| blob | fd5a7085e91307ecde12774abee04bb7de100656 |
1 /* Fold a constant sub-tree into a single node for C-compiler
2 Copyright (C) 1987, 1988, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999,
3 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007
4 Free Software Foundation, Inc.
6 This file is part of GCC.
8 GCC is free software; you can redistribute it and/or modify it under
9 the terms of the GNU General Public License as published by the Free
10 Software Foundation; either version 3, or (at your option) any later
11 version.
13 GCC is distributed in the hope that it will be useful, but WITHOUT ANY
14 WARRANTY; without even the implied warranty of MERCHANTABILITY or
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
16 for more details.
18 You should have received a copy of the GNU General Public License
19 along with GCC; see the file COPYING3. If not see
20 <http://www.gnu.org/licenses/>. */
22 /*@@ This file should be rewritten to use an arbitrary precision
23 @@ representation for "struct tree_int_cst" and "struct tree_real_cst".
24 @@ Perhaps the routines could also be used for bc/dc, and made a lib.
25 @@ The routines that translate from the ap rep should
26 @@ warn if precision et. al. is lost.
27 @@ This would also make life easier when this technology is used
28 @@ for cross-compilers. */
30 /* The entry points in this file are fold, size_int_wide, size_binop
31 and force_fit_type_double.
33 fold takes a tree as argument and returns a simplified tree.
35 size_binop takes a tree code for an arithmetic operation
36 and two operands that are trees, and produces a tree for the
37 result, assuming the type comes from `sizetype'.
39 size_int takes an integer value, and creates a tree constant
40 with type from `sizetype'.
42 force_fit_type_double takes a constant, an overflowable flag and a
43 prior overflow indicator. It forces the value to fit the type and
44 sets TREE_OVERFLOW.
46 Note: Since the folders get called on non-gimple code as well as
47 gimple code, we need to handle GIMPLE tuples as well as their
48 corresponding tree equivalents. */
68 /* Nonzero if we are folding constants inside an initializer; zero
69 otherwise. */
72 /* The following constants represent a bit based encoding of GCC's
73 comparison operators. This encoding simplifies transformations
74 on relational comparison operators, such as AND and OR. */
92 };
126 tree);
148 /* We know that A1 + B1 = SUM1, using 2's complement arithmetic and ignoring
149 overflow. Suppose A, B and SUM have the same respective signs as A1, B1,
150 and SUM1. Then this yields nonzero if overflow occurred during the
151 addition.
153 Overflow occurs if A and B have the same sign, but A and SUM differ in
154 sign. Use `^' to test whether signs differ, and `< 0' to isolate the
155 sign. */
156 #define OVERFLOW_SUM_SIGN(a, b, sum) ((~((a) ^ (b)) & ((a) ^ (sum))) < 0)
157 \f
158 /* To do constant folding on INTEGER_CST nodes requires two-word arithmetic.
159 We do that by representing the two-word integer in 4 words, with only
160 HOST_BITS_PER_WIDE_INT / 2 bits stored in each word, as a positive
161 number. The value of the word is LOWPART + HIGHPART * BASE. */
163 #define LOWPART(x) \
164 ((x) & (((unsigned HOST_WIDE_INT) 1 << (HOST_BITS_PER_WIDE_INT / 2)) - 1))
165 #define HIGHPART(x) \
166 ((unsigned HOST_WIDE_INT) (x) >> HOST_BITS_PER_WIDE_INT / 2)
167 #define BASE ((unsigned HOST_WIDE_INT) 1 << HOST_BITS_PER_WIDE_INT / 2)
169 /* Unpack a two-word integer into 4 words.
170 LOW and HI are the integer, as two `HOST_WIDE_INT' pieces.
171 WORDS points to the array of HOST_WIDE_INTs. */
173 static void
175 {
180 }
182 /* Pack an array of 4 words into a two-word integer.
183 WORDS points to the array of words.
184 The integer is stored into *LOW and *HI as two `HOST_WIDE_INT' pieces. */
186 static void
189 {
192 }
193 \f
194 /* Force the double-word integer L1, H1 to be within the range of the
195 integer type TYPE. Stores the properly truncated and sign-extended
196 double-word integer in *LV, *HV. Returns true if the operation
197 overflows, that is, argument and result are different. */
199 int
202 {
211 else
214 /* Size types *are* sign extended. */
219 /* First clear all bits that are beyond the type's precision. */
221 ;
224 else
225 {
229 }
231 /* Then do sign extension if necessary. */
237 {
238 /* Sign extend top half? */
242 }
244 {
247 }
248 else
249 {
250 /* Sign extend bottom half? */
252 {
255 }
256 }
261 /* If the value didn't fit, signal overflow. */
263 }
265 /* We force the double-int HIGH:LOW to the range of the type TYPE by
266 sign or zero extending it.
267 OVERFLOWABLE indicates if we are interested
268 in overflow of the value, when >0 we are only interested in signed
269 overflow, for <0 we are interested in any overflow. OVERFLOWED
270 indicates whether overflow has already occurred. CONST_OVERFLOWED
271 indicates whether constant overflow has already occurred. We force
272 T's value to be within range of T's type (by setting to 0 or 1 all
273 the bits outside the type's range). We set TREE_OVERFLOWED if,
274 OVERFLOWED is nonzero,
275 or OVERFLOWABLE is >0 and signed overflow occurs
276 or OVERFLOWABLE is <0 and any overflow occurs
277 We return a new tree node for the extended double-int. The node
278 is shared if no overflow flags are set. */
280 tree
284 {
288 /* Size types *are* sign extended. */
295 /* If we need to set overflow flags, return a new unshared node. */
297 {
301 {
308 }
309 }
311 /* Else build a shared node. */
313 }
314 \f
315 /* Add two doubleword integers with doubleword result.
316 Return nonzero if the operation overflows according to UNSIGNED_P.
317 Each argument is given as two `HOST_WIDE_INT' pieces.
318 One argument is L1 and H1; the other, L2 and H2.
319 The value is stored as two `HOST_WIDE_INT' pieces in *LV and *HV. */
321 int
326 {
328 HOST_WIDE_INT h;
338 else
340 }
342 /* Negate a doubleword integer with doubleword result.
343 Return nonzero if the operation overflows, assuming it's signed.
344 The argument is given as two `HOST_WIDE_INT' pieces in L1 and H1.
345 The value is stored as two `HOST_WIDE_INT' pieces in *LV and *HV. */
347 int
350 {
352 {
356 }
357 else
358 {
362 }
363 }
364 \f
365 /* Multiply two doubleword integers with doubleword result.
366 Return nonzero if the operation overflows according to UNSIGNED_P.
367 Each argument is given as two `HOST_WIDE_INT' pieces.
368 One argument is L1 and H1; the other, L2 and H2.
369 The value is stored as two `HOST_WIDE_INT' pieces in *LV and *HV. */
371 int
376 {
391 {
394 {
396 /* This product is <= 0xFFFE0001, the sum <= 0xFFFF0000. */
398 /* Since prod[p] < 0xFFFF, this sum <= 0xFFFFFFFF. */
402 }
404 }
409 /* Unsigned overflow is immediate. */
413 /* Check for signed overflow by calculating the signed representation of the
414 top half of the result; it should agree with the low half's sign bit. */
416 {
419 }
421 {
424 }
426 }
427 \f
428 /* Shift the doubleword integer in L1, H1 left by COUNT places
429 keeping only PREC bits of result.
430 Shift right if COUNT is negative.
431 ARITH nonzero specifies arithmetic shifting; otherwise use logical shift.
432 Store the value as two `HOST_WIDE_INT' pieces in *LV and *HV. */
434 void
438 {
442 {
445 }
451 {
452 /* Shifting by the host word size is undefined according to the
453 ANSI standard, so we must handle this as a special case. */
456 }
458 {
461 }
462 else
463 {
467 }
469 /* Sign extend all bits that are beyond the precision. */
477 ;
479 {
482 }
483 else
484 {
488 }
489 }
491 /* Shift the doubleword integer in L1, H1 right by COUNT places
492 keeping only PREC bits of result. COUNT must be positive.
493 ARITH nonzero specifies arithmetic shifting; otherwise use logical shift.
494 Store the value as two `HOST_WIDE_INT' pieces in *LV and *HV. */
496 void
501 {
504 signmask = (arith
512 {
513 /* Shifting by the host word size is undefined according to the
514 ANSI standard, so we must handle this as a special case. */
517 }
519 {
522 }
523 else
524 {
528 }
530 /* Zero / sign extend all bits that are beyond the precision. */
533 {
536 }
538 ;
540 {
543 }
544 else
545 {
549 }
550 }
551 \f
552 /* Rotate the doubleword integer in L1, H1 left by COUNT places
553 keeping only PREC bits of result.
554 Rotate right if COUNT is negative.
555 Store the value as two `HOST_WIDE_INT' pieces in *LV and *HV. */
557 void
561 {
573 }
575 /* Rotate the doubleword integer in L1, H1 left by COUNT places
576 keeping only PREC bits of result. COUNT must be positive.
577 Store the value as two `HOST_WIDE_INT' pieces in *LV and *HV. */
579 void
583 {
595 }
596 \f
597 /* Divide doubleword integer LNUM, HNUM by doubleword integer LDEN, HDEN
598 for a quotient (stored in *LQUO, *HQUO) and remainder (in *LREM, *HREM).
599 CODE is a tree code for a kind of division, one of
600 TRUNC_DIV_EXPR, FLOOR_DIV_EXPR, CEIL_DIV_EXPR, ROUND_DIV_EXPR
601 or EXACT_DIV_EXPR
602 It controls how the quotient is rounded to an integer.
603 Return nonzero if the operation overflows.
604 UNS nonzero says do unsigned division. */
606 int
609 HOST_WIDE_INT hnum_orig,
611 HOST_WIDE_INT hden_orig,
615 {
631 /* Calculate quotient sign and convert operands to unsigned. */
633 {
635 {
637 /* (minimum integer) / (-1) is the only overflow case. */
641 }
643 {
646 }
647 }
652 /* This unsigned division rounds toward zero. */
655 }
659 /* hden != 0 already checked. */
664 }
674 /* Special code for when the divisor < BASE. */
676 {
677 /* hnum != 0 already checked. */
679 {
683 }
684 }
685 else
686 {
687 /* Full double precision division,
688 with thanks to Don Knuth's "Seminumerical Algorithms". */
692 /* Find the highest nonzero divisor digit. */
695 {
698 }
700 /* Insure that the first digit of the divisor is at least BASE/2.
701 This is required by the quotient digit estimation algorithm. */
708 {
712 }
717 {
722 }
723 }
727 /* Main loop */
729 {
730 /* Guess the next quotient digit, quo_est, by dividing the first
731 two remaining dividend digits by the high order quotient digit.
732 quo_est is never low and is at most 2 high. */
739 else
742 /* Refine quo_est so it's usually correct, and at most one high. */
747 quo_est--;
749 /* Try QUO_EST as the quotient digit, by multiplying the
750 divisor by QUO_EST and subtracting from the remaining dividend.
751 Keep in mind that QUO_EST is the I - 1st digit. */
755 {
761 }
763 /* If quo_est was high by one, then num[i] went negative and
764 we need to correct things. */
766 {
767 quo_est--;
770 {
774 }
777 }
779 /* Store the quotient digit. */
781 }
782 }
786 finish_up:
787 /* If result is negative, make it so. */
791 /* Compute trial remainder: rem = num - (quo * den) */
797 {
806 {
807 /* quo = quo - 1; */
810 }
811 else
818 {
821 }
822 else
828 {
834 /* Get absolute values. */
840 /* If (2 * abs (lrem) >= abs (lden)) */
849 {
851 /* quo = quo - 1; */
854 else
855 /* quo = quo + 1; */
858 }
859 else
861 }
866 }
868 /* Compute true remainder: rem = num - (quo * den) */
873 }
875 /* If ARG2 divides ARG1 with zero remainder, carries out the division
876 of type CODE and returns the quotient.
877 Otherwise returns NULL_TREE. */
879 static tree
881 {
891 /* &obj[0] + -128 really should be compiled as &obj[-8] rather than
892 &obj[some_exotic_number]. */
894 {
898 type);
899 }
900 else
911 }
912 \f
913 /* This is nonzero if we should defer warnings about undefined
914 overflow. This facility exists because these warnings are a
915 special case. The code to estimate loop iterations does not want
916 to issue any warnings, since it works with expressions which do not
917 occur in user code. Various bits of cleanup code call fold(), but
918 only use the result if it has certain characteristics (e.g., is a
919 constant); that code only wants to issue a warning if the result is
920 used. */
924 /* If a warning about undefined overflow is deferred, this is the
925 warning. Note that this may cause us to turn two warnings into
926 one, but that is fine since it is sufficient to only give one
927 warning per expression. */
931 /* If a warning about undefined overflow is deferred, this is the
932 level at which the warning should be emitted. */
936 /* Start deferring overflow warnings. We could use a stack here to
937 permit nested calls, but at present it is not necessary. */
939 void
941 {
943 }
945 /* Stop deferring overflow warnings. If there is a pending warning,
946 and ISSUE is true, then issue the warning if appropriate. STMT is
947 the statement with which the warning should be associated (used for
948 location information); STMT may be NULL. CODE is the level of the
949 warning--a warn_strict_overflow_code value. This function will use
950 the smaller of CODE and the deferred code when deciding whether to
951 issue the warning. CODE may be zero to mean to always use the
952 deferred code. */
954 void
956 {
958 location_t locus;
963 {
969 }
980 /* Use the smallest code level when deciding to issue the
981 warning. */
990 else
993 }
995 /* Stop deferring overflow warnings, ignoring any deferred
996 warnings. */
998 void
1000 {
1002 }
1004 /* Whether we are deferring overflow warnings. */
1006 bool
1008 {
1010 }
1012 /* This is called when we fold something based on the fact that signed
1013 overflow is undefined. */
1015 static void
1017 {
1020 {
1023 {
1026 }
1027 }
1030 }
1031 \f
1032 /* Return true if the built-in mathematical function specified by CODE
1033 is odd, i.e. -f(x) == f(-x). */
1035 static bool
1037 {
1039 {
1073 }
1075 }
1077 /* Check whether we may negate an integer constant T without causing
1078 overflow. */
1080 bool
1082 {
1085 tree type;
1095 {
1100 }
1101 else
1106 }
1108 /* Determine whether an expression T can be cheaply negated using
1109 the function negate_expr without introducing undefined overflow. */
1111 static bool
1113 {
1114 tree type;
1123 {
1128 /* Check that -CST will not overflow type. */
1154 /* -(A + B) -> (-B) - A. */
1159 /* -(A + B) -> (-A) - B. */
1163 /* We can't turn -(A-B) into B-A when we honor signed zeros. */
1173 /* Fall through. */
1186 /* In general we can't negate A / B, because if A is INT_MIN and
1187 B is 1, we may turn this into INT_MIN / -1 which is undefined
1188 and actually traps on some architectures. But if overflow is
1189 undefined, we can negate, because - (INT_MIN / 1) is an
1190 overflow. */
1198 /* Negate -((double)float) as (double)(-float). */
1200 {
1204 }
1208 /* Negate -f(x) as f(-x). */
1214 /* Optimize -((int)x >> 31) into (unsigned)x >> 31. */
1216 {
1222 }
1227 }
1229 }
1231 /* Given T, an expression, return a folded tree for -T or NULL_TREE, if no
1232 simplification is possible.
1233 If negate_expr_p would return true for T, NULL_TREE will never be
1234 returned. */
1236 static tree
1238 {
1240 tree tem;
1243 {
1244 /* Convert - (~A) to A + 1. */
1260 /* Two's complement FP formats, such as c4x, may overflow. */
1270 {
1279 }
1301 {
1302 /* -(A + B) -> (-B) - A. */
1306 {
1310 }
1312 /* -(A + B) -> (-A) - B. */
1314 {
1318 }
1319 }
1323 /* - (A - B) -> B - A */
1335 /* Fall through. */
1339 {
1348 }
1356 /* In general we can't negate A / B, because if A is INT_MIN and
1357 B is 1, we may turn this into INT_MIN / -1 which is undefined
1358 and actually traps on some architectures. But if overflow is
1359 undefined, we can negate, because - (INT_MIN / 1) is an
1360 overflow. */
1362 {
1367 {
1374 }
1377 {
1384 }
1385 }
1389 /* Convert -((double)float) into (double)(-float). */
1391 {
1395 }
1399 /* Negate -f(x) as f(-x). */
1402 {
1408 }
1412 /* Optimize -((int)x >> 31) into (unsigned)x >> 31. */
1414 {
1419 {
1426 }
1427 }
1432 }
1435 }
1437 /* Like fold_negate_expr, but return a NEGATE_EXPR tree, if T can not be
1438 negated in a simpler way. Also allow for T to be NULL_TREE, in which case
1439 return NULL_TREE. */
1441 static tree
1443 {
1456 }
1457 \f
1458 /* Split a tree IN into a constant, literal and variable parts that could be
1459 combined with CODE to make IN. "constant" means an expression with
1460 TREE_CONSTANT but that isn't an actual constant. CODE must be a
1461 commutative arithmetic operation. Store the constant part into *CONP,
1462 the literal in *LITP and return the variable part. If a part isn't
1463 present, set it to null. If the tree does not decompose in this way,
1464 return the entire tree as the variable part and the other parts as null.
1466 If CODE is PLUS_EXPR we also split trees that use MINUS_EXPR. In that
1467 case, we negate an operand that was subtracted. Except if it is a
1468 literal for which we use *MINUS_LITP instead.
1470 If NEGATE_P is true, we are negating all of IN, again except a literal
1471 for which we use *MINUS_LITP instead.
1473 If IN is itself a literal or constant, return it as appropriate.
1475 Note that we do not guarantee that any of the three values will be the
1476 same type as IN, but they will have the same signedness and mode. */
1478 static tree
1481 {
1488 /* Strip any conversions that don't change the machine mode or signedness. */
1497 /* We can associate addition and subtraction together (even
1498 though the C standard doesn't say so) for integers because
1499 the value is not affected. For reals, the value might be
1500 affected, so we can't. */
1503 {
1509 /* First see if either of the operands is a literal, then a constant. */
1522 /* If we haven't dealt with either operand, this is not a case we can
1523 decompose. Otherwise, VAR is either of the ones remaining, if any. */
1528 else
1531 /* Now do any needed negations. */
1538 }
1541 else
1545 {
1552 }
1555 }
1557 /* Re-associate trees split by the above function. T1 and T2 are either
1558 expressions to associate or null. Return the new expression, if any. If
1559 we build an operation, do it in TYPE and with CODE. */
1561 static tree
1563 {
1569 /* If either input is CODE, a PLUS_EXPR, or a MINUS_EXPR, don't
1570 try to fold this since we will have infinite recursion. But do
1571 deal with any NEGATE_EXPRs. */
1574 {
1576 {
1585 }
1587 {
1590 }
1594 }
1598 }
1599 \f
1600 /* Check whether TYPE1 and TYPE2 are equivalent integer types, suitable
1601 for use in int_const_binop, size_binop and size_diffop. */
1603 static bool
1605 {
1612 {
1621 }
1626 }
1629 /* Combine two integer constants ARG1 and ARG2 under operation CODE
1630 to produce a new constant. Return NULL_TREE if we don't know how
1631 to evaluate CODE at compile-time.
1633 If NOTRUNC is nonzero, do not truncate the result to fit the data type. */
1635 tree
1637 {
1641 HOST_WIDE_INT hi;
1643 HOST_WIDE_INT garbageh;
1644 tree t;
1647 int is_sizetype
1657 {
1673 /* It's unclear from the C standard whether shifts can overflow.
1674 The following code ignores overflow; perhaps a C standard
1675 interpretation ruling is needed. */
1704 /* This is a shortcut for a common special case. */
1709 {
1715 }
1717 /* ... fall through ... */
1723 {
1726 }
1729 {
1732 }
1739 /* This is a shortcut for a common special case. */
1744 {
1749 }
1751 /* ... fall through ... */
1769 else
1775 else
1781 }
1784 {
1787 /* Propagate overflow flags ourselves. */
1790 {
1793 }
1794 }
1795 else
1801 }
1803 /* Combine two constants ARG1 and ARG2 under operation CODE to produce a new
1804 constant. We assume ARG1 and ARG2 have the same data type, or at least
1805 are the same kind of constant and the same machine mode. Return zero if
1806 combining the constants is not allowed in the current operating mode.
1808 If NOTRUNC is nonzero, do not truncate the result to fit the data type. */
1810 static tree
1812 {
1813 /* Sanity check for the recursive cases. */
1824 {
1826 REAL_VALUE_TYPE d1;
1827 REAL_VALUE_TYPE d2;
1828 REAL_VALUE_TYPE value;
1829 REAL_VALUE_TYPE result;
1833 /* The following codes are handled by real_arithmetic. */
1835 {
1846 }
1854 /* Don't perform operation if we honor signaling NaNs and
1855 either operand is a NaN. */
1860 /* Don't perform operation if it would raise a division
1861 by zero exception. */
1867 /* If either operand is a NaN, just return it. Otherwise, set up
1868 for floating-point trap; we return an overflow. */
1877 /* Don't constant fold this floating point operation if
1878 the result has overflowed and flag_trapping_math. */
1886 /* Don't constant fold this floating point operation if the
1887 result may dependent upon the run-time rounding mode and
1888 flag_rounding_math is set, or if GCC's software emulation
1889 is unable to accurately represent the result. */
1900 }
1903 {
1904 FIXED_VALUE_TYPE f1;
1905 FIXED_VALUE_TYPE f2;
1906 FIXED_VALUE_TYPE result;
1911 /* The following codes are handled by fixed_arithmetic. */
1913 {
1930 }
1937 /* Propagate overflow flags. */
1939 {
1942 }
1946 }
1949 {
1958 {
1969 notrunc);
1973 notrunc);
1977 {
1978 tree magsquared
1982 notrunc);
1983 tree t1
1987 notrunc);
1988 tree t2
1992 notrunc);
1999 }
2004 }
2008 }
2011 }
2013 /* Create a size type INT_CST node with NUMBER sign extended. KIND
2014 indicates which particular sizetype to create. */
2016 tree
2018 {
2020 }
2021 \f
2022 /* Combine operands OP1 and OP2 with arithmetic operation CODE. CODE
2023 is a tree code. The type of the result is taken from the operands.
2024 Both must be equivalent integer types, ala int_binop_types_match_p.
2025 If the operands are constant, so is the result. */
2027 tree
2029 {
2038 /* Handle the special case of two integer constants faster. */
2040 {
2041 /* And some specific cases even faster than that. */
2043 {
2048 }
2050 {
2053 }
2055 {
2058 }
2060 /* Handle general case of two integer constants. */
2062 }
2065 }
2067 /* Given two values, either both of sizetype or both of bitsizetype,
2068 compute the difference between the two values. Return the value
2069 in signed type corresponding to the type of the operands. */
2071 tree
2073 {
2075 tree ctype;
2080 /* If the type is already signed, just do the simple thing. */
2088 else
2091 /* If either operand is not a constant, do the conversions to the signed
2092 type and subtract. The hardware will do the right thing with any
2093 overflow in the subtraction. */
2098 /* If ARG0 is larger than ARG1, subtract and return the result in CTYPE.
2099 Otherwise, subtract the other way, convert to CTYPE (we know that can't
2100 overflow) and negate (which can't either). Special-case a result
2101 of zero while we're here. */
2106 else
2110 }
2111 \f
2112 /* A subroutine of fold_convert_const handling conversions of an
2113 INTEGER_CST to another integer type. */
2115 static tree
2117 {
2118 tree t;
2120 /* Given an integer constant, make new constant with new type,
2121 appropriately sign-extended or truncated. */
2124 /* Don't set the overflow when
2125 converting a pointer */
2133 }
2135 /* A subroutine of fold_convert_const handling conversions a REAL_CST
2136 to an integer type. */
2138 static tree
2140 {
2142 tree t;
2144 /* The following code implements the floating point to integer
2145 conversion rules required by the Java Language Specification,
2146 that IEEE NaNs are mapped to zero and values that overflow
2147 the target precision saturate, i.e. values greater than
2148 INT_MAX are mapped to INT_MAX, and values less than INT_MIN
2149 are mapped to INT_MIN. These semantics are allowed by the
2150 C and C++ standards that simply state that the behavior of
2151 FP-to-integer conversion is unspecified upon overflow. */
2154 REAL_VALUE_TYPE r;
2158 {
2165 }
2167 /* If R is NaN, return zero and show we have an overflow. */
2169 {
2173 }
2175 /* See if R is less than the lower bound or greater than the
2176 upper bound. */
2179 {
2183 {
2187 }
2188 }
2191 {
2194 {
2197 {
2201 }
2202 }
2203 }
2211 }
2213 /* A subroutine of fold_convert_const handling conversions of a
2214 FIXED_CST to an integer type. */
2216 static tree
2218 {
2219 tree t;
2223 /* Right shift FIXED_CST to temp by fbit. */
2227 {
2232 /* Left shift temp to temp_trunc by fbit. */
2237 }
2238 else
2239 {
2244 }
2246 /* If FIXED_CST is negative, we need to round the value toward 0.
2247 By checking if the fractional bits are not zero to add 1 to temp. */
2250 {
2251 double_int one;
2255 }
2257 /* Given a fixed-point constant, make new constant with new type,
2258 appropriately sign-extended or truncated. */
2266 }
2268 /* A subroutine of fold_convert_const handling conversions a REAL_CST
2269 to another floating point type. */
2271 static tree
2273 {
2274 REAL_VALUE_TYPE value;
2275 tree t;
2282 }
2284 /* A subroutine of fold_convert_const handling conversions a FIXED_CST
2285 to a floating point type. */
2287 static tree
2289 {
2290 REAL_VALUE_TYPE value;
2291 tree t;
2300 }
2302 /* A subroutine of fold_convert_const handling conversions a FIXED_CST
2303 to another fixed-point type. */
2305 static tree
2307 {
2308 FIXED_VALUE_TYPE value;
2309 tree t;
2316 /* Propagate overflow flags. */
2318 {
2321 }
2325 }
2327 /* A subroutine of fold_convert_const handling conversions an INTEGER_CST
2328 to a fixed-point type. */
2330 static tree
2332 {
2333 FIXED_VALUE_TYPE value;
2334 tree t;
2343 /* Propagate overflow flags. */
2345 {
2348 }
2352 }
2354 /* A subroutine of fold_convert_const handling conversions a REAL_CST
2355 to a fixed-point type. */
2357 static tree
2359 {
2360 FIXED_VALUE_TYPE value;
2361 tree t;
2369 /* Propagate overflow flags. */
2371 {
2374 }
2378 }
2380 /* Attempt to fold type conversion operation CODE of expression ARG1 to
2381 type TYPE. If no simplification can be done return NULL_TREE. */
2383 static tree
2385 {
2390 {
2397 }
2399 {
2406 }
2408 {
2415 }
2417 }
2419 /* Construct a vector of zero elements of vector type TYPE. */
2421 static tree
2423 {
2434 }
2436 /* Returns true, if ARG is convertible to TYPE using a NOP_EXPR. */
2438 bool
2440 {
2455 {
2467 }
2468 }
2470 /* Convert expression ARG to type TYPE. Used by the middle-end for
2471 simple conversions in preference to calling the front-end's convert. */
2473 tree
2475 {
2477 tree tem;
2491 {
2496 {
2500 }
2505 {
2508 }
2515 {
2519 }
2521 {
2525 }
2527 {
2531 }
2534 {
2552 }
2557 {
2561 }
2564 {
2578 }
2582 {
2592 {
2596 {
2600 }
2608 }
2612 }
2630 }
2631 }
2632 \f
2633 /* Return false if expr can be assumed not to be an lvalue, true
2634 otherwise. */
2636 static bool
2638 {
2639 /* We only need to wrap lvalue tree codes. */
2641 {
2676 /* Assume the worst for front-end tree codes. */
2680 }
2683 }
2685 /* Return an expr equal to X but certainly not valid as an lvalue. */
2687 tree
2689 {
2690 /* While we are in GIMPLE, NON_LVALUE_EXPR doesn't mean anything to
2691 us. */
2698 }
2700 /* Nonzero means lvalues are limited to those valid in pedantic ANSI C.
2701 Zero means allow extended lvalues. */
2705 /* When pedantic, return an expr equal to X but certainly not valid as a
2706 pedantic lvalue. Otherwise, return X. */
2708 static tree
2710 {
2713 else
2715 }
2716 \f
2717 /* Given a tree comparison code, return the code that is the logical inverse
2718 of the given code. It is not safe to do this for floating-point
2719 comparisons, except for NE_EXPR and EQ_EXPR, so we receive a machine mode
2720 as well: if reversing the comparison is unsafe, return ERROR_MARK. */
2722 enum tree_code
2724 {
2729 {
2760 }
2761 }
2763 /* Similar, but return the comparison that results if the operands are
2764 swapped. This is safe for floating-point. */
2766 enum tree_code
2768 {
2770 {
2796 }
2797 }
2800 /* Convert a comparison tree code from an enum tree_code representation
2801 into a compcode bit-based encoding. This function is the inverse of
2802 compcode_to_comparison. */
2804 static enum comparison_code
2806 {
2808 {
2839 }
2840 }
2842 /* Convert a compcode bit-based encoding of a comparison operator back
2843 to GCC's enum tree_code representation. This function is the
2844 inverse of comparison_to_compcode. */
2846 static enum tree_code
2848 {
2850 {
2881 }
2882 }
2884 /* Return a tree for the comparison which is the combination of
2885 doing the AND or OR (depending on CODE) of the two operations LCODE
2886 and RCODE on the identical operands LL_ARG and LR_ARG. Take into account
2887 the possibility of trapping if the mode has NaNs, and return NULL_TREE
2888 if this makes the transformation invalid. */
2890 tree
2894 {
2901 {
2912 }
2915 {
2916 /* Eliminate unordered comparisons, as well as LTGT and ORD
2917 which are not used unless the mode has NaNs. */
2923 }
2925 {
2926 /* Check that the original operation and the optimized ones will trap
2927 under the same condition. */
2938 /* In a short-circuited boolean expression the LHS might be
2939 such that the RHS, if evaluated, will never trap. For
2940 example, in ORD (x, y) && (x < y), we evaluate the RHS only
2941 if neither x nor y is NaN. (This is a mixed blessing: for
2942 example, the expression above will never trap, hence
2943 optimizing it to x < y would be invalid). */
2948 /* If the comparison was short-circuited, and only the RHS
2949 trapped, we may now generate a spurious trap. */
2954 /* If we changed the conditions that cause a trap, we lose. */
2957 }
2963 else
2966 }
2968 /* Return nonzero if CODE is a tree code that represents a truth value. */
2970 static int
2972 {
2977 }
2978 \f
2979 /* Return nonzero if two operands (typically of the same tree node)
2980 are necessarily equal. If either argument has side-effects this
2981 function returns zero. FLAGS modifies behavior as follows:
2983 If OEP_ONLY_CONST is set, only return nonzero for constants.
2984 This function tests whether the operands are indistinguishable;
2985 it does not test whether they are equal using C's == operation.
2986 The distinction is important for IEEE floating point, because
2987 (1) -0.0 and 0.0 are distinguishable, but -0.0==0.0, and
2988 (2) two NaNs may be indistinguishable, but NaN!=NaN.
2990 If OEP_ONLY_CONST is unset, a VAR_DECL is considered equal to itself
2991 even though it may hold multiple values during a function.
2992 This is because a GCC tree node guarantees that nothing else is
2993 executed between the evaluation of its "operands" (which may often
2994 be evaluated in arbitrary order). Hence if the operands themselves
2995 don't side-effect, the VAR_DECLs, PARM_DECLs etc... must hold the
2996 same value in each operand/subexpression. Hence leaving OEP_ONLY_CONST
2997 unset means assuming isochronic (or instantaneous) tree equivalence.
2998 Unless comparing arbitrary expression trees, such as from different
2999 statements, this flag can usually be left unset.
3001 If OEP_PURE_SAME is set, then pure functions with identical arguments
3002 are considered the same. It is used when the caller has other ways
3003 to ensure that global memory is unchanged in between. */
3005 int
3007 {
3008 /* If either is ERROR_MARK, they aren't equal. */
3012 /* If both types don't have the same signedness, then we can't consider
3013 them equal. We must check this before the STRIP_NOPS calls
3014 because they may change the signedness of the arguments. */
3018 /* If both types don't have the same precision, then it is not safe
3019 to strip NOPs. */
3026 /* In case both args are comparisons but with different comparison
3027 code, try to swap the comparison operands of one arg to produce
3028 a match and compare that variant. */
3032 {
3040 }
3043 /* This is needed for conversions and for COMPONENT_REF.
3044 Might as well play it safe and always test this. */
3050 /* If ARG0 and ARG1 are the same SAVE_EXPR, they are necessarily equal.
3051 We don't care about side effects in that case because the SAVE_EXPR
3052 takes care of that for us. In all other cases, two expressions are
3053 equal if they have no side effects. If we have two identical
3054 expressions with side effects that should be treated the same due
3055 to the only side effects being identical SAVE_EXPR's, that will
3056 be detected in the recursive calls below. */
3062 /* Next handle constant cases, those for which we can return 1 even
3063 if ONLY_CONST is set. */
3066 {
3081 {
3082 /* If we do not distinguish between signed and unsigned zero,
3083 consider them equal. */
3086 }
3090 {
3096 {
3098 flags))
3102 }
3105 }
3109 flags)
3111 flags));
3124 }
3129 /* Define macros to test an operand from arg0 and arg1 for equality and a
3130 variant that allows null and views null as being different from any
3131 non-null value. In the latter case, if either is null, the both
3132 must be; otherwise, do the normal comparison. */
3133 #define OP_SAME(N) operand_equal_p (TREE_OPERAND (arg0, N), \
3134 TREE_OPERAND (arg1, N), flags)
3136 #define OP_SAME_WITH_NULL(N) \
3137 ((!TREE_OPERAND (arg0, N) || !TREE_OPERAND (arg1, N)) \
3138 ? TREE_OPERAND (arg0, N) == TREE_OPERAND (arg1, N) : OP_SAME (N))
3141 {
3143 /* Two conversions are equal only if signedness and modes match. */
3145 {
3155 }
3165 /* For commutative ops, allow the other order. */
3173 /* If either of the pointer (or reference) expressions we are
3174 dereferencing contain a side effect, these cannot be equal. */
3180 {
3190 /* Operands 2 and 3 may be null.
3191 Compare the array index by value if it is constant first as we
3192 may have different types but same value here. */
3201 /* Handle operand 2 the same as for ARRAY_REF. Operand 0
3202 may be NULL when we're called to compare MEM_EXPRs. */
3212 }
3216 {
3231 /* Otherwise take into account this is a commutative operation. */
3239 }
3243 {
3245 /* If the CALL_EXPRs call different functions, then they
3246 clearly can not be equal. */
3248 flags))
3251 {
3255 else
3259 }
3261 /* Now see if all the arguments are the same. */
3262 {
3273 /* If we get here and both argument lists are exhausted
3274 then the CALL_EXPRs are equal. */
3276 }
3279 }
3282 /* Consider __builtin_sqrt equal to sqrt. */
3290 }
3292 #undef OP_SAME
3293 #undef OP_SAME_WITH_NULL
3294 }
3295 \f
3296 /* Similar to operand_equal_p, but see if ARG0 might have been made by
3297 shorten_compare from ARG1 when ARG1 was being compared with OTHER.
3299 When in doubt, return 0. */
3301 static int
3303 {
3315 /* Discard any conversions that don't change the modes of ARG0 and ARG1
3316 and see if the inner values are the same. This removes any
3317 signedness comparison, which doesn't matter here. */
3324 /* Duplicate what shorten_compare does to ARG1 and see if that gives the
3325 actual comparison operand, ARG0.
3327 First throw away any conversions to wider types
3328 already present in the operands. */
3337 {
3340 /* Make sure shorter operand is extended the right way
3341 to match the longer operand. */
3347 }
3350 }
3351 \f
3352 /* See if ARG is an expression that is either a comparison or is performing
3353 arithmetic on comparisons. The comparisons must only be comparing
3354 two different values, which will be stored in *CVAL1 and *CVAL2; if
3355 they are nonzero it means that some operands have already been found.
3356 No variables may be used anywhere else in the expression except in the
3357 comparisons. If SAVE_P is true it means we removed a SAVE_EXPR around
3358 the expression and save_expr needs to be called with CVAL1 and CVAL2.
3360 If this is true, return 1. Otherwise, return zero. */
3362 static int
3364 {
3368 /* We can handle some of the tcc_expression cases here. */
3378 {
3379 /* If we've already found a CVAL1 or CVAL2, this expression is
3380 two complex to handle. */
3386 }
3389 {
3412 /* First see if we can handle the first operand, then the second. For
3413 the second operand, we know *CVAL1 can't be zero. It must be that
3414 one side of the comparison is each of the values; test for the
3415 case where this isn't true by failing if the two operands
3416 are the same. */
3425 ;
3429 ;
3430 else
3434 ;
3438 ;
3439 else
3446 }
3447 }
3448 \f
3449 /* ARG is a tree that is known to contain just arithmetic operations and
3450 comparisons. Evaluate the operations in the tree substituting NEW0 for
3451 any occurrence of OLD0 as an operand of a comparison and likewise for
3452 NEW1 and OLD1. */
3454 static tree
3456 {
3461 /* We can handle some of the tcc_expression cases here. */
3469 {
3484 {
3501 }
3502 /* Fall through - ??? */
3505 {
3509 /* We need to check both for exact equality and tree equality. The
3510 former will be true if the operand has a side-effect. In that
3511 case, we know the operand occurred exactly once. */
3524 }
3528 }
3529 }
3530 \f
3531 /* Return a tree for the case when the result of an expression is RESULT
3532 converted to TYPE and OMITTED was previously an operand of the expression
3533 but is now not needed (e.g., we folded OMITTED * 0).
3535 If OMITTED has side effects, we must evaluate it. Otherwise, just do
3536 the conversion of RESULT to TYPE. */
3538 tree
3540 {
3543 /* If the resulting operand is an empty statement, just return the omitted
3544 statement casted to void. */
3552 }
3554 /* Similar, but call pedantic_non_lvalue instead of non_lvalue. */
3556 static tree
3558 {
3561 /* If the resulting operand is an empty statement, just return the omitted
3562 statement casted to void. */
3570 }
3572 /* Return a tree for the case when the result of an expression is RESULT
3573 converted to TYPE and OMITTED1 and OMITTED2 were previously operands
3574 of the expression but are now not needed.
3576 If OMITTED1 or OMITTED2 has side effects, they must be evaluated.
3577 If both OMITTED1 and OMITTED2 have side effects, OMITTED1 is
3578 evaluated before OMITTED2. Otherwise, if neither has side effects,
3579 just do the conversion of RESULT to TYPE. */
3581 tree
3583 {
3592 }
3594 \f
3595 /* Return a simplified tree node for the truth-negation of ARG. This
3596 never alters ARG itself. We assume that ARG is an operation that
3597 returns a truth value (0 or 1).
3599 FIXME: one would think we would fold the result, but it causes
3600 problems with the dominator optimizer. */
3602 tree
3604 {
3608 /* If this is a comparison, we can simply invert it, except for
3609 floating-point non-equality comparisons, in which case we just
3610 enclose a TRUTH_NOT_EXPR around what we have. */
3613 {
3616 && flag_trapping_math
3620 else
3621 {
3626 else
3629 }
3630 }
3633 {
3648 /* Here we can invert either operand. We invert the first operand
3649 unless the second operand is a TRUTH_NOT_EXPR in which case our
3650 result is the XOR of the first operand with the inside of the
3651 negation of the second operand. */
3656 else
3675 {
3678 /* A COND_EXPR may have a throw as one operand, which
3679 then has void type. Just leave void operands
3680 as they are. */
3686 }
3719 }
3722 }
3724 /* Return a simplified tree node for the truth-negation of ARG. This
3725 never alters ARG itself. We assume that ARG is an operation that
3726 returns a truth value (0 or 1).
3728 FIXME: one would think we would fold the result, but it causes
3729 problems with the dominator optimizer. */
3731 tree
3733 {
3734 tree tem;
3744 }
3746 /* Given a bit-wise operation CODE applied to ARG0 and ARG1, see if both
3747 operands are another bit-wise operation with a common input. If so,
3748 distribute the bit operations to save an operation and possibly two if
3749 constants are involved. For example, convert
3750 (A | B) & (A | C) into A | (B & C)
3751 Further simplification will occur if B and C are constants.
3753 If this optimization cannot be done, 0 will be returned. */
3755 static tree
3757 {
3758 tree common;
3768 {
3772 }
3774 {
3778 }
3780 {
3784 }
3786 {
3790 }
3791 else
3796 }
3798 /* Knowing that ARG0 and ARG1 are both RDIV_EXPRs, simplify a binary operation
3799 with code CODE. This optimization is unsafe. */
3800 static tree
3802 {
3806 /* (A / C) +- (B / C) -> (A +- B) / C. */
3816 /* (A / C1) +- (A / C2) -> A * (1 / C1 +- 1 / C2). */
3821 {
3833 }
3836 }
3837 \f
3838 /* Return a BIT_FIELD_REF of type TYPE to refer to BITSIZE bits of INNER
3839 starting at BITPOS. The field is unsigned if UNSIGNEDP is nonzero. */
3841 static tree
3844 {
3845 tree result;
3848 {
3855 }
3863 }
3865 /* Optimize a bit-field compare.
3867 There are two cases: First is a compare against a constant and the
3868 second is a comparison of two items where the fields are at the same
3869 bit position relative to the start of a chunk (byte, halfword, word)
3870 large enough to contain it. In these cases we can avoid the shift
3871 implicit in bitfield extractions.
3873 For constants, we emit a compare of the shifted constant with the
3874 BIT_AND_EXPR of a mask and a byte, halfword, or word of the operand being
3875 compared. For two fields at the same position, we do the ANDs with the
3876 similar mask and compare the result of the ANDs.
3878 CODE is the comparison code, known to be either NE_EXPR or EQ_EXPR.
3879 COMPARE_TYPE is the type of the comparison, and LHS and RHS
3880 are the left and right operands of the comparison, respectively.
3882 If the optimization described above can be done, we return the resulting
3883 tree. Otherwise we return zero. */
3885 static tree
3888 {
3897 tree mask;
3898 tree offset;
3900 /* Get all the information about the extractions being done. If the bit size
3901 if the same as the size of the underlying object, we aren't doing an
3902 extraction at all and so can do nothing. We also don't want to
3903 do anything if the inner expression is a PLACEHOLDER_EXPR since we
3904 then will no longer be able to replace it. */
3912 {
3913 /* If this is not a constant, we can only do something if bit positions,
3914 sizes, and signedness are the same. */
3922 }
3924 /* See if we can find a mode to refer to this field. We should be able to,
3925 but fail if we can't. */
3934 /* Set signed and unsigned types of the precision of this mode for the
3935 shifts below. */
3939 /* Compute the bit position and size for the new reference and our offset
3940 within it. If the new reference is the same size as the original, we
3941 won't optimize anything, so return zero. */
3951 /* Make the mask to be used against the extracted field. */
3958 /* If not comparing with constant, just rework the comparison
3959 and return. */
3963 unsigned_type,
3966 mask),
3969 unsigned_type,
3972 mask));
3974 /* Otherwise, we are handling the constant case. See if the constant is too
3975 big for the field. Warn and return a tree of for 0 (false) if so. We do
3976 this not only for its own sake, but to avoid having to test for this
3977 error case below. If we didn't, we might generate wrong code.
3979 For unsigned fields, the constant shifted right by the field length should
3980 be all zero. For signed fields, the high-order bits should agree with
3981 the sign bit. */
3984 {
3988 {
3992 }
3993 }
3994 else
3995 {
3999 {
4003 }
4004 }
4006 /* Single-bit compares should always be against zero. */
4008 {
4011 }
4013 /* Make a new bitfield reference, shift the constant over the
4014 appropriate number of bits and mask it with the computed mask
4015 (in case this was a signed field). If we changed it, make a new one. */
4018 {
4021 }
4031 rhs);
4032 }
4033 \f
4034 /* Subroutine for fold_truthop: decode a field reference.
4036 If EXP is a comparison reference, we return the innermost reference.
4038 *PBITSIZE is set to the number of bits in the reference, *PBITPOS is
4039 set to the starting bit number.
4041 If the innermost field can be completely contained in a mode-sized
4042 unit, *PMODE is set to that mode. Otherwise, it is set to VOIDmode.
4044 *PVOLATILEP is set to 1 if the any expression encountered is volatile;
4045 otherwise it is not changed.
4047 *PUNSIGNEDP is set to the signedness of the field.
4049 *PMASK is set to the mask used. This is either contained in a
4050 BIT_AND_EXPR or derived from the width of the field.
4052 *PAND_MASK is set to the mask found in a BIT_AND_EXPR, if any.
4054 Return 0 if this is not a component reference or is one that we can't
4055 do anything with. */
4057 static tree
4062 {
4066 tree unsigned_type;
4069 /* All the optimizations using this function assume integer fields.
4070 There are problems with FP fields since the type_for_size call
4071 below can fail for, e.g., XFmode. */
4075 /* We are interested in the bare arrangement of bits, so strip everything
4076 that doesn't affect the machine mode. However, record the type of the
4077 outermost expression if it may matter below. */
4085 {
4091 }
4100 /* If the number of bits in the reference is the same as the bitsize of
4101 the outer type, then the outer type gives the signedness. Otherwise
4102 (in case of a small bitfield) the signedness is unchanged. */
4106 /* Compute the mask to access the bitfield. */
4115 /* Merge it with the mask we found in the BIT_AND_EXPR, if any. */
4123 }
4125 /* Return nonzero if MASK represents a mask of SIZE ones in the low-order
4126 bit positions. */
4128 static int
4130 {
4133 tree tmask;
4137 return
4144 }
4146 /* Subroutine for fold: determine if VAL is the INTEGER_CONST that
4147 represents the sign bit of EXP's type. If EXP represents a sign
4148 or zero extension, also test VAL against the unextended type.
4149 The return value is the (sub)expression whose sign bit is VAL,
4150 or NULL_TREE otherwise. */
4152 static tree
4154 {
4158 tree t;
4160 /* Tree EXP must have an integral type. */
4165 /* Tree VAL must be an integer constant. */
4172 {
4179 }
4180 else
4181 {
4188 }
4190 /* We mask off those bits beyond TREE_TYPE (exp) so that we can
4191 treat VAL as if it were unsigned. */
4196 /* Handle extension from a narrower type. */
4202 }
4204 /* Subroutine for fold_truthop: determine if an operand is simple enough
4205 to be evaluated unconditionally. */
4207 static int
4209 {
4210 /* Strip any conversions that don't change the machine mode. */
4219 /* Don't regard global variables as simple. They may be
4220 allocated in ways unknown to the compiler (shared memory,
4221 #pragma weak, etc). */
4224 /* Loading a static variable is unduly expensive, but global
4225 registers aren't expensive. */
4227 }
4228 \f
4229 /* The following functions are subroutines to fold_range_test and allow it to
4230 try to change a logical combination of comparisons into a range test.
4232 For example, both
4233 X == 2 || X == 3 || X == 4 || X == 5
4234 and
4235 X >= 2 && X <= 5
4236 are converted to
4237 (unsigned) (X - 2) <= 3
4239 We describe each set of comparisons as being either inside or outside
4240 a range, using a variable named like IN_P, and then describe the
4241 range with a lower and upper bound. If one of the bounds is omitted,
4242 it represents either the highest or lowest value of the type.
4244 In the comments below, we represent a range by two numbers in brackets
4245 preceded by a "+" to designate being inside that range, or a "-" to
4246 designate being outside that range, so the condition can be inverted by
4247 flipping the prefix. An omitted bound is represented by a "-". For
4248 example, "- [-, 10]" means being outside the range starting at the lowest
4249 possible value and ending at 10, in other words, being greater than 10.
4250 The range "+ [-, -]" is always true and hence the range "- [-, -]" is
4251 always false.
4253 We set up things so that the missing bounds are handled in a consistent
4254 manner so neither a missing bound nor "true" and "false" need to be
4255 handled using a special case. */
4257 /* Return the result of applying CODE to ARG0 and ARG1, but handle the case
4258 of ARG0 and/or ARG1 being omitted, meaning an unlimited range. UPPER0_P
4259 and UPPER1_P are nonzero if the respective argument is an upper bound
4260 and zero for a lower. TYPE, if nonzero, is the type of the result; it
4261 must be specified for a comparison. ARG1 will be converted to ARG0's
4262 type if both are specified. */
4264 static tree
4267 {
4268 tree tem;
4272 /* If neither arg represents infinity, do the normal operation.
4273 Else, if not a comparison, return infinity. Else handle the special
4274 comparison rules. Note that most of the cases below won't occur, but
4275 are handled for consistency. */
4278 {
4283 }
4288 /* Set SGN[01] to -1 if ARG[01] is a lower bound, 1 for upper, and 0
4289 for neither. In real maths, we cannot assume open ended ranges are
4290 the same. But, this is computer arithmetic, where numbers are finite.
4291 We can therefore make the transformation of any unbounded range with
4292 the value Z, Z being greater than any representable number. This permits
4293 us to treat unbounded ranges as equal. */
4297 {
4318 }
4321 }
4322 \f
4323 /* Given EXP, a logical expression, set the range it is testing into
4324 variables denoted by PIN_P, PLOW, and PHIGH. Return the expression
4325 actually being tested. *PLOW and *PHIGH will be made of the same
4326 type as the returned expression. If EXP is not a comparison, we
4327 will most likely not be returning a useful value and range. Set
4328 *STRICT_OVERFLOW_P to true if the return value is only valid
4329 because signed overflow is undefined; otherwise, do not change
4330 *STRICT_OVERFLOW_P. */
4332 static tree
4335 {
4342 /* Start with simply saying "EXP != 0" and then look at the code of EXP
4343 and see if we can refine the range. Some of the cases below may not
4344 happen, but it doesn't seem worth worrying about this. We "continue"
4345 the outer loop when we've changed something; otherwise we "break"
4346 the switch, which will "break" the while. */
4352 {
4357 {
4369 }
4372 {
4379 /* We can only do something if the range is testing for zero
4380 and if the second operand is an integer constant. Note that
4381 saying something is "in" the range we make is done by
4382 complementing IN_P since it will set in the initial case of
4383 being not equal to zero; "out" is leaving it alone. */
4390 {
4411 }
4413 /* If this is an unsigned comparison, we also know that EXP is
4414 greater than or equal to zero. We base the range tests we make
4415 on that fact, so we record it here so we can parse existing
4416 range tests. We test arg0_type since often the return type
4417 of, e.g. EQ_EXPR, is boolean. */
4419 {
4423 NULL_TREE))
4428 /* If the high bound is missing, but we have a nonzero low
4429 bound, reverse the range so it goes from zero to the low bound
4430 minus 1. */
4432 {
4437 }
4438 }
4444 /* (-x) IN [a,b] -> x in [-b, -a] */
4456 /* ~ X -> -X - 1 */
4465 /* If flag_wrapv and ARG0_TYPE is signed, then we cannot
4466 move a constant to the other side. */
4471 /* If EXP is signed, any overflow in the computation is undefined,
4472 so we don't worry about it so long as our computations on
4473 the bounds don't overflow. For unsigned, overflow is defined
4474 and this is exactly the right thing. */
4486 /* Check for an unsigned range which has wrapped around the maximum
4487 value thus making n_high < n_low, and normalize it. */
4489 {
4495 /* If the range is of the form +/- [ x+1, x ], we won't
4496 be able to normalize it. But then, it represents the
4497 whole range or the empty set, so make it
4498 +/- [ -, - ]. */
4502 else
4504 }
4505 else
4529 /* If we're converting arg0 from an unsigned type, to exp,
4530 a signed type, we will be doing the comparison as unsigned.
4531 The tests above have already verified that LOW and HIGH
4532 are both positive.
4534 So we have to ensure that we will handle large unsigned
4535 values the same way that the current signed bounds treat
4536 negative values. */
4539 {
4540 tree high_positive;
4541 tree equiv_type;
4542 /* For fixed-point modes, we need to pass the saturating flag
4543 as the 2nd parameter. */
4548 else
4552 /* A range without an upper bound is, naturally, unbounded.
4553 Since convert would have cropped a very large value, use
4554 the max value for the destination type. */
4555 high_positive
4562 high_positive),
4565 /* If the low bound is specified, "and" the range with the
4566 range for which the original unsigned value will be
4567 positive. */
4569 {
4573 integer_zero_node),
4574 high_positive))
4578 }
4579 else
4580 {
4581 /* Otherwise, "or" the range with the range of the input
4582 that will be interpreted as negative. */
4586 integer_zero_node),
4587 high_positive))
4591 }
4592 }
4600 }
4603 }
4605 /* If EXP is a constant, we can evaluate whether this is true or false. */
4607 {
4614 }
4618 }
4619 \f
4620 /* Given a range, LOW, HIGH, and IN_P, an expression, EXP, and a result
4621 type, TYPE, return an expression to test if EXP is in (or out of, depending
4622 on IN_P) the range. Return 0 if the test couldn't be created. */
4624 static tree
4626 {
4628 tree value;
4630 #ifdef HAVE_canonicalize_funcptr_for_compare
4631 /* Disable this optimization for function pointer expressions
4632 on targets that require function pointer canonicalization. */
4637 #endif
4640 {
4646 }
4664 {
4666 {
4670 }
4672 }
4674 /* Optimize (c>=1) && (c<=127) into (signed char)c > 0. */
4676 {
4678 HOST_WIDE_INT hi;
4683 {
4686 }
4687 else
4688 {
4691 }
4694 {
4696 {
4699 }
4702 }
4703 }
4705 /* Optimize (c>=low) && (c<=high) into (c-low>=0) && (c-low<=high-low).
4706 This requires wrap-around arithmetics for the type of the expression. */
4708 {
4710 /* There is no requirement that LOW be within the range of ETYPE
4711 if the latter is a subtype. It must, however, be within the base
4712 type of ETYPE. So be sure we do the subtraction in that type. */
4725 }
4727 /* If we don't have wrap-around arithmetics upfront, try to force it. */
4730 {
4733 /* Check if (unsigned) INT_MAX + 1 == (unsigned) INT_MIN
4734 for the type in question, as we rely on this here. */
4744 else
4746 }
4756 {
4758 {
4764 }
4766 }
4774 }
4775 \f
4776 /* Return the predecessor of VAL in its type, handling the infinite case. */
4778 static tree
4780 {
4786 else
4788 }
4790 /* Return the successor of VAL in its type, handling the infinite case. */
4792 static tree
4794 {
4800 else
4802 }
4804 /* Given two ranges, see if we can merge them into one. Return 1 if we
4805 can, 0 if we can't. Set the output range into the specified parameters. */
4807 static int
4810 {
4814 tree tem;
4824 /* Make range 0 be the range that starts first, or ends last if they
4825 start at the same value. Swap them if it isn't. */
4828 || (lowequal
4831 {
4835 }
4837 /* Now flag two cases, whether the ranges are disjoint or whether the
4838 second range is totally subsumed in the first. Note that the tests
4839 below are simplified by the ones above. */
4845 /* We now have four cases, depending on whether we are including or
4846 excluding the two ranges. */
4848 {
4849 /* If they don't overlap, the result is false. If the second range
4850 is a subset it is the result. Otherwise, the range is from the start
4851 of the second to the end of the first. */
4856 else
4858 }
4861 {
4862 /* If they don't overlap, the result is the first range. If they are
4863 equal, the result is false. If the second range is a subset of the
4864 first, and the ranges begin at the same place, we go from just after
4865 the end of the second range to the end of the first. If the second
4866 range is not a subset of the first, or if it is a subset and both
4867 ranges end at the same place, the range starts at the start of the
4868 first range and ends just before the second range.
4869 Otherwise, we can't describe this as a single range. */
4875 {
4880 {
4881 /* We are in the weird situation where high0 > high1 but
4882 high1 has no successor. Punt. */
4884 }
4885 }
4887 {
4892 {
4893 /* low0 < low1 but low1 has no predecessor. Punt. */
4895 }
4896 }
4897 else
4899 }
4902 {
4903 /* If they don't overlap, the result is the second range. If the second
4904 is a subset of the first, the result is false. Otherwise,
4905 the range starts just after the first range and ends at the
4906 end of the second. */
4911 else
4912 {
4917 {
4918 /* high1 > high0 but high0 has no successor. Punt. */
4920 }
4921 }
4922 }
4924 else
4925 {
4926 /* The case where we are excluding both ranges. Here the complex case
4927 is if they don't overlap. In that case, the only time we have a
4928 range is if they are adjacent. If the second is a subset of the
4929 first, the result is the first. Otherwise, the range to exclude
4930 starts at the beginning of the first range and ends at the end of the
4931 second. */
4933 {
4938 else
4939 {
4940 /* Canonicalize - [min, x] into - [-, x]. */
4943 {
4948 /* FALLTHROUGH */
4961 }
4963 /* Canonicalize - [x, max] into - [x, -]. */
4966 {
4971 /* FALLTHROUGH */
4986 }
4988 /* The ranges might be also adjacent between the maximum and
4989 minimum values of the given type. For
4990 - [{min,-}, x] and - [y, {max,-}] ranges where x + 1 < y
4991 return + [x + 1, y - 1]. */
4993 {
5000 }
5001 else
5003 }
5004 }
5007 else
5009 }
5013 }
5014 \f
5016 /* Subroutine of fold, looking inside expressions of the form
5017 A op B ? A : C, where ARG0, ARG1 and ARG2 are the three operands
5018 of the COND_EXPR. This function is being used also to optimize
5019 A op B ? C : A, by reversing the comparison first.
5021 Return a folded expression whose code is not a COND_EXPR
5022 anymore, or NULL_TREE if no folding opportunity is found. */
5024 static tree
5026 {
5031 tree tem;
5036 /* If we have A op 0 ? A : -A, consider applying the following
5037 transformations:
5039 A == 0? A : -A same as -A
5040 A != 0? A : -A same as A
5041 A >= 0? A : -A same as abs (A)
5042 A > 0? A : -A same as abs (A)
5043 A <= 0? A : -A same as -abs (A)
5044 A < 0? A : -A same as -abs (A)
5046 None of these transformations work for modes with signed
5047 zeros. If A is +/-0, the first two transformations will
5048 change the sign of the result (from +0 to -0, or vice
5049 versa). The last four will fix the sign of the result,
5050 even though the original expressions could be positive or
5051 negative, depending on the sign of A.
5053 Note that all these transformations are correct if A is
5054 NaN, since the two alternatives (A and -A) are also NaNs. */
5060 /* In the case that A is of the form X-Y, '-A' (arg2) may
5061 have already been folded to Y-X, check for that. */
5069 {
5081 /* Fall through. */
5103 }
5105 /* A != 0 ? A : 0 is simply A, unless A is -0. Likewise
5106 A == 0 ? A : 0 is always 0 unless A is -0. Note that
5107 both transformations are correct when A is NaN: A != 0
5108 is then true, and A == 0 is false. */
5111 {
5116 }
5118 /* Try some transformations of A op B ? A : B.
5120 A == B? A : B same as B
5121 A != B? A : B same as A
5122 A >= B? A : B same as max (A, B)
5123 A > B? A : B same as max (B, A)
5124 A <= B? A : B same as min (A, B)
5125 A < B? A : B same as min (B, A)
5127 As above, these transformations don't work in the presence
5128 of signed zeros. For example, if A and B are zeros of
5129 opposite sign, the first two transformations will change
5130 the sign of the result. In the last four, the original
5131 expressions give different results for (A=+0, B=-0) and
5132 (A=-0, B=+0), but the transformed expressions do not.
5134 The first two transformations are correct if either A or B
5135 is a NaN. In the first transformation, the condition will
5136 be false, and B will indeed be chosen. In the case of the
5137 second transformation, the condition A != B will be true,
5138 and A will be chosen.
5140 The conversions to max() and min() are not correct if B is
5141 a number and A is not. The conditions in the original
5142 expressions will be false, so all four give B. The min()
5143 and max() versions would give a NaN instead. */
5145 /* Avoid these transformations if the COND_EXPR may be used
5146 as an lvalue in the C++ front-end. PR c++/19199. */
5147 && (in_gimple_form
5152 {
5157 /* Avoid adding NOP_EXPRs in case this is an lvalue. */
5159 {
5163 }
5166 {
5175 /* In C++ a ?: expression can be an lvalue, so put the
5176 operand which will be used if they are equal first
5177 so that we can convert this back to the
5178 corresponding COND_EXPR. */
5180 {
5187 }
5194 {
5201 }
5214 }
5215 }
5217 /* If this is A op C1 ? A : C2 with C1 and C2 constant integers,
5218 we might still be able to simplify this. For example,
5219 if C1 is one less or one more than C2, this might have started
5220 out as a MIN or MAX and been transformed by this function.
5221 Only good for INTEGER_TYPEs, because we need TYPE_MAX_VALUE. */
5227 {
5229 /* We can replace A with C1 in this case. */
5234 /* If C1 is C2 + 1, this is min(A, C2). */
5236 OEP_ONLY_CONST)
5240 OEP_ONLY_CONST))
5242 type,
5244 arg2));
5248 /* If C1 is C2 - 1, this is min(A, C2). */
5250 OEP_ONLY_CONST)
5254 OEP_ONLY_CONST))
5256 type,
5258 arg2));
5262 /* If C1 is C2 - 1, this is max(A, C2). */
5264 OEP_ONLY_CONST)
5268 OEP_ONLY_CONST))
5270 type,
5272 arg2));
5276 /* If C1 is C2 + 1, this is max(A, C2). */
5278 OEP_ONLY_CONST)
5282 OEP_ONLY_CONST))
5284 type,
5286 arg2));
5292 }
5295 }
5298 \f
5299 #ifndef LOGICAL_OP_NON_SHORT_CIRCUIT
5300 #define LOGICAL_OP_NON_SHORT_CIRCUIT (BRANCH_COST >= 2)
5301 #endif
5303 /* EXP is some logical combination of boolean tests. See if we can
5304 merge it into some range test. Return the new tree if so. */
5306 static tree
5308 {
5316 tree tem;
5320 /* If this is an OR operation, invert both sides; we will invert
5321 again at the end. */
5325 /* If both expressions are the same, if we can merge the ranges, and we
5326 can build the range test, return it or it inverted. If one of the
5327 ranges is always true or always false, consider it to be the same
5328 expression as the other. */
5336 {
5340 }
5342 /* On machines where the branch cost is expensive, if this is a
5343 short-circuited branch and the underlying object on both sides
5344 is the same, make a non-short-circuit operation. */
5350 {
5351 /* If simple enough, just rewrite. Otherwise, make a SAVE_EXPR
5352 unless we are at top level or LHS contains a PLACEHOLDER_EXPR, in
5353 which cases we can't do this. */
5361 {
5370 {
5373 WARN_STRICT_OVERFLOW_COMPARISON);
5377 }
5378 }
5379 }
5382 }
5383 \f
5384 /* Subroutine for fold_truthop: C is an INTEGER_CST interpreted as a P
5385 bit value. Arrange things so the extra bits will be set to zero if and
5386 only if C is signed-extended to its full width. If MASK is nonzero,
5387 it is an INTEGER_CST that should be AND'ed with the extra bits. */
5389 static tree
5391 {
5394 tree temp;
5399 /* We work by getting just the sign bit into the low-order bit, then
5400 into the high-order bit, then sign-extend. We then XOR that value
5401 with C. */
5405 /* We must use a signed type in order to get an arithmetic right shift.
5406 However, we must also avoid introducing accidental overflows, so that
5407 a subsequent call to integer_zerop will work. Hence we must
5408 do the type conversion here. At this point, the constant is either
5409 zero or one, and the conversion to a signed type can never overflow.
5410 We could get an overflow if this conversion is done anywhere else. */
5419 /* If necessary, convert the type back to match the type of C. */
5424 }
5425 \f
5426 /* Find ways of folding logical expressions of LHS and RHS:
5427 Try to merge two comparisons to the same innermost item.
5428 Look for range tests like "ch >= '0' && ch <= '9'".
5429 Look for combinations of simple terms on machines with expensive branches
5430 and evaluate the RHS unconditionally.
5432 For example, if we have p->a == 2 && p->b == 4 and we can make an
5433 object large enough to span both A and B, we can do this with a comparison
5434 against the object ANDed with the a mask.
5436 If we have p->a == q->a && p->b == q->b, we may be able to use bit masking
5437 operations to do this with one comparison.
5439 We check for both normal comparisons and the BIT_AND_EXPRs made this by
5440 function and the one above.
5442 CODE is the logical operation being done. It can be TRUTH_ANDIF_EXPR,
5443 TRUTH_AND_EXPR, TRUTH_ORIF_EXPR, or TRUTH_OR_EXPR.
5445 TRUTH_TYPE is the type of the logical operand and LHS and RHS are its
5446 two operands.
5448 We return the simplified tree or 0 if no optimization is possible. */
5450 static tree
5452 {
5453 /* If this is the "or" of two comparisons, we can do something if
5454 the comparisons are NE_EXPR. If this is the "and", we can do something
5455 if the comparisons are EQ_EXPR. I.e.,
5456 (a->b == 2 && a->c == 4) can become (a->new == NEW).
5458 WANTED_CODE is this operation code. For single bit fields, we can
5459 convert EQ_EXPR to NE_EXPR so we need not reject the "wrong"
5460 comparison for one-bit fields. */
5482 /* Start by getting the comparison codes. Fail if anything is volatile.
5483 If one operand is a BIT_AND_EXPR with the constant one, treat it as if
5484 it were surrounded with a NE_EXPR. */
5493 {
5497 }
5500 {
5504 }
5515 /* Simplify (x<y) && (x==y) into (x<=y) and related optimizations. */
5518 {
5519 tree result;
5522 {
5527 }
5530 {
5536 }
5537 }
5542 /* If the RHS can be evaluated unconditionally and its operands are
5543 simple, it wins to evaluate the RHS unconditionally on machines
5544 with expensive branches. In this case, this isn't a comparison
5545 that can be merged. Avoid doing this if the RHS is a floating-point
5546 comparison since those can trap. */
5552 {
5553 /* Convert (a != 0) || (b != 0) into (a | b) != 0. */
5563 /* Convert (a == 0) && (b == 0) into (a | b) == 0. */
5574 {
5578 }
5579 }
5581 /* See if the comparisons can be merged. Then get all the parameters for
5582 each side. */
5606 /* It must be true that the inner operation on the lhs of each
5607 comparison must be the same if we are to be able to do anything.
5608 Then see if we have constants. If not, the same must be true for
5609 the rhs's. */
5620 else
5623 /* If either comparison code is not correct for our logical operation,
5624 fail. However, we can convert a one-bit comparison against zero into
5625 the opposite comparison against that bit being set in the field. */
5629 {
5631 {
5632 /* Make the left operand unsigned, since we are only interested
5633 in the value of one bit. Otherwise we are doing the wrong
5634 thing below. */
5637 }
5638 else
5640 }
5642 /* This is analogous to the code for l_const above. */
5644 {
5646 {
5649 }
5650 else
5652 }
5654 /* See if we can find a mode that contains both fields being compared on
5655 the left. If we can't, fail. Otherwise, update all constants and masks
5656 to be relative to a field of that size. */
5661 volatilep);
5671 {
5674 }
5682 {
5690 {
5694 }
5695 }
5697 {
5705 {
5709 }
5710 }
5712 /* If the right sides are not constant, do the same for it. Also,
5713 disallow this optimization if a size or signedness mismatch occurs
5714 between the left and right sides. */
5716 {
5719 /* Make sure the two fields on the right
5720 correspond to the left without being swapped. */
5728 volatilep);
5738 {
5741 }
5748 /* Make a mask that corresponds to both fields being compared.
5749 Do this for both items being compared. If the operands are the
5750 same size and the bits being compared are in the same position
5751 then we can do this by masking both and comparing the masked
5752 results. */
5756 {
5768 }
5770 /* There is still another way we can do something: If both pairs of
5771 fields being compared are adjacent, we may be able to make a wider
5772 field containing them both.
5774 Note that we still must mask the lhs/rhs expressions. Furthermore,
5775 the mask must be shifted to account for the shift done by
5776 make_bit_field_ref. */
5781 {
5782 tree type;
5794 /* Convert to the smaller type before masking out unwanted bits. */
5797 {
5799 {
5803 }
5805 {
5809 }
5810 }
5819 }
5822 }
5824 /* Handle the case of comparisons with constants. If there is something in
5825 common between the masks, those bits of the constants must be the same.
5826 If not, the condition is always false. Test for this to avoid generating
5827 incorrect code below. */
5832 {
5834 {
5837 }
5838 else
5839 {
5842 }
5843 }
5845 /* Construct the expression we will return. First get the component
5846 reference we will make. Unless the mask is all ones the width of
5847 that field, perform the mask operation. Then compare with the
5848 merged constant. */
5858 }
5859 \f
5860 /* Optimize T, which is a comparison of a MIN_EXPR or MAX_EXPR with a
5861 constant. */
5863 static tree
5865 {
5869 tree minmax_const;
5871 tree inner;
5881 /* If something does not permit us to optimize, return the original tree. */
5889 /* Now handle all the various comparison codes. We only handle EQ_EXPR
5890 and GT_EXPR, doing the rest with recursive calls using logical
5891 simplifications. */
5893 {
5895 {
5901 }
5904 return
5906 optimize_minmax_comparison
5908 optimize_minmax_comparison
5913 /* MAX (X, 0) == 0 -> X <= 0 */
5917 /* MAX (X, 0) == 5 -> X == 5 */
5921 /* MAX (X, 0) == -1 -> false */
5925 /* MIN (X, 0) == 0 -> X >= 0 */
5929 /* MIN (X, 0) == 5 -> false */
5932 else
5933 /* MIN (X, 0) == -1 -> X == -1 */
5938 /* MAX (X, 0) > 0 -> X > 0
5939 MAX (X, 0) > 5 -> X > 5 */
5943 /* MAX (X, 0) > -1 -> true */
5947 /* MIN (X, 0) > 0 -> false
5948 MIN (X, 0) > 5 -> false */
5951 else
5952 /* MIN (X, 0) > -1 -> X > -1 */
5957 }
5958 }
5959 \f
5960 /* T is an integer expression that is being multiplied, divided, or taken a
5961 modulus (CODE says which and what kind of divide or modulus) by a
5962 constant C. See if we can eliminate that operation by folding it with
5963 other operations already in T. WIDE_TYPE, if non-null, is a type that
5964 should be used for the computation if wider than our type.
5966 For example, if we are dividing (X * 8) + (Y * 16) by 4, we can return
5967 (X * 2) + (Y * 4). We must, however, be assured that either the original
5968 expression would not overflow or that overflow is undefined for the type
5969 in the language in question.
5971 We also canonicalize (X + 7) * 4 into X * 4 + 28 in the hope that either
5972 the machine has a multiply-accumulate insn or that this is part of an
5973 addressing calculation.
5975 If we return a non-null expression, it is an equivalent form of the
5976 original computation, but need not be in the original type.
5978 We set *STRICT_OVERFLOW_P to true if the return values depends on
5979 signed overflow being undefined. Otherwise we do not change
5980 *STRICT_OVERFLOW_P. */
5982 static tree
5985 {
5986 /* To avoid exponential search depth, refuse to allow recursion past
5987 three levels. Beyond that (1) it's highly unlikely that we'll find
5988 something interesting and (2) we've probably processed it before
5989 when we built the inner expression. */
5992 tree ret;
5997 depth++;
5999 depth--;
6002 }
6004 static tree
6007 {
6018 /* Don't deal with constants of zero here; they confuse the code below. */
6028 /* Note that we need not handle conditional operations here since fold
6029 already handles those cases. So just do arithmetic here. */
6031 {
6033 /* For a constant, we can always simplify if we are a multiply
6034 or (for divide and modulus) if it is a multiple of our constant. */
6042 /* If op0 is an expression ... */
6048 /* ... and is unsigned, and its type is smaller than ctype,
6049 then we cannot pass through as widening. */
6055 /* ... or this is a truncation (t is narrower than op0),
6056 then we cannot pass through this narrowing. */
6059 /* ... or signedness changes for division or modulus,
6060 then we cannot pass through this conversion. */
6066 /* Pass the constant down and see if we can make a simplification. If
6067 we can, replace this expression with the inner simplification for
6068 possible later conversion to our or some other type. */
6073 code == MULT_EXPR
6075 strict_overflow_p))))
6080 /* If widening the type changes it from signed to unsigned, then we
6081 must avoid building ABS_EXPR itself as unsigned. */
6083 {
6087 {
6090 }
6092 }
6093 /* FALLTHROUGH */
6101 /* If widening the type changes the signedness, then we can't perform
6102 this optimization as that changes the result. */
6106 /* MIN (a, b) / 5 -> MIN (a / 5, b / 5) */
6112 {
6119 }
6123 /* If the second operand is constant, this is a multiplication
6124 or floor division, by a power of two, so we can treat it that
6125 way unless the multiplier or divisor overflows. Signed
6126 left-shift overflow is implementation-defined rather than
6127 undefined in C90, so do not convert signed left shift into
6128 multiplication. */
6131 /* const_binop may not detect overflow correctly,
6132 so check for it explicitly here. */
6137 size_one_node,
6147 /* See if we can eliminate the operation on both sides. If we can, we
6148 can return a new PLUS or MINUS. If we can't, the only remaining
6149 cases where we can do anything are if the second operand is a
6150 constant. */
6156 /* If not multiplication, we can only do this if both operands
6157 are divisible by c. */
6160 {
6165 }
6167 /* If this was a subtraction, negate OP1 and set it to be an addition.
6168 This simplifies the logic below. */
6175 /* If either OP1 or C are negative, this optimization is not safe for
6176 some of the division and remainder types while for others we need
6177 to change the code. */
6179 {
6187 }
6189 /* If it's a multiply or a division/modulus operation of a multiple
6190 of our constant, do the operation and verify it doesn't overflow. */
6193 {
6196 /* We allow the constant to overflow with wrapping semantics. */
6200 }
6201 else
6204 /* If we have an unsigned type is not a sizetype, we cannot widen
6205 the operation since it will change the result if the original
6206 computation overflowed. */
6212 /* If we were able to eliminate our operation from the first side,
6213 apply our operation to the second side and reform the PLUS. */
6217 /* The last case is if we are a multiply. In that case, we can
6218 apply the distributive law to commute the multiply and addition
6219 if the multiplication of the constants doesn't overflow. */
6225 op1);
6230 /* We have a special case here if we are doing something like
6231 (C * 8) % 4 since we know that's zero. */
6238 /* ... fall through ... */
6242 /* If we can extract our operation from the LHS, do so and return a
6243 new operation. Likewise for the RHS from a MULT_EXPR. Otherwise,
6244 do something only if the second operand is a constant. */
6258 /* If these are the same operation types, we can associate them
6259 assuming no overflow. */
6266 /* If these operations "cancel" each other, we have the main
6267 optimizations of this pass, which occur when either constant is a
6268 multiple of the other, in which case we replace this with either an
6269 operation or CODE or TCODE.
6271 If we have an unsigned type that is not a sizetype, we cannot do
6272 this since it will change the result if the original computation
6273 overflowed. */
6281 {
6283 {
6290 }
6292 {
6299 }
6300 }
6305 }
6308 }
6309 \f
6310 /* Return a node which has the indicated constant VALUE (either 0 or
6311 1), and is of the indicated TYPE. */
6313 tree
6315 {
6320 else
6322 }
6325 /* Transform `a + (b ? x : y)' into `b ? (a + x) : (a + y)'.
6326 Transform, `a + (x < y)' into `(x < y) ? (a + 1) : (a + 0)'. Here
6327 CODE corresponds to the `+', COND to the `(b ? x : y)' or `(x < y)'
6328 expression, and ARG to `a'. If COND_FIRST_P is nonzero, then the
6329 COND is the first argument to CODE; otherwise (as in the example
6330 given here), it is the second argument. TYPE is the type of the
6331 original expression. Return NULL_TREE if no simplification is
6332 possible. */
6334 static tree
6338 {
6345 /* This transformation is only worthwhile if we don't have to wrap
6346 arg in a SAVE_EXPR, and the operation can be simplified on at least
6347 one of the branches once its pushed inside the COND_EXPR. */
6352 {
6356 /* If this operand throws an expression, then it does not make
6357 sense to try to perform a logical or arithmetic operation
6358 involving it. */
6363 }
6364 else
6365 {
6370 }
6374 {
6378 else
6380 }
6382 {
6386 else
6388 }
6392 }
6394 \f
6395 /* Subroutine of fold() that checks for the addition of +/- 0.0.
6397 If !NEGATE, return true if ADDEND is +/-0.0 and, for all X of type
6398 TYPE, X + ADDEND is the same as X. If NEGATE, return true if X -
6399 ADDEND is the same as X.
6401 X + 0 and X - 0 both give X when X is NaN, infinite, or nonzero
6402 and finite. The problematic cases are when X is zero, and its mode
6403 has signed zeros. In the case of rounding towards -infinity,
6404 X - 0 is not the same as X because 0 - 0 is -0. In other rounding
6405 modes, X + 0 is not the same as X because -0 + 0 is 0. */
6407 static bool
6409 {
6413 /* Don't allow the fold with -fsignaling-nans. */
6417 /* Allow the fold if zeros aren't signed, or their sign isn't important. */
6421 /* Treat x + -0 as x - 0 and x - -0 as x + 0. */
6426 /* The mode has signed zeros, and we have to honor their sign.
6427 In this situation, there is only one case we can return true for.
6428 X - 0 is the same as X unless rounding towards -infinity is
6429 supported. */
6431 }
6433 /* Subroutine of fold() that checks comparisons of built-in math
6434 functions against real constants.
6436 FCODE is the DECL_FUNCTION_CODE of the built-in, CODE is the comparison
6437 operator: EQ_EXPR, NE_EXPR, GT_EXPR, LT_EXPR, GE_EXPR or LE_EXPR. TYPE
6438 is the type of the result and ARG0 and ARG1 are the operands of the
6439 comparison. ARG1 must be a TREE_REAL_CST.
6441 The function returns the constant folded tree if a simplification
6442 can be made, and NULL_TREE otherwise. */
6444 static tree
6447 {
6448 REAL_VALUE_TYPE c;
6451 {
6457 {
6458 /* sqrt(x) < y is always false, if y is negative. */
6462 /* sqrt(x) > y is always true, if y is negative and we
6463 don't care about NaNs, i.e. negative values of x. */
6467 /* sqrt(x) > y is the same as x >= 0, if y is negative. */
6470 }
6472 {
6473 REAL_VALUE_TYPE c2;
6479 {
6480 /* sqrt(x) > y is x == +Inf, when y is very large. */
6485 /* sqrt(x) > y is always false, when y is very large
6486 and we don't care about infinities. */
6488 }
6490 /* sqrt(x) > c is the same as x > c*c. */
6493 }
6495 {
6496 REAL_VALUE_TYPE c2;
6502 {
6503 /* sqrt(x) < y is always true, when y is a very large
6504 value and we don't care about NaNs or Infinities. */
6508 /* sqrt(x) < y is x != +Inf when y is very large and we
6509 don't care about NaNs. */
6514 /* sqrt(x) < y is x >= 0 when y is very large and we
6515 don't care about Infinities. */
6520 /* sqrt(x) < y is x >= 0 && x != +Inf, when y is large. */
6529 dconst0)),
6532 c2)));
6533 }
6535 /* sqrt(x) < c is the same as x < c*c, if we ignore NaNs. */
6540 /* sqrt(x) < c is the same as x >= 0 && x < c*c. */
6543 {
6548 dconst0)),
6551 c2)));
6552 }
6553 }
6554 }
6557 }
6559 /* Subroutine of fold() that optimizes comparisons against Infinities,
6560 either +Inf or -Inf.
6562 CODE is the comparison operator: EQ_EXPR, NE_EXPR, GT_EXPR, LT_EXPR,
6563 GE_EXPR or LE_EXPR. TYPE is the type of the result and ARG0 and ARG1
6564 are the operands of the comparison. ARG1 must be a TREE_REAL_CST.
6566 The function returns the constant folded tree if a simplification
6567 can be made, and NULL_TREE otherwise. */
6569 static tree
6571 {
6573 REAL_VALUE_TYPE max;
6574 tree temp;
6579 /* For negative infinity swap the sense of the comparison. */
6585 {
6587 /* x > +Inf is always false, if with ignore sNANs. */
6593 /* x <= +Inf is always true, if we don't case about NaNs. */
6597 /* x <= +Inf is the same as x == x, i.e. isfinite(x). */
6600 {
6603 }
6608 /* x == +Inf and x >= +Inf are always equal to x > DBL_MAX. */
6614 /* x < +Inf is always equal to x <= DBL_MAX. */
6620 /* x != +Inf is always equal to !(x > DBL_MAX). */
6632 }
6635 }
6637 /* Subroutine of fold() that optimizes comparisons of a division by
6638 a nonzero integer constant against an integer constant, i.e.
6639 X/C1 op C2.
6641 CODE is the comparison operator: EQ_EXPR, NE_EXPR, GT_EXPR, LT_EXPR,
6642 GE_EXPR or LE_EXPR. TYPE is the type of the result and ARG0 and ARG1
6643 are the operands of the comparison. ARG1 must be a TREE_REAL_CST.
6645 The function returns the constant folded tree if a simplification
6646 can be made, and NULL_TREE otherwise. */
6648 static tree
6650 {
6655 HOST_WIDE_INT hpart;
6660 /* We have to do this the hard way to detect unsigned overflow.
6661 prod = int_const_binop (MULT_EXPR, arg01, arg1, 0); */
6672 {
6677 /* Likewise hi = int_const_binop (PLUS_EXPR, prod, tmp, 0). */
6685 }
6687 {
6691 {
6710 }
6711 }
6712 else
6713 {
6714 /* A negative divisor reverses the relational operators. */
6720 {
6739 }
6740 }
6743 {
6764 {
6767 }
6772 {
6775 }
6780 {
6783 }
6788 {
6791 }
6796 }
6799 }
6802 /* If CODE with arguments ARG0 and ARG1 represents a single bit
6803 equality/inequality test, then return a simplified form of the test
6804 using a sign testing. Otherwise return NULL. TYPE is the desired
6805 result type. */
6807 static tree
6809 tree result_type)
6810 {
6811 /* If this is testing a single bit, we can optimize the test. */
6815 {
6816 /* If we have (A & C) != 0 where C is the sign bit of A, convert
6817 this into A < 0. Similarly for (A & C) == 0 into A >= 0. */
6821 /* This is only a win if casting to a signed type is cheap,
6822 i.e. when arg00's type is not a partial mode. */
6825 {
6830 }
6831 }
6834 }
6836 /* If CODE with arguments ARG0 and ARG1 represents a single bit
6837 equality/inequality test, then return a simplified form of
6838 the test using shifts and logical operations. Otherwise return
6839 NULL. TYPE is the desired result type. */
6841 tree
6843 tree result_type)
6844 {
6845 /* If this is testing a single bit, we can optimize the test. */
6849 {
6858 /* First, see if we can fold the single bit test into a sign-bit
6859 test. */
6861 result_type);
6865 /* Otherwise we have (A & C) != 0 where C is a single bit,
6866 convert that into ((A >> C2) & 1). Where C2 = log2(C).
6867 Similarly for (A & C) == 0. */
6869 /* If INNER is a right shift of a constant and it plus BITNUM does
6870 not overflow, adjust BITNUM and INNER. */
6877 {
6880 }
6882 /* If we are going to be able to omit the AND below, we must do our
6883 operations as unsigned. If we must use the AND, we have a choice.
6884 Normally unsigned is faster, but for some machines signed is. */
6885 #ifdef LOAD_EXTEND_OP
6888 #else
6890 #endif
6906 /* Put the AND last so it can combine with more things. */
6909 /* Make sure to return the proper type. */
6913 }
6915 }
6917 /* Check whether we are allowed to reorder operands arg0 and arg1,
6918 such that the evaluation of arg1 occurs before arg0. */
6920 static bool
6922 {
6929 }
6931 /* Test whether it is preferable two swap two operands, ARG0 and
6932 ARG1, for example because ARG0 is an integer constant and ARG1
6933 isn't. If REORDER is true, only recommend swapping if we can
6934 evaluate the operands in reverse order. */
6936 bool
6938 {
6974 /* It is preferable to swap two SSA_NAME to ensure a canonical form
6975 for commutative and comparison operators. Ensuring a canonical
6976 form allows the optimizers to find additional redundancies without
6977 having to explicitly check for both orderings. */
6983 /* Put SSA_NAMEs last. */
6989 /* Put variables last. */
6996 }
6998 /* Fold comparison ARG0 CODE ARG1 (with result in TYPE), where
6999 ARG0 is extended to a wider type. */
7001 static tree
7003 {
7005 tree arg1_unw;
7014 #ifdef HAVE_canonicalize_funcptr_for_compare
7015 /* Disable this optimization if we're casting a function pointer
7016 type on targets that require function pointer canonicalization. */
7021 #endif
7028 /* If possible, express the comparison in the shorter mode. */
7044 /* If we are comparing with the integer that does not fit into the range
7045 of the shorter type, the result is known. */
7056 {
7083 }
7086 }
7088 /* Fold comparison ARG0 CODE ARG1 (with result in TYPE), where for
7089 ARG0 just the signedness is changed. */
7091 static tree
7094 {
7095 tree arg0_inner;
7106 #ifdef HAVE_canonicalize_funcptr_for_compare
7107 /* Disable this optimization if we're casting a function pointer
7108 type on targets that require function pointer canonicalization. */
7113 #endif
7133 else
7137 }
7139 /* Tries to replace &a[idx] p+ s * delta with &a[idx + delta], if s is
7140 step of the array. Reconstructs s and delta in the case of s * delta
7141 being an integer constant (and thus already folded).
7142 ADDR is the address. MULT is the multiplicative expression.
7143 If the function succeeds, the new address expression is returned. Otherwise
7144 NULL_TREE is returned. */
7146 static tree
7148 {
7152 tree itype;
7155 /* Strip the nops that might be added when converting op1 to sizetype. */
7158 /* Canonicalize op1 into a possibly non-constant delta
7159 and an INTEGER_CST s. */
7161 {
7168 {
7171 }
7173 {
7176 }
7177 else
7179 }
7181 {
7184 }
7185 else
7186 {
7187 /* Simulate we are delta * 1. */
7190 }
7193 {
7195 {
7196 /* Remember if this was a multi-dimensional array. */
7209 {
7212 }
7213 else
7214 {
7215 /* Try if delta is a multiple of step. */
7220 }
7222 /* Only fold here if we can verify we do not overflow one
7223 dimension of a multi-dimensional array. */
7225 {
7226 tree tmp;
7242 }
7245 }
7246 else
7251 }
7253 /* We found the suitable array reference. So copy everything up to it,
7254 and replace the index. */
7261 {
7265 }
7273 }
7276 /* Fold A < X && A + 1 > Y to A < X && A >= Y. Normally A + 1 > Y
7277 means A >= Y && A != MAX, but in this case we know that
7278 A < X <= MAX. INEQ is A + 1 > Y, BOUND is A < X. */
7280 static tree
7282 {
7289 else
7298 {
7301 }
7303 {
7306 }
7307 else
7314 {
7315 /* Convert the pointer types into integer before taking the difference. */
7319 }
7320 else
7327 }
7329 /* Fold a sum or difference of at least one multiplication.
7330 Returns the folded tree or NULL if no simplification could be made. */
7332 static tree
7334 {
7338 /* (A * C) +- (B * C) -> (A+-B) * C.
7339 (A * C) +- A -> A * (C+-1).
7340 We are most concerned about the case where C is a constant,
7341 but other combinations show up during loop reduction. Since
7342 it is not difficult, try all four possibilities. */
7345 {
7348 }
7350 {
7353 }
7354 else
7355 {
7356 /* We cannot generate constant 1 for fract. */
7361 }
7363 {
7366 }
7368 {
7371 }
7372 else
7373 {
7374 /* We cannot generate constant 1 for fract. */
7379 }
7391 /* No identical multiplicands; see if we can find a common
7392 power-of-two factor in non-power-of-two multiplies. This
7393 can help in multi-dimensional array access. */
7396 {
7399 tree maybe_same;
7403 /* Move min of absolute values to int11. */
7406 {
7411 }
7412 else
7416 {
7424 }
7425 }
7435 }
7437 /* Subroutine of native_encode_expr. Encode the INTEGER_CST
7438 specified by EXPR into the buffer PTR of length LEN bytes.
7439 Return the number of bytes placed in the buffer, or zero
7440 upon failure. */
7442 static int
7444 {
7455 {
7459 else
7464 {
7471 else
7473 }
7474 else
7477 }
7479 }
7482 /* Subroutine of native_encode_expr. Encode the REAL_CST
7483 specified by EXPR into the buffer PTR of length LEN bytes.
7484 Return the number of bytes placed in the buffer, or zero
7485 upon failure. */
7487 static int
7489 {
7495 /* There are always 32 bits in each long, no matter the size of
7496 the hosts long. We handle floating point representations with
7497 up to 192 bits. */
7508 {
7513 {
7520 else
7522 }
7523 else
7526 }
7528 }
7530 /* Subroutine of native_encode_expr. Encode the COMPLEX_CST
7531 specified by EXPR into the buffer PTR of length LEN bytes.
7532 Return the number of bytes placed in the buffer, or zero
7533 upon failure. */
7535 static int
7537 {
7539 tree part;
7550 }
7553 /* Subroutine of native_encode_expr. Encode the VECTOR_CST
7554 specified by EXPR into the buffer PTR of length LEN bytes.
7555 Return the number of bytes placed in the buffer, or zero
7556 upon failure. */
7558 static int
7560 {
7570 {
7572 {
7575 }
7576 else
7580 {
7583 }
7584 else
7585 {
7589 }
7591 }
7593 }
7596 /* Subroutine of fold_view_convert_expr. Encode the INTEGER_CST,
7597 REAL_CST, COMPLEX_CST or VECTOR_CST specified by EXPR into the
7598 buffer PTR of length LEN bytes. Return the number of bytes
7599 placed in the buffer, or zero upon failure. */
7601 int
7603 {
7605 {
7620 }
7621 }
7624 /* Subroutine of native_interpret_expr. Interpret the contents of
7625 the buffer PTR of length LEN as an INTEGER_CST of type TYPE.
7626 If the buffer cannot be interpreted, return NULL_TREE. */
7628 static tree
7630 {
7644 {
7647 {
7654 else
7656 }
7657 else
7663 else
7666 }
7669 }
7672 /* Subroutine of native_interpret_expr. Interpret the contents of
7673 the buffer PTR of length LEN as a REAL_CST of type TYPE.
7674 If the buffer cannot be interpreted, return NULL_TREE. */
7676 static tree
7678 {
7683 /* There are always 32 bits in each long, no matter the size of
7684 the hosts long. We handle floating point representations with
7685 up to 192 bits. */
7686 REAL_VALUE_TYPE r;
7697 {
7700 {
7707 else
7709 }
7710 else
7715 }
7719 }
7722 /* Subroutine of native_interpret_expr. Interpret the contents of
7723 the buffer PTR of length LEN as a COMPLEX_CST of type TYPE.
7724 If the buffer cannot be interpreted, return NULL_TREE. */
7726 static tree
7728 {
7743 }
7746 /* Subroutine of native_interpret_expr. Interpret the contents of
7747 the buffer PTR of length LEN as a VECTOR_CST of type TYPE.
7748 If the buffer cannot be interpreted, return NULL_TREE. */
7750 static tree
7752 {
7764 {
7769 }
7771 }
7774 /* Subroutine of fold_view_convert_expr. Interpret the contents of
7775 the buffer PTR of length LEN as a constant of type TYPE. For
7776 INTEGRAL_TYPE_P we return an INTEGER_CST, for SCALAR_FLOAT_TYPE_P
7777 we return a REAL_CST, etc... If the buffer cannot be interpreted,
7778 return NULL_TREE. */
7780 tree
7782 {
7784 {
7801 }
7802 }
7805 /* Fold a VIEW_CONVERT_EXPR of a constant expression EXPR to type
7806 TYPE at compile-time. If we're unable to perform the conversion
7807 return NULL_TREE. */
7809 static tree
7811 {
7812 /* We support up to 512-bit values (for V8DFmode). */
7816 /* Check that the host and target are sane. */
7825 }
7827 /* Build an expression for the address of T. Folds away INDIRECT_REF
7828 to avoid confusing the gimplify process. When IN_FOLD is true
7829 avoid modifications of T. */
7831 static tree
7833 {
7834 /* The size of the object is not relevant when talking about its address. */
7838 /* Note: doesn't apply to ALIGN_INDIRECT_REF */
7841 {
7846 }
7848 {
7858 }
7859 else
7863 }
7865 /* Build an expression for the address of T with type PTRTYPE. This
7866 function modifies the input parameter 'T' by sometimes setting the
7867 TREE_ADDRESSABLE flag. */
7869 tree
7871 {
7873 }
7875 /* Build an expression for the address of T. This function modifies
7876 the input parameter 'T' by sometimes setting the TREE_ADDRESSABLE
7877 flag. When called from fold functions, use fold_addr_expr instead. */
7879 tree
7881 {
7885 }
7887 /* Same as build_fold_addr_expr, builds an expression for the address
7888 of T, but avoids touching the input node 't'. Fold functions
7889 should use this version. */
7891 static tree
7893 {
7897 }
7899 /* Fold a unary expression of code CODE and type TYPE with operand
7900 OP0. Return the folded expression if folding is successful.
7901 Otherwise, return NULL_TREE. */
7903 tree
7905 {
7906 tree tem;
7907 tree arg0;
7915 {
7918 {
7919 /* Don't use STRIP_NOPS, because signedness of argument type
7920 matters. */
7922 }
7923 else
7924 {
7925 /* Strip any conversions that don't change the mode. This
7926 is safe for every expression, except for a comparison
7927 expression because its signedness is derived from its
7928 operands.
7930 Note that this is done as an internal manipulation within
7931 the constant folder, in order to find the simplest
7932 representation of the arguments so that their form can be
7933 studied. In any cases, the appropriate type conversions
7934 should be put back in the tree that will get out of the
7935 constant folder. */
7937 }
7938 }
7941 {
7946 {
7956 /* If this was a conversion, and all we did was to move into
7957 inside the COND_EXPR, bring it back out. But leave it if
7958 it is a conversion from integer to integer and the
7959 result precision is no wider than a word since such a
7960 conversion is cheap and may be optimized away by combine,
7961 while it couldn't if it were outside the COND_EXPR. Then return
7962 so we don't get into an infinite recursion loop taking the
7963 conversion out and then back in. */
7975 && (INTEGRAL_TYPE_P
7987 }
7989 {
7991 {
7995 }
7999 integer_one_node),
8001 integer_zero_node));
8002 }
8003 }
8006 {
8014 /* If we have (type) (a CMP b) and type is an integral type, return
8015 new expression involving the new type. */
8020 /* Handle cases of two conversions in a row. */
8023 {
8045 /* In addition to the cases of two conversions in a row
8046 handled below, if we are converting something to its own
8047 type via an object of identical or wider precision, neither
8048 conversion is needed. */
8055 /* Likewise, if the intermediate and final types are either both
8056 float or both integer, we don't need the middle conversion if
8057 it is wider than the final type and doesn't change the signedness
8058 (for integers). Avoid this if the final type is a pointer
8059 since then we sometimes need the inner conversion. Likewise if
8060 the outer has a precision not equal to the size of its mode. */
8069 && ! final_ptr
8073 /* If we have a sign-extension of a zero-extended value, we can
8074 replace that by a single zero-extension. */
8080 /* Two conversions in a row are not needed unless:
8081 - some conversion is floating-point (overstrict for now), or
8082 - some conversion is a vector (overstrict for now), or
8083 - the intermediate type is narrower than both initial and
8084 final, or
8085 - the intermediate type and innermost type differ in signedness,
8086 and the outermost type is wider than the intermediate, or
8087 - the initial type is a pointer type and the precisions of the
8088 intermediate and final types differ, or
8089 - the final type is a pointer type and the precisions of the
8090 initial and intermediate types differ.
8091 - the initial type is a pointer to an array and the final type
8092 not. */
8109 }
8111 /* Handle (T *)&A.B.C for A being of type T and B and C
8112 living at offset zero. This occurs frequently in
8113 C++ upcasting and then accessing the base. */
8117 {
8119 tree offset;
8125 /* If the reference was to a (constant) zero offset, we can use
8126 the address of the base if it has the same base type
8127 as the result type. */
8132 }
8137 /* Detect assigning a bitfield. */
8139 && DECL_BIT_FIELD
8141 {
8142 /* Don't leave an assignment inside a conversion
8143 unless assigning a bitfield. */
8145 /* First do the assignment, then return converted constant. */
8150 }
8152 /* Convert (T)(x & c) into (T)x & (T)c, if c is an integer
8153 constants (if x has signed type, the sign bit cannot be set
8154 in c). This folds extension into the BIT_AND_EXPR. */
8159 {
8169 <= HOST_BITS_PER_WIDE_INT
8171 {
8178 #ifdef LOAD_EXTEND_OP
8180 && !flag_syntax_only
8183 {
8187 }
8188 #endif
8189 }
8191 {
8197 }
8198 }
8200 /* Convert (T1)(X p+ Y) into ((T1)X p+ Y), for pointer type,
8201 when one of the new casts will fold away. Conservatively we assume
8202 that this happens when X or Y is NOP_EXPR or Y is INTEGER_CST. */
8208 {
8214 }
8216 /* Convert (T1)(~(T2)X) into ~(T1)X if T1 and T2 are integral types
8217 of the same precision, and X is an integer type not narrower than
8218 types T1 or T2, i.e. the cast (T2)X isn't an extension. */
8225 {
8230 }
8257 /* Convert fabs((double)float) into (double)fabsf(float). */
8260 {
8265 targ0));
8266 }
8267 /* ABS_EXPR<ABS_EXPR<x>> = ABS_EXPR<x> even if flag_wrapv is on. */
8273 /* Strip sign ops from argument. */
8275 {
8279 }
8286 {
8291 }
8293 {
8298 }
8308 /* Convert ~ (-A) to A - 1. */
8313 /* Convert ~ (A - 1) or ~ (A + -1) to -A. */
8321 /* Convert ~(X ^ Y) to ~X ^ Y or X ^ ~Y if ~X or ~Y simplify. */
8334 /* Perform BIT_NOT_EXPR on each element individually. */
8336 {
8341 {
8343 {
8349 }
8350 else
8353 }
8356 }
8361 /* The argument to invert_truthvalue must have Boolean type. */
8365 /* Note that the operand of this must be an int
8366 and its values must be 0 or 1.
8367 ("true" is a fixed value perhaps depending on the language,
8368 but we don't handle values other than 1 correctly yet.) */
8383 {
8391 }
8393 {
8397 }
8399 {
8403 {
8412 }
8413 }
8425 {
8433 }
8435 {
8439 }
8441 {
8445 {
8454 }
8455 }
8461 }
8463 /* Fold a binary expression of code CODE and type TYPE with operands
8464 OP0 and OP1, containing either a MIN-MAX or a MAX-MIN combination.
8465 Return the folded expression if folding is successful. Otherwise,
8466 return NULL_TREE. */
8468 static tree
8470 {
8477 else
8480 /* MIN (MAX (a, b), b) == b. */
8485 /* MIN (MAX (b, a), b) == b. */
8491 /* MIN (a, MAX (a, b)) == a. */
8497 /* MIN (a, MAX (b, a)) == a. */
8504 }
8506 /* Helper that tries to canonicalize the comparison ARG0 CODE ARG1
8507 by changing CODE to reduce the magnitude of constants involved in
8508 ARG0 of the comparison.
8509 Returns a canonicalized comparison tree if a simplification was
8510 possible, otherwise returns NULL_TREE.
8511 Set *STRICT_OVERFLOW_P to true if the canonicalization is only
8512 valid if signed overflow is undefined. */
8514 static tree
8518 {
8524 /* Match A +- CST code arg1 and CST code arg1. */
8531 /* Identify the constant in arg0 and its sign. */
8534 else
8538 /* Overflowed constants and zero will cause problems. */
8543 /* See if we can reduce the magnitude of the constant in
8544 arg0 by changing the comparison code. */
8546 {
8547 /* CST <= arg1 -> CST-1 < arg1. */
8550 /* -CST < arg1 -> -CST-1 <= arg1. */
8553 /* CST > arg1 -> CST-1 >= arg1. */
8556 /* -CST >= arg1 -> -CST-1 > arg1. */
8559 else
8561 /* arg1 code' CST' might be more canonical. */
8563 }
8564 else
8565 {
8566 /* A - CST < arg1 -> A - CST-1 <= arg1. */
8570 /* A + CST > arg1 -> A + CST-1 >= arg1. */
8574 /* A + CST <= arg1 -> A + CST-1 < arg1. */
8578 /* A - CST >= arg1 -> A - CST-1 > arg1. */
8582 else
8585 }
8587 /* Now build the constant reduced in magnitude. */
8593 /* If swapping might yield to a more canonical form, do so. */
8596 else
8598 }
8600 /* Canonicalize the comparison ARG0 CODE ARG1 with type TYPE with undefined
8601 overflow further. Try to decrease the magnitude of constants involved
8602 by changing LE_EXPR and GE_EXPR to LT_EXPR and GT_EXPR or vice versa
8603 and put sole constants at the second argument position.
8604 Returns the canonicalized tree if changed, otherwise NULL_TREE. */
8606 static tree
8609 {
8610 tree t;
8615 /* In principle pointers also have undefined overflow behavior,
8616 but that causes problems elsewhere. */
8621 /* Try canonicalization by simplifying arg0. */
8626 {
8630 }
8632 /* Try canonicalization by simplifying arg1 using the swapped
8633 comparison. */
8641 }
8643 /* Subroutine of fold_binary. This routine performs all of the
8644 transformations that are common to the equality/inequality
8645 operators (EQ_EXPR and NE_EXPR) and the ordering operators
8646 (LT_EXPR, LE_EXPR, GE_EXPR and GT_EXPR). Callers other than
8647 fold_binary should call fold_binary. Fold a comparison with
8648 tree code CODE and type TYPE with operands OP0 and OP1. Return
8649 the folded comparison or NULL_TREE. */
8651 static tree
8653 {
8666 /* If one arg is a real or integer constant, put it last. */
8670 /* Transform comparisons of the form X +- C1 CMP C2 to X CMP C2 +- C1. */
8677 {
8681 tree lhs;
8688 /* If the constant operation overflowed this can be
8689 simplified as a comparison against INT_MAX/INT_MIN. */
8692 {
8696 /* Get the sign of the constant on the lhs if the
8697 operation were VARIABLE + CONST1. */
8701 /* The sign of the constant determines if we overflowed
8702 INT_MAX (const1_sgn == -1) or INT_MIN (const1_sgn == 1).
8703 Canonicalize to the INT_MIN overflow by swapping the comparison
8704 if necessary. */
8708 /* We now can look at the canonicalized case
8709 VARIABLE + 1 CODE2 INT_MIN
8710 and decide on the result. */
8719 }
8724 {
8726 "when changing X +- C1 cmp C2 to "
8728 WARN_STRICT_OVERFLOW_COMPARISON);
8730 }
8731 }
8733 /* For comparisons of pointers we can decompose it to a compile time
8734 comparison of the base objects and the offsets into the object.
8735 This requires at least one operand being an ADDR_EXPR or a
8736 POINTER_PLUS_EXPR to do more than the operand_equal_p test below. */
8742 {
8749 /* Get base and offset for the access. Strip ADDR_EXPR for
8750 get_inner_reference, but put it back by stripping INDIRECT_REF
8751 off the base object if possible. */
8754 {
8760 else
8762 }
8764 {
8767 }
8771 {
8775 /* We have to make sure to have an indirect/non-indirect base1
8776 just the same as we did for base0. */
8782 }
8784 {
8787 }
8791 /* If we have equivalent bases we might be able to simplify. */
8794 {
8795 /* We can fold this expression to a constant if the non-constant
8796 offset parts are equal. */
8800 {
8802 {
8816 }
8817 }
8818 /* We can simplify the comparison to a comparison of the variable
8819 offset parts if the constant offset parts are equal.
8820 Be careful to use signed size type here because otherwise we
8821 mess with array offsets in the wrong way. This is possible
8822 because pointer arithmetic is restricted to retain within an
8823 object and overflow on pointer differences is undefined as of
8824 6.5.6/8 and /9 with respect to the signed ptrdiff_t. */
8826 {
8827 tree signed_size_type_node;
8830 /* By converting to signed size type we cover middle-end pointer
8831 arithmetic which operates on unsigned pointer types of size
8832 type size and ARRAY_REF offsets which are properly sign or
8833 zero extended from their type in case it is narrower than
8834 size type. */
8837 else
8841 else
8845 }
8846 }
8847 }
8849 /* Transform comparisons of the form X +- C1 CMP Y +- C2 to
8850 X CMP Y +- C2 +- C1 for signed X, Y. This is valid if
8851 the resulting offset is smaller in absolute value than the
8852 original one. */
8860 {
8865 tree cst;
8867 "occur when combining constants around "
8870 /* Put the constant on the side where it doesn't overflow and is
8871 of lower absolute value than before. */
8877 {
8880 variable1,
8883 }
8890 {
8895 variable2);
8896 }
8897 }
8899 /* Transform comparisons of the form X * C1 CMP 0 to X CMP 0 in the
8900 signed arithmetic case. That form is created by the compiler
8901 often enough for folding it to be of value. One example is in
8902 computing loop trip counts after Operator Strength Reduction. */
8908 {
8917 "eliminating multiplication in comparison "
8919 WARN_STRICT_OVERFLOW_COMPARISON);
8921 /* If const1 is negative we swap the sense of the comparison. */
8926 }
8933 {
8941 /* Fold (double)float1 CMP (double)float2 into float1 CMP float2. */
8946 /* (-a) CMP (-b) -> b CMP a */
8953 {
8954 REAL_VALUE_TYPE cst;
8957 /* (-a) CMP CST -> a swap(CMP) (-CST) */
8964 /* IEEE doesn't distinguish +0 and -0 in comparisons. */
8965 /* a CMP (-0) -> a CMP 0 */
8970 /* x != NaN is always true, other ops are always false. */
8973 {
8976 }
8978 /* Fold comparisons against infinity. */
8980 {
8984 }
8985 }
8987 /* If this is a comparison of a real constant with a PLUS_EXPR
8988 or a MINUS_EXPR of a real constant, we can convert it into a
8989 comparison with a revised real constant as long as no overflow
8990 occurs when unsafe_math_optimizations are enabled. */
9002 /* Likewise, we can simplify a comparison of a real constant with
9003 a MINUS_EXPR whose first operand is also a real constant, i.e.
9004 (c1 - x) < c2 becomes x > c1-c2. Reordering is allowed on
9005 floating-point types only if -fassociative-math is set. */
9016 /* Fold comparisons against built-in math functions. */
9018 && flag_unsafe_math_optimizations
9020 {
9024 {
9028 }
9029 }
9030 }
9035 {
9036 /* If we are widening one operand of an integer comparison,
9037 see if the other operand is similarly being widened. Perhaps we
9038 can do the comparison in the narrower type. */
9043 /* Or if we are changing signedness. */
9047 }
9049 /* If this is comparing a constant with a MIN_EXPR or a MAX_EXPR of a
9050 constant, we can simplify it. */
9055 {
9059 }
9061 /* Simplify comparison of something with itself. (For IEEE
9062 floating-point, we can only do some of these simplifications.) */
9064 {
9066 {
9081 /* For NE, we can only do this simplification if integer
9082 or we don't honor IEEE floating point NaNs. */
9086 /* ... fall through ... */
9092 }
9093 }
9095 /* If we are comparing an expression that just has comparisons
9096 of two integer values, arithmetic expressions of those comparisons,
9097 and constants, we can simplify it. There are only three cases
9098 to check: the two values can either be equal, the first can be
9099 greater, or the second can be greater. Fold the expression for
9100 those three values. Since each value must be 0 or 1, we have
9101 eight possibilities, each of which corresponds to the constant 0
9102 or 1 or one of the six possible comparisons.
9104 This handles common cases like (a > b) == 0 but also handles
9105 expressions like ((x > y) - (y > x)) > 0, which supposedly
9106 occur in macroized code. */
9109 {
9114 /* Don't handle degenerate cases here; they should already
9115 have been handled anyway. */
9124 {
9128 /* We can't just pass T to eval_subst in case cval1 or cval2
9129 was the same as ARG1. */
9131 tree high_result
9135 arg1);
9136 tree equal_result
9140 arg1);
9141 tree low_result
9145 arg1);
9147 /* All three of these results should be 0 or 1. Confirm they are.
9148 Then use those values to select the proper code to use. */
9153 {
9154 /* Make a 3-bit mask with the high-order bit being the
9155 value for `>', the next for '=', and the low for '<'. */
9159 {
9161 /* Always false. */
9182 /* Always true. */
9184 }
9189 }
9190 }
9191 }
9193 /* Fold a comparison of the address of COMPONENT_REFs with the same
9194 type and component to a comparison of the address of the base
9195 object. In short, &x->a OP &y->a to x OP y and
9196 &x->a OP &y.a to x OP &y */
9201 {
9205 {
9211 }
9212 }
9214 /* We can fold X/C1 op C2 where C1 and C2 are integer constants
9215 into a single range test. */
9223 {
9227 }
9229 /* Fold ~X op ~Y as Y op X. */
9232 {
9237 }
9239 /* Fold ~X op C as X op' ~C, where op' is the swapped comparison. */
9242 {
9248 }
9251 }
9254 /* Subroutine of fold_binary. Optimize complex multiplications of the
9255 form z * conj(z), as pow(realpart(z),2) + pow(imagpart(z),2). The
9256 argument EXPR represents the expression "z" of type TYPE. */
9258 static tree
9260 {
9265 {
9268 }
9270 {
9273 }
9274 else
9275 {
9279 }
9288 }
9291 /* Subroutine of fold_binary. If P is the value of EXPR, computes
9292 power-of-two M and (arbitrary) N such that M divides (P-N). This condition
9293 guarantees that P and N have the same least significant log2(M) bits.
9294 N is not otherwise constrained. In particular, N is not normalized to
9295 0 <= N < M as is common. In general, the precise value of P is unknown.
9296 M is chosen as large as possible such that constant N can be determined.
9298 Returns M and sets *RESIDUE to N. */
9300 static unsigned HOST_WIDE_INT
9302 {
9309 {
9312 {
9314 tree offset;
9322 {
9325 else
9326 /* We don't handle more complicated offset expressions. */
9328 }
9329 }
9333 }
9335 {
9348 {
9351 }
9353 {
9356 {
9359 /* Compute the greatest power-of-2 divisor of op1. */
9363 /* If align is non-zero and less than *modulus, replace
9364 *modulus with align., If align is 0, then either op1 is 0
9365 or the greatest power-of-2 divisor of op1 doesn't fit in an
9366 unsigned HOST_WIDE_INT. In either case, no additional
9367 constraint is imposed. */
9372 }
9373 }
9374 }
9376 /* If we get here, we were unable to determine anything useful about the
9377 expression. */
9379 }
9382 /* Fold a binary expression of code CODE and type TYPE with operands
9383 OP0 and OP1. Return the folded expression if folding is
9384 successful. Otherwise, return NULL_TREE. */
9386 tree
9388 {
9403 /* Strip any conversions that don't change the mode. This is
9404 safe for every expression, except for a comparison expression
9405 because its signedness is derived from its operands. So, in
9406 the latter case, only strip conversions that don't change the
9407 signedness.
9409 Note that this is done as an internal manipulation within the
9410 constant folder, in order to find the simplest representation
9411 of the arguments so that their form can be studied. In any
9412 cases, the appropriate type conversions should be put back in
9413 the tree that will get out of the constant folder. */
9416 {
9419 }
9420 else
9421 {
9424 }
9426 /* Note that TREE_CONSTANT isn't enough: static var addresses are
9427 constant but we can't do arithmetic on them. */
9434 {
9436 {
9437 /* Make sure type and arg0 have the same saturating flag. */
9441 }
9444 else
9448 {
9452 }
9453 }
9455 /* If this is a commutative operation, and ARG0 is a constant, move it
9456 to ARG1 to reduce the number of tests below. */
9461 /* ARG0 is the first operand of EXPR, and ARG1 is the second operand.
9463 First check for cases where an arithmetic operation is applied to a
9464 compound, conditional, or comparison operation. Push the arithmetic
9465 operation inside the compound or conditional to see if any folding
9466 can then be done. Convert comparison to conditional for this purpose.
9467 The also optimizes non-constant cases that used to be done in
9468 expand_expr.
9470 Before we do that, see if this is a BIT_AND_EXPR or a BIT_IOR_EXPR,
9471 one of the operands is a comparison and the other is a comparison, a
9472 BIT_AND_EXPR with the constant 1, or a truth value. In that case, the
9473 code below would make the expression more complex. Change it to a
9474 TRUTH_{AND,OR}_EXPR. Likewise, convert a similar NE_EXPR to
9475 TRUTH_XOR_EXPR and an EQ_EXPR to the inversion of a TRUTH_XOR_EXPR. */
9487 {
9491 boolean_type_node,
9499 }
9503 {
9515 {
9521 }
9524 {
9530 }
9531 }
9534 {
9536 /* 0 +p index -> (type)index */
9540 /* PTR +p 0 -> PTR */
9544 /* INT +p INT -> (PTR)(INT + INT). Stripping types allows for this. */
9551 /* index +p PTR -> PTR +p index */
9558 /* (PTR +p B) +p A -> PTR +p (B + A) */
9560 {
9561 tree inner;
9569 }
9571 /* PTR_CST +p CST -> CST1 */
9575 /* Try replacing &a[i1] +p c * i2 with &a[i1 + i2], if c is step
9576 of the array. Loop optimizer sometimes produce this type of
9577 expressions. */
9579 {
9583 }
9588 /* PTR + INT -> (INT)(PTR p+ INT) */
9593 arg0,
9595 /* INT + PTR -> (INT)(PTR p+ INT) */
9600 arg1,
9602 /* A + (-B) -> A - B */
9607 /* (-A) + B -> B - A */
9615 {
9616 /* Convert ~A + 1 to -A. */
9621 /* ~X + X is -1. */
9624 {
9629 {
9632 }
9633 }
9635 /* X + ~X is -1. */
9638 {
9643 {
9646 }
9647 }
9648 }
9650 /* Handle (A1 * C1) + (A2 * C2) with A1, A2 or C1, C2 being the
9651 same or one. Make sure type is not saturating.
9652 fold_plusminus_mult_expr will re-associate. */
9657 {
9661 }
9664 {
9668 /* If we are adding two BIT_AND_EXPR's, both of which are and'ing
9669 with a constant, and the two constants have no bits in common,
9670 we should treat this as a BIT_IOR_EXPR since this may produce more
9671 simplifications. */
9679 {
9682 }
9684 /* Reassociate (plus (plus (mult) (foo)) (mult)) as
9685 (plus (plus (mult) (mult)) (foo)) so that we can
9686 take advantage of the factoring cases below. */
9693 {
9699 else
9721 parg1)));
9722 }
9723 }
9724 else
9725 {
9726 /* See if ARG1 is zero and X + ARG1 reduces to X. */
9730 /* Likewise if the operands are reversed. */
9734 /* Convert X + -C into X - C. */
9737 {
9743 }
9745 /* Fold __complex__ ( x, 0 ) + __complex__ ( 0, y )
9746 to __complex__ ( x, y ). This is not the same for SNaNs or
9747 if signed zeros are involved. */
9751 {
9758 {
9762 {
9768 }
9770 {
9776 }
9777 }
9778 }
9786 /* Convert x+x into x*2.0. */
9792 /* Convert a + (b*c + d*e) into (a + b*c) + d*e.
9793 We associate floats only if the user has specified
9794 -fassociative-math. */
9798 {
9803 {
9804 tree tree0;
9807 }
9808 }
9809 /* Convert (b*c + d*e) + a into b*c + (d*e +a).
9810 We associate floats only if the user has specified
9811 -fassociative-math. */
9815 {
9820 {
9821 tree tree0;
9824 }
9825 }
9826 }
9828 bit_rotate:
9829 /* (A << C1) + (A >> C2) if A is unsigned and C1+C2 is the size of A
9830 is a rotate of A by C1 bits. */
9831 /* (A << B) + (A >> (Z - B)) if A is unsigned and Z is the size of A
9832 is a rotate of A by B bits. */
9833 {
9842 {
9861 {
9869 TYPE_PRECISION
9874 ? LROTATE_EXPR
9877 }
9879 {
9887 TYPE_PRECISION
9892 ? LROTATE_EXPR
9895 }
9896 }
9897 }
9899 associate:
9900 /* In most languages, can't associate operations on floats through
9901 parentheses. Rather than remember where the parentheses were, we
9902 don't associate floats at all, unless the user has specified
9903 -fassociative-math.
9904 And, we need to make sure type is not saturating. */
9908 {
9913 /* Split both trees into variables, constants, and literals. Then
9914 associate each group together, the constants with literals,
9915 then the result with variables. This increases the chances of
9916 literals being recombined later and of generating relocatable
9917 expressions for the sum of a constant and literal. */
9922 /* With undefined overflow we can only associate constants
9923 with one variable. */
9927 {
9935 /* The only case we can still associate with two variables
9936 is if they are the same, modulo negation. */
9939 }
9941 /* Only do something if we found more than two objects. Otherwise,
9942 nothing has changed and we risk infinite recursion. */
9948 {
9949 /* Recombine MINUS_EXPR operands by using PLUS_EXPR. */
9958 /* Preserve the MINUS_EXPR if the negative part of the literal is
9959 greater than the positive part. Otherwise, the multiplicative
9960 folding code (i.e extract_muldiv) may be fooled in case
9961 unsigned constants are subtracted, like in the following
9962 example: ((X*2 + 4) - 8U)/2. */
9964 {
9968 {
9972 }
9973 else
9974 {
9978 }
9979 }
9981 {
9986 else
9987 {
9993 }
9994 }
9999 }
10000 }
10005 /* Pointer simplifications for subtraction, simple reassociations. */
10007 {
10008 /* (PTR0 p+ A) - (PTR1 p+ B) -> (PTR0 - PTR1) + (A - B) */
10011 {
10019 }
10020 /* (PTR0 p+ A) - PTR1 -> (PTR0 - PTR1) + A, assuming PTR0 - PTR1 simplifies. */
10022 {
10028 }
10029 }
10030 /* A - (-B) -> A + B */
10034 /* (-A) - B -> (-B) - A where B is easily negated and we can swap. */
10043 /* Convert -A - 1 to ~A. */
10051 /* Convert -1 - A to ~A. */
10057 {
10063 /* Fold A - (A & B) into ~B & A. */
10066 {
10068 {
10073 }
10075 {
10080 }
10081 }
10083 /* Fold (A & ~B) - (A & B) into (A ^ B) - B, where B is
10084 any power of 2 minus 1. */
10089 {
10095 {
10099 }
10100 }
10101 }
10103 /* See if ARG1 is zero and X - ARG1 reduces to X. */
10107 /* (ARG0 - ARG1) is the same as (-ARG1 + ARG0). So check whether
10108 ARG0 is zero and X + ARG0 reduces to X, since that would mean
10109 (-ARG1 + ARG0) reduces to -ARG1. */
10113 /* Fold __complex__ ( x, 0 ) - __complex__ ( 0, y ) to
10114 __complex__ ( x, -y ). This is not the same for SNaNs or if
10115 signed zeros are involved. */
10119 {
10126 {
10130 {
10132 arg1r ? arg1r
10137 }
10139 {
10143 arg1i ? arg1i
10146 }
10147 }
10148 }
10150 /* Fold &x - &x. This can happen from &x.foo - &x.
10151 This is unsafe for certain floats even in non-IEEE formats.
10152 In IEEE, it is unsafe because it does wrong for NaNs.
10153 Also note that operand_equal_p is always false if an operand
10154 is volatile. */
10160 /* A - B -> A + (-B) if B is easily negatable. */
10163 /* Avoid this transformation if B is a positive REAL_CST. */
10171 /* Try folding difference of addresses. */
10172 {
10173 HOST_WIDE_INT diff;
10179 }
10181 /* Fold &a[i] - &a[j] to i-j. */
10186 {
10191 {
10199 }
10200 }
10208 /* Handle (A1 * C1) - (A2 * C2) with A1, A2 or C1, C2 being the
10209 same or one. Make sure type is not saturating.
10210 fold_plusminus_mult_expr will re-associate. */
10215 {
10219 }
10224 /* (-A) * (-B) -> A * B */
10235 {
10240 /* Transform x * -1 into -x. Make sure to do the negation
10241 on the original operand with conversions not stripped
10242 because we can only strip non-sign-changing conversions. */
10245 /* Transform x * -C into -x * C if x is easily negatable. */
10254 /* (a * (1 << b)) is (a << b) */
10270 {
10273 "occur when simplifying "
10275 WARN_STRICT_OVERFLOW_MISC);
10277 }
10279 /* Optimize z * conj(z) for integer complex numbers. */
10286 }
10287 else
10288 {
10289 /* Maybe fold x * 0 to 0. The expressions aren't the same
10290 when x is NaN, since x * 0 is also NaN. Nor are they the
10291 same in modes with signed zeros, since multiplying a
10292 negative value by 0 gives -0, not +0. */
10297 /* In IEEE floating point, x*1 is not equivalent to x for snans. */
10302 /* Transform x * -1.0 into -x. */
10307 /* Convert (C1/X)*C2 into (C1*C2)/X. This transformation may change
10308 the result for floating point types due to rounding so it is applied
10309 only if -fassociative-math was specify. */
10314 {
10320 }
10322 /* Strip sign operations from X in X*X, i.e. -Y*-Y -> Y*Y. */
10324 {
10327 {
10330 }
10331 }
10333 /* Fold z * +-I to __complex__ (-+__imag z, +-__real z).
10334 This is not the same for NaNs or if signed zeros are
10335 involved. */
10341 {
10353 }
10355 /* Optimize z * conj(z) for floating point complex numbers.
10356 Guarded by flag_unsafe_math_optimizations as non-finite
10357 imaginary components don't produce scalar results. */
10368 {
10372 /* Optimizations of root(...)*root(...). */
10374 {
10379 /* Optimize sqrt(x)*sqrt(x) as x. */
10385 /* Optimize root(x)*root(y) as root(x*y). */
10389 }
10391 /* Optimize expN(x)*expN(y) as expN(x+y). */
10393 {
10399 }
10401 /* Optimizations of pow(...)*pow(...). */
10405 {
10411 /* Optimize pow(x,y)*pow(z,y) as pow(x*z,y). */
10413 {
10417 }
10419 /* Optimize pow(x,y)*pow(x,z) as pow(x,y+z). */
10421 {
10425 }
10426 }
10428 /* Optimize tan(x)*cos(x) as sin(x). */
10437 {
10442 }
10444 /* Optimize x*pow(x,c) as pow(x,c+1). */
10448 {
10454 {
10456 REAL_VALUE_TYPE c;
10457 tree arg;
10463 }
10464 }
10466 /* Optimize pow(x,c)*x as pow(x,c+1). */
10470 {
10476 {
10478 REAL_VALUE_TYPE c;
10479 tree arg;
10485 }
10486 }
10488 /* Optimize x*x as pow(x,2.0), which is expanded as x*x. */
10491 {
10495 {
10498 }
10499 }
10500 }
10501 }
10505 bit_ior:
10513 /* ~X | X is -1. */
10516 {
10520 }
10522 /* X | ~X is -1. */
10525 {
10529 }
10531 /* Canonicalize (X & C1) | C2. */
10535 {
10543 /* If (C1&C2) == C1, then (X&C1)|C2 becomes (X,C2). */
10548 {
10552 }
10553 else
10554 {
10558 }
10560 /* If (C1|C2) == ~0 then (X&C1)|C2 becomes X|C2. */
10565 /* Minimize the number of bits set in C1, i.e. C1 := C1 & ~C2. */
10575 arg1);
10576 }
10578 /* (X & Y) | Y is (X, Y). */
10582 /* (X & Y) | X is (Y, X). */
10587 /* X | (X & Y) is (Y, X). */
10592 /* X | (Y & X) is (Y, X). */
10602 /* Convert (or (not arg0) (not arg1)) to (not (and (arg0) (arg1))).
10604 This results in more efficient code for machines without a NAND
10605 instruction. Combine will canonicalize to the first form
10606 which will allow use of NAND instructions provided by the
10607 backend if they exist. */
10610 {
10615 }
10617 /* See if this can be simplified into a rotate first. If that
10618 is unsuccessful continue in the association code. */
10629 /* ~X ^ X is -1. */
10632 {
10636 }
10638 /* X ^ ~X is -1. */
10641 {
10645 }
10647 /* If we are XORing two BIT_AND_EXPR's, both of which are and'ing
10648 with a constant, and the two constants have no bits in common,
10649 we should treat this as a BIT_IOR_EXPR since this may produce more
10650 simplifications. */
10658 {
10661 }
10663 /* (X | Y) ^ X -> Y & ~ X*/
10666 {
10669 arg1);
10673 }
10675 /* (Y | X) ^ X -> Y & ~ X*/
10678 {
10681 arg1);
10685 }
10687 /* X ^ (X | Y) -> Y & ~ X*/
10690 {
10693 arg0);
10697 }
10699 /* X ^ (Y | X) -> Y & ~ X*/
10702 {
10705 arg0);
10709 }
10711 /* Convert ~X ^ ~Y to X ^ Y. */
10718 /* Convert ~X ^ C to X ^ ~C. */
10725 /* Fold (X & 1) ^ 1 as (X & 1) == 0. */
10732 /* Fold (X & Y) ^ Y as ~X & Y. */
10735 {
10740 }
10741 /* Fold (X & Y) ^ X as ~Y & X. */
10745 {
10750 }
10751 /* Fold X ^ (X & Y) as X & ~Y. */
10754 {
10759 }
10760 /* Fold X ^ (Y & X) as ~Y & X. */
10764 {
10769 }
10771 /* See if this can be simplified into a rotate first. If that
10772 is unsuccessful continue in the association code. */
10783 /* ~X & X is always zero. */
10788 /* X & ~X is always zero. */
10793 /* Canonicalize (X | C1) & C2 as (X & C2) | (C1 & C2). */
10797 {
10806 }
10808 /* (X | Y) & Y is (X, Y). */
10812 /* (X | Y) & X is (Y, X). */
10817 /* X & (X | Y) is (Y, X). */
10822 /* X & (Y | X) is (Y, X). */
10828 /* Fold (X ^ 1) & 1 as (X & 1) == 0. */
10832 {
10838 }
10839 /* Fold ~X & 1 as (X & 1) == 0. */
10842 {
10848 }
10850 /* Fold (X ^ Y) & Y as ~X & Y. */
10853 {
10858 }
10859 /* Fold (X ^ Y) & X as ~Y & X. */
10863 {
10868 }
10869 /* Fold X & (X ^ Y) as X & ~Y. */
10872 {
10877 }
10878 /* Fold X & (Y ^ X) as ~Y & X. */
10882 {
10887 }
10892 /* Simplify ((int)c & 0377) into (int)c, if c is unsigned char. */
10895 {
10896 unsigned int prec
10903 }
10905 /* Convert (and (not arg0) (not arg1)) to (not (or (arg0) (arg1))).
10907 This results in more efficient code for machines without a NOR
10908 instruction. Combine will canonicalize to the first form
10909 which will allow use of NOR instructions provided by the
10910 backend if they exist. */
10913 {
10920 }
10922 /* If arg0 is derived from the address of an object or function, we may
10923 be able to fold this expression using the object or function's
10924 alignment. */
10926 {
10932 /* This works because modulus is a power of 2. If this weren't the
10933 case, we'd have to replace it by its greatest power-of-2
10934 divisor: modulus & -modulus. */
10937 }
10942 /* Don't touch a floating-point divide by zero unless the mode
10943 of the constant can represent infinity. */
10949 /* Optimize A / A to 1.0 if we don't care about
10950 NaNs or Infinities. Skip the transformation
10951 for non-real operands. */
10956 {
10960 }
10962 /* The complex version of the above A / A optimization. */
10965 {
10969 {
10971 /* omit_two_operands will call fold_convert for us. */
10973 }
10974 }
10976 /* (-A) / (-B) -> A / B */
10986 /* In IEEE floating point, x/1 is not equivalent to x for snans. */
10991 /* In IEEE floating point, x/-1 is not equivalent to -x for snans. */
10996 /* If ARG1 is a constant, we can convert this to a multiply by the
10997 reciprocal. This does not have the same rounding properties,
10998 so only do this if -freciprocal-math. We can actually
10999 always safely do it if ARG1 is a power of two, but it's hard to
11000 tell if it is or not in a portable manner. */
11002 {
11007 /* Find the reciprocal if optimizing and the result is exact. */
11009 {
11010 REAL_VALUE_TYPE r;
11013 {
11017 }
11018 }
11019 }
11020 /* Convert A/B/C to A/(B*C). */
11027 /* Convert A/(B/C) to (A/B)*C. */
11035 /* Convert C1/(X*C2) into (C1/C2)/X. */
11040 {
11046 }
11049 {
11053 /* Optimize sin(x)/cos(x) as tan(x). */
11059 {
11064 }
11066 /* Optimize cos(x)/sin(x) as 1.0/tan(x). */
11072 {
11076 {
11080 }
11081 }
11083 /* Optimize sin(x)/tan(x) as cos(x) if we don't care about
11084 NaNs or Infinities. */
11088 {
11095 {
11100 }
11101 }
11103 /* Optimize tan(x)/sin(x) as 1.0/cos(x) if we don't care about
11104 NaNs or Infinities. */
11108 {
11115 {
11119 {
11123 tmp);
11124 }
11125 }
11126 }
11128 /* Optimize pow(x,c)/x as pow(x,c-1). */
11132 {
11138 {
11140 REAL_VALUE_TYPE c;
11141 tree arg;
11147 }
11148 }
11150 /* Optimize a/root(b/c) into a*root(c/b). */
11152 {
11156 {
11165 }
11166 }
11168 /* Optimize x/expN(y) into x*expN(-y). */
11170 {
11175 }
11177 /* Optimize x/pow(y,z) into x*pow(y,-z). */
11181 {
11188 }
11189 }
11194 /* Simplify A / (B << N) where A and B are positive and B is
11195 a power of 2, to A >> (N + log2(B)). */
11200 {
11203 {
11210 WARN_STRICT_OVERFLOW_MISC);
11216 }
11217 }
11218 /* Fall thru */
11227 /* X / -1 is -X. */
11234 /* Convert -A / -B to A / B when the type is signed and overflow is
11235 undefined. */
11239 {
11242 "when distributing negation across "
11244 WARN_STRICT_OVERFLOW_MISC);
11248 }
11252 {
11255 "when distributing negation across "
11257 WARN_STRICT_OVERFLOW_MISC);
11260 }
11262 /* If arg0 is a multiple of arg1, then rewrite to the fastest div
11263 operation, EXACT_DIV_EXPR.
11265 Note that only CEIL_DIV_EXPR and FLOOR_DIV_EXPR are rewritten now.
11266 At one time others generated faster code, it's not clear if they do
11267 after the last round to changes to the DIV code in expmed.c. */
11276 {
11280 WARN_STRICT_OVERFLOW_MISC);
11282 }
11290 /* X % 1 is always zero, but be sure to preserve any side
11291 effects in X. */
11295 /* X % 0, return X % 0 unchanged so that we can get the
11296 proper warnings and errors. */
11300 /* 0 % X is always zero, but be sure to preserve any side
11301 effects in X. Place this after checking for X == 0. */
11305 /* X % -1 is zero. */
11312 /* Optimize TRUNC_MOD_EXPR by a power of two into a BIT_AND_EXPR,
11313 i.e. "X % C" into "X & (C - 1)", if X and C are positive. */
11318 {
11320 /* Also optimize A % (C << N) where C is a power of 2,
11321 to A & ((C << N) - 1). */
11326 {
11331 "occur when simplifying "
11333 WARN_STRICT_OVERFLOW_MISC);
11337 }
11338 }
11340 /* X % -C is the same as X % C. */
11347 /* Avoid this transformation if C is INT_MIN, i.e. C == -C. */
11352 /* X % -Y is the same as X % Y. */
11363 {
11367 WARN_STRICT_OVERFLOW_MISC);
11369 }
11380 /* Optimize -1 >> x for arithmetic right shifts. */
11383 /* ... fall through ... */
11386 shift:
11392 /* Since negative shift count is not well-defined,
11393 don't try to compute it in the compiler. */
11397 /* Turn (a OP c1) OP c2 into a OP (c1+c2). */
11402 {
11406 /* Deal with a OP (c1 + c2) being undefined but (a OP c1) OP c2
11407 being well defined. */
11409 {
11414 else
11416 }
11420 }
11422 /* Transform (x >> c) << c into x & (-1<<c), or transform (x << c) >> c
11423 into x & ((unsigned)-1 >> c) for unsigned types. */
11431 {
11434 tree lshift;
11435 tree arg00;
11438 {
11445 }
11446 }
11448 /* Rewrite an LROTATE_EXPR by a constant into an
11449 RROTATE_EXPR by a new constant. */
11451 {
11456 }
11458 /* If we have a rotate of a bit operation with the rotate count and
11459 the second operand of the bit operation both constant,
11460 permute the two operations. */
11472 /* Two consecutive rotates adding up to the width of the mode can
11473 be ignored. */
11510 /* Note that the operands of this must be ints
11511 and their values must be 0 or 1.
11512 ("true" is a fixed value perhaps depending on the language.) */
11513 /* If first arg is constant zero, return it. */
11517 /* If either arg is constant true, drop it. */
11521 /* Preserve sequence points. */
11524 /* If second arg is constant zero, result is zero, but first arg
11525 must be evaluated. */
11528 /* Likewise for first arg, but note that only the TRUTH_AND_EXPR
11529 case will be handled here. */
11533 /* !X && X is always false. */
11537 /* X && !X is always false. */
11542 /* A < X && A + 1 > Y ==> A < X && A >= Y. Normally A + 1 > Y
11543 means A >= Y && A != MAX, but in this case we know that
11544 A < X <= MAX. */
11548 {
11556 }
11558 truth_andor:
11559 /* We only do these simplifications if we are optimizing. */
11563 /* Check for things like (A || B) && (A || C). We can convert this
11564 to A || (B && C). Note that either operator can be any of the four
11565 truth and/or operations and the transformation will still be
11566 valid. Also note that we only care about order for the
11567 ANDIF and ORIF operators. If B contains side effects, this
11568 might change the truth-value of A. */
11575 {
11595 /* This case if tricky because we must either have commutative
11596 operators or else A10 must not have side-effects. */
11602 a01);
11603 }
11605 /* See if we can build a range comparison. */
11609 /* Check for the possibility of merging component references. If our
11610 lhs is another similar operation, try to merge its rhs with our
11611 rhs. Then try to merge our lhs and rhs. */
11623 /* Note that the operands of this must be ints
11624 and their values must be 0 or true.
11625 ("true" is a fixed value perhaps depending on the language.) */
11626 /* If first arg is constant true, return it. */
11630 /* If either arg is constant zero, drop it. */
11634 /* Preserve sequence points. */
11637 /* If second arg is constant true, result is true, but we must
11638 evaluate first arg. */
11641 /* Likewise for first arg, but note this only occurs here for
11642 TRUTH_OR_EXPR. */
11646 /* !X || X is always true. */
11650 /* X || !X is always true. */
11658 /* If the second arg is constant zero, drop it. */
11661 /* If the second arg is constant true, this is a logical inversion. */
11663 {
11664 /* Only call invert_truthvalue if operand is a truth value. */
11667 else
11670 }
11671 /* Identical arguments cancel to zero. */
11675 /* !X ^ X is always true. */
11680 /* X ^ !X is always true. */
11693 /* bool_var != 0 becomes bool_var. */
11698 /* bool_var == 1 becomes bool_var. */
11703 /* bool_var != 1 becomes !bool_var. */
11708 /* bool_var == 0 becomes !bool_var. */
11713 /* If this is an equality comparison of the address of two non-weak,
11714 unaliased symbols neither of which are extern (since we do not
11715 have access to attributes for externs), then we know the result. */
11728 {
11729 /* We know that we're looking at the address of two
11730 non-weak, unaliased, static _DECL nodes.
11732 It is both wasteful and incorrect to call operand_equal_p
11733 to compare the two ADDR_EXPR nodes. It is wasteful in that
11734 all we need to do is test pointer equality for the arguments
11735 to the two ADDR_EXPR nodes. It is incorrect to use
11736 operand_equal_p as that function is NOT equivalent to a
11737 C equality test. It can in fact return false for two
11738 objects which would test as equal using the C equality
11739 operator. */
11743 type);
11744 }
11746 /* If this is an EQ or NE comparison of a constant with a PLUS_EXPR or
11747 a MINUS_EXPR of a constant, we can convert it into a comparison with
11748 a revised constant as long as no overflow occurs. */
11760 /* Similarly for a NEGATE_EXPR. */
11768 /* Similarly for a BIT_XOR_EXPR; X ^ C1 == C2 is X == (C1 ^ C2). */
11777 /* Transform comparisons of the form X +- C CMP X. */
11783 {
11790 else
11793 }
11795 /* If we have X - Y == 0, we can convert that to X == Y and similarly
11796 for !=. Don't do this for ordered comparisons due to overflow. */
11802 /* Convert ABS_EXPR<x> == 0 or ABS_EXPR<x> != 0 to x == 0 or x != 0. */
11807 /* If this is an EQ or NE comparison with zero and ARG0 is
11808 (1 << foo) & bar, convert it to (bar >> foo) & 1. Both require
11809 two operations, but the latter can be done in one less insn
11810 on machines that have only two-operand insns or on which a
11811 constant cannot be the first operand. */
11814 {
11819 return
11825 integer_one_node)),
11826 arg1);
11829 return
11835 integer_one_node)),
11836 arg1);
11837 }
11839 /* If this is an NE or EQ comparison of zero against the result of a
11840 signed MOD operation whose second operand is a power of 2, make
11841 the MOD operation unsigned since it is simpler and equivalent. */
11849 {
11859 }
11861 /* Fold ((X >> C1) & C2) == 0 and ((X >> C1) & C2) != 0 where
11862 C1 is a valid shift constant, and C2 is a power of two, i.e.
11863 a single bit. */
11867 == INTEGER_CST
11870 {
11875 /* Check for a valid shift count. */
11878 {
11882 /* If (C2 << C1) doesn't overflow, then ((X >> C1) & C2) != 0
11883 can be rewritten as (X & (C2 << C1)) != 0. */
11885 {
11889 }
11890 /* Otherwise, for signed (arithmetic) shifts,
11891 ((X >> C1) & C2) != 0 is rewritten as X < 0, and
11892 ((X >> C1) & C2) == 0 is rewritten as X >= 0. */
11896 /* Otherwise, of unsigned (logical) shifts,
11897 ((X >> C1) & C2) != 0 is rewritten as (X,false), and
11898 ((X >> C1) & C2) == 0 is rewritten as (X,true). */
11899 else
11903 arg000);
11904 }
11905 }
11907 /* If this is an NE comparison of zero with an AND of one, remove the
11908 comparison since the AND will give the correct value. */
11915 /* If we have (A & C) == C where C is a power of 2, convert this into
11916 (A & C) != 0. Similarly for NE_EXPR. */
11922 integer_zero_node));
11924 /* If we have (A & C) != 0 or (A & C) == 0 and C is the sign
11925 bit, then fold the expression into A < 0 or A >= 0. */
11930 /* If we have (A & C) == D where D & ~C != 0, convert this into 0.
11931 Similarly for NE_EXPR. */
11935 {
11944 }
11946 /* If we have (A | C) == D where C & ~D != 0, convert this into 0.
11947 Similarly for NE_EXPR. */
11951 {
11958 }
11960 /* If this is a comparison of a field, we may be able to simplify it. */
11963 /* Handle the constant case even without -O
11964 to make sure the warnings are given. */
11966 {
11970 }
11972 /* Optimize comparisons of strlen vs zero to a compare of the
11973 first character of the string vs zero. To wit,
11974 strlen(ptr) == 0 => *ptr == 0
11975 strlen(ptr) != 0 => *ptr != 0
11976 Other cases should reduce to one of these two (or a constant)
11977 due to the return value of strlen being unsigned. */
11980 {
11988 {
11992 }
11993 }
11995 /* Fold (X >> C) != 0 into X < 0 if C is one less than the width
11996 of X. Similarly fold (X >> C) == 0 into X >= 0. */
12000 {
12007 {
12009 {
12012 }
12015 }
12016 }
12018 /* (X ^ Y) == 0 becomes X == Y, and (X ^ Y) != 0 becomes X != Y. */
12024 /* (X ^ Y) == Y becomes X == 0. We know that Y has no side-effects. */
12029 /* Likewise (X ^ Y) == X becomes Y == 0. X has no side-effects. */
12036 /* (X ^ C1) op C2 can be rewritten as X op (C1 ^ C2). */
12044 /* Fold (~X & C) == 0 into (X & C) != 0 and (~X & C) != 0 into
12045 (X & C) == 0 when C is a single bit. */
12050 {
12056 }
12058 /* Fold ((X & C) ^ C) eq/ne 0 into (X & C) ne/eq 0, when the
12059 constant C is a power of two, i.e. a single bit. */
12066 {
12070 }
12072 /* Likewise, fold ((X ^ C) & C) eq/ne 0 into (X & C) ne/eq 0,
12073 when is C is a power of two, i.e. a single bit. */
12080 {
12086 }
12090 {
12093 }
12095 /* Fold -X op -Y as X op Y, where op is eq/ne. */
12102 /* Fold (X & C) op (Y & C) as (X ^ Y) & C op 0", and symmetries. */
12105 {
12117 arg01),
12125 arg01),
12133 arg00),
12141 arg00),
12143 }
12147 {
12154 /* Optimize (X ^ Z) op (Y ^ Z) as X op Y, and symmetries.
12155 operand_equal_p guarantees no side-effects so we don't need
12156 to use omit_one_operand on Z. */
12166 /* Optimize (X ^ C1) op (Y ^ C2) as (X ^ (C1 ^ C2)) op Y. */
12173 arg10);
12174 }
12176 /* Attempt to simplify equality/inequality comparisons of complex
12177 values. Only lower the comparison if the result is known or
12178 can be simplified to a single scalar comparison. */
12183 {
12188 {
12191 }
12192 else
12193 {
12196 }
12199 {
12202 }
12203 else
12204 {
12207 }
12211 {
12213 {
12218 }
12219 else
12220 {
12225 }
12226 }
12230 {
12232 {
12237 }
12238 else
12239 {
12244 }
12245 }
12246 }
12258 /* Transform comparisons of the form X +- C CMP X. */
12265 {
12272 else
12275 /* (X - c) > X becomes false. */
12279 {
12283 "occur when assuming that (X - c) > X "
12285 WARN_STRICT_OVERFLOW_ALL);
12287 }
12289 /* Likewise (X + c) < X becomes false. */
12293 {
12297 "occur when assuming that "
12299 WARN_STRICT_OVERFLOW_ALL);
12301 }
12303 /* Convert (X - c) <= X to true. */
12308 {
12312 "occur when assuming that "
12314 WARN_STRICT_OVERFLOW_ALL);
12316 }
12318 /* Convert (X + c) >= X to true. */
12323 {
12327 "occur when assuming that "
12329 WARN_STRICT_OVERFLOW_ALL);
12331 }
12334 {
12335 /* Convert X + c > X and X - c < X to true for integers. */
12339 {
12342 "not occur when assuming that "
12344 WARN_STRICT_OVERFLOW_ALL);
12346 }
12351 {
12354 "not occur when assuming that "
12356 WARN_STRICT_OVERFLOW_ALL);
12358 }
12360 /* Convert X + c <= X and X - c >= X to false for integers. */
12364 {
12367 "not occur when assuming that "
12369 WARN_STRICT_OVERFLOW_ALL);
12371 }
12376 {
12379 "not occur when assuming that "
12381 WARN_STRICT_OVERFLOW_ALL);
12383 }
12384 }
12385 }
12387 /* Change X >= C to X > (C - 1) and X < C to X <= (C - 1) if C > 0.
12388 This transformation affects the cases which are handled in later
12389 optimizations involving comparisons with non-negative constants. */
12393 {
12395 {
12400 }
12402 {
12407 }
12408 }
12410 /* Comparisons with the highest or lowest possible integer of
12411 the specified precision will have known values. */
12412 {
12420 {
12421 HOST_WIDE_INT signed_max_hi;
12426 {
12433 {
12437 }
12438 else
12439 {
12443 }
12444 }
12445 else
12446 {
12455 {
12458 }
12459 else
12460 {
12463 }
12464 }
12469 {
12482 /* The GE_EXPR and LT_EXPR cases above are not normally
12483 reached because of previous transformations. */
12487 }
12489 == max_hi
12492 {
12498 arg1);
12504 arg1);
12507 }
12509 == min_hi
12512 {
12527 }
12529 == min_hi
12532 {
12537 arg1);
12542 arg1);
12545 }
12550 /* We will flip the signedness of the comparison operator
12551 associated with the mode of arg1, so the sign bit is
12552 specified by this mode. Check that arg1 is the signed
12553 max associated with this sign bit. */
12555 /* signed_type does not work on pointer types. */
12557 {
12558 /* The following case also applies to X < signed_max+1
12559 and X >= signed_max+1 because previous transformations. */
12561 {
12562 tree st;
12567 }
12568 }
12569 }
12570 }
12572 /* If we are comparing an ABS_EXPR with a constant, we can
12573 convert all the cases into explicit comparisons, but they may
12574 well not be faster than doing the ABS and one comparison.
12575 But ABS (X) <= C is a range comparison, which becomes a subtraction
12576 and a comparison, and is probably faster. */
12590 /* Convert ABS_EXPR<x> >= 0 to true. */
12597 {
12600 "when simplifying comparison of "
12602 WARN_STRICT_OVERFLOW_CONDITIONAL);
12604 }
12606 /* Convert ABS_EXPR<x> < 0 to false. */
12611 {
12614 "when simplifying comparison of "
12616 WARN_STRICT_OVERFLOW_CONDITIONAL);
12618 }
12620 /* If X is unsigned, convert X < (1 << Y) into X >> Y == 0
12621 and similarly for >= into !=. */
12637 return
12656 {
12660 }
12662 /* If the first operand is NaN, the result is constant. */
12666 {
12668 ? integer_zero_node
12671 }
12673 /* If the second operand is NaN, the result is constant. */
12677 {
12679 ? integer_zero_node
12682 }
12684 /* Simplify unordered comparison of something with itself. */
12690 && !flag_trapping_math
12694 /* Fold (double)float1 CMP (double)float2 into float1 CMP float2. */
12695 {
12706 }
12711 /* When pedantic, a compound expression can be neither an lvalue
12712 nor an integer constant expression. */
12715 /* Don't let (0, 0) be null pointer constant. */
12729 /* An ASSERT_EXPR should never be passed to fold_binary. */
12735 }
12737 /* Callback for walk_tree, looking for LABEL_EXPR.
12738 Returns tree TP if it is LABEL_EXPR. Otherwise it returns NULL_TREE.
12739 Do not check the sub-tree of GOTO_EXPR. */
12741 static tree
12745 {
12747 {
12752 /* no break */
12755 }
12756 }
12758 /* Checks whether the sub-tree ST contains a label LABEL_EXPR which is
12759 accessible from outside the sub-tree. Returns NULL_TREE if no
12760 addressable label is found. */
12762 static bool
12764 {
12766 }
12768 /* Fold a ternary expression of code CODE and type TYPE with operands
12769 OP0, OP1, and OP2. Return the folded expression if folding is
12770 successful. Otherwise, return NULL_TREE. */
12772 tree
12774 {
12775 tree tem;
12782 /* Strip any conversions that don't change the mode. This is safe
12783 for every expression, except for a comparison expression because
12784 its signedness is derived from its operands. So, in the latter
12785 case, only strip conversions that don't change the signedness.
12787 Note that this is done as an internal manipulation within the
12788 constant folder, in order to find the simplest representation of
12789 the arguments so that their form can be studied. In any cases,
12790 the appropriate type conversions should be put back in the tree
12791 that will get out of the constant folder. */
12793 {
12796 }
12799 {
12802 }
12805 {
12809 {
12815 }
12819 /* Pedantic ANSI C says that a conditional expression is never an lvalue,
12820 so all simple results must be passed through pedantic_non_lvalue. */
12822 {
12825 /* Only optimize constant conditions when the selected branch
12826 has the same type as the COND_EXPR. This avoids optimizing
12827 away "c ? x : throw", where the throw has a void type.
12828 Avoid throwing away that operand which contains label. */
12835 }
12839 /* If we have A op B ? A : C, we may be able to convert this to a
12840 simpler expression, depending on the operation and the values
12841 of B and C. Signed zeros prevent all of these transformations,
12842 for reasons given above each one.
12844 Also try swapping the arguments and inverting the conditional. */
12849 {
12853 }
12857 op2,
12860 {
12863 {
12867 }
12868 }
12870 /* If the second operand is simpler than the third, swap them
12871 since that produces better jump optimization results. */
12874 {
12875 /* See if this can be inverted. If it can't, possibly because
12876 it was a floating-point inequality comparison, don't do
12877 anything. */
12881 }
12883 /* Convert A ? 1 : 0 to simply A. */
12886 /* If we try to convert OP0 to our type, the
12887 call to fold will try to move the conversion inside
12888 a COND, which will recurse. In that case, the COND_EXPR
12889 is probably the best choice, so leave it alone. */
12893 /* Convert A ? 0 : 1 to !A. This prefers the use of NOT_EXPR
12894 over COND_EXPR in cases such as floating point comparisons. */
12901 /* A < 0 ? <sign bit of A> : 0 is simply (A & <sign bit of A>). */
12906 {
12907 /* sign_bit_p only checks ARG1 bits within A's precision.
12908 If <sign bit of A> has wider type than A, bits outside
12909 of A's precision in <sign bit of A> need to be checked.
12910 If they are all 0, this optimization needs to be done
12911 in unsigned A's type, if they are all 1 in signed A's type,
12912 otherwise this can't be done. */
12917 {
12919 HOST_WIDE_INT mask_hi;
12921 tree tem_type;
12929 {
12933 }
12934 else
12935 {
12939 }
12941 {
12945 }
12946 else
12952 {
12955 }
12958 {
12961 }
12962 else
12964 }
12971 arg1)));
12972 }
12974 /* (A >> N) & 1 ? (1 << N) : 0 is simply A & (1 << N). A & 1 was
12975 already handled above. */
12980 {
12989 }
12991 /* A & N ? N : 0 is simply A & N if N is a power of two. This
12992 is probably obsolete because the first operand should be a
12993 truth value (that's why we have the two cases above), but let's
12994 leave it in until we can confirm this for all front-ends. */
13005 /* Convert A ? B : 0 into A && B if A and B are truth values. */
13011 arg1);
13013 /* Convert A ? B : 1 into !A || B if A and B are truth values. */
13017 {
13018 /* Only perform transformation if ARG0 is easily inverted. */
13023 arg1);
13024 }
13026 /* Convert A ? 0 : B into !A && B if A and B are truth values. */
13030 {
13031 /* Only perform transformation if ARG0 is easily inverted. */
13036 op2);
13037 }
13039 /* Convert A ? 1 : B into A || B if A and B are truth values. */
13045 op2);
13050 /* CALL_EXPRs used to be ternary exprs. Catch any mistaken uses
13051 of fold_ternary on them. */
13060 {
13069 {
13074 else
13075 {
13077 tree value;
13081 }
13086 else
13088 }
13089 }
13095 }
13097 /* Perform constant folding and related simplification of EXPR.
13098 The related simplifications include x*1 => x, x*0 => 0, etc.,
13099 and application of the associative law.
13100 NOP_EXPR conversions may be removed freely (as long as we
13101 are careful not to change the type of the overall expression).
13102 We cannot simplify through a CONVERT_EXPR, FIX_EXPR or FLOAT_EXPR,
13103 but we can constant-fold them if they have constant operands. */
13105 #ifdef ENABLE_FOLD_CHECKING
13106 # define fold(x) fold_1 (x)
13108 static
13109 #endif
13110 tree
13112 {
13116 tree tem;
13118 /* Return right away if a constant. */
13122 /* CALL_EXPR-like objects with variable numbers of operands are
13123 treated specially. */
13125 {
13127 {
13130 }
13132 }
13136 {
13141 {
13159 }
13160 }
13163 {
13170 }
13172 #ifdef ENABLE_FOLD_CHECKING
13173 #undef fold
13179 /* When --enable-checking=fold, compute a digest of expr before
13180 and after actual fold call to see if fold did not accidentally
13181 change original expr. */
13183 tree
13185 {
13186 tree ret;
13189 htab_t ht;
13208 }
13210 void
13212 {
13215 htab_t ht;
13225 }
13227 static void
13229 {
13231 }
13233 static void
13235 {
13241 recursive_label:
13255 {
13256 /* Allow DECL_ASSEMBLER_NAME to be modified. */
13260 }
13265 {
13266 /* Allow these fields to be modified. */
13267 tree tmp;
13274 {
13277 }
13278 }
13287 {
13290 {
13304 }
13308 {
13321 }
13338 {
13344 }
13349 {
13353 }
13364 {
13367 }
13377 }
13378 }
13380 /* Helper function for outputting the checksum of a tree T. When
13381 debugging with gdb, you can "define mynext" to be "next" followed
13382 by "call debug_fold_checksum (op0)", then just trace down till the
13383 outputs differ. */
13385 void
13387 {
13402 }
13404 #endif
13406 /* Fold a unary tree expression with code CODE of type TYPE with an
13407 operand OP0. Return a folded expression if successful. Otherwise,
13408 return a tree expression with code CODE of type TYPE with an
13409 operand OP0. */
13411 tree
13413 {
13414 tree tem;
13415 #ifdef ENABLE_FOLD_CHECKING
13418 htab_t ht;
13425 #endif
13431 #ifdef ENABLE_FOLD_CHECKING
13439 #endif
13441 }
13443 /* Fold a binary tree expression with code CODE of type TYPE with
13444 operands OP0 and OP1. Return a folded expression if successful.
13445 Otherwise, return a tree expression with code CODE of type TYPE
13446 with operands OP0 and OP1. */
13448 tree
13450 MEM_STAT_DECL)
13451 {
13452 tree tem;
13453 #ifdef ENABLE_FOLD_CHECKING
13459 htab_t ht;
13471 #endif
13477 #ifdef ENABLE_FOLD_CHECKING
13493 #endif
13495 }
13497 /* Fold a ternary tree expression with code CODE of type TYPE with
13498 operands OP0, OP1, and OP2. Return a folded expression if
13499 successful. Otherwise, return a tree expression with code CODE of
13500 type TYPE with operands OP0, OP1, and OP2. */
13502 tree
13504 MEM_STAT_DECL)
13505 {
13506 tree tem;
13507 #ifdef ENABLE_FOLD_CHECKING
13515 htab_t ht;
13532 #endif
13539 #ifdef ENABLE_FOLD_CHECKING
13563 #endif
13565 }
13567 /* Fold a CALL_EXPR expression of type TYPE with operands FN and NARGS
13568 arguments in ARGARRAY, and a null static chain.
13569 Return a folded expression if successful. Otherwise, return a CALL_EXPR
13570 of type TYPE from the given operands as constructed by build_call_array. */
13572 tree
13574 {
13575 tree tem;
13576 #ifdef ENABLE_FOLD_CHECKING
13582 htab_t ht;
13596 #endif
13600 #ifdef ENABLE_FOLD_CHECKING
13617 #endif
13619 }
13621 /* Perform constant folding and related simplification of initializer
13622 expression EXPR. These behave identically to "fold_buildN" but ignore
13623 potential run-time traps and exceptions that fold must preserve. */
13625 #define START_FOLD_INIT \
13626 int saved_signaling_nans = flag_signaling_nans;\
13627 int saved_trapping_math = flag_trapping_math;\
13628 int saved_rounding_math = flag_rounding_math;\
13629 int saved_trapv = flag_trapv;\
13630 int saved_folding_initializer = folding_initializer;\
13631 flag_signaling_nans = 0;\
13632 flag_trapping_math = 0;\
13633 flag_rounding_math = 0;\
13634 flag_trapv = 0;\
13635 folding_initializer = 1;
13637 #define END_FOLD_INIT \
13638 flag_signaling_nans = saved_signaling_nans;\
13639 flag_trapping_math = saved_trapping_math;\
13640 flag_rounding_math = saved_rounding_math;\
13641 flag_trapv = saved_trapv;\
13642 folding_initializer = saved_folding_initializer;
13644 tree
13646 {
13647 tree result;
13648 START_FOLD_INIT;
13652 END_FOLD_INIT;
13654 }
13656 tree
13658 {
13659 tree result;
13660 START_FOLD_INIT;
13664 END_FOLD_INIT;
13666 }
13668 tree
13670 tree op2)
13671 {
13672 tree result;
13673 START_FOLD_INIT;
13677 END_FOLD_INIT;
13679 }
13681 tree
13684 {
13685 tree result;
13686 START_FOLD_INIT;
13690 END_FOLD_INIT;
13692 }
13694 #undef START_FOLD_INIT
13695 #undef END_FOLD_INIT
13697 /* Determine if first argument is a multiple of second argument. Return 0 if
13698 it is not, or we cannot easily determined it to be.
13700 An example of the sort of thing we care about (at this point; this routine
13701 could surely be made more general, and expanded to do what the *_DIV_EXPR's
13702 fold cases do now) is discovering that
13704 SAVE_EXPR (I) * SAVE_EXPR (J * 8)
13706 is a multiple of
13708 SAVE_EXPR (J * 8)
13710 when we know that the two SAVE_EXPR (J * 8) nodes are the same node.
13712 This code also handles discovering that
13714 SAVE_EXPR (I) * SAVE_EXPR (J * 8)
13716 is a multiple of 8 so we don't have to worry about dealing with a
13717 possible remainder.
13719 Note that we *look* inside a SAVE_EXPR only to determine how it was
13720 calculated; it is not safe for fold to do much of anything else with the
13721 internals of a SAVE_EXPR, since it cannot know when it will be evaluated
13722 at run time. For example, the latter example above *cannot* be implemented
13723 as SAVE_EXPR (I) * J or any variant thereof, since the value of J at
13724 evaluation time of the original SAVE_EXPR is not necessarily the same at
13725 the time the new expression is evaluated. The only optimization of this
13726 sort that would be valid is changing
13728 SAVE_EXPR (I) * SAVE_EXPR (SAVE_EXPR (J) * 8)
13730 divided by 8 to
13732 SAVE_EXPR (I) * SAVE_EXPR (J)
13734 (where the same SAVE_EXPR (J) is used in the original and the
13735 transformed version). */
13737 int
13739 {
13747 {
13749 /* Bitwise and provides a power of two multiple. If the mask is
13750 a multiple of BOTTOM then TOP is a multiple of BOTTOM. */
13753 /* FALLTHRU */
13766 {
13770 /* const_binop may not detect overflow correctly,
13771 so check for it explicitly here. */
13777 size_one_node,
13781 }
13785 /* Can't handle conversions from non-integral or wider integral type. */
13791 /* .. fall through ... */
13808 }
13809 }
13811 /* Return true if `t' is known to be non-negative. If the return
13812 value is based on the assumption that signed overflow is undefined,
13813 set *STRICT_OVERFLOW_P to true; otherwise, don't change
13814 *STRICT_OVERFLOW_P. */
13816 bool
13818 {
13826 {
13828 /* Query VRP to see if it has recorded any information about
13829 the range of this object. */
13833 /* We can't return 1 if flag_wrapv is set because
13834 ABS_EXPR<INT_MIN> = INT_MIN. */
13838 {
13841 }
13857 strict_overflow_p)
13859 strict_overflow_p));
13861 /* zero_extend(x) + zero_extend(y) is non-negative if x and y are
13862 both unsigned and at least 2 bits shorter than the result. */
13866 {
13871 {
13875 }
13876 }
13881 {
13882 /* x * x for floating point x is always non-negative. */
13886 strict_overflow_p)
13888 strict_overflow_p));
13889 }
13891 /* zero_extend(x) * zero_extend(y) is non-negative if x and y are
13892 both unsigned and their total bits is shorter than the result. */
13896 {
13903 }
13909 strict_overflow_p)
13911 strict_overflow_p));
13922 strict_overflow_p)
13924 strict_overflow_p));
13935 strict_overflow_p);
13941 strict_overflow_p);
13945 strict_overflow_p);
13949 strict_overflow_p)
13951 strict_overflow_p));
13954 {
13959 {
13962 strict_overflow_p);
13964 {
13968 strict_overflow_p);
13969 }
13970 }
13972 {
13975 strict_overflow_p);
13979 }
13980 }
13984 {
13988 /* If the initializer is non-void, then it's a normal expression
13989 that will be assigned to the slot. */
13993 /* Otherwise, the initializer sets the slot in some way. One common
13994 way is an assignment statement at the end of the initializer. */
13996 {
14004 else
14006 }
14011 strict_overflow_p);
14014 }
14017 {
14021 {
14039 /* Always true. */
14043 /* sqrt(-0.0) is -0.0. */
14047 strict_overflow_p);
14080 /* True if the 1st argument is nonnegative. */
14082 strict_overflow_p);
14085 /* True if the 1st OR 2nd arguments are nonnegative. */
14087 strict_overflow_p)
14089 strict_overflow_p)));
14092 /* True if the 1st AND 2nd arguments are nonnegative. */
14094 strict_overflow_p)
14096 strict_overflow_p)));
14099 /* True if the 2nd argument is nonnegative. */
14101 strict_overflow_p);
14104 /* True if the 1st argument is nonnegative or the second
14105 argument is an even integer. */
14107 {
14111 }
14113 strict_overflow_p);
14116 /* True if the 1st argument is nonnegative or the second
14117 argument is an even integer valued real. */
14119 {
14120 REAL_VALUE_TYPE c;
14121 HOST_WIDE_INT n;
14126 {
14127 REAL_VALUE_TYPE cint;
14132 }
14133 }
14135 strict_overflow_p);
14139 }
14140 }
14142 /* ... fall through ... */
14145 {
14149 /* Truth values evaluate to 0 or 1, which is nonnegative unless we
14150 have a signed:1 type (where the value is -1 and 0). */
14152 }
14153 }
14155 /* We don't know sign of `t', so be conservative and return false. */
14157 }
14159 /* Return true if `t' is known to be non-negative. Handle warnings
14160 about undefined signed overflow. */
14162 bool
14164 {
14171 "determining that expression is always "
14173 WARN_STRICT_OVERFLOW_MISC);
14175 }
14177 /* Return true when T is an address and is known to be nonzero.
14178 For floating point we further ensure that T is not denormal.
14179 Similar logic is present in nonzero_address in rtlanal.h.
14181 If the return value is based on the assumption that signed overflow
14182 is undefined, set *STRICT_OVERFLOW_P to true; otherwise, don't
14183 change *STRICT_OVERFLOW_P. */
14185 bool
14187 {
14191 /* Doing something useful for floating point would need more work. */
14196 {
14198 /* Query VRP to see if it has recorded any information about
14199 the range of this object. */
14204 strict_overflow_p);
14212 {
14213 /* With the presence of negative values it is hard
14214 to say something. */
14221 /* One of operands must be positive and the other non-negative. */
14222 /* We don't set *STRICT_OVERFLOW_P here: even if this value
14223 overflows, on a twos-complement machine the sum of two
14224 nonnegative numbers can never be zero. */
14226 strict_overflow_p)
14228 strict_overflow_p));
14229 }
14234 {
14236 strict_overflow_p)
14238 strict_overflow_p))
14239 {
14242 }
14243 }
14247 {
14253 strict_overflow_p));
14254 }
14258 {
14264 /* Weak declarations may link to NULL. */
14268 /* Constants are never weak. */
14273 }
14281 {
14285 }
14294 {
14297 }
14304 {
14308 /* When both operands are nonzero, then MAX must be too. */
14310 strict_overflow_p))
14313 /* MAX where operand 0 is positive is positive. */
14315 strict_overflow_p);
14316 }
14317 /* MAX where operand 1 is positive is positive. */
14322 {
14326 }
14334 strict_overflow_p);
14339 strict_overflow_p);
14343 strict_overflow_p)
14345 strict_overflow_p));
14352 }
14354 }
14356 /* Return true when T is an address and is known to be nonzero.
14357 Handle warnings about undefined signed overflow. */
14359 bool
14361 {
14368 "determining that expression is always "
14370 WARN_STRICT_OVERFLOW_MISC);
14372 }
14374 /* Given the components of a binary expression CODE, TYPE, OP0 and OP1,
14375 attempt to fold the expression to a constant without modifying TYPE,
14376 OP0 or OP1.
14378 If the expression could be simplified to a constant, then return
14379 the constant. If the expression would not be simplified to a
14380 constant, then return NULL_TREE. */
14382 tree
14384 {
14387 }
14389 /* Given the components of a unary expression CODE, TYPE and OP0,
14390 attempt to fold the expression to a constant without modifying
14391 TYPE or OP0.
14393 If the expression could be simplified to a constant, then return
14394 the constant. If the expression would not be simplified to a
14395 constant, then return NULL_TREE. */
14397 tree
14399 {
14402 }
14404 /* If EXP represents referencing an element in a constant string
14405 (either via pointer arithmetic or array indexing), return the
14406 tree representing the value accessed, otherwise return NULL. */
14408 tree
14410 {
14414 {
14416 tree index;
14417 tree string;
14421 else
14422 {
14426 /* Optimize the special-case of a zero lower bound.
14428 We convert the low_bound to sizetype to avoid some problems
14429 with constant folding. (E.g. suppose the lower bound is 1,
14430 and its mode is QI. Without the conversion,l (ARRAY
14431 +(INDEX-(unsigned char)1)) becomes ((ARRAY+(-(unsigned char)1))
14432 +INDEX), which becomes (ARRAY+255+INDEX). Opps!) */
14437 }
14450 }
14452 }
14454 /* Return the tree for neg (ARG0) when ARG0 is known to be either
14455 an integer constant, real, or fixed-point constant.
14457 TYPE is the type of the result. */
14459 static tree
14461 {
14465 {
14467 {
14469 HOST_WIDE_INT high;
14477 }
14484 {
14485 FIXED_VALUE_TYPE f;
14490 /* Propagate overflow flags. */
14492 {
14495 }
14499 }
14503 }
14506 }
14508 /* Return the tree for abs (ARG0) when ARG0 is known to be either
14509 an integer constant or real constant.
14511 TYPE is the type of the result. */
14513 tree
14515 {
14519 {
14521 /* If the value is unsigned, then the absolute value is
14522 the same as the ordinary value. */
14525 /* Similarly, if the value is non-negative. */
14528 /* If the value is negative, then the absolute value is
14529 its negation. */
14530 else
14531 {
14533 HOST_WIDE_INT high;
14539 }
14545 else
14551 }
14554 }
14556 /* Return the tree for not (ARG0) when ARG0 is known to be an integer
14557 constant. TYPE is the type of the result. */
14559 static tree
14561 {
14571 }
14573 /* Given CODE, a relational operator, the target type, TYPE and two
14574 constant operands OP0 and OP1, return the result of the
14575 relational operation. If the result is not a compile time
14576 constant, then return NULL_TREE. */
14578 static tree
14580 {
14583 /* From here on, the only cases we handle are when the result is
14584 known to be a constant. */
14587 {
14591 /* Handle the cases where either operand is a NaN. */
14593 {
14595 {
14623 }
14626 }
14629 }
14632 {
14636 }
14638 /* Handle equality/inequality of complex constants. */
14640 {
14651 else
14653 }
14655 /* From here on we only handle LT, LE, GT, GE, EQ and NE.
14657 To compute GT, swap the arguments and do LT.
14658 To compute GE, do LT and invert the result.
14659 To compute LE, swap the arguments, do LT and invert the result.
14660 To compute NE, do EQ and invert the result.
14662 Therefore, the code below must handle only EQ and LT. */
14665 {
14670 }
14672 /* Note that it is safe to invert for real values here because we
14673 have already handled the one case that it matters. */
14677 {
14680 }
14682 /* Compute a result for LT or EQ if args permit;
14683 Otherwise return T. */
14685 {
14690 else
14692 }
14693 else
14699 }
14701 /* If necessary, return a CLEANUP_POINT_EXPR for EXPR with the
14702 indicated TYPE. If no CLEANUP_POINT_EXPR is necessary, return EXPR
14703 itself. */
14705 tree
14707 {
14708 /* If the expression does not have side effects then we don't have to wrap
14709 it with a cleanup point expression. */
14713 /* If the expression is a return, check to see if the expression inside the
14714 return has no side effects or the right hand side of the modify expression
14715 inside the return. If either don't have side effects set we don't need to
14716 wrap the expression in a cleanup point expression. Note we don't check the
14717 left hand side of the modify because it should always be a return decl. */
14719 {
14726 }
14729 }
14731 /* Given a pointer value OP0 and a type TYPE, return a simplified version
14732 of an indirection through OP0, or NULL_TREE if no simplification is
14733 possible. */
14735 tree
14737 {
14739 tree subtype;
14747 {
14750 /* *&CONST_DECL -> to the value of the const decl. */
14753 /* *&p => p; make sure to handle *&"str"[cst] here. */
14755 {
14759 else
14761 }
14762 /* *(foo *)&fooarray => fooarray[0] */
14765 {
14771 }
14772 /* *(foo *)&complexfoo => __real__ complexfoo */
14776 /* *(foo *)&vectorfoo => BIT_FIELD_REF<vectorfoo,...> */
14779 {
14783 }
14784 }
14786 /* ((foo*)&complexfoo)[1] => __imag__ complexfoo */
14789 {
14792 tree op00type;
14799 {
14803 }
14804 }
14806 /* *(foo *)fooarrptr => (*fooarrptr)[0] */
14809 {
14810 tree type_domain;
14817 }
14820 }
14822 /* Builds an expression for an indirection through T, simplifying some
14823 cases. */
14825 tree
14827 {
14833 else
14835 }
14837 /* Given an INDIRECT_REF T, return either T or a simplified version. */
14839 tree
14841 {
14846 else
14848 }
14850 /* Strip non-trapping, non-side-effecting tree nodes from an expression
14851 whose result is ignored. The type of the returned tree need not be
14852 the same as the original expression. */
14854 tree
14856 {
14862 {
14873 else
14879 {
14895 }
14900 }
14901 }
14903 /* Return the value of VALUE, rounded up to a multiple of DIVISOR.
14904 This can only be applied to objects of a sizetype. */
14906 tree
14908 {
14915 /* See if VALUE is already a multiple of DIVISOR. If so, we don't
14916 have to do anything. Only do this when we are not given a const,
14917 because in that case, this check is more expensive than just
14918 doing it. */
14920 {
14925 }
14927 /* If divisor is a power of two, simplify this to bit manipulation. */
14929 {
14931 {
14944 {
14945 high++;
14948 }
14952 }
14953 else
14954 {
14955 tree t;
14961 }
14962 }
14963 else
14964 {
14969 }
14972 }
14974 /* Likewise, but round down. */
14976 tree
14978 {
14985 /* See if VALUE is already a multiple of DIVISOR. If so, we don't
14986 have to do anything. Only do this when we are not given a const,
14987 because in that case, this check is more expensive than just
14988 doing it. */
14990 {
14995 }
14997 /* If divisor is a power of two, simplify this to bit manipulation. */
14999 {
15000 tree t;
15004 }
15005 else
15006 {
15011 }
15014 }
15016 /* Returns the pointer to the base of the object addressed by EXP and
15017 extracts the information about the offset of the access, storing it
15018 to PBITPOS and POFFSET. */
15020 static tree
15023 {
15024 tree core;
15027 HOST_WIDE_INT bitsize;
15030 {
15035 }
15036 else
15037 {
15041 }
15044 }
15046 /* Returns true if addresses of E1 and E2 differ by a constant, false
15047 otherwise. If they do, E1 - E2 is stored in *DIFF. */
15049 bool
15051 {
15065 {
15075 }
15077 {
15078 /* If only one of the offsets is non-constant, the difference cannot
15079 be a constant. */
15081 }
15082 else
15087 }
15089 /* Simplify the floating point expression EXP when the sign of the
15090 result is not significant. Return NULL_TREE if no simplification
15091 is possible. */
15093 tree
15095 {
15099 {
15134 {
15137 {
15139 /* Strip copysign function call, return the 1st argument. */
15145 /* Strip sign ops from the argument of "odd" math functions. */
15147 {
15151 }
15153 }
15154 }
15159 }
15161 }