_cst_type (type
, -1)));
133 if (flow_loop_nested_p (loop1
, loop0
))
135 if (code
== PLUS_EXPR
)
136 return build_polynomial_chrec
137 (CHREC_VARIABLE (poly0
),
138 chrec_fold_plus (type
, CHREC_LEFT (poly0
), poly1
),
139 CHREC_RIGHT (poly0
));
141 return build_polynomial_chrec
142 (CHREC_VARIABLE (poly0
),
143 chrec_fold_minus (type
, CHREC_LEFT (poly0
), poly1
),
144 CHREC_RIGHT (poly0
));
147 /* This function should never be called for chrecs of loops that
148 do not belong to the same loop nest. */
149 gcc_assert (loop0
== loop1
);
151 if (code
== PLUS_EXPR
)
153 left
= chrec_fold_plus
154 (type
, CHREC_LEFT (poly0
), CHREC_LEFT (poly1
));
155 right
= chrec_fold_plus
156 (type
, CHREC_RIGHT (poly0
), CHREC_RIGHT (poly1
));
160 left
= chrec_fold_minus
161 (type
, CHREC_LEFT (poly0
), CHREC_LEFT (poly1
));
162 right
= chrec_fold_minus
163 (type
, CHREC_RIGHT (poly0
), CHREC_RIGHT (poly1
));
166 if (chrec_zerop (right
))
169 return build_polynomial_chrec
170 (CHREC_VARIABLE (poly0
), left
, right
);
175 /* Fold the multiplication of two polynomial functions. */
178 chrec_fold_multiply_poly_poly (tree type
,
184 struct loop
*loop0
= get_chrec_loop (poly0
);
185 struct loop
*loop1
= get_chrec_loop (poly1
);
189 gcc_assert (TREE_CODE (poly0
) == POLYNOMIAL_CHREC
);
190 gcc_assert (TREE_CODE (poly1
) == POLYNOMIAL_CHREC
);
191 gcc_assert (chrec_type (poly0
) == chrec_type (poly1
));
192 gcc_assert (type
== chrec_type (poly0
));
194 /* {a, +, b}_1 * {c, +, d}_2 -> {c*{a, +, b}_1, +, d}_2,
195 {a, +, b}_2 * {c, +, d}_1 -> {a*{c, +, d}_1, +, b}_2,
196 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */
197 if (flow_loop_nested_p (loop0
, loop1
))
198 /* poly0 is a constant wrt. poly1. */
199 return build_polynomial_chrec
200 (CHREC_VARIABLE (poly1
),
201 chrec_fold_multiply (type
, CHREC_LEFT (poly1
), poly0
),
202 CHREC_RIGHT (poly1
));
204 if (flow_loop_nested_p (loop1
, loop0
))
205 /* poly1 is a constant wrt. poly0. */
206 return build_polynomial_chrec
207 (CHREC_VARIABLE (poly0
),
208 chrec_fold_multiply (type
, CHREC_LEFT (poly0
), poly1
),
209 CHREC_RIGHT (poly0
));
211 gcc_assert (loop0
== loop1
);
213 /* poly0 and poly1 are two polynomials in the same variable,
214 {a, +, b}_x * {c, +, d}_x -> {a*c, +, a*d + b*c + b*d, +, 2*b*d}_x. */
217 t0
= chrec_fold_multiply (type
, CHREC_LEFT (poly0
), CHREC_LEFT (poly1
));
219 /* "a*d + b*c + b*d". */
220 t1
= chrec_fold_multiply (type
, CHREC_LEFT (poly0
), CHREC_RIGHT (poly1
));
221 t1
= chrec_fold_plus (type
, t1
, chrec_fold_multiply (type
,
223 CHREC_LEFT (poly1
)));
224 t1
= chrec_fold_plus (type
, t1
, chrec_fold_multiply (type
,
226 CHREC_RIGHT (poly1
)));
228 t2
= chrec_fold_multiply (type
, CHREC_RIGHT (poly0
), CHREC_RIGHT (poly1
));
229 t2
= chrec_fold_multiply (type
, SCALAR_FLOAT_TYPE_P (type
)
230 ? build_real (type
, dconst2
)
231 : build_int_cst (type
, 2), t2
);
233 var
= CHREC_VARIABLE (poly0
);
234 return build_polynomial_chrec (var
, t0
,
235 build_polynomial_chrec (var
, t1
, t2
));
238 /* When the operands are automatically_generated_chrec_p, the fold has
239 to respect the semantics of the operands. */
242 chrec_fold_automatically_generated_operands (tree op0
,
245 if (op0
== chrec_dont_know
246 || op1
== chrec_dont_know
)
247 return chrec_dont_know
;
249 if (op0
== chrec_known
250 || op1
== chrec_known
)
253 if (op0
== chrec_not_analyzed_yet
254 || op1
== chrec_not_analyzed_yet
)
255 return chrec_not_analyzed_yet
;
257 /* The default case produces a safe result. */
258 return chrec_dont_know
;
261 /* Fold the addition of two chrecs. */
264 chrec_fold_plus_1 (enum tree_code code
, tree type
,
267 if (automatically_generated_chrec_p (op0
)
268 || automatically_generated_chrec_p (op1
))
269 return chrec_fold_automatically_generated_operands (op0
, op1
);
271 switch (TREE_CODE (op0
))
273 case POLYNOMIAL_CHREC
:
274 switch (TREE_CODE (op1
))
276 case POLYNOMIAL_CHREC
:
277 return chrec_fold_plus_poly_poly (code
, type
, op0
, op1
);
280 if (code
== PLUS_EXPR
)
281 return build_polynomial_chrec
282 (CHREC_VARIABLE (op0
),
283 chrec_fold_plus (type
, CHREC_LEFT (op0
), op1
),
286 return build_polynomial_chrec
287 (CHREC_VARIABLE (op0
),
288 chrec_fold_minus (type
, CHREC_LEFT (op0
), op1
),
293 switch (TREE_CODE (op1
))
295 case POLYNOMIAL_CHREC
:
296 if (code
== PLUS_EXPR
)
297 return build_polynomial_chrec
298 (CHREC_VARIABLE (op1
),
299 chrec_fold_plus (type
, op0
, CHREC_LEFT (op1
)),
302 return build_polynomial_chrec
303 (CHREC_VARIABLE (op1
),
304 chrec_fold_minus (type
, op0
, CHREC_LEFT (op1
)),
305 chrec_fold_multiply (type
, CHREC_RIGHT (op1
),
306 SCALAR_FLOAT_TYPE_P (type
)
307 ? build_real (type
, dconstm1
)
308 : build_int_cst_type (type
, -1)));
313 if ((tree_contains_chrecs (op0
, &size
)
314 || tree_contains_chrecs (op1
, &size
))
315 && size
< PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE
))
316 return build2 (code
, type
, op0
, op1
);
317 else if (size
< PARAM_VALUE (PARAM_SCEV_MAX_EXPR_SIZE
))
318 return fold_build2 (code
, type
,
319 fold_convert (type
, op0
),
320 fold_convert (type
, op1
));
322 return chrec_dont_know
;
328 /* Fold the addition of two chrecs. */
331 chrec_fold_plus (tree type
,
335 if (automatically_generated_chrec_p (op0
)
336 || automatically_generated_chrec_p (op1
))
337 return chrec_fold_automatically_generated_operands (op0
, op1
);
339 if (integer_zerop (op0
))
341 if (integer_zerop (op1
))
344 return chrec_fold_plus_1 (PLUS_EXPR
, type
, op0
, op1
);
347 /* Fold the subtraction of two chrecs. */
350 chrec_fold_minus (tree type
,
354 if (automatically_generated_chrec_p (op0
)
355 || automatically_generated_chrec_p (op1
))
356 return chrec_fold_automatically_generated_operands (op0
, op1
);
358 if (integer_zerop (op1
))
361 return chrec_fold_plus_1 (MINUS_EXPR
, type
, op0
, op1
);
364 /* Fold the multiplication of two chrecs. */
367 chrec_fold_multiply (tree type
,
371 if (automatically_generated_chrec_p (op0
)
372 || automatically_generated_chrec_p (op1
))
373 return chrec_fold_automatically_generated_operands (op0
, op1
);
375 switch (TREE_CODE (op0
))
377 case POLYNOMIAL_CHREC
:
378 switch (TREE_CODE (op1
))
380 case POLYNOMIAL_CHREC
:
381 return chrec_fold_multiply_poly_poly (type
, op0
, op1
);
384 if (integer_onep (op1
))
386 if (integer_zerop (op1
))
387 return build_int_cst (type
, 0);
389 return build_polynomial_chrec
390 (CHREC_VARIABLE (op0
),
391 chrec_fold_multiply (type
, CHREC_LEFT (op0
), op1
),
392 chrec_fold_multiply (type
, CHREC_RIGHT (op0
), op1
));
396 if (integer_onep (op0
))
399 if (integer_zerop (op0
))
400 return build_int_cst (type
, 0);
402 switch (TREE_CODE (op1
))
404 case POLYNOMIAL_CHREC
:
405 return build_polynomial_chrec
406 (CHREC_VARIABLE (op1
),
407 chrec_fold_multiply (type
, CHREC_LEFT (op1
), op0
),
408 chrec_fold_multiply (type
, CHREC_RIGHT (op1
), op0
));
411 if (integer_onep (op1
))
413 if (integer_zerop (op1
))
414 return build_int_cst (type
, 0);
415 return fold_build2 (MULT_EXPR
, type
, op0
, op1
);
424 /* Evaluate the binomial coefficient. Return NULL_TREE if the intermediate
425 calculation overflows, otherwise return C(n,k) with type TYPE. */
428 tree_fold_binomial (tree type
, tree n
, unsigned int k
)
430 unsigned HOST_WIDE_INT lidx
, lnum
, ldenom
, lres
, ldum
;
431 HOST_WIDE_INT hidx
, hnum
, hdenom
, hres
, hdum
;
435 /* Handle the most frequent cases. */
437 return build_int_cst (type
, 1);
439 return fold_convert (type
, n
);
441 /* Check that k <= n. */
442 if (TREE_INT_CST_HIGH (n
) == 0
443 && TREE_INT_CST_LOW (n
) < k
)
447 lnum
= TREE_INT_CST_LOW (n
);
448 hnum
= TREE_INT_CST_HIGH (n
);
450 /* Denominator = 2. */
454 /* Index = Numerator-1. */
458 lidx
= ~ (unsigned HOST_WIDE_INT
) 0;
466 /* Numerator = Numerator*Index = n*(n-1). */
467 if (mul_double (lnum
, hnum
, lidx
, hidx
, &lnum
, &hnum
))
470 for (i
= 3; i
<= k
; i
++)
476 lidx
= ~ (unsigned HOST_WIDE_INT
) 0;
481 /* Numerator *= Index. */
482 if (mul_double (lnum
, hnum
, lidx
, hidx
, &lnum
, &hnum
))
485 /* Denominator *= i. */
486 mul_double (ldenom
, hdenom
, i
, 0, &ldenom
, &hdenom
);
489 /* Result = Numerator / Denominator. */
490 div_and_round_double (EXACT_DIV_EXPR
, 1, lnum
, hnum
, ldenom
, hdenom
,
491 &lres
, &hres
, &ldum
, &hdum
);
493 res
= build_int_cst_wide (type
, lres
, hres
);
494 return int_fits_type_p (res
, type
) ? res
: NULL_TREE
;
497 /* Helper function. Use the Newton's interpolating formula for
498 evaluating the value of the evolution function. */
501 chrec_evaluate (unsigned var
, tree chrec
, tree n
, unsigned int k
)
503 tree arg0
, arg1
, binomial_n_k
;
504 tree type
= TREE_TYPE (chrec
);
505 struct loop
*var_loop
= get_loop (var
);
507 while (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
508 && flow_loop_nested_p (var_loop
, get_chrec_loop (chrec
)))
509 chrec
= CHREC_LEFT (chrec
);
511 if (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
512 && CHREC_VARIABLE (chrec
) == var
)
514 arg0
= chrec_evaluate (var
, CHREC_RIGHT (chrec
), n
, k
+ 1);
515 if (arg0
== chrec_dont_know
)
516 return chrec_dont_know
;
517 binomial_n_k
= tree_fold_binomial (type
, n
, k
);
519 return chrec_dont_know
;
520 arg1
= fold_build2 (MULT_EXPR
, type
,
521 CHREC_LEFT (chrec
), binomial_n_k
);
522 return chrec_fold_plus (type
, arg0
, arg1
);
525 binomial_n_k
= tree_fold_binomial (type
, n
, k
);
527 return chrec_dont_know
;
529 return fold_build2 (MULT_EXPR
, type
, chrec
, binomial_n_k
);
532 /* Evaluates "CHREC (X)" when the varying variable is VAR.
533 Example: Given the following parameters,
539 The result is given by the Newton's interpolating formula:
540 3 * \binom{10}{0} + 4 * \binom{10}{1}.
544 chrec_apply (unsigned var
,
548 tree type
= chrec_type (chrec
);
549 tree res
= chrec_dont_know
;
551 if (automatically_generated_chrec_p (chrec
)
552 || automatically_generated_chrec_p (x
)
554 /* When the symbols are defined in an outer loop, it is possible
555 to symbolically compute the apply, since the symbols are
556 constants with respect to the varying loop. */
557 || chrec_contains_symbols_defined_in_loop (chrec
, var
))
558 return chrec_dont_know
;
560 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
561 fprintf (dump_file
, "(chrec_apply \n");
563 if (TREE_CODE (x
) == INTEGER_CST
&& SCALAR_FLOAT_TYPE_P (type
))
564 x
= build_real_from_int_cst (type
, x
);
566 if (evolution_function_is_affine_p (chrec
))
568 /* "{a, +, b} (x)" -> "a + b*x". */
569 x
= chrec_convert (type
, x
, NULL_TREE
);
570 res
= chrec_fold_multiply (type
, CHREC_RIGHT (chrec
), x
);
571 if (!integer_zerop (CHREC_LEFT (chrec
)))
572 res
= chrec_fold_plus (type
, CHREC_LEFT (chrec
), res
);
575 else if (TREE_CODE (chrec
) != POLYNOMIAL_CHREC
)
578 else if (TREE_CODE (x
) == INTEGER_CST
579 && tree_int_cst_sgn (x
) == 1)
580 /* testsuite/.../ssa-chrec-38.c. */
581 res
= chrec_evaluate (var
, chrec
, x
, 0);
583 res
= chrec_dont_know
;
585 if (dump_file
&& (dump_flags
& TDF_DETAILS
))
587 fprintf (dump_file
, " (varying_loop = %d\n", var
);
588 fprintf (dump_file
, ")\n (chrec = ");
589 print_generic_expr (dump_file
, chrec
, 0);
590 fprintf (dump_file
, ")\n (x = ");
591 print_generic_expr (dump_file
, x
, 0);
592 fprintf (dump_file
, ")\n (res = ");
593 print_generic_expr (dump_file
, res
, 0);
594 fprintf (dump_file
, "))\n");
600 /* Replaces the initial condition in CHREC with INIT_COND. */
603 chrec_replace_initial_condition (tree chrec
,
606 if (automatically_generated_chrec_p (chrec
))
609 gcc_assert (chrec_type (chrec
) == chrec_type (init_cond
));
611 switch (TREE_CODE (chrec
))
613 case POLYNOMIAL_CHREC
:
614 return build_polynomial_chrec
615 (CHREC_VARIABLE (chrec
),
616 chrec_replace_initial_condition (CHREC_LEFT (chrec
), init_cond
),
617 CHREC_RIGHT (chrec
));
624 /* Returns the initial condition of a given CHREC. */
627 initial_condition (tree chrec
)
629 if (automatically_generated_chrec_p (chrec
))
632 if (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
)
633 return initial_condition (CHREC_LEFT (chrec
));
638 /* Returns a univariate function that represents the evolution in
639 LOOP_NUM. Mask the evolution of any other loop. */
642 hide_evolution_in_other_loops_than_loop (tree chrec
,
645 struct loop
*loop
= get_loop (loop_num
), *chloop
;
646 if (automatically_generated_chrec_p (chrec
))
649 switch (TREE_CODE (chrec
))
651 case POLYNOMIAL_CHREC
:
652 chloop
= get_chrec_loop (chrec
);
655 return build_polynomial_chrec
657 hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec
),
659 CHREC_RIGHT (chrec
));
661 else if (flow_loop_nested_p (chloop
, loop
))
662 /* There is no evolution in this loop. */
663 return initial_condition (chrec
);
667 gcc_assert (flow_loop_nested_p (loop
, chloop
));
668 return hide_evolution_in_other_loops_than_loop (CHREC_LEFT (chrec
),
677 /* Returns the evolution part of CHREC in LOOP_NUM when RIGHT is
678 true, otherwise returns the initial condition in LOOP_NUM. */
681 chrec_component_in_loop_num (tree chrec
,
686 struct loop
*loop
= get_loop (loop_num
), *chloop
;
688 if (automatically_generated_chrec_p (chrec
))
691 switch (TREE_CODE (chrec
))
693 case POLYNOMIAL_CHREC
:
694 chloop
= get_chrec_loop (chrec
);
699 component
= CHREC_RIGHT (chrec
);
701 component
= CHREC_LEFT (chrec
);
703 if (TREE_CODE (CHREC_LEFT (chrec
)) != POLYNOMIAL_CHREC
704 || CHREC_VARIABLE (CHREC_LEFT (chrec
)) != CHREC_VARIABLE (chrec
))
708 return build_polynomial_chrec
710 chrec_component_in_loop_num (CHREC_LEFT (chrec
),
716 else if (flow_loop_nested_p (chloop
, loop
))
717 /* There is no evolution part in this loop. */
722 gcc_assert (flow_loop_nested_p (loop
, chloop
));
723 return chrec_component_in_loop_num (CHREC_LEFT (chrec
),
736 /* Returns the evolution part in LOOP_NUM. Example: the call
737 evolution_part_in_loop_num ({{0, +, 1}_1, +, 2}_1, 1) returns
741 evolution_part_in_loop_num (tree chrec
,
744 return chrec_component_in_loop_num (chrec
, loop_num
, true);
747 /* Returns the initial condition in LOOP_NUM. Example: the call
748 initial_condition_in_loop_num ({{0, +, 1}_1, +, 2}_2, 2) returns
752 initial_condition_in_loop_num (tree chrec
,
755 return chrec_component_in_loop_num (chrec
, loop_num
, false);
758 /* Set or reset the evolution of CHREC to NEW_EVOL in loop LOOP_NUM.
759 This function is essentially used for setting the evolution to
760 chrec_dont_know, for example after having determined that it is
761 impossible to say how many times a loop will execute. */
764 reset_evolution_in_loop (unsigned loop_num
,
768 struct loop
*loop
= get_loop (loop_num
);
770 gcc_assert (chrec_type (chrec
) == chrec_type (new_evol
));
772 if (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
773 && flow_loop_nested_p (loop
, get_chrec_loop (chrec
)))
775 tree left
= reset_evolution_in_loop (loop_num
, CHREC_LEFT (chrec
),
777 tree right
= reset_evolution_in_loop (loop_num
, CHREC_RIGHT (chrec
),
779 return build3 (POLYNOMIAL_CHREC
, TREE_TYPE (left
),
780 build_int_cst (NULL_TREE
, CHREC_VARIABLE (chrec
)),
784 while (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
785 && CHREC_VARIABLE (chrec
) == loop_num
)
786 chrec
= CHREC_LEFT (chrec
);
788 return build_polynomial_chrec (loop_num
, chrec
, new_evol
);
791 /* Merges two evolution functions that were found by following two
792 alternate paths of a conditional expression. */
795 chrec_merge (tree chrec1
,
798 if (chrec1
== chrec_dont_know
799 || chrec2
== chrec_dont_know
)
800 return chrec_dont_know
;
802 if (chrec1
== chrec_known
803 || chrec2
== chrec_known
)
806 if (chrec1
== chrec_not_analyzed_yet
)
808 if (chrec2
== chrec_not_analyzed_yet
)
811 if (eq_evolutions_p (chrec1
, chrec2
))
814 return chrec_dont_know
;
821 /* Helper function for is_multivariate_chrec. */
824 is_multivariate_chrec_rec (tree chrec
, unsigned int rec_var
)
826 if (chrec
== NULL_TREE
)
829 if (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
)
831 if (CHREC_VARIABLE (chrec
) != rec_var
)
834 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec
), rec_var
)
835 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec
), rec_var
));
841 /* Determine whether the given chrec is multivariate or not. */
844 is_multivariate_chrec (tree chrec
)
846 if (chrec
== NULL_TREE
)
849 if (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
)
850 return (is_multivariate_chrec_rec (CHREC_LEFT (chrec
),
851 CHREC_VARIABLE (chrec
))
852 || is_multivariate_chrec_rec (CHREC_RIGHT (chrec
),
853 CHREC_VARIABLE (chrec
)));
858 /* Determines whether the chrec contains symbolic names or not. */
861 chrec_contains_symbols (tree chrec
)
865 if (chrec
== NULL_TREE
)
868 if (TREE_CODE (chrec
) == SSA_NAME
869 || TREE_CODE (chrec
) == VAR_DECL
870 || TREE_CODE (chrec
) == PARM_DECL
871 || TREE_CODE (chrec
) == FUNCTION_DECL
872 || TREE_CODE (chrec
) == LABEL_DECL
873 || TREE_CODE (chrec
) == RESULT_DECL
874 || TREE_CODE (chrec
) == FIELD_DECL
)
877 n
= TREE_OPERAND_LENGTH (chrec
);
878 for (i
= 0; i
< n
; i
++)
879 if (chrec_contains_symbols (TREE_OPERAND (chrec
, i
)))
884 /* Determines whether the chrec contains undetermined coefficients. */
887 chrec_contains_undetermined (tree chrec
)
891 if (chrec
== chrec_dont_know
)
894 if (chrec
== NULL_TREE
)
897 n
= TREE_OPERAND_LENGTH (chrec
);
898 for (i
= 0; i
< n
; i
++)
899 if (chrec_contains_undetermined (TREE_OPERAND (chrec
, i
)))
904 /* Determines whether the tree EXPR contains chrecs, and increment
905 SIZE if it is not a NULL pointer by an estimation of the depth of
909 tree_contains_chrecs (tree expr
, int *size
)
913 if (expr
== NULL_TREE
)
919 if (tree_is_chrec (expr
))
922 n
= TREE_OPERAND_LENGTH (expr
);
923 for (i
= 0; i
< n
; i
++)
924 if (tree_contains_chrecs (TREE_OPERAND (expr
, i
), size
))
929 /* Recursive helper function. */
932 evolution_function_is_invariant_rec_p (tree chrec
, int loopnum
)
934 if (evolution_function_is_constant_p (chrec
))
937 if (TREE_CODE (chrec
) == SSA_NAME
938 && expr_invariant_in_loop_p (get_loop (loopnum
), chrec
))
941 if (TREE_CODE (chrec
) == POLYNOMIAL_CHREC
)
943 if (CHREC_VARIABLE (chrec
) == (unsigned) loopnum
944 || !evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec
),
946 || !evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec
),
952 switch (TREE_OPERAND_LENGTH (chrec
))
955 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec
, 1),
960 if (!evolution_function_is_invariant_rec_p (TREE_OPERAND (chrec
, 0),
972 /* Return true if CHREC is invariant in loop LOOPNUM, false otherwise. */
975 evolution_function_is_invariant_p (tree chrec
, int loopnum
)
977 return evolution_function_is_invariant_rec_p (chrec
, loopnum
);
980 /* Determine whether the given tree is an affine multivariate
984 evolution_function_is_affine_multivariate_p (tree chrec
, int loopnum
)
986 if (chrec
== NULL_TREE
)
989 switch (TREE_CODE (chrec
))
991 case POLYNOMIAL_CHREC
:
992 if (evolution_function_is_invariant_rec_p (CHREC_LEFT (chrec
), loopnum
))
994 if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec
), loopnum
))
998 if (TREE_CODE (CHREC_RIGHT (chrec
)) == POLYNOMIAL_CHREC
999 && CHREC_VARIABLE (CHREC_RIGHT (chrec
))
1000 != CHREC_VARIABLE (chrec
)
1001 && evolution_function_is_affine_multivariate_p
1002 (CHREC_RIGHT (chrec
), loopnum
))
1010 if (evolution_function_is_invariant_rec_p (CHREC_RIGHT (chrec
), loopnum
)
1011 && TREE_CODE (CHREC_LEFT (chrec
)) == POLYNOMIAL_CHREC
1012 && CHREC_VARIABLE (CHREC_LEFT (chrec
)) != CHREC_VARIABLE (chrec
)
1013 && evolution_function_is_affine_multivariate_p
1014 (CHREC_LEFT (chrec
), loopnum
))
1025 /* Determine whether the given tree is a function in zero or one
1029 evolution_function_is_univariate_p (tree chrec
)
1031 if (chrec
== NULL_TREE
)
1034 switch (TREE_CODE (chrec
))
1036 case POLYNOMIAL_CHREC
:
1037 switch (TREE_CODE (CHREC_LEFT (chrec
)))
1039 case POLYNOMIAL_CHREC
:
1040 if (CHREC_VARIABLE (chrec
) != CHREC_VARIABLE (CHREC_LEFT (chrec
)))
1042 if (!evolution_function_is_univariate_p (CHREC_LEFT (chrec
)))
1050 switch (TREE_CODE (CHREC_RIGHT (chrec
)))
1052 case POLYNOMIAL_CHREC
:
1053 if (CHREC_VARIABLE (chrec
) != CHREC_VARIABLE (CHREC_RIGHT (chrec
)))
1055 if (!evolution_function_is_univariate_p (CHREC_RIGHT (chrec
)))
1068 /* Returns the number of variables of CHREC. Example: the call
1069 nb_vars_in_chrec ({{0, +, 1}_5, +, 2}_6) returns 2. */
1072 nb_vars_in_chrec (tree chrec
)
1074 if (chrec
== NULL_TREE
)
1077 switch (TREE_CODE (chrec
))
1079 case POLYNOMIAL_CHREC
:
1080 return 1 + nb_vars_in_chrec
1081 (initial_condition_in_loop_num (chrec
, CHREC_VARIABLE (chrec
)));
1088 /* Returns true if TYPE is a type in that we cannot directly perform
1089 arithmetics, even though it is a scalar type. */
1092 avoid_arithmetics_in_type_p (tree type
)
1094 /* Ada frontend uses subtypes -- an arithmetic cannot be directly performed
1095 in the subtype, but a base type must be used, and the result then can
1096 be casted to the subtype. */
1097 if (TREE_CODE (type
) == INTEGER_TYPE
&& TREE_TYPE (type
) != NULL_TREE
)
1103 static tree
chrec_convert_1 (tree
, tree
, tree
, bool);
1105 /* Converts BASE and STEP of affine scev to TYPE. LOOP is the loop whose iv
1106 the scev corresponds to. AT_STMT is the statement at that the scev is
1107 evaluated. USE_OVERFLOW_SEMANTICS is true if this function should assume that
1108 the rules for overflow of the given language apply (e.g., that signed
1109 arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1110 tests, but also to enforce that the result follows them. Returns true if the
1111 conversion succeeded, false otherwise. */
1114 convert_affine_scev (struct loop
*loop
, tree type
,
1115 tree
*base
, tree
*step
, tree at_stmt
,
1116 bool use_overflow_semantics
)
1118 tree ct
= TREE_TYPE (*step
);
1119 bool enforce_overflow_semantics
;
1120 bool must_check_src_overflow
, must_check_rslt_overflow
;
1121 tree new_base
, new_step
;
1123 /* If we cannot perform arithmetic in TYPE, avoid creating an scev. */
1124 if (avoid_arithmetics_in_type_p (type
))
1128 (TYPE) (BASE + STEP * i) = (TYPE) BASE + (TYPE -- sign extend) STEP * i,
1129 but we must check some assumptions.
1131 1) If [BASE, +, STEP] wraps, the equation is not valid when precision
1132 of CT is smaller than the precision of TYPE. For example, when we
1133 cast unsigned char [254, +, 1] to unsigned, the values on left side
1134 are 254, 255, 0, 1, ..., but those on the right side are
1135 254, 255, 256, 257, ...
1136 2) In case that we must also preserve the fact that signed ivs do not
1137 overflow, we must additionally check that the new iv does not wrap.
1138 For example, unsigned char [125, +, 1] casted to signed char could
1139 become a wrapping variable with values 125, 126, 127, -128, -127, ...,
1140 which would confuse optimizers that assume that this does not
1142 must_check_src_overflow
= TYPE_PRECISION (ct
) < TYPE_PRECISION (type
);
1144 enforce_overflow_semantics
= (use_overflow_semantics
1145 && nowrap_type_p (type
));
1146 if (enforce_overflow_semantics
)
1148 /* We can avoid checking whether the result overflows in the following
1151 -- must_check_src_overflow is true, and the range of TYPE is superset
1152 of the range of CT -- i.e., in all cases except if CT signed and
1154 -- both CT and TYPE have the same precision and signedness, and we
1155 verify instead that the source does not overflow (this may be
1156 easier than verifying it for the result, as we may use the
1157 information about the semantics of overflow in CT). */
1158 if (must_check_src_overflow
)
1160 if (TYPE_UNSIGNED (type
) && !TYPE_UNSIGNED (ct
))
1161 must_check_rslt_overflow
= true;
1163 must_check_rslt_overflow
= false;
1165 else if (TYPE_UNSIGNED (ct
) == TYPE_UNSIGNED (type
)
1166 && TYPE_PRECISION (ct
) == TYPE_PRECISION (type
))
1168 must_check_rslt_overflow
= false;
1169 must_check_src_overflow
= true;
1172 must_check_rslt_overflow
= true;
1175 must_check_rslt_overflow
= false;
1177 if (must_check_src_overflow
1178 && scev_probably_wraps_p (*base
, *step
, at_stmt
, loop
,
1179 use_overflow_semantics
))
1182 new_base
= chrec_convert_1 (type
, *base
, at_stmt
,
1183 use_overflow_semantics
);
1184 /* The step must be sign extended, regardless of the signedness
1185 of CT and TYPE. This only needs to be handled specially when
1186 CT is unsigned -- to avoid e.g. unsigned char [100, +, 255]
1187 (with values 100, 99, 98, ...) from becoming signed or unsigned
1188 [100, +, 255] with values 100, 355, ...; the sign-extension is
1189 performed by default when CT is signed. */
1191 if (TYPE_PRECISION (type
) > TYPE_PRECISION (ct
) && TYPE_UNSIGNED (ct
))
1192 new_step
= chrec_convert_1 (signed_type_for (ct
), new_step
, at_stmt
,
1193 use_overflow_semantics
);
1194 new_step
= chrec_convert_1 (type
, new_step
, at_stmt
, use_overflow_semantics
);
1196 if (automatically_generated_chrec_p (new_base
)
1197 || automatically_generated_chrec_p (new_step
))
1200 if (must_check_rslt_overflow
1201 /* Note that in this case we cannot use the fact that signed variables
1202 do not overflow, as this is what we are verifying for the new iv. */
1203 && scev_probably_wraps_p (new_base
, new_step
, at_stmt
, loop
, false))
1212 /* Convert CHREC to TYPE. When the analyzer knows the context in
1213 which the CHREC is built, it sets AT_STMT to the statement that
1214 contains the definition of the analyzed variable, otherwise the
1215 conversion is less accurate: the information is used for
1216 determining a more accurate estimation of the number of iterations.
1217 By default AT_STMT could be safely set to NULL_TREE.
1219 The following rule is always true: TREE_TYPE (chrec) ==
1220 TREE_TYPE (CHREC_LEFT (chrec)) == TREE_TYPE (CHREC_RIGHT (chrec)).
1221 An example of what could happen when adding two chrecs and the type
1222 of the CHREC_RIGHT is different than CHREC_LEFT is:
1224 {(uint) 0, +, (uchar) 10} +
1225 {(uint) 0, +, (uchar) 250}
1227 that would produce a wrong result if CHREC_RIGHT is not (uint):
1229 {(uint) 0, +, (uchar) 4}
1233 {(uint) 0, +, (uint) 260}
1237 chrec_convert (tree type
, tree chrec
, tree at_stmt
)
1239 return chrec_convert_1 (type
, chrec
, at_stmt
, true);
1242 /* Convert CHREC to TYPE. When the analyzer knows the context in
1243 which the CHREC is built, it sets AT_STMT to the statement that
1244 contains the definition of the analyzed variable, otherwise the
1245 conversion is less accurate: the information is used for
1246 determining a more accurate estimation of the number of iterations.
1247 By default AT_STMT could be safely set to NULL_TREE.
1249 USE_OVERFLOW_SEMANTICS is true if this function should assume that
1250 the rules for overflow of the given language apply (e.g., that signed
1251 arithmetics in C does not overflow) -- i.e., to use them to avoid unnecessary
1252 tests, but also to enforce that the result follows them. */
1255 chrec_convert_1 (tree type
, tree chrec
, tree at_stmt
,
1256 bool use_overflow_semantics
)
1262 if (automatically_generated_chrec_p (chrec
))
1265 ct
= chrec_type (chrec
);
1269 if (!evolution_function_is_affine_p (chrec
))
1272 loop
= get_chrec_loop (chrec
);
1273 base
= CHREC_LEFT (chrec
);
1274 step
= CHREC_RIGHT (chrec
);
1276 if (convert_affine_scev (loop
, type
, &base
, &step
, at_stmt
,
1277 use_overflow_semantics
))
1278 return build_polynomial_chrec (loop
->num
, base
, step
);
1280 /* If we cannot propagate the cast inside the chrec, just keep the cast. */
1282 res
= fold_convert (type
, chrec
);
1284 /* Don't propagate overflows. */
1285 if (CONSTANT_CLASS_P (res
))
1286 TREE_OVERFLOW (res
) = 0;
1288 /* But reject constants that don't fit in their type after conversion.
1289 This can happen if TYPE_MIN_VALUE or TYPE_MAX_VALUE are not the
1290 natural values associated with TYPE_PRECISION and TYPE_UNSIGNED,
1291 and can cause problems later when computing niters of loops. Note
1292 that we don't do the check before converting because we don't want
1293 to reject conversions of negative chrecs to unsigned types. */
1294 if (TREE_CODE (res
) == INTEGER_CST
1295 && TREE_CODE (type
) == INTEGER_TYPE
1296 && !int_fits_type_p (res
, type
))
1297 res
= chrec_dont_know
;
1302 /* Convert CHREC to TYPE, without regard to signed overflows. Returns the new
1303 chrec if something else than what chrec_convert would do happens, NULL_TREE
1307 chrec_convert_aggressive (tree type
, tree chrec
)
1309 tree inner_type
, left
, right
, lc
, rc
;
1311 if (automatically_generated_chrec_p (chrec
)
1312 || TREE_CODE (chrec
) != POLYNOMIAL_CHREC
)
1315 inner_type
= TREE_TYPE (chrec
);
1316 if (TYPE_PRECISION (type
) > TYPE_PRECISION (inner_type
))
1319 /* If we cannot perform arithmetic in TYPE, avoid creating an scev. */
1320 if (avoid_arithmetics_in_type_p (type
))
1323 left
= CHREC_LEFT (chrec
);
1324 right
= CHREC_RIGHT (chrec
);
1325 lc
= chrec_convert_aggressive (type
, left
);
1327 lc
= chrec_convert (type
, left
, NULL_TREE
);
1328 rc
= chrec_convert_aggressive (type
, right
);
1330 rc
= chrec_convert (type
, right
, NULL_TREE
);
1332 return build_polynomial_chrec (CHREC_VARIABLE (chrec
), lc
, rc
);
1335 /* Returns true when CHREC0 == CHREC1. */
1338 eq_evolutions_p (tree chrec0
,
1341 if (chrec0
== NULL_TREE
1342 || chrec1
== NULL_TREE
1343 || TREE_CODE (chrec0
) != TREE_CODE (chrec1
))
1346 if (chrec0
== chrec1
)
1349 switch (TREE_CODE (chrec0
))
1352 return operand_equal_p (chrec0
, chrec1
, 0);
1354 case POLYNOMIAL_CHREC
:
1355 return (CHREC_VARIABLE (chrec0
) == CHREC_VARIABLE (chrec1
)
1356 && eq_evolutions_p (CHREC_LEFT (chrec0
), CHREC_LEFT (chrec1
))
1357 && eq_evolutions_p (CHREC_RIGHT (chrec0
), CHREC_RIGHT (chrec1
)));
1363 /* Returns EV_GROWS if CHREC grows (assuming that it does not overflow),
1364 EV_DECREASES if it decreases, and EV_UNKNOWN if we cannot determine
1365 which of these cases happens. */
1368 scev_direction (tree chrec
)
1372 if (!evolution_function_is_affine_p (chrec
))
1373 return EV_DIR_UNKNOWN
;
1375 step
= CHREC_RIGHT (chrec
);
1376 if (TREE_CODE (step
) != INTEGER_CST
)
1377 return EV_DIR_UNKNOWN
;
1379 if (tree_int_cst_sign_bit (step
))
1380 return EV_DIR_DECREASES
;
1382 return EV_DIR_GROWS
;