PR67945: Fix oscillation between pow representations

[gcc.git] / gcc / match.pd

/* Match-and-simplify patterns for shared GENERIC and GIMPLE folding.
   This file is consumed by genmatch which produces gimple-match.c
   and generic-match.c from it.

   Copyright (C) 2014-2015 Free Software Foundation, Inc.
   Contributed by Richard Biener <rguenther@suse.de>
   and Prathamesh Kulkarni  <bilbotheelffriend@gmail.com>

This file is part of GCC.

GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.

GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

You should have received a copy of the GNU General Public License
along with GCC; see the file COPYING3.  If not see
<http://www.gnu.org/licenses/>.  */


/* Generic tree predicates we inherit.  */
(define_predicates
   integer_onep integer_zerop integer_all_onesp integer_minus_onep
   integer_each_onep integer_truep integer_nonzerop
   real_zerop real_onep real_minus_onep
   zerop
   CONSTANT_CLASS_P
   tree_expr_nonnegative_p
   integer_pow2p
   HONOR_NANS)

/* Operator lists.  */
(define_operator_list tcc_comparison
  lt   le   eq ne ge   gt   unordered ordered   unlt unle ungt unge uneq ltgt)
(define_operator_list inverted_tcc_comparison
  ge   gt   ne eq lt   le   ordered   unordered ge   gt   le   lt   ltgt uneq)
(define_operator_list inverted_tcc_comparison_with_nans
  unge ungt ne eq unlt unle ordered   unordered ge   gt   le   lt   ltgt uneq)
(define_operator_list swapped_tcc_comparison
  gt   ge   eq ne le   lt   unordered ordered   ungt unge unlt unle uneq ltgt)
(define_operator_list simple_comparison         lt   le   eq ne ge   gt)
(define_operator_list swapped_simple_comparison gt   ge   eq ne le   lt)

(define_operator_list LOG BUILT_IN_LOGF BUILT_IN_LOG BUILT_IN_LOGL)
(define_operator_list EXP BUILT_IN_EXPF BUILT_IN_EXP BUILT_IN_EXPL)
(define_operator_list LOG2 BUILT_IN_LOG2F BUILT_IN_LOG2 BUILT_IN_LOG2L)
(define_operator_list EXP2 BUILT_IN_EXP2F BUILT_IN_EXP2 BUILT_IN_EXP2L)
(define_operator_list LOG10 BUILT_IN_LOG10F BUILT_IN_LOG10 BUILT_IN_LOG10L)
(define_operator_list EXP10 BUILT_IN_EXP10F BUILT_IN_EXP10 BUILT_IN_EXP10L)
(define_operator_list POW BUILT_IN_POWF BUILT_IN_POW BUILT_IN_POWL)
(define_operator_list POW10 BUILT_IN_POW10F BUILT_IN_POW10 BUILT_IN_POW10L)
(define_operator_list SQRT BUILT_IN_SQRTF BUILT_IN_SQRT BUILT_IN_SQRTL)
(define_operator_list CBRT BUILT_IN_CBRTF BUILT_IN_CBRT BUILT_IN_CBRTL)
(define_operator_list SIN BUILT_IN_SINF BUILT_IN_SIN BUILT_IN_SINL)
(define_operator_list COS BUILT_IN_COSF BUILT_IN_COS BUILT_IN_COSL)
(define_operator_list TAN BUILT_IN_TANF BUILT_IN_TAN BUILT_IN_TANL)
(define_operator_list COSH BUILT_IN_COSHF BUILT_IN_COSH BUILT_IN_COSHL)
(define_operator_list CEXPI BUILT_IN_CEXPIF BUILT_IN_CEXPI BUILT_IN_CEXPIL)

/* Simplifications of operations with one constant operand and
   simplifications to constants or single values.  */

(for op (plus pointer_plus minus bit_ior bit_xor)
  (simplify
    (op @0 integer_zerop)
    (non_lvalue @0)))

/* 0 +p index -> (type)index */
(simplify
 (pointer_plus integer_zerop @1)
 (non_lvalue (convert @1)))

/* See if ARG1 is zero and X + ARG1 reduces to X.
   Likewise if the operands are reversed.  */
(simplify
 (plus:c @0 real_zerop@1)
 (if (fold_real_zero_addition_p (type, @1, 0))
  (non_lvalue @0)))

/* See if ARG1 is zero and X - ARG1 reduces to X.  */
(simplify
 (minus @0 real_zerop@1)
 (if (fold_real_zero_addition_p (type, @1, 1))
  (non_lvalue @0)))

/* Simplify x - x.
   This is unsafe for certain floats even in non-IEEE formats.
   In IEEE, it is unsafe because it does wrong for NaNs.
   Also note that operand_equal_p is always false if an operand
   is volatile.  */
(simplify
 (minus @0 @0)
 (if (!FLOAT_TYPE_P (type) || !HONOR_NANS (type))
  { build_zero_cst (type); }))

(simplify
 (mult @0 integer_zerop@1)
 @1)

/* Maybe fold x * 0 to 0.  The expressions aren't the same
   when x is NaN, since x * 0 is also NaN.  Nor are they the
   same in modes with signed zeros, since multiplying a
   negative value by 0 gives -0, not +0.  */
(simplify
 (mult @0 real_zerop@1)
 (if (!HONOR_NANS (type) && !HONOR_SIGNED_ZEROS (type))
  @1))

/* In IEEE floating point, x*1 is not equivalent to x for snans.
   Likewise for complex arithmetic with signed zeros.  */
(simplify
 (mult @0 real_onep)
 (if (!HONOR_SNANS (type)
      && (!HONOR_SIGNED_ZEROS (type)
          || !COMPLEX_FLOAT_TYPE_P (type)))
  (non_lvalue @0)))

/* Transform x * -1.0 into -x.  */
(simplify
 (mult @0 real_minus_onep)
  (if (!HONOR_SNANS (type)
       && (!HONOR_SIGNED_ZEROS (type)
           || !COMPLEX_FLOAT_TYPE_P (type)))
   (negate @0)))

/* Make sure to preserve divisions by zero.  This is the reason why
   we don't simplify x / x to 1 or 0 / x to 0.  */
(for op (mult trunc_div ceil_div floor_div round_div exact_div)
  (simplify
    (op @0 integer_onep)
    (non_lvalue @0)))

/* X / -1 is -X.  */
(for div (trunc_div ceil_div floor_div round_div exact_div)
 (simplify
   (div @0 integer_minus_onep@1)
   (if (!TYPE_UNSIGNED (type))
    (negate @0))))

/* For unsigned integral types, FLOOR_DIV_EXPR is the same as
   TRUNC_DIV_EXPR.  Rewrite into the latter in this case.  */
(simplify
 (floor_div @0 @1)
 (if ((INTEGRAL_TYPE_P (type) || VECTOR_INTEGER_TYPE_P (type))
      && TYPE_UNSIGNED (type))
  (trunc_div @0 @1)))

/* Combine two successive divisions.  Note that combining ceil_div
   and floor_div is trickier and combining round_div even more so.  */
(for div (trunc_div exact_div)
 (simplify
  (div (div @0 INTEGER_CST@1) INTEGER_CST@2)
  (with {
    bool overflow_p;
    wide_int mul = wi::mul (@1, @2, TYPE_SIGN (type), &overflow_p);
   }
   (if (!overflow_p)
    (div @0 { wide_int_to_tree (type, mul); })
    (if (TYPE_UNSIGNED (type)
         || mul != wi::min_value (TYPE_PRECISION (type), SIGNED))
     { build_zero_cst (type); })))))

/* Optimize A / A to 1.0 if we don't care about
   NaNs or Infinities.  */
(simplify
 (rdiv @0 @0)
 (if (FLOAT_TYPE_P (type)
      && ! HONOR_NANS (type)
      && ! HONOR_INFINITIES (type))
  { build_one_cst (type); }))

/* Optimize -A / A to -1.0 if we don't care about
   NaNs or Infinities.  */
(simplify
 (rdiv:c @0 (negate @0))
 (if (FLOAT_TYPE_P (type)
      && ! HONOR_NANS (type)
      && ! HONOR_INFINITIES (type))
  { build_minus_one_cst (type); }))

/* In IEEE floating point, x/1 is not equivalent to x for snans.  */
(simplify
 (rdiv @0 real_onep)
 (if (!HONOR_SNANS (type))
  (non_lvalue @0)))

/* In IEEE floating point, x/-1 is not equivalent to -x for snans.  */
(simplify
 (rdiv @0 real_minus_onep)
 (if (!HONOR_SNANS (type))
  (negate @0)))

/* If ARG1 is a constant, we can convert this to a multiply by the
   reciprocal.  This does not have the same rounding properties,
   so only do this if -freciprocal-math.  We can actually
   always safely do it if ARG1 is a power of two, but it's hard to
   tell if it is or not in a portable manner.  */
(for cst (REAL_CST COMPLEX_CST VECTOR_CST)
 (simplify
  (rdiv @0 cst@1)
  (if (optimize)
   (if (flag_reciprocal_math
        && !real_zerop (@1))
    (with
     { tree tem = const_binop (RDIV_EXPR, type, build_one_cst (type), @1); }
     (if (tem)
      (mult @0 { tem; } )))
    (if (cst != COMPLEX_CST)
     (with { tree inverse = exact_inverse (type, @1); }
      (if (inverse)
       (mult @0 { inverse; } ))))))))

/* Same applies to modulo operations, but fold is inconsistent here
   and simplifies 0 % x to 0, only preserving literal 0 % 0.  */
(for mod (ceil_mod floor_mod round_mod trunc_mod)
 /* 0 % X is always zero.  */
 (simplify
  (mod integer_zerop@0 @1)
  /* But not for 0 % 0 so that we can get the proper warnings and errors.  */
  (if (!integer_zerop (@1))
   @0))
 /* X % 1 is always zero.  */
 (simplify
  (mod @0 integer_onep)
  { build_zero_cst (type); })
 /* X % -1 is zero.  */
 (simplify
  (mod @0 integer_minus_onep@1)
  (if (!TYPE_UNSIGNED (type))
   { build_zero_cst (type); }))
 /* (X % Y) % Y is just X % Y.  */
 (simplify
  (mod (mod@2 @0 @1) @1)
  @2)
 /* From extract_muldiv_1: (X * C1) % C2 is zero if C1 is a multiple of C2.  */
 (simplify
  (mod (mult @0 INTEGER_CST@1) INTEGER_CST@2)
  (if (ANY_INTEGRAL_TYPE_P (type)
       && TYPE_OVERFLOW_UNDEFINED (type)
       && wi::multiple_of_p (@1, @2, TYPE_SIGN (type)))
   { build_zero_cst (type); })))

/* X % -C is the same as X % C.  */
(simplify
 (trunc_mod @0 INTEGER_CST@1)
  (if (TYPE_SIGN (type) == SIGNED
       && !TREE_OVERFLOW (@1)
       && wi::neg_p (@1)
       && !TYPE_OVERFLOW_TRAPS (type)
       /* Avoid this transformation if C is INT_MIN, i.e. C == -C.  */
       && !sign_bit_p (@1, @1))
   (trunc_mod @0 (negate @1))))

/* X % -Y is the same as X % Y.  */
(simplify
 (trunc_mod @0 (convert? (negate @1)))
 (if (!TYPE_UNSIGNED (type)
      && !TYPE_OVERFLOW_TRAPS (type)
      && tree_nop_conversion_p (type, TREE_TYPE (@1)))
  (trunc_mod @0 (convert @1))))

/* X - (X / Y) * Y is the same as X % Y.  */
(simplify
 (minus (convert1? @0) (convert2? (mult (trunc_div @0 @1) @1)))
 (if ((INTEGRAL_TYPE_P (type) || VECTOR_INTEGER_TYPE_P (type))
      && TYPE_UNSIGNED (TREE_TYPE (@0)) == TYPE_UNSIGNED (type))
  (trunc_mod (convert @0) (convert @1))))

/* Optimize TRUNC_MOD_EXPR by a power of two into a BIT_AND_EXPR,
   i.e. "X % C" into "X & (C - 1)", if X and C are positive.
   Also optimize A % (C << N)  where C is a power of 2,
   to A & ((C << N) - 1).  */
(match (power_of_two_cand @1)
 INTEGER_CST@1)
(match (power_of_two_cand @1)
 (lshift INTEGER_CST@1 @2))
(for mod (trunc_mod floor_mod)
 (simplify
  (mod @0 (convert?@3 (power_of_two_cand@1 @2)))
  (if ((TYPE_UNSIGNED (type)
        || tree_expr_nonnegative_p (@0))
        && tree_nop_conversion_p (type, TREE_TYPE (@3))
        && integer_pow2p (@2) && tree_int_cst_sgn (@2) > 0)
   (bit_and @0 (convert (minus @1 { build_int_cst (TREE_TYPE (@1), 1); }))))))

/* Simplify (unsigned t * 2)/2 -> unsigned t & 0x7FFFFFFF.  */
(simplify
 (trunc_div (mult @0 integer_pow2p@1) @1)
 (if (TYPE_UNSIGNED (TREE_TYPE (@0)))
  (bit_and @0 { wide_int_to_tree
                (type, wi::mask (TYPE_PRECISION (type) - wi::exact_log2 (@1),
                                 false, TYPE_PRECISION (type))); })))

/* Simplify (unsigned t / 2) * 2 -> unsigned t & ~1.  */
(simplify
 (mult (trunc_div @0 integer_pow2p@1) @1)
 (if (TYPE_UNSIGNED (TREE_TYPE (@0)))
  (bit_and @0 (negate @1))))

/* Simplify (t * 2) / 2) -> t.  */
(for div (trunc_div ceil_div floor_div round_div exact_div)
 (simplify
  (div (mult @0 @1) @1)
  (if (ANY_INTEGRAL_TYPE_P (type)
       && TYPE_OVERFLOW_UNDEFINED (type))
   @0)))

(for op (negate abs)
 /* Simplify cos(-x) and cos(|x|) -> cos(x).  Similarly for cosh.  */
 (for coss (COS COSH)
  (simplify
   (coss (op @0))
    (coss @0)))
 /* Simplify pow(-x, y) and pow(|x|,y) -> pow(x,y) if y is an even integer.  */
 (for pows (POW)
  (simplify
   (pows (op @0) REAL_CST@1)
   (with { HOST_WIDE_INT n; }
    (if (real_isinteger (&TREE_REAL_CST (@1), &n) && (n & 1) == 0)
     (pows @0 @1))))))

/* X % Y is smaller than Y.  */
(for cmp (lt ge)
 (simplify
  (cmp (trunc_mod @0 @1) @1)
  (if (TYPE_UNSIGNED (TREE_TYPE (@0)))
   { constant_boolean_node (cmp == LT_EXPR, type); })))
(for cmp (gt le)
 (simplify
  (cmp @1 (trunc_mod @0 @1))
  (if (TYPE_UNSIGNED (TREE_TYPE (@0)))
   { constant_boolean_node (cmp == GT_EXPR, type); })))

/* x | ~0 -> ~0  */
(simplify
  (bit_ior @0 integer_all_onesp@1)
  @1)

/* x & 0 -> 0  */
(simplify
  (bit_and @0 integer_zerop@1)
  @1)

/* ~x | x -> -1 */
/* ~x ^ x -> -1 */
/* ~x + x -> -1 */
(for op (bit_ior bit_xor plus)
 (simplify
  (op:c (convert? @0) (convert? (bit_not @0)))
  (convert { build_all_ones_cst (TREE_TYPE (@0)); })))

/* x ^ x -> 0 */
(simplify
  (bit_xor @0 @0)
  { build_zero_cst (type); })

/* Canonicalize X ^ ~0 to ~X.  */
(simplify
  (bit_xor @0 integer_all_onesp@1)
  (bit_not @0))

/* x & ~0 -> x  */
(simplify
 (bit_and @0 integer_all_onesp)
  (non_lvalue @0))

/* x & x -> x,  x | x -> x  */
(for bitop (bit_and bit_ior)
 (simplify
  (bitop @0 @0)
  (non_lvalue @0)))

/* x + (x & 1) -> (x + 1) & ~1 */
(simplify
 (plus:c @0 (bit_and:s @0 integer_onep@1))
 (bit_and (plus @0 @1) (bit_not @1)))

/* x & ~(x & y) -> x & ~y */
/* x | ~(x | y) -> x | ~y  */
(for bitop (bit_and bit_ior)
 (simplify
  (bitop:c @0 (bit_not (bitop:cs @0 @1)))
  (bitop @0 (bit_not @1))))

/* (x | y) & ~x -> y & ~x */
/* (x & y) | ~x -> y | ~x */
(for bitop (bit_and bit_ior)
     rbitop (bit_ior bit_and)
 (simplify
  (bitop:c (rbitop:c @0 @1) (bit_not@2 @0))
  (bitop @1 @2)))

/* (x & y) ^ (x | y) -> x ^ y */
(simplify
 (bit_xor:c (bit_and @0 @1) (bit_ior @0 @1))
 (bit_xor @0 @1))

/* (x ^ y) ^ (x | y) -> x & y */
(simplify
 (bit_xor:c (bit_xor @0 @1) (bit_ior @0 @1))
 (bit_and @0 @1))

/* (x & y) + (x ^ y) -> x | y */
/* (x & y) | (x ^ y) -> x | y */
/* (x & y) ^ (x ^ y) -> x | y */
(for op (plus bit_ior bit_xor)
 (simplify
  (op:c (bit_and @0 @1) (bit_xor @0 @1))
  (bit_ior @0 @1)))

/* (x & y) + (x | y) -> x + y */
(simplify
 (plus:c (bit_and @0 @1) (bit_ior @0 @1))
 (plus @0 @1))

/* (x + y) - (x | y) -> x & y */
(simplify
 (minus (plus @0 @1) (bit_ior @0 @1))
 (if (!TYPE_OVERFLOW_SANITIZED (type) && !TYPE_OVERFLOW_TRAPS (type)
      && !TYPE_SATURATING (type))
  (bit_and @0 @1)))

/* (x + y) - (x & y) -> x | y */
(simplify
 (minus (plus @0 @1) (bit_and @0 @1))
 (if (!TYPE_OVERFLOW_SANITIZED (type) && !TYPE_OVERFLOW_TRAPS (type)
      && !TYPE_SATURATING (type))
  (bit_ior @0 @1)))

/* (x | y) - (x ^ y) -> x & y */
(simplify
 (minus (bit_ior @0 @1) (bit_xor @0 @1))
 (bit_and @0 @1))

/* (x | y) - (x & y) -> x ^ y */
(simplify
 (minus (bit_ior @0 @1) (bit_and @0 @1))
 (bit_xor @0 @1))

/* (x | y) & ~(x & y) -> x ^ y */
(simplify
 (bit_and:c (bit_ior @0 @1) (bit_not (bit_and @0 @1)))
 (bit_xor @0 @1))

/* (x | y) & (~x ^ y) -> x & y */
(simplify
 (bit_and:c (bit_ior:c @0 @1) (bit_xor:c @1 (bit_not @0)))
 (bit_and @0 @1))

/* ~x & ~y -> ~(x | y)
   ~x | ~y -> ~(x & y) */
(for op (bit_and bit_ior)
     rop (bit_ior bit_and)
 (simplify
  (op (convert1? (bit_not @0)) (convert2? (bit_not @1)))
  (if (tree_nop_conversion_p (type, TREE_TYPE (@0))
       && tree_nop_conversion_p (type, TREE_TYPE (@1)))
   (bit_not (rop (convert @0) (convert @1))))))

/* If we are XORing or adding two BIT_AND_EXPR's, both of which are and'ing
   with a constant, and the two constants have no bits in common,
   we should treat this as a BIT_IOR_EXPR since this may produce more
   simplifications.  */
(for op (bit_xor plus)
 (simplify
  (op (convert1? (bit_and@4 @0 INTEGER_CST@1))
      (convert2? (bit_and@5 @2 INTEGER_CST@3)))
  (if (tree_nop_conversion_p (type, TREE_TYPE (@0))
       && tree_nop_conversion_p (type, TREE_TYPE (@2))
       && wi::bit_and (@1, @3) == 0)
   (bit_ior (convert @4) (convert @5)))))

/* (X | Y) ^ X -> Y & ~ X*/
(simplify
 (bit_xor:c (convert? (bit_ior:c @0 @1)) (convert? @0))
 (if (tree_nop_conversion_p (type, TREE_TYPE (@0)))
  (convert (bit_and @1 (bit_not @0)))))

/* Convert ~X ^ ~Y to X ^ Y.  */
(simplify
 (bit_xor (convert1? (bit_not @0)) (convert2? (bit_not @1)))
 (if (tree_nop_conversion_p (type, TREE_TYPE (@0))
      && tree_nop_conversion_p (type, TREE_TYPE (@1)))
  (bit_xor (convert @0) (convert @1))))

/* Convert ~X ^ C to X ^ ~C.  */
(simplify
 (bit_xor (convert? (bit_not @0)) INTEGER_CST@1)
 (if (tree_nop_conversion_p (type, TREE_TYPE (@0)))
  (bit_xor (convert @0) (bit_not @1))))

/* Fold (X & Y) ^ Y as ~X & Y.  */
(simplify
 (bit_xor:c (bit_and:c @0 @1) @1)
 (bit_and (bit_not @0) @1))

/* Given a bit-wise operation CODE applied to ARG0 and ARG1, see if both
   operands are another bit-wise operation with a common input.  If so,
   distribute the bit operations to save an operation and possibly two if
   constants are involved.  For example, convert
     (A | B) & (A | C) into A | (B & C)
   Further simplification will occur if B and C are constants.  */
(for op (bit_and bit_ior)
     rop (bit_ior bit_and)
 (simplify
  (op (convert? (rop:c @0 @1)) (convert? (rop @0 @2)))
  (if (tree_nop_conversion_p (type, TREE_TYPE (@0)))
   (rop (convert @0) (op (convert @1) (convert @2))))))


(simplify
 (abs (abs@1 @0))
 @1)
(simplify
 (abs (negate @0))
 (abs @0))
(simplify
 (abs tree_expr_nonnegative_p@0)
 @0)

/* A few cases of fold-const.c negate_expr_p predicate.  */
(match negate_expr_p
 INTEGER_CST
 (if ((INTEGRAL_TYPE_P (type)
       && TYPE_OVERFLOW_WRAPS (type))
      || (!TYPE_OVERFLOW_SANITIZED (type)
          && may_negate_without_overflow_p (t)))))
(match negate_expr_p
 FIXED_CST)
(match negate_expr_p
 (negate @0)
 (if (!TYPE_OVERFLOW_SANITIZED (type))))
(match negate_expr_p
 REAL_CST
 (if (REAL_VALUE_NEGATIVE (TREE_REAL_CST (t)))))
/* VECTOR_CST handling of non-wrapping types would recurse in unsupported
   ways.  */
(match negate_expr_p
 VECTOR_CST
 (if (FLOAT_TYPE_P (TREE_TYPE (type)) || TYPE_OVERFLOW_WRAPS (type))))
 
/* -(A + B) -> (-B) - A.  */
(simplify
 (negate (plus:c @0 negate_expr_p@1))
 (if (!HONOR_SIGN_DEPENDENT_ROUNDING (element_mode (type))
      && !HONOR_SIGNED_ZEROS (element_mode (type)))
  (minus (negate @1) @0)))

/* A - B -> A + (-B) if B is easily negatable.  */
(simplify
 (minus @0 negate_expr_p@1)
 (if (!FIXED_POINT_TYPE_P (type))
 (plus @0 (negate @1))))

/* Try to fold (type) X op CST -> (type) (X op ((type-x) CST))
   when profitable.
   For bitwise binary operations apply operand conversions to the
   binary operation result instead of to the operands.  This allows
   to combine successive conversions and bitwise binary operations.
   We combine the above two cases by using a conditional convert.  */
(for bitop (bit_and bit_ior bit_xor)
 (simplify
  (bitop (convert @0) (convert? @1))
  (if (((TREE_CODE (@1) == INTEGER_CST
         && INTEGRAL_TYPE_P (TREE_TYPE (@0))
         && int_fits_type_p (@1, TREE_TYPE (@0)))
        || types_match (@0, @1))
       /* ???  This transform conflicts with fold-const.c doing
          Convert (T)(x & c) into (T)x & (T)c, if c is an integer
          constants (if x has signed type, the sign bit cannot be set
          in c).  This folds extension into the BIT_AND_EXPR.
          Restrict it to GIMPLE to avoid endless recursions.  */
       && (bitop != BIT_AND_EXPR || GIMPLE)
       && (/* That's a good idea if the conversion widens the operand, thus
              after hoisting the conversion the operation will be narrower.  */
           TYPE_PRECISION (TREE_TYPE (@0)) < TYPE_PRECISION (type)
           /* It's also a good idea if the conversion is to a non-integer
              mode.  */
           || GET_MODE_CLASS (TYPE_MODE (type)) != MODE_INT
           /* Or if the precision of TO is not the same as the precision
              of its mode.  */
           || TYPE_PRECISION (type) != GET_MODE_PRECISION (TYPE_MODE (type))))
   (convert (bitop @0 (convert @1))))))

(for bitop (bit_and bit_ior)
     rbitop (bit_ior bit_and)
  /* (x | y) & x -> x */
  /* (x & y) | x -> x */
 (simplify
  (bitop:c (rbitop:c @0 @1) @0)
  @0)
 /* (~x | y) & x -> x & y */
 /* (~x & y) | x -> x | y */
 (simplify
  (bitop:c (rbitop:c (bit_not @0) @1) @0)
  (bitop @0 @1)))

/* Simplify (A & B) OP0 (C & B) to (A OP0 C) & B. */
(for bitop (bit_and bit_ior bit_xor)
 (simplify
  (bitop (bit_and:c @0 @1) (bit_and @2 @1))
  (bit_and (bitop @0 @2) @1)))

/* (x | CST1) & CST2 -> (x & CST2) | (CST1 & CST2) */
(simplify
  (bit_and (bit_ior @0 CONSTANT_CLASS_P@1) CONSTANT_CLASS_P@2)
  (bit_ior (bit_and @0 @2) (bit_and @1 @2)))

/* Combine successive equal operations with constants.  */
(for bitop (bit_and bit_ior bit_xor)
 (simplify
  (bitop (bitop @0 CONSTANT_CLASS_P@1) CONSTANT_CLASS_P@2)
  (bitop @0 (bitop @1 @2))))

/* Try simple folding for X op !X, and X op X with the help
   of the truth_valued_p and logical_inverted_value predicates.  */
(match truth_valued_p
 @0
 (if (INTEGRAL_TYPE_P (type) && TYPE_PRECISION (type) == 1)))
(for op (tcc_comparison truth_and truth_andif truth_or truth_orif truth_xor)
 (match truth_valued_p
  (op @0 @1)))
(match truth_valued_p
  (truth_not @0))

(match (logical_inverted_value @0)
 (bit_not truth_valued_p@0))
(match (logical_inverted_value @0)
 (eq @0 integer_zerop))
(match (logical_inverted_value @0)
 (ne truth_valued_p@0 integer_truep))
(match (logical_inverted_value @0)
 (bit_xor truth_valued_p@0 integer_truep))

/* X & !X -> 0.  */
(simplify
 (bit_and:c @0 (logical_inverted_value @0))
 { build_zero_cst (type); })
/* X | !X and X ^ !X -> 1, , if X is truth-valued.  */
(for op (bit_ior bit_xor)
 (simplify
  (op:c truth_valued_p@0 (logical_inverted_value @0))
  { constant_boolean_node (true, type); }))
/* X ==/!= !X is false/true.  */
(for op (eq ne)
 (simplify
  (op:c truth_valued_p@0 (logical_inverted_value @0))
  { constant_boolean_node (op == NE_EXPR ? true : false, type); }))

/* If arg1 and arg2 are booleans (or any single bit type)
   then try to simplify:

   (~X & Y) -> X < Y
   (X & ~Y) -> Y < X
   (~X | Y) -> X <= Y
   (X | ~Y) -> Y <= X

   But only do this if our result feeds into a comparison as
   this transformation is not always a win, particularly on
   targets with and-not instructions.
   -> simplify_bitwise_binary_boolean */
(simplify
  (ne (bit_and:c (bit_not @0) @1) integer_zerop)
  (if (INTEGRAL_TYPE_P (TREE_TYPE (@1))
       && TYPE_PRECISION (TREE_TYPE (@1)) == 1)
   (lt @0 @1)))
(simplify
  (ne (bit_ior:c (bit_not @0) @1) integer_zerop)
  (if (INTEGRAL_TYPE_P (TREE_TYPE (@1))
       && TYPE_PRECISION (TREE_TYPE (@1)) == 1)
   (le @0 @1)))

/* ~~x -> x */
(simplify
  (bit_not (bit_not @0))
  @0)

/* Convert ~ (-A) to A - 1.  */
(simplify
 (bit_not (convert? (negate @0)))
 (if (tree_nop_conversion_p (type, TREE_TYPE (@0)))
  (convert (minus @0 { build_each_one_cst (TREE_TYPE (@0)); }))))

/* Convert ~ (A - 1) or ~ (A + -1) to -A.  */
(simplify
 (bit_not (convert? (minus @0 integer_each_onep)))
 (if (tree_nop_conversion_p (type, TREE_TYPE (@0)))
  (convert (negate @0))))
(simplify
 (bit_not (convert? (plus @0 integer_all_onesp)))
 (if (tree_nop_conversion_p (type, TREE_TYPE (@0)))
  (convert (negate @0))))

/* Part of convert ~(X ^ Y) to ~X ^ Y or X ^ ~Y if ~X or ~Y simplify.  */
(simplify
 (bit_not (convert? (bit_xor @0 INTEGER_CST@1)))
 (if (tree_nop_conversion_p (type, TREE_TYPE (@0)))
  (convert (bit_xor @0 (bit_not @1)))))
(simplify
 (bit_not (convert? (bit_xor:c (bit_not @0) @1)))
 (if (tree_nop_conversion_p (type, TREE_TYPE (@0)))
  (convert (bit_xor @0 @1))))

/* (x & ~m) | (y & m) -> ((x ^ y) & m) ^ x */
(simplify
 (bit_ior:c (bit_and:cs @0 (bit_not @2)) (bit_and:cs @1 @2))
 (bit_xor (bit_and (bit_xor @0 @1) @2) @0))

/* Fold A - (A & B) into ~B & A.  */
(simplify
 (minus (convert? @0) (convert?:s (bit_and:cs @0 @1)))
 (if (tree_nop_conversion_p (type, TREE_TYPE (@0))
      && tree_nop_conversion_p (type, TREE_TYPE (@1)))
  (convert (bit_and (bit_not @1) @0))))



/* ((X inner_op C0) outer_op C1)
   With X being a tree where value_range has reasoned certain bits to always be
   zero throughout its computed value range,
   inner_op = {|,^}, outer_op = {|,^} and inner_op != outer_op
   where zero_mask has 1's for all bits that are sure to be 0 in
   and 0's otherwise.
   if (inner_op == '^') C0 &= ~C1;
   if ((C0 & ~zero_mask) == 0) then emit (X outer_op (C0 outer_op C1)
   if ((C1 & ~zero_mask) == 0) then emit (X inner_op (C0 outer_op C1)
*/
(for inner_op (bit_ior bit_xor)
     outer_op (bit_xor bit_ior)
(simplify
 (outer_op
  (inner_op:s @2 INTEGER_CST@0) INTEGER_CST@1)
 (with
  {
    bool fail = false;
    wide_int zero_mask_not;
    wide_int C0;
    wide_int cst_emit;

    if (TREE_CODE (@2) == SSA_NAME)
      zero_mask_not = get_nonzero_bits (@2);
    else
      fail = true;

    if (inner_op == BIT_XOR_EXPR)
      {
        C0 = wi::bit_and_not (@0, @1);
        cst_emit = wi::bit_or (C0, @1);
      }
    else
      {
        C0 = @0;
        cst_emit = wi::bit_xor (@0, @1);
      }
  }
  (if (!fail && wi::bit_and (C0, zero_mask_not) == 0)
   (outer_op @2 { wide_int_to_tree (type, cst_emit); })
   (if (!fail && wi::bit_and (@1, zero_mask_not) == 0)
    (inner_op @2 { wide_int_to_tree (type, cst_emit); }))))))

/* Associate (p +p off1) +p off2 as (p +p (off1 + off2)).  */
(simplify
  (pointer_plus (pointer_plus:s @0 @1) @3)
  (pointer_plus @0 (plus @1 @3)))

/* Pattern match
     tem1 = (long) ptr1;
     tem2 = (long) ptr2;
     tem3 = tem2 - tem1;
     tem4 = (unsigned long) tem3;
     tem5 = ptr1 + tem4;
   and produce
     tem5 = ptr2;  */
(simplify
  (pointer_plus @0 (convert?@2 (minus@3 (convert @1) (convert @0))))
  /* Conditionally look through a sign-changing conversion.  */
  (if (TYPE_PRECISION (TREE_TYPE (@2)) == TYPE_PRECISION (TREE_TYPE (@3))
       && ((GIMPLE && useless_type_conversion_p (type, TREE_TYPE (@1)))
            || (GENERIC && type == TREE_TYPE (@1))))
   @1))

/* Pattern match
     tem = (sizetype) ptr;
     tem = tem & algn;
     tem = -tem;
     ... = ptr p+ tem;
   and produce the simpler and easier to analyze with respect to alignment
     ... = ptr & ~algn;  */
(simplify
  (pointer_plus @0 (negate (bit_and (convert @0) INTEGER_CST@1)))
  (with { tree algn = wide_int_to_tree (TREE_TYPE (@0), wi::bit_not (@1)); }
   (bit_and @0 { algn; })))

/* Try folding difference of addresses.  */
(simplify
 (minus (convert ADDR_EXPR@0) (convert @1))
 (if (tree_nop_conversion_p (type, TREE_TYPE (@0)))
  (with { HOST_WIDE_INT diff; }
   (if (ptr_difference_const (@0, @1, &diff))
    { build_int_cst_type (type, diff); }))))
(simplify
 (minus (convert @0) (convert ADDR_EXPR@1))
 (if (tree_nop_conversion_p (type, TREE_TYPE (@0)))
  (with { HOST_WIDE_INT diff; }
   (if (ptr_difference_const (@0, @1, &diff))
    { build_int_cst_type (type, diff); }))))

/* If arg0 is derived from the address of an object or function, we may
   be able to fold this expression using the object or function's
   alignment.  */
(simplify
 (bit_and (convert? @0) INTEGER_CST@1)
 (if (POINTER_TYPE_P (TREE_TYPE (@0))
      && tree_nop_conversion_p (type, TREE_TYPE (@0)))
  (with
   {
     unsigned int align;
     unsigned HOST_WIDE_INT bitpos;
     get_pointer_alignment_1 (@0, &align, &bitpos);
   }
   (if (wi::ltu_p (@1, align / BITS_PER_UNIT))
    { wide_int_to_tree (type, wi::bit_and (@1, bitpos / BITS_PER_UNIT)); }))))


/* We can't reassociate at all for saturating types.  */
(if (!TYPE_SATURATING (type))

 /* Contract negates.  */
 /* A + (-B) -> A - B */
 (simplify
  (plus:c (convert1? @0) (convert2? (negate @1)))
  /* Apply STRIP_NOPS on @0 and the negate.  */
  (if (tree_nop_conversion_p (type, TREE_TYPE (@0))
       && tree_nop_conversion_p (type, TREE_TYPE (@1))
       && !TYPE_OVERFLOW_SANITIZED (type))
   (minus (convert @0) (convert @1))))
 /* A - (-B) -> A + B */
 (simplify
  (minus (convert1? @0) (convert2? (negate @1)))
  (if (tree_nop_conversion_p (type, TREE_TYPE (@0))
       && tree_nop_conversion_p (type, TREE_TYPE (@1))
       && !TYPE_OVERFLOW_SANITIZED (type))
   (plus (convert @0) (convert @1))))
 /* -(-A) -> A */
 (simplify
  (negate (convert? (negate @1)))
  (if (tree_nop_conversion_p (type, TREE_TYPE (@1))
       && !TYPE_OVERFLOW_SANITIZED (type))
   (convert @1)))

 /* We can't reassociate floating-point unless -fassociative-math
    or fixed-point plus or minus because of saturation to +-Inf.  */
 (if ((!FLOAT_TYPE_P (type) || flag_associative_math)
      && !FIXED_POINT_TYPE_P (type))

  /* Match patterns that allow contracting a plus-minus pair
     irrespective of overflow issues.  */
  /* (A +- B) - A       ->  +- B */
  /* (A +- B) -+ B      ->  A */
  /* A - (A +- B)       -> -+ B */
  /* A +- (B -+ A)      ->  +- B */
  (simplify
    (minus (plus:c @0 @1) @0)
    @1)
  (simplify
    (minus (minus @0 @1) @0)
    (negate @1))
  (simplify
    (plus:c (minus @0 @1) @1)
    @0)
  (simplify
   (minus @0 (plus:c @0 @1))
   (negate @1))
  (simplify
   (minus @0 (minus @0 @1))
   @1)

  /* (A +- CST) +- CST -> A + CST  */
  (for outer_op (plus minus)
   (for inner_op (plus minus)
    (simplify
     (outer_op (inner_op @0 CONSTANT_CLASS_P@1) CONSTANT_CLASS_P@2)
     /* If the constant operation overflows we cannot do the transform
        as we would introduce undefined overflow, for example
        with (a - 1) + INT_MIN.  */
     (with { tree cst = fold_binary (outer_op == inner_op
                                     ? PLUS_EXPR : MINUS_EXPR, type, @1, @2); }
      (if (cst && !TREE_OVERFLOW (cst))
       (inner_op @0 { cst; } ))))))

  /* (CST - A) +- CST -> CST - A  */
  (for outer_op (plus minus)
   (simplify
    (outer_op (minus CONSTANT_CLASS_P@1 @0) CONSTANT_CLASS_P@2)
    (with { tree cst = fold_binary (outer_op, type, @1, @2); }
     (if (cst && !TREE_OVERFLOW (cst))
      (minus { cst; } @0)))))

  /* ~A + A -> -1 */
  (simplify
   (plus:c (bit_not @0) @0)
   (if (!TYPE_OVERFLOW_TRAPS (type))
    { build_all_ones_cst (type); }))

  /* ~A + 1 -> -A */
  (simplify
   (plus (convert? (bit_not @0)) integer_each_onep)
   (if (tree_nop_conversion_p (type, TREE_TYPE (@0)))
    (negate (convert @0))))

  /* -A - 1 -> ~A */
  (simplify
   (minus (convert? (negate @0)) integer_each_onep)
   (if (!TYPE_OVERFLOW_TRAPS (type)
        && tree_nop_conversion_p (type, TREE_TYPE (@0)))
    (bit_not (convert @0))))

  /* -1 - A -> ~A */
  (simplify
   (minus integer_all_onesp @0)
   (bit_not @0))

  /* (T)(P + A) - (T)P -> (T) A */
  (for add (plus pointer_plus)
   (simplify
    (minus (convert (add @0 @1))
     (convert @0))
    (if (element_precision (type) <= element_precision (TREE_TYPE (@1))
         /* For integer types, if A has a smaller type
            than T the result depends on the possible
            overflow in P + A.
            E.g. T=size_t, A=(unsigned)429497295, P>0.
            However, if an overflow in P + A would cause
            undefined behavior, we can assume that there
            is no overflow.  */
         || (INTEGRAL_TYPE_P (TREE_TYPE (@0))
             && TYPE_OVERFLOW_UNDEFINED (TREE_TYPE (@0)))
         /* For pointer types, if the conversion of A to the
            final type requires a sign- or zero-extension,
            then we have to punt - it is not defined which
            one is correct.  */
         || (POINTER_TYPE_P (TREE_TYPE (@0))
             && TREE_CODE (@1) == INTEGER_CST
             && tree_int_cst_sign_bit (@1) == 0))
     (convert @1))))))


/* Simplifications of MIN_EXPR and MAX_EXPR.  */

(for minmax (min max)
 (simplify
  (minmax @0 @0)
  @0))
(simplify
 (min @0 @1)
 (if (INTEGRAL_TYPE_P (type)
      && TYPE_MIN_VALUE (type)
      && operand_equal_p (@1, TYPE_MIN_VALUE (type), OEP_ONLY_CONST))
  @1))
(simplify
 (max @0 @1)
 (if (INTEGRAL_TYPE_P (type)
      && TYPE_MAX_VALUE (type)
      && operand_equal_p (@1, TYPE_MAX_VALUE (type), OEP_ONLY_CONST))
  @1))


/* Simplifications of shift and rotates.  */

(for rotate (lrotate rrotate)
 (simplify
  (rotate integer_all_onesp@0 @1)
  @0))

/* Optimize -1 >> x for arithmetic right shifts.  */
(simplify
 (rshift integer_all_onesp@0 @1)
 (if (!TYPE_UNSIGNED (type)
      && tree_expr_nonnegative_p (@1))
  @0))

/* Optimize (x >> c) << c into x & (-1<<c).  */
(simplify
 (lshift (rshift @0 INTEGER_CST@1) @1)
 (if (wi::ltu_p (@1, element_precision (type)))
  (bit_and @0 (lshift { build_minus_one_cst (type); } @1))))

/* Optimize (x << c) >> c into x & ((unsigned)-1 >> c) for unsigned
   types.  */
(simplify
 (rshift (lshift @0 INTEGER_CST@1) @1)
 (if (TYPE_UNSIGNED (type)
      && (wi::ltu_p (@1, element_precision (type))))
  (bit_and @0 (rshift { build_minus_one_cst (type); } @1))))

(for shiftrotate (lrotate rrotate lshift rshift)
 (simplify
  (shiftrotate @0 integer_zerop)
  (non_lvalue @0))
 (simplify
  (shiftrotate integer_zerop@0 @1)
  @0)
 /* Prefer vector1 << scalar to vector1 << vector2
    if vector2 is uniform.  */
 (for vec (VECTOR_CST CONSTRUCTOR)
  (simplify
   (shiftrotate @0 vec@1)
   (with { tree tem = uniform_vector_p (@1); }
    (if (tem)
     (shiftrotate @0 { tem; }))))))

/* Rewrite an LROTATE_EXPR by a constant into an
   RROTATE_EXPR by a new constant.  */
(simplify
 (lrotate @0 INTEGER_CST@1)
 (rrotate @0 { fold_binary (MINUS_EXPR, TREE_TYPE (@1),
                            build_int_cst (TREE_TYPE (@1),
                                           element_precision (type)), @1); }))

/* Turn (a OP c1) OP c2 into a OP (c1+c2).  */
(for op (lrotate rrotate rshift lshift)
 (simplify
  (op (op @0 INTEGER_CST@1) INTEGER_CST@2)
  (with { unsigned int prec = element_precision (type); }
   (if (wi::ge_p (@1, 0, TYPE_SIGN (TREE_TYPE (@1)))
        && wi::lt_p (@1, prec, TYPE_SIGN (TREE_TYPE (@1)))
        && wi::ge_p (@2, 0, TYPE_SIGN (TREE_TYPE (@2)))
        && wi::lt_p (@2, prec, TYPE_SIGN (TREE_TYPE (@2))))
    (with { unsigned int low = wi::add (@1, @2).to_uhwi (); }
     /* Deal with a OP (c1 + c2) being undefined but (a OP c1) OP c2
        being well defined.  */
     (if (low >= prec)
      (if (op == LROTATE_EXPR || op == RROTATE_EXPR)
       (op @0 { build_int_cst (TREE_TYPE (@1), low % prec); })
       (if (TYPE_UNSIGNED (type) || op == LSHIFT_EXPR)
        { build_zero_cst (type); }
        (op @0 { build_int_cst (TREE_TYPE (@1), prec - 1); })))
      (op @0 { build_int_cst (TREE_TYPE (@1), low); })))))))


/* ((1 << A) & 1) != 0 -> A == 0
   ((1 << A) & 1) == 0 -> A != 0 */
(for cmp (ne eq)
     icmp (eq ne)
 (simplify
  (cmp (bit_and (lshift integer_onep @0) integer_onep) integer_zerop)
  (icmp @0 { build_zero_cst (TREE_TYPE (@0)); })))

/* (CST1 << A) == CST2 -> A == ctz (CST2) - ctz (CST1)
   (CST1 << A) != CST2 -> A != ctz (CST2) - ctz (CST1)
   if CST2 != 0.  */
(for cmp (ne eq)
 (simplify
  (cmp (lshift INTEGER_CST@0 @1) INTEGER_CST@2)
  (with { int cand = wi::ctz (@2) - wi::ctz (@0); }
   (if (cand < 0
        || (!integer_zerop (@2)
            && wi::ne_p (wi::lshift (@0, cand), @2)))
    { constant_boolean_node (cmp == NE_EXPR, type); }
    (if (!integer_zerop (@2)
         && wi::eq_p (wi::lshift (@0, cand), @2))
     (cmp @1 { build_int_cst (TREE_TYPE (@1), cand); }))))))

/* Fold (X << C1) & C2 into (X << C1) & (C2 | ((1 << C1) - 1))
        (X >> C1) & C2 into (X >> C1) & (C2 | ~((type) -1 >> C1))
   if the new mask might be further optimized.  */
(for shift (lshift rshift)
 (simplify
  (bit_and (convert?:s@4 (shift:s@5 (convert1?@3 @0) INTEGER_CST@1))
           INTEGER_CST@2)
   (if (tree_nop_conversion_p (TREE_TYPE (@4), TREE_TYPE (@5))
        && TYPE_PRECISION (type) <= HOST_BITS_PER_WIDE_INT
        && tree_fits_uhwi_p (@1)
        && tree_to_uhwi (@1) > 0
        && tree_to_uhwi (@1) < TYPE_PRECISION (type))
    (with
     {
       unsigned int shiftc = tree_to_uhwi (@1);
       unsigned HOST_WIDE_INT mask = TREE_INT_CST_LOW (@2);
       unsigned HOST_WIDE_INT newmask, zerobits = 0;
       tree shift_type = TREE_TYPE (@3);
       unsigned int prec;

       if (shift == LSHIFT_EXPR)
         zerobits = ((((unsigned HOST_WIDE_INT) 1) << shiftc) - 1);
       else if (shift == RSHIFT_EXPR
                && (TYPE_PRECISION (shift_type)
                    == GET_MODE_PRECISION (TYPE_MODE (shift_type))))
         {
           prec = TYPE_PRECISION (TREE_TYPE (@3));
           tree arg00 = @0;
           /* See if more bits can be proven as zero because of
              zero extension.  */
           if (@3 != @0
               && TYPE_UNSIGNED (TREE_TYPE (@0)))
             {
               tree inner_type = TREE_TYPE (@0);
               if ((TYPE_PRECISION (inner_type)
                    == GET_MODE_PRECISION (TYPE_MODE (inner_type)))
                   && TYPE_PRECISION (inner_type) < prec)
                 {
                   prec = TYPE_PRECISION (inner_type);
                   /* See if we can shorten the right shift.  */
                   if (shiftc < prec)
                     shift_type = inner_type;
                   /* Otherwise X >> C1 is all zeros, so we'll optimize
                      it into (X, 0) later on by making sure zerobits
                      is all ones.  */
                 }
             }
           zerobits = ~(unsigned HOST_WIDE_INT) 0;
           if (shiftc < prec)
             {
               zerobits >>= HOST_BITS_PER_WIDE_INT - shiftc;
               zerobits <<= prec - shiftc;
             }
           /* For arithmetic shift if sign bit could be set, zerobits
              can contain actually sign bits, so no transformation is
              possible, unless MASK masks them all away.  In that
              case the shift needs to be converted into logical shift.  */
           if (!TYPE_UNSIGNED (TREE_TYPE (@3))
               && prec == TYPE_PRECISION (TREE_TYPE (@3)))
             {
               if ((mask & zerobits) == 0)
                 shift_type = unsigned_type_for (TREE_TYPE (@3));
               else
                 zerobits = 0;
             }
         }
     }
     /* ((X << 16) & 0xff00) is (X, 0).  */
     (if ((mask & zerobits) == mask)
      { build_int_cst (type, 0); }
      (with { newmask = mask | zerobits; }
       (if (newmask != mask && (newmask & (newmask + 1)) == 0)
        (with
         {
           /* Only do the transformation if NEWMASK is some integer
              mode's mask.  */
           for (prec = BITS_PER_UNIT;
                prec < HOST_BITS_PER_WIDE_INT; prec <<= 1)
             if (newmask == (((unsigned HOST_WIDE_INT) 1) << prec) - 1)
               break;
         }
         (if (prec < HOST_BITS_PER_WIDE_INT
              || newmask == ~(unsigned HOST_WIDE_INT) 0)
          (with
           { tree newmaskt = build_int_cst_type (TREE_TYPE (@2), newmask); }
           (if (!tree_int_cst_equal (newmaskt, @2))
            (if (shift_type != TREE_TYPE (@3))
             (bit_and (convert (shift:shift_type (convert @3) @1)) { newmaskt; })
             (bit_and @4 { newmaskt; })))))))))))))

/* Fold (X {&,^,|} C2) << C1 into (X << C1) {&,^,|} (C2 << C1)
   (X {&,^,|} C2) >> C1 into (X >> C1) & (C2 >> C1).  */
(for shift (lshift rshift)
 (for bit_op (bit_and bit_xor bit_ior)
  (simplify
   (shift (convert?:s (bit_op:s @0 INTEGER_CST@2)) INTEGER_CST@1)
   (if (tree_nop_conversion_p (type, TREE_TYPE (@0)))
    (with { tree mask = int_const_binop (shift, fold_convert (type, @2), @1); }
     (bit_op (shift (convert @0) @1) { mask; }))))))


/* Simplifications of conversions.  */

/* Basic strip-useless-type-conversions / strip_nops.  */
(for cvt (convert view_convert float fix_trunc)
 (simplify
  (cvt @0)
  (if ((GIMPLE && useless_type_conversion_p (type, TREE_TYPE (@0)))
       || (GENERIC && type == TREE_TYPE (@0)))
   @0)))

/* Contract view-conversions.  */
(simplify
  (view_convert (view_convert @0))
  (view_convert @0))

/* For integral conversions with the same precision or pointer
   conversions use a NOP_EXPR instead.  */
(simplify
  (view_convert @0)
  (if ((INTEGRAL_TYPE_P (type) || POINTER_TYPE_P (type))
       && (INTEGRAL_TYPE_P (TREE_TYPE (@0)) || POINTER_TYPE_P (TREE_TYPE (@0)))
       && TYPE_PRECISION (type) == TYPE_PRECISION (TREE_TYPE (@0)))
   (convert @0)))

/* Strip inner integral conversions that do not change precision or size.  */
(simplify
  (view_convert (convert@0 @1))
  (if ((INTEGRAL_TYPE_P (TREE_TYPE (@0)) || POINTER_TYPE_P (TREE_TYPE (@0)))
       && (INTEGRAL_TYPE_P (TREE_TYPE (@1)) || POINTER_TYPE_P (TREE_TYPE (@1)))
       && (TYPE_PRECISION (TREE_TYPE (@0)) == TYPE_PRECISION (TREE_TYPE (@1)))
       && (TYPE_SIZE (TREE_TYPE (@0)) == TYPE_SIZE (TREE_TYPE (@1))))
   (view_convert @1)))

/* Re-association barriers around constants and other re-association
   barriers can be removed.  */
(simplify
 (paren CONSTANT_CLASS_P@0)
 @0)
(simplify
 (paren (paren@1 @0))
 @1)

/* Handle cases of two conversions in a row.  */
(for ocvt (convert float fix_trunc)
 (for icvt (convert float)
  (simplify
   (ocvt (icvt@1 @0))
   (with
    {
      tree inside_type = TREE_TYPE (@0);
      tree inter_type = TREE_TYPE (@1);
      int inside_int = INTEGRAL_TYPE_P (inside_type);
      int inside_ptr = POINTER_TYPE_P (inside_type);
      int inside_float = FLOAT_TYPE_P (inside_type);
      int inside_vec = VECTOR_TYPE_P (inside_type);
      unsigned int inside_prec = TYPE_PRECISION (inside_type);
      int inside_unsignedp = TYPE_UNSIGNED (inside_type);
      int inter_int = INTEGRAL_TYPE_P (inter_type);
      int inter_ptr = POINTER_TYPE_P (inter_type);
      int inter_float = FLOAT_TYPE_P (inter_type);
      int inter_vec = VECTOR_TYPE_P (inter_type);
      unsigned int inter_prec = TYPE_PRECISION (inter_type);
      int inter_unsignedp = TYPE_UNSIGNED (inter_type);
      int final_int = INTEGRAL_TYPE_P (type);
      int final_ptr = POINTER_TYPE_P (type);
      int final_float = FLOAT_TYPE_P (type);
      int final_vec = VECTOR_TYPE_P (type);
      unsigned int final_prec = TYPE_PRECISION (type);
      int final_unsignedp = TYPE_UNSIGNED (type);
    }
   (switch
    /* In addition to the cases of two conversions in a row
       handled below, if we are converting something to its own
       type via an object of identical or wider precision, neither
       conversion is needed.  */
    (if (((GIMPLE && useless_type_conversion_p (type, inside_type))
          || (GENERIC
              && TYPE_MAIN_VARIANT (type) == TYPE_MAIN_VARIANT (inside_type)))
         && (((inter_int || inter_ptr) && final_int)
             || (inter_float && final_float))
         && inter_prec >= final_prec)
     (ocvt @0))

    /* Likewise, if the intermediate and initial types are either both
       float or both integer, we don't need the middle conversion if the
       former is wider than the latter and doesn't change the signedness
       (for integers).  Avoid this if the final type is a pointer since
       then we sometimes need the middle conversion.  Likewise if the
       final type has a precision not equal to the size of its mode.  */
    (if (((inter_int && inside_int) || (inter_float && inside_float))
         && (final_int || final_float)
         && inter_prec >= inside_prec
         && (inter_float || inter_unsignedp == inside_unsignedp)
         && ! (final_prec != GET_MODE_PRECISION (TYPE_MODE (type))
               && TYPE_MODE (type) == TYPE_MODE (inter_type)))
     (ocvt @0))

    /* If we have a sign-extension of a zero-extended value, we can
       replace that by a single zero-extension.  Likewise if the
       final conversion does not change precision we can drop the
       intermediate conversion.  */
    (if (inside_int && inter_int && final_int
         && ((inside_prec < inter_prec && inter_prec < final_prec
              && inside_unsignedp && !inter_unsignedp)
             || final_prec == inter_prec))
     (ocvt @0))

    /* Two conversions in a row are not needed unless:
        - some conversion is floating-point (overstrict for now), or
        - some conversion is a vector (overstrict for now), or
        - the intermediate type is narrower than both initial and
          final, or
        - the intermediate type and innermost type differ in signedness,
          and the outermost type is wider than the intermediate, or
        - the initial type is a pointer type and the precisions of the
          intermediate and final types differ, or
        - the final type is a pointer type and the precisions of the
          initial and intermediate types differ.  */
    (if (! inside_float && ! inter_float && ! final_float
         && ! inside_vec && ! inter_vec && ! final_vec
         && (inter_prec >= inside_prec || inter_prec >= final_prec)
         && ! (inside_int && inter_int
               && inter_unsignedp != inside_unsignedp
               && inter_prec < final_prec)
         && ((inter_unsignedp && inter_prec > inside_prec)
             == (final_unsignedp && final_prec > inter_prec))
         && ! (inside_ptr && inter_prec != final_prec)
         && ! (final_ptr && inside_prec != inter_prec)
         && ! (final_prec != GET_MODE_PRECISION (TYPE_MODE (type))
               && TYPE_MODE (type) == TYPE_MODE (inter_type)))
     (ocvt @0))

    /* A truncation to an unsigned type (a zero-extension) should be
       canonicalized as bitwise and of a mask.  */
    (if (final_int && inter_int && inside_int
         && final_prec == inside_prec
         && final_prec > inter_prec
         && inter_unsignedp)
     (convert (bit_and @0 { wide_int_to_tree
                              (inside_type,
                               wi::mask (inter_prec, false,
                                         TYPE_PRECISION (inside_type))); })))

    /* If we are converting an integer to a floating-point that can
       represent it exactly and back to an integer, we can skip the
       floating-point conversion.  */
    (if (GIMPLE /* PR66211 */
         && inside_int && inter_float && final_int &&
         (unsigned) significand_size (TYPE_MODE (inter_type))
         >= inside_prec - !inside_unsignedp)
     (convert @0)))))))

/* If we have a narrowing conversion to an integral type that is fed by a
   BIT_AND_EXPR, we might be able to remove the BIT_AND_EXPR if it merely
   masks off bits outside the final type (and nothing else).  */
(simplify
  (convert (bit_and @0 INTEGER_CST@1))
  (if (INTEGRAL_TYPE_P (type)
       && INTEGRAL_TYPE_P (TREE_TYPE (@0))
       && TYPE_PRECISION (type) <= TYPE_PRECISION (TREE_TYPE (@0))
       && operand_equal_p (@1, build_low_bits_mask (TREE_TYPE (@1),
                                                    TYPE_PRECISION (type)), 0))
   (convert @0)))


/* (X /[ex] A) * A -> X.  */
(simplify
  (mult (convert? (exact_div @0 @1)) @1)
  /* Look through a sign-changing conversion.  */
  (convert @0))

/* Canonicalization of binary operations.  */

/* Convert X + -C into X - C.  */
(simplify
 (plus @0 REAL_CST@1)
 (if (REAL_VALUE_NEGATIVE (TREE_REAL_CST (@1)))
  (with { tree tem = fold_unary (NEGATE_EXPR, type, @1); }
   (if (!TREE_OVERFLOW (tem) || !flag_trapping_math)
    (minus @0 { tem; })))))

/* Convert x+x into x*2.0.  */
(simplify
 (plus @0 @0)
 (if (SCALAR_FLOAT_TYPE_P (type))
  (mult @0 { build_real (type, dconst2); })))

(simplify
 (minus integer_zerop @1)
 (negate @1))

/* (ARG0 - ARG1) is the same as (-ARG1 + ARG0).  So check whether
   ARG0 is zero and X + ARG0 reduces to X, since that would mean
   (-ARG1 + ARG0) reduces to -ARG1.  */
(simplify
 (minus real_zerop@0 @1)
 (if (fold_real_zero_addition_p (type, @0, 0))
  (negate @1)))

/* Transform x * -1 into -x.  */
(simplify
 (mult @0 integer_minus_onep)
 (negate @0))

/* COMPLEX_EXPR and REALPART/IMAGPART_EXPR cancellations.  */
(simplify
 (complex (realpart @0) (imagpart @0))
 @0)
(simplify
 (realpart (complex @0 @1))
 @0)
(simplify
 (imagpart (complex @0 @1))
 @1)

/* Sometimes we only care about half of a complex expression.  */
(simplify
 (realpart (convert?:s (conj:s @0)))
 (convert (realpart @0)))
(simplify
 (imagpart (convert?:s (conj:s @0)))
 (convert (negate (imagpart @0))))
(for part (realpart imagpart)
 (for op (plus minus)
  (simplify
   (part (convert?:s@2 (op:s @0 @1)))
   (convert (op (part @0) (part @1))))))
(simplify
 (realpart (convert?:s (CEXPI:s @0)))
 (convert (COS @0)))
(simplify
 (imagpart (convert?:s (CEXPI:s @0)))
 (convert (SIN @0)))

/* conj(conj(x)) -> x  */
(simplify
 (conj (convert? (conj @0)))
 (if (tree_nop_conversion_p (TREE_TYPE (@0), type))
  (convert @0)))

/* conj({x,y}) -> {x,-y}  */
(simplify
 (conj (convert?:s (complex:s @0 @1)))
 (with { tree itype = TREE_TYPE (type); }
  (complex (convert:itype @0) (negate (convert:itype @1)))))

/* BSWAP simplifications, transforms checked by gcc.dg/builtin-bswap-8.c.  */
(for bswap (BUILT_IN_BSWAP16 BUILT_IN_BSWAP32 BUILT_IN_BSWAP64)
 (simplify
  (bswap (bswap @0))
  @0)
 (simplify
  (bswap (bit_not (bswap @0)))
  (bit_not @0))
 (for bitop (bit_xor bit_ior bit_and)
  (simplify
   (bswap (bitop:c (bswap @0) @1))
   (bitop @0 (bswap @1)))))


/* Combine COND_EXPRs and VEC_COND_EXPRs.  */

/* Simplify constant conditions.
   Only optimize constant conditions when the selected branch
   has the same type as the COND_EXPR.  This avoids optimizing
   away "c ? x : throw", where the throw has a void type.
   Note that we cannot throw away the fold-const.c variant nor
   this one as we depend on doing this transform before possibly
   A ? B : B -> B triggers and the fold-const.c one can optimize
   0 ? A : B to B even if A has side-effects.  Something
   genmatch cannot handle.  */
(simplify
 (cond INTEGER_CST@0 @1 @2)
 (if (integer_zerop (@0))
  (if (!VOID_TYPE_P (TREE_TYPE (@2)) || VOID_TYPE_P (type))
   @2)
  (if (!VOID_TYPE_P (TREE_TYPE (@1)) || VOID_TYPE_P (type))
   @1)))
(simplify
 (vec_cond VECTOR_CST@0 @1 @2)
 (if (integer_all_onesp (@0))
  @1
  (if (integer_zerop (@0))
   @2)))

(for cnd (cond vec_cond)
 /* A ? B : (A ? X : C) -> A ? B : C.  */
 (simplify
  (cnd @0 (cnd @0 @1 @2) @3)
  (cnd @0 @1 @3))
 (simplify
  (cnd @0 @1 (cnd @0 @2 @3))
  (cnd @0 @1 @3))

 /* A ? B : B -> B.  */
 (simplify
  (cnd @0 @1 @1)
  @1)

 /* !A ? B : C -> A ? C : B.  */
 (simplify
  (cnd (logical_inverted_value truth_valued_p@0) @1 @2)
  (cnd @0 @2 @1)))

/* A + (B vcmp C ? 1 : 0) -> A - (B vcmp C), since vector comparisons
   return all-1 or all-0 results.  */
/* ??? We could instead convert all instances of the vec_cond to negate,
   but that isn't necessarily a win on its own.  */
(simplify
 (plus:c @3 (view_convert? (vec_cond @0 integer_each_onep@1 integer_zerop@2)))
 (if (VECTOR_TYPE_P (type)
      && TYPE_VECTOR_SUBPARTS (type) == TYPE_VECTOR_SUBPARTS (TREE_TYPE (@0))
      && (TYPE_MODE (TREE_TYPE (type))
          == TYPE_MODE (TREE_TYPE (TREE_TYPE (@0)))))
  (minus @3 (view_convert @0))))

/* ... likewise A - (B vcmp C ? 1 : 0) -> A + (B vcmp C).  */
(simplify
 (minus @3 (view_convert? (vec_cond @0 integer_each_onep@1 integer_zerop@2)))
 (if (VECTOR_TYPE_P (type)
      && TYPE_VECTOR_SUBPARTS (type) == TYPE_VECTOR_SUBPARTS (TREE_TYPE (@0))
      && (TYPE_MODE (TREE_TYPE (type))
          == TYPE_MODE (TREE_TYPE (TREE_TYPE (@0)))))
  (plus @3 (view_convert @0))))


/* Simplifications of comparisons.  */

/* See if we can reduce the magnitude of a constant involved in a
   comparison by changing the comparison code.  This is a canonicalization
   formerly done by maybe_canonicalize_comparison_1.  */
(for cmp  (le gt)
     acmp (lt ge)
 (simplify
  (cmp @0 INTEGER_CST@1)
  (if (tree_int_cst_sgn (@1) == -1)
   (acmp @0 { wide_int_to_tree (TREE_TYPE (@1), wi::add (@1, 1)); }))))
(for cmp  (ge lt)
     acmp (gt le)
 (simplify
  (cmp @0 INTEGER_CST@1)
  (if (tree_int_cst_sgn (@1) == 1)
   (acmp @0 { wide_int_to_tree (TREE_TYPE (@1), wi::sub (@1, 1)); }))))


/* We can simplify a logical negation of a comparison to the
   inverted comparison.  As we cannot compute an expression
   operator using invert_tree_comparison we have to simulate
   that with expression code iteration.  */
(for cmp (tcc_comparison)
     icmp (inverted_tcc_comparison)
     ncmp (inverted_tcc_comparison_with_nans)
 /* Ideally we'd like to combine the following two patterns
    and handle some more cases by using
      (logical_inverted_value (cmp @0 @1))
    here but for that genmatch would need to "inline" that.
    For now implement what forward_propagate_comparison did.  */
 (simplify
  (bit_not (cmp @0 @1))
  (if (VECTOR_TYPE_P (type)
       || (INTEGRAL_TYPE_P (type) && TYPE_PRECISION (type) == 1))
   /* Comparison inversion may be impossible for trapping math,
      invert_tree_comparison will tell us.  But we can't use
      a computed operator in the replacement tree thus we have
      to play the trick below.  */
   (with { enum tree_code ic = invert_tree_comparison
             (cmp, HONOR_NANS (@0)); }
    (if (ic == icmp)
     (icmp @0 @1)
     (if (ic == ncmp)
      (ncmp @0 @1))))))
 (simplify
  (bit_xor (cmp @0 @1) integer_truep)
  (with { enum tree_code ic = invert_tree_comparison
            (cmp, HONOR_NANS (@0)); }
   (if (ic == icmp)
    (icmp @0 @1)
    (if (ic == ncmp)
     (ncmp @0 @1))))))

/* Transform comparisons of the form X - Y CMP 0 to X CMP Y.
   ??? The transformation is valid for the other operators if overflow
   is undefined for the type, but performing it here badly interacts
   with the transformation in fold_cond_expr_with_comparison which
   attempts to synthetize ABS_EXPR.  */
(for cmp (eq ne)
 (simplify
  (cmp (minus@2 @0 @1) integer_zerop)
  (if (single_use (@2))
   (cmp @0 @1))))

/* Transform comparisons of the form X * C1 CMP 0 to X CMP 0 in the
   signed arithmetic case.  That form is created by the compiler
   often enough for folding it to be of value.  One example is in
   computing loop trip counts after Operator Strength Reduction.  */
(for cmp (simple_comparison)
     scmp (swapped_simple_comparison)
 (simplify
  (cmp (mult @0 INTEGER_CST@1) integer_zerop@2)
  /* Handle unfolded multiplication by zero.  */
  (if (integer_zerop (@1))
   (cmp @1 @2)
   (if (ANY_INTEGRAL_TYPE_P (TREE_TYPE (@0))
        && TYPE_OVERFLOW_UNDEFINED (TREE_TYPE (@0)))
    /* If @1 is negative we swap the sense of the comparison.  */
    (if (tree_int_cst_sgn (@1) < 0)
     (scmp @0 @2)
     (cmp @0 @2))))))
 
/* Simplify comparison of something with itself.  For IEEE
   floating-point, we can only do some of these simplifications.  */
(simplify
 (eq @0 @0)
 (if (! FLOAT_TYPE_P (TREE_TYPE (@0))
      || ! HONOR_NANS (TYPE_MODE (TREE_TYPE (@0))))
  { constant_boolean_node (true, type); }))
(for cmp (ge le)
 (simplify
  (cmp @0 @0)
  (eq @0 @0)))
(for cmp (ne gt lt)
 (simplify
  (cmp @0 @0)
  (if (cmp != NE_EXPR
       || ! FLOAT_TYPE_P (TREE_TYPE (@0))
       || ! HONOR_NANS (TYPE_MODE (TREE_TYPE (@0))))
   { constant_boolean_node (false, type); })))
(for cmp (unle unge uneq)
 (simplify
  (cmp @0 @0)
  { constant_boolean_node (true, type); }))
(simplify
 (ltgt @0 @0)
 (if (!flag_trapping_math)
  { constant_boolean_node (false, type); }))

/* Fold ~X op ~Y as Y op X.  */
(for cmp (simple_comparison)
 (simplify
  (cmp (bit_not @0) (bit_not @1))
  (cmp @1 @0)))

/* Fold ~X op C as X op' ~C, where op' is the swapped comparison.  */
(for cmp (simple_comparison)
     scmp (swapped_simple_comparison)
 (simplify
  (cmp (bit_not @0) CONSTANT_CLASS_P@1)
  (if (TREE_CODE (@1) == INTEGER_CST || TREE_CODE (@1) == VECTOR_CST)
   (scmp @0 (bit_not @1)))))

(for cmp (simple_comparison)
 /* Fold (double)float1 CMP (double)float2 into float1 CMP float2.  */
 (simplify
  (cmp (convert@2 @0) (convert? @1))
  (if (FLOAT_TYPE_P (TREE_TYPE (@0))
       && (DECIMAL_FLOAT_TYPE_P (TREE_TYPE (@2))
           == DECIMAL_FLOAT_TYPE_P (TREE_TYPE (@0)))
       && (DECIMAL_FLOAT_TYPE_P (TREE_TYPE (@2))
           == DECIMAL_FLOAT_TYPE_P (TREE_TYPE (@1))))
   (with
    {
      tree type1 = TREE_TYPE (@1);
      if (TREE_CODE (@1) == REAL_CST && !DECIMAL_FLOAT_TYPE_P (type1))
        {
          REAL_VALUE_TYPE orig = TREE_REAL_CST (@1);
          if (TYPE_PRECISION (type1) > TYPE_PRECISION (float_type_node)
              && exact_real_truncate (TYPE_MODE (float_type_node), &orig))
            type1 = float_type_node;
          if (TYPE_PRECISION (type1) > TYPE_PRECISION (double_type_node)
              && exact_real_truncate (TYPE_MODE (double_type_node), &orig))
            type1 = double_type_node;
        }
      tree newtype
        = (TYPE_PRECISION (TREE_TYPE (@0)) > TYPE_PRECISION (type1)
           ? TREE_TYPE (@0) : type1); 
    }
    (if (TYPE_PRECISION (TREE_TYPE (@2)) > TYPE_PRECISION (newtype))
     (cmp (convert:newtype @0) (convert:newtype @1))))))
 
 (simplify
  (cmp @0 REAL_CST@1)
  /* IEEE doesn't distinguish +0 and -0 in comparisons.  */
  (switch
   /* a CMP (-0) -> a CMP 0  */
   (if (REAL_VALUE_MINUS_ZERO (TREE_REAL_CST (@1)))
    (cmp @0 { build_real (TREE_TYPE (@1), dconst0); }))
   /* x != NaN is always true, other ops are always false.  */
   (if (REAL_VALUE_ISNAN (TREE_REAL_CST (@1))
        && ! HONOR_SNANS (@1))
    { constant_boolean_node (cmp == NE_EXPR, type); })
   /* Fold comparisons against infinity.  */
   (if (REAL_VALUE_ISINF (TREE_REAL_CST (@1))
        && MODE_HAS_INFINITIES (TYPE_MODE (TREE_TYPE (@1))))
    (with
     {
       REAL_VALUE_TYPE max;
       enum tree_code code = cmp;
       bool neg = REAL_VALUE_NEGATIVE (TREE_REAL_CST (@1));
       if (neg)
         code = swap_tree_comparison (code);
     }
     (switch
      /* x > +Inf is always false, if with ignore sNANs.  */
      (if (code == GT_EXPR
           && ! HONOR_SNANS (@0))
       { constant_boolean_node (false, type); })
      (if (code == LE_EXPR)
       /* x <= +Inf is always true, if we don't case about NaNs.  */
       (if (! HONOR_NANS (@0))
        { constant_boolean_node (true, type); }
        /* x <= +Inf is the same as x == x, i.e. !isnan(x).  */
        (eq @0 @0)))
      /* x == +Inf and x >= +Inf are always equal to x > DBL_MAX.  */
      (if (code == EQ_EXPR || code == GE_EXPR)
       (with { real_maxval (&max, neg, TYPE_MODE (TREE_TYPE (@0))); }
        (if (neg)
         (lt @0 { build_real (TREE_TYPE (@0), max); })
         (gt @0 { build_real (TREE_TYPE (@0), max); }))))
      /* x < +Inf is always equal to x <= DBL_MAX.  */
      (if (code == LT_EXPR)
       (with { real_maxval (&max, neg, TYPE_MODE (TREE_TYPE (@0))); }
        (if (neg)
         (ge @0 { build_real (TREE_TYPE (@0), max); })
         (le @0 { build_real (TREE_TYPE (@0), max); }))))
      /* x != +Inf is always equal to !(x > DBL_MAX).  */
      (if (code == NE_EXPR)
       (with { real_maxval (&max, neg, TYPE_MODE (TREE_TYPE (@0))); }
        (if (! HONOR_NANS (@0))
         (if (neg)
          (ge @0 { build_real (TREE_TYPE (@0), max); })
          (le @0 { build_real (TREE_TYPE (@0), max); }))
         (if (neg)
          (bit_xor (lt @0 { build_real (TREE_TYPE (@0), max); })
           { build_one_cst (type); })
          (bit_xor (gt @0 { build_real (TREE_TYPE (@0), max); })
           { build_one_cst (type); }))))))))))

 /* If this is a comparison of a real constant with a PLUS_EXPR
    or a MINUS_EXPR of a real constant, we can convert it into a
    comparison with a revised real constant as long as no overflow
    occurs when unsafe_math_optimizations are enabled.  */
 (if (flag_unsafe_math_optimizations)
  (for op (plus minus)
   (simplify
    (cmp (op @0 REAL_CST@1) REAL_CST@2)
    (with
     {
       tree tem = const_binop (op == PLUS_EXPR ? MINUS_EXPR : PLUS_EXPR,
                               TREE_TYPE (@1), @2, @1);
     }
     (if (tem && !TREE_OVERFLOW (tem))
      (cmp @0 { tem; }))))))

 /* Likewise, we can simplify a comparison of a real constant with
    a MINUS_EXPR whose first operand is also a real constant, i.e.
    (c1 - x) < c2 becomes x > c1-c2.  Reordering is allowed on
    floating-point types only if -fassociative-math is set.  */
 (if (flag_associative_math)
  (simplify
   (cmp (minus REAL_CST@0 @1) REAL_CST@2)
   (with { tree tem = const_binop (MINUS_EXPR, TREE_TYPE (@1), @0, @2); }
    (if (tem && !TREE_OVERFLOW (tem))
     (cmp { tem; } @1)))))

 /* Fold comparisons against built-in math functions.  */
 (if (flag_unsafe_math_optimizations
      && ! flag_errno_math)
  (for sq (SQRT)
   (simplify
    (cmp (sq @0) REAL_CST@1)
    (switch
     (if (REAL_VALUE_NEGATIVE (TREE_REAL_CST (@1)))
      (switch
       /* sqrt(x) < y is always false, if y is negative.  */
       (if (cmp == EQ_EXPR || cmp == LT_EXPR || cmp == LE_EXPR)
        { constant_boolean_node (false, type); })
       /* sqrt(x) > y is always true, if y is negative and we
          don't care about NaNs, i.e. negative values of x.  */
       (if (cmp == NE_EXPR || !HONOR_NANS (@0))
        { constant_boolean_node (true, type); })
       /* sqrt(x) > y is the same as x >= 0, if y is negative.  */
       (ge @0 { build_real (TREE_TYPE (@0), dconst0); })))
     (if (cmp == GT_EXPR || cmp == GE_EXPR)
      (with
       {
         REAL_VALUE_TYPE c2;
         real_arithmetic (&c2, MULT_EXPR,
                          &TREE_REAL_CST (@1), &TREE_REAL_CST (@1));
         real_convert (&c2, TYPE_MODE (TREE_TYPE (@0)), &c2);
       }
       (if (REAL_VALUE_ISINF (c2))
        /* sqrt(x) > y is x == +Inf, when y is very large.  */
        (if (HONOR_INFINITIES (@0))
         (eq @0 { build_real (TREE_TYPE (@0), c2); })
         { constant_boolean_node (false, type); })
        /* sqrt(x) > c is the same as x > c*c.  */
        (cmp @0 { build_real (TREE_TYPE (@0), c2); }))))
     (if (cmp == LT_EXPR || cmp == LE_EXPR)
      (with
       {
         REAL_VALUE_TYPE c2;
         real_arithmetic (&c2, MULT_EXPR,
                          &TREE_REAL_CST (@1), &TREE_REAL_CST (@1));
         real_convert (&c2, TYPE_MODE (TREE_TYPE (@0)), &c2);
       }
       (if (REAL_VALUE_ISINF (c2))
        (switch
         /* sqrt(x) < y is always true, when y is a very large
            value and we don't care about NaNs or Infinities.  */
         (if (! HONOR_NANS (@0) && ! HONOR_INFINITIES (@0))
          { constant_boolean_node (true, type); })
         /* sqrt(x) < y is x != +Inf when y is very large and we
            don't care about NaNs.  */
         (if (! HONOR_NANS (@0))
          (ne @0 { build_real (TREE_TYPE (@0), c2); }))
         /* sqrt(x) < y is x >= 0 when y is very large and we
            don't care about Infinities.  */
         (if (! HONOR_INFINITIES (@0))
          (ge @0 { build_real (TREE_TYPE (@0), dconst0); }))
         /* sqrt(x) < y is x >= 0 && x != +Inf, when y is large.  */
         (if (GENERIC)
          (truth_andif
           (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
           (ne @0 { build_real (TREE_TYPE (@0), c2); }))))
        /* sqrt(x) < c is the same as x < c*c, if we ignore NaNs.  */
        (if (! HONOR_NANS (@0))
         (cmp @0 { build_real (TREE_TYPE (@0), c2); })
         /* sqrt(x) < c is the same as x >= 0 && x < c*c.  */
         (if (GENERIC)
          (truth_andif
           (ge @0 { build_real (TREE_TYPE (@0), dconst0); })
           (cmp @0 { build_real (TREE_TYPE (@0), c2); }))))))))))))

/* Unordered tests if either argument is a NaN.  */
(simplify
 (bit_ior (unordered @0 @0) (unordered @1 @1))
 (if (types_match (@0, @1))
  (unordered @0 @1)))
(simplify
 (bit_and (ordered @0 @0) (ordered @1 @1))
 (if (types_match (@0, @1))
  (ordered @0 @1)))
(simplify
 (bit_ior:c (unordered @0 @0) (unordered:c@2 @0 @1))
 @2)
(simplify
 (bit_and:c (ordered @0 @0) (ordered:c@2 @0 @1))
 @2)

/* -A CMP -B -> B CMP A.  */
(for cmp (tcc_comparison)
     scmp (swapped_tcc_comparison)
 (simplify
  (cmp (negate @0) (negate @1))
  (if (FLOAT_TYPE_P (TREE_TYPE (@0))
       || (ANY_INTEGRAL_TYPE_P (TREE_TYPE (@0))
           && TYPE_OVERFLOW_UNDEFINED (TREE_TYPE (@0))))
   (scmp @0 @1)))
 (simplify
  (cmp (negate @0) CONSTANT_CLASS_P@1)
  (if (FLOAT_TYPE_P (TREE_TYPE (@0))
       || (ANY_INTEGRAL_TYPE_P (TREE_TYPE (@0))
           && TYPE_OVERFLOW_UNDEFINED (TREE_TYPE (@0))))
   (with { tree tem = fold_unary (NEGATE_EXPR, TREE_TYPE (@0), @1); }
    (if (tem && !TREE_OVERFLOW (tem))
     (scmp @0 { tem; }))))))

/* Convert ABS_EXPR<x> == 0 or ABS_EXPR<x> != 0 to x == 0 or x != 0.  */
(for op (eq ne)
 (simplify
  (op (abs @0) zerop@1)
  (op @0 @1)))

/* From fold_sign_changed_comparison and fold_widened_comparison.  */
(for cmp (simple_comparison)
 (simplify
  (cmp (convert@0 @00) (convert?@1 @10))
  (if (TREE_CODE (TREE_TYPE (@0)) == INTEGER_TYPE
       /* Disable this optimization if we're casting a function pointer
          type on targets that require function pointer canonicalization.  */
       && !(targetm.have_canonicalize_funcptr_for_compare ()
            && TREE_CODE (TREE_TYPE (@00)) == POINTER_TYPE
            && TREE_CODE (TREE_TYPE (TREE_TYPE (@00))) == FUNCTION_TYPE)
       && single_use (@0))
   (if (TYPE_PRECISION (TREE_TYPE (@00)) == TYPE_PRECISION (TREE_TYPE (@0))
        && (TREE_CODE (@10) == INTEGER_CST
            || (@1 != @10 && types_match (TREE_TYPE (@10), TREE_TYPE (@00))))
        && (TYPE_UNSIGNED (TREE_TYPE (@00)) == TYPE_UNSIGNED (TREE_TYPE (@0))
            || cmp == NE_EXPR
            || cmp == EQ_EXPR)
        && (POINTER_TYPE_P (TREE_TYPE (@00)) == POINTER_TYPE_P (TREE_TYPE (@0))))
    /* ???  The special-casing of INTEGER_CST conversion was in the original
       code and here to avoid a spurious overflow flag on the resulting
       constant which fold_convert produces.  */
    (if (TREE_CODE (@1) == INTEGER_CST)
     (cmp @00 { force_fit_type (TREE_TYPE (@00), wi::to_widest (@1), 0,
                                TREE_OVERFLOW (@1)); })
     (cmp @00 (convert @1)))

    (if (TYPE_PRECISION (TREE_TYPE (@0)) > TYPE_PRECISION (TREE_TYPE (@00)))
     /* If possible, express the comparison in the shorter mode.  */
     (if ((cmp == EQ_EXPR || cmp == NE_EXPR
           || TYPE_UNSIGNED (TREE_TYPE (@0)) == TYPE_UNSIGNED (TREE_TYPE (@00)))
          && (types_match (TREE_TYPE (@10), TREE_TYPE (@00))
              || ((TYPE_PRECISION (TREE_TYPE (@00))
                   >= TYPE_PRECISION (TREE_TYPE (@10)))
                  && (TYPE_UNSIGNED (TREE_TYPE (@00))
                      == TYPE_UNSIGNED (TREE_TYPE (@10))))
              || (TREE_CODE (@10) == INTEGER_CST
                  && (TREE_CODE (TREE_TYPE (@00)) == INTEGER_TYPE
                      || TREE_CODE (TREE_TYPE (@00)) == BOOLEAN_TYPE)
                  && int_fits_type_p (@10, TREE_TYPE (@00)))))
      (cmp @00 (convert @10))
      (if (TREE_CODE (@10) == INTEGER_CST
           && TREE_CODE (TREE_TYPE (@00)) == INTEGER_TYPE
           && !int_fits_type_p (@10, TREE_TYPE (@00)))
       (with
        {
          tree min = lower_bound_in_type (TREE_TYPE (@10), TREE_TYPE (@00));
          tree max = upper_bound_in_type (TREE_TYPE (@10), TREE_TYPE (@00));
          bool above = integer_nonzerop (const_binop (LT_EXPR, type, max, @10));
          bool below = integer_nonzerop (const_binop (LT_EXPR, type, @10, min));
        }
        (if (above || below)
         (if (cmp == EQ_EXPR || cmp == NE_EXPR)
          { constant_boolean_node (cmp == EQ_EXPR ? false : true, type); }
          (if (cmp == LT_EXPR || cmp == LE_EXPR)
           { constant_boolean_node (above ? true : false, type); }
           (if (cmp == GT_EXPR || cmp == GE_EXPR)
            { constant_boolean_node (above ? false : true, type); }))))))))))))

(for cmp (eq ne)
 /* A local variable can never be pointed to by
    the default SSA name of an incoming parameter.
    SSA names are canonicalized to 2nd place.  */
 (simplify
  (cmp addr@0 SSA_NAME@1)
  (if (SSA_NAME_IS_DEFAULT_DEF (@1)
       && TREE_CODE (SSA_NAME_VAR (@1)) == PARM_DECL)
   (with { tree base = get_base_address (TREE_OPERAND (@0, 0)); }
    (if (TREE_CODE (base) == VAR_DECL
         && auto_var_in_fn_p (base, current_function_decl))
     (if (cmp == NE_EXPR)
      { constant_boolean_node (true, type); }
      { constant_boolean_node (false, type); }))))))

/* Equality compare simplifications from fold_binary  */
(for cmp (eq ne)

 /* If we have (A | C) == D where C & ~D != 0, convert this into 0.
    Similarly for NE_EXPR.  */
 (simplify
  (cmp (convert?@3 (bit_ior @0 INTEGER_CST@1)) INTEGER_CST@2)
  (if (tree_nop_conversion_p (TREE_TYPE (@3), TREE_TYPE (@0))
       && wi::bit_and_not (@1, @2) != 0)
   { constant_boolean_node (cmp == NE_EXPR, type); }))

 /* (X ^ Y) == 0 becomes X == Y, and (X ^ Y) != 0 becomes X != Y.  */
 (simplify
  (cmp (bit_xor @0 @1) integer_zerop)
  (cmp @0 @1))

 /* (X ^ Y) == Y becomes X == 0.
    Likewise (X ^ Y) == X becomes Y == 0.  */
 (simplify
  (cmp:c (bit_xor:c @0 @1) @0)
  (cmp @1 { build_zero_cst (TREE_TYPE (@1)); }))

 /* (X ^ C1) op C2 can be rewritten as X op (C1 ^ C2).  */
 (simplify
  (cmp (convert?@3 (bit_xor @0 INTEGER_CST@1)) INTEGER_CST@2)
  (if (tree_nop_conversion_p (TREE_TYPE (@3), TREE_TYPE (@0)))
   (cmp @0 (bit_xor @1 (convert @2)))))

 (simplify
  (cmp (convert? addr@0) integer_zerop)
  (if (tree_single_nonzero_warnv_p (@0, NULL))
   { constant_boolean_node (cmp == NE_EXPR, type); })))

/* If we have (A & C) == C where C is a power of 2, convert this into
   (A & C) != 0.  Similarly for NE_EXPR.  */
(for cmp (eq ne)
     icmp (ne eq)
 (simplify
  (cmp (bit_and@2 @0 integer_pow2p@1) @1)
  (icmp @2 { build_zero_cst (TREE_TYPE (@0)); })))
 
/* If we have (A & C) != 0 where C is the sign bit of A, convert
   this into A < 0.  Similarly for (A & C) == 0 into A >= 0.  */
(for cmp (eq ne)
     ncmp (ge lt)
 (simplify
  (cmp (bit_and (convert?@2 @0) integer_pow2p@1) integer_zerop)
  (if (INTEGRAL_TYPE_P (TREE_TYPE (@0))
       && (TYPE_PRECISION (TREE_TYPE (@0))
           == GET_MODE_PRECISION (TYPE_MODE (TREE_TYPE (@0))))
       && element_precision (@2) >= element_precision (@0)
       && wi::only_sign_bit_p (@1, element_precision (@0)))
   (with { tree stype = signed_type_for (TREE_TYPE (@0)); }
    (ncmp (convert:stype @0) { build_zero_cst (stype); })))))

/* When the addresses are not directly of decls compare base and offset.
   This implements some remaining parts of fold_comparison address
   comparisons but still no complete part of it.  Still it is good
   enough to make fold_stmt not regress when not dispatching to fold_binary.  */
(for cmp (simple_comparison)
 (simplify
  (cmp (convert1?@2 addr@0) (convert2? addr@1))
  (with
   {
     HOST_WIDE_INT off0, off1;
     tree base0 = get_addr_base_and_unit_offset (TREE_OPERAND (@0, 0), &off0);
     tree base1 = get_addr_base_and_unit_offset (TREE_OPERAND (@1, 0), &off1);
     if (base0 && TREE_CODE (base0) == MEM_REF)
       {
         off0 += mem_ref_offset (base0).to_short_addr ();
         base0 = TREE_OPERAND (base0, 0);
       }
     if (base1 && TREE_CODE (base1) == MEM_REF)
       {
         off1 += mem_ref_offset (base1).to_short_addr ();
         base1 = TREE_OPERAND (base1, 0);
       }
   }
   (if (base0 && base1)
    (with
     {
       int equal = 2;
       if (decl_in_symtab_p (base0)
           && decl_in_symtab_p (base1))
         equal = symtab_node::get_create (base0)
                   ->equal_address_to (symtab_node::get_create (base1));
       else if ((DECL_P (base0)
                 || TREE_CODE (base0) == SSA_NAME
                 || TREE_CODE (base0) == STRING_CST)
                && (DECL_P (base1)
                    || TREE_CODE (base1) == SSA_NAME
                    || TREE_CODE (base1) == STRING_CST))
         equal = (base0 == base1);
     }
     (if (equal == 1
          && (cmp == EQ_EXPR || cmp == NE_EXPR
              /* If the offsets are equal we can ignore overflow.  */
              || off0 == off1
              || POINTER_TYPE_OVERFLOW_UNDEFINED
              /* Or if we compare using pointers to decls or strings.  */
              || (POINTER_TYPE_P (TREE_TYPE (@2))
                  && (DECL_P (base0) || TREE_CODE (base0) == STRING_CST))))
      (switch
       (if (cmp == EQ_EXPR)
        { constant_boolean_node (off0 == off1, type); })
       (if (cmp == NE_EXPR)
        { constant_boolean_node (off0 != off1, type); })
       (if (cmp == LT_EXPR)
        { constant_boolean_node (off0 < off1, type); })
       (if (cmp == LE_EXPR)
        { constant_boolean_node (off0 <= off1, type); })
       (if (cmp == GE_EXPR)
        { constant_boolean_node (off0 >= off1, type); })
       (if (cmp == GT_EXPR)
        { constant_boolean_node (off0 > off1, type); }))
      (if (equal == 0
           && DECL_P (base0) && DECL_P (base1)
           /* If we compare this as integers require equal offset.  */
           && (!INTEGRAL_TYPE_P (TREE_TYPE (@2))
               || off0 == off1))
       (switch
        (if (cmp == EQ_EXPR)
         { constant_boolean_node (false, type); })
        (if (cmp == NE_EXPR)
         { constant_boolean_node (true, type); })))))))))

/* Non-equality compare simplifications from fold_binary  */
(for cmp (lt gt le ge)
 /* Comparisons with the highest or lowest possible integer of
    the specified precision will have known values.  */
 (simplify
  (cmp (convert?@2 @0) INTEGER_CST@1)
  (if ((INTEGRAL_TYPE_P (TREE_TYPE (@1)) || POINTER_TYPE_P (TREE_TYPE (@1)))
       && tree_nop_conversion_p (TREE_TYPE (@2), TREE_TYPE (@0)))
   (with
    {
      tree arg1_type = TREE_TYPE (@1);
      unsigned int prec = TYPE_PRECISION (arg1_type);
      wide_int max = wi::max_value (arg1_type);
      wide_int signed_max = wi::max_value (prec, SIGNED);
      wide_int min = wi::min_value (arg1_type);
    }
    (switch
     (if (wi::eq_p (@1, max))
      (switch
       (if (cmp == GT_EXPR)
        { constant_boolean_node (false, type); })
       (if (cmp == GE_EXPR)
        (eq @2 @1))
       (if (cmp == LE_EXPR)
        { constant_boolean_node (true, type); })
       (if (cmp == LT_EXPR)
        (ne @2 @1))))
     (if (wi::eq_p (@1, min))
      (switch
       (if (cmp == LT_EXPR)
        { constant_boolean_node (false, type); })
       (if (cmp == LE_EXPR)
        (eq @2 @1))
       (if (cmp == GE_EXPR)
        { constant_boolean_node (true, type); })
       (if (cmp == GT_EXPR)
        (ne @2 @1))))
     (if (wi::eq_p (@1, max - 1))
      (switch
       (if (cmp == GT_EXPR)
        (eq @2 { wide_int_to_tree (TREE_TYPE (@1), wi::add (@1, 1)); }))
       (if (cmp == LE_EXPR)
        (ne @2 { wide_int_to_tree (TREE_TYPE (@1), wi::add (@1, 1)); }))))
     (if (wi::eq_p (@1, min + 1))
      (switch
       (if (cmp == GE_EXPR)
        (ne @2 { wide_int_to_tree (TREE_TYPE (@1), wi::sub (@1, 1)); }))
       (if (cmp == LT_EXPR)
        (eq @2 { wide_int_to_tree (TREE_TYPE (@1), wi::sub (@1, 1)); }))))
     (if (wi::eq_p (@1, signed_max)
          && TYPE_UNSIGNED (arg1_type)
          /* We will flip the signedness of the comparison operator
             associated with the mode of @1, so the sign bit is
             specified by this mode.  Check that @1 is the signed
             max associated with this sign bit.  */
          && prec == GET_MODE_PRECISION (TYPE_MODE (arg1_type))
          /* signed_type does not work on pointer types.  */
          && INTEGRAL_TYPE_P (arg1_type))
      /* The following case also applies to X < signed_max+1
         and X >= signed_max+1 because previous transformations.  */
      (if (cmp == LE_EXPR || cmp == GT_EXPR)
       (with { tree st = signed_type_for (arg1_type); }
        (if (cmp == LE_EXPR)
         (ge (convert:st @0) { build_zero_cst (st); })
         (lt (convert:st @0) { build_zero_cst (st); }))))))))))
 
(for cmp (unordered ordered unlt unle ungt unge uneq ltgt)
 /* If the second operand is NaN, the result is constant.  */
 (simplify
  (cmp @0 REAL_CST@1)
  (if (REAL_VALUE_ISNAN (TREE_REAL_CST (@1))
       && (cmp != LTGT_EXPR || ! flag_trapping_math))
   { constant_boolean_node (cmp == ORDERED_EXPR || cmp == LTGT_EXPR
                            ? false : true, type); })))

/* bool_var != 0 becomes bool_var.  */
(simplify
 (ne @0 integer_zerop)
 (if (TREE_CODE (TREE_TYPE (@0)) == BOOLEAN_TYPE
      && types_match (type, TREE_TYPE (@0)))
  (non_lvalue @0)))
/* bool_var == 1 becomes bool_var.  */
(simplify
 (eq @0 integer_onep)
 (if (TREE_CODE (TREE_TYPE (@0)) == BOOLEAN_TYPE
      && types_match (type, TREE_TYPE (@0)))
  (non_lvalue @0)))
/* Do not handle
   bool_var == 0 becomes !bool_var or
   bool_var != 1 becomes !bool_var
   here because that only is good in assignment context as long
   as we require a tcc_comparison in GIMPLE_CONDs where we'd
   replace if (x == 0) with tem = ~x; if (tem != 0) which is
   clearly less optimal and which we'll transform again in forwprop.  */


/* Simplification of math builtins.  These rules must all be optimizations
   as well as IL simplifications.  If there is a possibility that the new
   form could be a pessimization, the rule should go in the canonicalization
   section that follows this one.

   Rules can generally go in this section if they satisfy one of
   the following:

   - the rule describes an identity

   - the rule replaces calls with something as simple as addition or
     multiplication

   - the rule contains unary calls only and simplifies the surrounding
     arithmetic.  (The idea here is to exclude non-unary calls in which
     one operand is constant and in which the call is known to be cheap
     when the operand has that value.)  */

(if (flag_unsafe_math_optimizations)
 /* Simplify sqrt(x) * sqrt(x) -> x.  */
 (simplify
  (mult (SQRT@1 @0) @1)
  (if (!HONOR_SNANS (type))
   @0))

 /* Simplify sqrt(x) * sqrt(y) -> sqrt(x*y).  */
 (for root (SQRT CBRT)
  (simplify
   (mult (root:s @0) (root:s @1))
    (root (mult @0 @1))))

 /* Simplify expN(x) * expN(y) -> expN(x+y). */
 (for exps (EXP EXP2 EXP10 POW10)
  (simplify
   (mult (exps:s @0) (exps:s @1))
    (exps (plus @0 @1))))

 /* Simplify a/root(b/c) into a*root(c/b).  */
 (for root (SQRT CBRT)
  (simplify
   (rdiv @0 (root:s (rdiv:s @1 @2)))
    (mult @0 (root (rdiv @2 @1)))))

 /* Simplify x/expN(y) into x*expN(-y).  */
 (for exps (EXP EXP2 EXP10 POW10)
  (simplify
   (rdiv @0 (exps:s @1))
    (mult @0 (exps (negate @1)))))

 /* Special case, optimize logN(expN(x)) = x.  */
 (for logs (LOG LOG2 LOG10 LOG10)
      exps (EXP EXP2 EXP10 POW10)
  (simplify
   (logs (exps @0))
    @0))

 /* Optimize logN(func()) for various exponential functions.  We
    want to determine the value "x" and the power "exponent" in
    order to transform logN(x**exponent) into exponent*logN(x).  */
 (for logs (LOG  LOG   LOG   LOG2 LOG2  LOG2  LOG10 LOG10)
      exps (EXP2 EXP10 POW10 EXP  EXP10 POW10 EXP   EXP2)
  (simplify
   (logs (exps @0))
   (with {
     tree x;
     switch (exps)
       {
       CASE_FLT_FN (BUILT_IN_EXP):
         /* Prepare to do logN(exp(exponent)) -> exponent*logN(e).  */
         x = build_real_truncate (type, dconst_e ());
         break;
       CASE_FLT_FN (BUILT_IN_EXP2):
         /* Prepare to do logN(exp2(exponent)) -> exponent*logN(2).  */
         x = build_real (type, dconst2);
         break;
       CASE_FLT_FN (BUILT_IN_EXP10):
       CASE_FLT_FN (BUILT_IN_POW10):
         /* Prepare to do logN(exp10(exponent)) -> exponent*logN(10).  */
         {
           REAL_VALUE_TYPE dconst10;
           real_from_integer (&dconst10, VOIDmode, 10, SIGNED);
           x = build_real (type, dconst10);
         }
         break;
       default:
         gcc_unreachable ();
       }
     }
    (mult (logs { x; }) @0))))

 (for logs (LOG LOG
            LOG2 LOG2
            LOG10 LOG10)
      exps (SQRT CBRT)
  (simplify
   (logs (exps @0))
   (with {
     tree x;
     switch (exps)
       {
       CASE_FLT_FN (BUILT_IN_SQRT):
         /* Prepare to do logN(sqrt(x)) -> 0.5*logN(x).  */
         x = build_real (type, dconsthalf);
         break;
       CASE_FLT_FN (BUILT_IN_CBRT):
         /* Prepare to do logN(cbrt(x)) -> (1/3)*logN(x).  */
         x = build_real_truncate (type, dconst_third ());
         break;
       default:
         gcc_unreachable ();
       }
     }
    (mult { x; } (logs @0)))))

 /* logN(pow(x,exponent)) -> exponent*logN(x).  */
 (for logs (LOG LOG2 LOG10)
      pows (POW)
  (simplify
   (logs (pows @0 @1))
   (mult @1 (logs @0))))

 (for sqrts (SQRT)
      cbrts (CBRT)
      exps (EXP EXP2 EXP10 POW10)
  /* sqrt(expN(x)) -> expN(x*0.5).  */
  (simplify
   (sqrts (exps @0))
   (exps (mult @0 { build_real (type, dconsthalf); })))
  /* cbrt(expN(x)) -> expN(x/3).  */
  (simplify
   (cbrts (exps @0))
   (exps (mult @0 { build_real_truncate (type, dconst_third ()); })))))

/* Canonicalization of sequences of math builtins.  These rules represent
   IL simplifications but are not necessarily optimizations.

   The sincos pass is responsible for picking "optimal" implementations
   of math builtins, which may be more complicated and can sometimes go
   the other way, e.g. converting pow into a sequence of sqrts.
   We only want to do these canonicalizations before the pass has run.  */

(if (flag_unsafe_math_optimizations && canonicalize_math_p ())
 /* Simplify tan(x) * cos(x) -> sin(x). */
 (simplify
  (mult:c (TAN:s @0) (COS:s @0))
   (SIN @0))

 /* Simplify x * pow(x,c) -> pow(x,c+1). */
 (simplify
  (mult @0 (POW:s @0 REAL_CST@1))
  (if (!TREE_OVERFLOW (@1))
   (POW @0 (plus @1 { build_one_cst (type); }))))

 /* Simplify sin(x) / cos(x) -> tan(x). */
 (simplify
  (rdiv (SIN:s @0) (COS:s @0))
   (TAN @0))

 /* Simplify cos(x) / sin(x) -> 1 / tan(x). */
 (simplify
  (rdiv (COS:s @0) (SIN:s @0))
   (rdiv { build_one_cst (type); } (TAN @0)))

 /* Simplify sin(x) / tan(x) -> cos(x). */
 (simplify
  (rdiv (SIN:s @0) (TAN:s @0))
  (if (! HONOR_NANS (@0)
       && ! HONOR_INFINITIES (@0))
   (cos @0)))

 /* Simplify tan(x) / sin(x) -> 1.0 / cos(x). */
 (simplify
  (rdiv (TAN:s @0) (SIN:s @0))
  (if (! HONOR_NANS (@0)
       && ! HONOR_INFINITIES (@0))
   (rdiv { build_one_cst (type); } (COS @0))))

 /* Simplify pow(x,y) * pow(x,z) -> pow(x,y+z). */
 (simplify
  (mult (POW:s @0 @1) (POW:s @0 @2))
   (POW @0 (plus @1 @2)))

 /* Simplify pow(x,y) * pow(z,y) -> pow(x*z,y). */
 (simplify
  (mult (POW:s @0 @1) (POW:s @2 @1))
   (POW (mult @0 @2) @1))

 /* Simplify pow(x,c) / x -> pow(x,c-1). */
 (simplify
  (rdiv (POW:s @0 REAL_CST@1) @0)
  (if (!TREE_OVERFLOW (@1))
   (POW @0 (minus @1 { build_one_cst (type); }))))

 /* Simplify x / pow (y,z) -> x * pow(y,-z). */
 (simplify
  (rdiv @0 (POW:s @1 @2))
   (mult @0 (POW @1 (negate @2))))

 (for sqrts (SQRT)
      cbrts (CBRT)
      pows (POW)
  /* sqrt(sqrt(x)) -> pow(x,1/4).  */
  (simplify
   (sqrts (sqrts @0))
   (pows @0 { build_real (type, dconst_quarter ()); }))
  /* sqrt(cbrt(x)) -> pow(x,1/6).  */
  (simplify
   (sqrts (cbrts @0))
   (pows @0 { build_real_truncate (type, dconst_sixth ()); }))
  /* cbrt(sqrt(x)) -> pow(x,1/6).  */
  (simplify
   (cbrts (sqrts @0))
   (pows @0 { build_real_truncate (type, dconst_sixth ()); }))
  /* cbrt(cbrt(x)) -> pow(x,1/9), iff x is nonnegative.  */
  (simplify
   (cbrts (cbrts tree_expr_nonnegative_p@0))
   (pows @0 { build_real_truncate (type, dconst_ninth ()); }))
  /* sqrt(pow(x,y)) -> pow(|x|,y*0.5).  */
  (simplify
   (sqrts (pows @0 @1))
   (pows (abs @0) (mult @1 { build_real (type, dconsthalf); })))
  /* cbrt(pow(x,y)) -> pow(x,y/3), iff x is nonnegative.  */
  (simplify
   (cbrts (pows tree_expr_nonnegative_p@0 @1))
   (pows @0 (mult @1 { build_real_truncate (type, dconst_third ()); })))))

/* Narrowing of arithmetic and logical operations. 

   These are conceptually similar to the transformations performed for
   the C/C++ front-ends by shorten_binary_op and shorten_compare.  Long
   term we want to move all that code out of the front-ends into here.  */

/* If we have a narrowing conversion of an arithmetic operation where
   both operands are widening conversions from the same type as the outer
   narrowing conversion.  Then convert the innermost operands to a suitable
   unsigned type (to avoid introducing undefined behaviour), perform the
   operation and convert the result to the desired type.  */
(for op (plus minus)
  (simplify
    (convert (op:s (convert@2 @0) (convert@3 @1)))
    (if (INTEGRAL_TYPE_P (type)
         /* We check for type compatibility between @0 and @1 below,
            so there's no need to check that @1/@3 are integral types.  */
         && INTEGRAL_TYPE_P (TREE_TYPE (@0))
         && INTEGRAL_TYPE_P (TREE_TYPE (@2))
         /* The precision of the type of each operand must match the
            precision of the mode of each operand, similarly for the
            result.  */
         && (TYPE_PRECISION (TREE_TYPE (@0))
             == GET_MODE_PRECISION (TYPE_MODE (TREE_TYPE (@0))))
         && (TYPE_PRECISION (TREE_TYPE (@1))
             == GET_MODE_PRECISION (TYPE_MODE (TREE_TYPE (@1))))
         && TYPE_PRECISION (type) == GET_MODE_PRECISION (TYPE_MODE (type))
         /* The inner conversion must be a widening conversion.  */
         && TYPE_PRECISION (TREE_TYPE (@2)) > TYPE_PRECISION (TREE_TYPE (@0))
         && types_match (@0, @1)
         && types_match (@0, type))
      (if (TYPE_OVERFLOW_WRAPS (TREE_TYPE (@0)))
        (convert (op @0 @1))
        (with { tree utype = unsigned_type_for (TREE_TYPE (@0)); }
         (convert (op (convert:utype @0) (convert:utype @1))))))))

/* This is another case of narrowing, specifically when there's an outer
   BIT_AND_EXPR which masks off bits outside the type of the innermost
   operands.   Like the previous case we have to convert the operands
   to unsigned types to avoid introducing undefined behaviour for the
   arithmetic operation.  */
(for op (minus plus)
 (simplify
  (bit_and (op:s (convert@2 @0) (convert@3 @1)) INTEGER_CST@4)
  (if (INTEGRAL_TYPE_P (type)
       /* We check for type compatibility between @0 and @1 below,
          so there's no need to check that @1/@3 are integral types.  */
       && INTEGRAL_TYPE_P (TREE_TYPE (@0))
       && INTEGRAL_TYPE_P (TREE_TYPE (@2))
       /* The precision of the type of each operand must match the
          precision of the mode of each operand, similarly for the
          result.  */
       && (TYPE_PRECISION (TREE_TYPE (@0))
           == GET_MODE_PRECISION (TYPE_MODE (TREE_TYPE (@0))))
       && (TYPE_PRECISION (TREE_TYPE (@1))
           == GET_MODE_PRECISION (TYPE_MODE (TREE_TYPE (@1))))
       && TYPE_PRECISION (type) == GET_MODE_PRECISION (TYPE_MODE (type))
       /* The inner conversion must be a widening conversion.  */
       && TYPE_PRECISION (TREE_TYPE (@2)) > TYPE_PRECISION (TREE_TYPE (@0))
       && types_match (@0, @1)
       && (tree_int_cst_min_precision (@4, TYPE_SIGN (TREE_TYPE (@0)))
           <= TYPE_PRECISION (TREE_TYPE (@0)))
       && (TYPE_OVERFLOW_WRAPS (TREE_TYPE (@0))
           || tree_int_cst_sgn (@4) >= 0))
   (if (TYPE_OVERFLOW_WRAPS (TREE_TYPE (@0)))
    (with { tree ntype = TREE_TYPE (@0); }
     (convert (bit_and (op @0 @1) (convert:ntype @4))))
    (with { tree utype = unsigned_type_for (TREE_TYPE (@0)); }
     (convert (bit_and (op (convert:utype @0) (convert:utype @1))
               (convert:utype @4))))))))