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[official-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) 2014-2017 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
   tree_expr_nonzero_p
   integer_valued_real_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)

#include "cfn-operators.pd"

/* Define operand lists for math rounding functions {,i,l,ll}FN,
   where the versions prefixed with "i" return an int, those prefixed with
   "l" return a long and those prefixed with "ll" return a long long.

   Also define operand lists:

     X<FN>F for all float functions, in the order i, l, ll
     X<FN> for all double functions, in the same order
     X<FN>L for all long double functions, in the same order.  */
#define DEFINE_INT_AND_FLOAT_ROUND_FN(FN) \
  (define_operator_list X##FN##F BUILT_IN_I##FN##F \
                                 BUILT_IN_L##FN##F \
                                 BUILT_IN_LL##FN##F) \
  (define_operator_list X##FN BUILT_IN_I##FN \
                              BUILT_IN_L##FN \
                              BUILT_IN_LL##FN) \
  (define_operator_list X##FN##L BUILT_IN_I##FN##L \
                                 BUILT_IN_L##FN##L \
                                 BUILT_IN_LL##FN##L)

DEFINE_INT_AND_FLOAT_ROUND_FN (FLOOR)
DEFINE_INT_AND_FLOAT_ROUND_FN (CEIL)
DEFINE_INT_AND_FLOAT_ROUND_FN (ROUND)
DEFINE_INT_AND_FLOAT_ROUND_FN (RINT)

/* 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)))

/* X * 1, X / 1 -> X.  */
(for op (mult trunc_div ceil_div floor_div round_div exact_div)
  (simplify
    (op @0 integer_onep)
    (non_lvalue @0)))

/* Preserve explicit divisions by 0: the C++ front-end wants to detect
   undefined behavior in constexpr evaluation, and assuming that the division
   traps enables better optimizations than these anyway.  */
(for div (trunc_div ceil_div floor_div round_div exact_div)
 /* 0 / X is always zero.  */
 (simplify
  (div 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 -X.  */
 (simplify
   (div @0 integer_minus_onep@1)
   (if (!TYPE_UNSIGNED (type))
    (negate @0)))
 /* X / X is one.  */
 (simplify
  (div @0 @0)
  /* But not for 0 / 0 so that we can get the proper warnings and errors.  */
  (if (!integer_zerop (@0))
   { build_one_cst (type); }))
 /* X / abs (X) is X < 0 ? -1 : 1.  */ 
 (simplify
   (div:C @0 (abs @0))
   (if (INTEGRAL_TYPE_P (type)
        && TYPE_OVERFLOW_UNDEFINED (type))
    (cond (lt @0 { build_zero_cst (type); })
          { build_minus_one_cst (type); } { build_one_cst (type); })))
 /* X / -X is -1.  */
 (simplify
   (div:C @0 (negate @0))
   (if ((INTEGRAL_TYPE_P (type) || VECTOR_INTEGER_TYPE_P (type))
        && TYPE_OVERFLOW_UNDEFINED (type))
    { build_minus_one_cst (type); })))

/* 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); }))

/* PR71078: x / abs(x) -> copysign (1.0, x) */
(simplify
 (rdiv:C (convert? @0) (convert? (abs @0)))
  (if (SCALAR_FLOAT_TYPE_P (type)
       && ! HONOR_NANS (type)
       && ! HONOR_INFINITIES (type))
   (switch
    (if (types_match (type, float_type_node))
     (BUILT_IN_COPYSIGNF { build_one_cst (type); } (convert @0)))
    (if (types_match (type, double_type_node))
     (BUILT_IN_COPYSIGN { build_one_cst (type); } (convert @0)))
    (if (types_match (type, long_double_type_node))
     (BUILT_IN_COPYSIGNL { build_one_cst (type); } (convert @0))))))

/* 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 (flag_reciprocal_math)
 /* Convert (A/B)/C to A/(B*C)  */
 (simplify
  (rdiv (rdiv:s @0 @1) @2)
   (rdiv @0 (mult @1 @2)))

 /* Convert A/(B/C) to (A/B)*C  */
 (simplify
  (rdiv @0 (rdiv:s @1 @2))
   (mult (rdiv @0 @1) @2)))

/* Optimize (X & (-A)) / A where A is a power of 2, to X >> log2(A) */
(for div (trunc_div ceil_div floor_div round_div exact_div)
 (simplify
  (div (convert? (bit_and @0 INTEGER_CST@1)) INTEGER_CST@2)
  (if (integer_pow2p (@2)
       && tree_int_cst_sgn (@2) > 0
       && wi::add (@2, @1) == 0
       && tree_nop_conversion_p (type, TREE_TYPE (@0)))
   (rshift (convert @0) { build_int_cst (integer_type_node,
                                         wi::exact_log2 (@2)); }))))

/* 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; } ))))))))

(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 % X is zero.  */
 (simplify
  (mod @0 @0)
  /* But not for 0 % 0 so that we can get the proper warnings and errors.  */
  (if (!integer_zerop (@0))
   { 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 (INTEGRAL_TYPE_P (type)
      && !TYPE_UNSIGNED (type)
      && !TYPE_OVERFLOW_TRAPS (type)
      && tree_nop_conversion_p (type, TREE_TYPE (@1))
      /* Avoid this transformation if X might be INT_MIN or
         Y might be -1, because we would then change valid
         INT_MIN % -(-1) into invalid INT_MIN % -1.  */
      && (expr_not_equal_to (@0, TYPE_MIN_VALUE (type))
          || expr_not_equal_to (@1, wi::minus_one (TYPE_PRECISION
                                                        (TREE_TYPE (@1))))))
  (trunc_mod @0 (convert @1))))

/* X - (X / Y) * Y is the same as X % Y.  */
(simplify
 (minus (convert1? @0) (convert2? (mult:c (trunc_div @@0 @@1) @1)))
 (if (INTEGRAL_TYPE_P (type) || VECTOR_INTEGER_TYPE_P (type))
  (convert (trunc_mod @0 @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)))))
 /* Likewise for powi.  */
 (for pows (POWI)
  (simplify
   (pows (op @0) INTEGER_CST@1)
   (if (wi::bit_and (@1, 1) == 0)
    (pows @0 @1))))
 /* Strip negate and abs from both operands of hypot.  */
 (for hypots (HYPOT)
  (simplify
   (hypots (op @0) @1)
   (hypots @0 @1))
  (simplify
   (hypots @0 (op @1))
   (hypots @0 @1)))
 /* copysign(-x, y) and copysign(abs(x), y) -> copysign(x, y).  */
 (for copysigns (COPYSIGN)
  (simplify
   (copysigns (op @0) @1)
   (copysigns @0 @1))))

/* abs(x)*abs(x) -> x*x.  Should be valid for all types.  */
(simplify
 (mult (abs@1 @0) @1)
 (mult @0 @0))

/* cos(copysign(x, y)) -> cos(x).  Similarly for cosh.  */
(for coss (COS COSH)
     copysigns (COPYSIGN)
 (simplify
  (coss (copysigns @0 @1))
   (coss @0)))

/* pow(copysign(x, y), z) -> pow(x, z) if z is an even integer.  */
(for pows (POW)
     copysigns (COPYSIGN)
 (simplify
  (pows (copysigns @0 @2) REAL_CST@1)
  (with { HOST_WIDE_INT n; }
   (if (real_isinteger (&TREE_REAL_CST (@1), &n) && (n & 1) == 0)
    (pows @0 @1)))))
/* Likewise for powi.  */
(for pows (POWI)
     copysigns (COPYSIGN)
 (simplify
  (pows (copysigns @0 @2) INTEGER_CST@1)
  (if (wi::bit_and (@1, 1) == 0)
   (pows @0 @1))))

(for hypots (HYPOT)
     copysigns (COPYSIGN)
 /* hypot(copysign(x, y), z) -> hypot(x, z).  */
 (simplify
  (hypots (copysigns @0 @1) @2)
  (hypots @0 @2))
 /* hypot(x, copysign(y, z)) -> hypot(x, y).  */
 (simplify
  (hypots @0 (copysigns @1 @2))
  (hypots @0 @1)))

/* copysign(x, CST) -> [-]abs (x).  */
(for copysigns (COPYSIGN)
 (simplify
  (copysigns @0 REAL_CST@1)
  (if (REAL_VALUE_NEGATIVE (TREE_REAL_CST (@1)))
   (negate (abs @0))
   (abs @0))))

/* copysign(copysign(x, y), z) -> copysign(x, z).  */
(for copysigns (COPYSIGN)
 (simplify
  (copysigns (copysigns @0 @1) @2)
  (copysigns @0 @2)))

/* copysign(x,y)*copysign(x,y) -> x*x.  */
(for copysigns (COPYSIGN)
 (simplify
  (mult (copysigns@2 @0 @1) @2)
  (mult @0 @0)))

/* ccos(-x) -> ccos(x).  Similarly for ccosh.  */
(for ccoss (CCOS CCOSH)
 (simplify
  (ccoss (negate @0))
   (ccoss @0)))

/* cabs(-x) and cos(conj(x)) -> cabs(x).  */
(for ops (conj negate)
 (for cabss (CABS)
  (simplify
   (cabss (ops @0))
   (cabss @0))))

/* Fold (a * (1 << b)) into (a << b)  */
(simplify
 (mult:c @0 (convert? (lshift integer_onep@1 @2)))
  (if (! FLOAT_TYPE_P (type)
       && tree_nop_conversion_p (type, TREE_TYPE (@1)))
   (lshift @0 @2)))

/* Fold (C1/X)*C2 into (C1*C2)/X.  */
(simplify
 (mult (rdiv@3 REAL_CST@0 @1) REAL_CST@2)
  (if (flag_associative_math
       && single_use (@3))
   (with
    { tree tem = const_binop (MULT_EXPR, type, @0, @2); }
    (if (tem)
     (rdiv { tem; } @1)))))

/* Convert C1/(X*C2) into (C1/C2)/X  */
(simplify
 (rdiv REAL_CST@0 (mult @1 REAL_CST@2))
  (if (flag_reciprocal_math)
   (with
    { tree tem = const_binop (RDIV_EXPR, type, @0, @2); }
    (if (tem)
     (rdiv { tem; } @1)))))

/* Simplify ~X & X as zero.  */
(simplify
 (bit_and:c (convert? @0) (convert? (bit_not @0)))
  { build_zero_cst (type); })

/* PR71636: Transform x & ((1U << b) - 1) -> x & ~(~0U << b);  */
(simplify
  (bit_and:c @0 (plus:s (lshift:s integer_onep @1) integer_minus_onep))
  (if (TYPE_UNSIGNED (type))
    (bit_and @0 (bit_not (lshift { build_all_ones_cst (type); } @1)))))

/* PR35691: Transform
   (x == 0 & y == 0) -> (x | typeof(x)(y)) == 0.
   (x != 0 | y != 0) -> (x | typeof(x)(y)) != 0.  */
(for bitop (bit_and bit_ior)
     cmp (eq ne)
 (simplify
  (bitop (cmp @0 integer_zerop@2) (cmp @1 integer_zerop))
   (if (INTEGRAL_TYPE_P (TREE_TYPE (@0))
       && INTEGRAL_TYPE_P (TREE_TYPE (@1))
       && TYPE_PRECISION (TREE_TYPE (@0)) == TYPE_PRECISION (TREE_TYPE (@1)))
    (cmp (bit_ior @0 (convert @1)) @2))))

/* Fold (A & ~B) - (A & B) into (A ^ B) - B.  */
(simplify
 (minus (bit_and:cs @0 (bit_not @1)) (bit_and:cs @0 @1))
  (minus (bit_xor @0 @1) @1))
(simplify
 (minus (bit_and:s @0 INTEGER_CST@2) (bit_and:s @0 INTEGER_CST@1))
 (if (wi::bit_not (@2) == @1)
  (minus (bit_xor @0 @1) @1)))

/* Fold (A & B) - (A & ~B) into B - (A ^ B).  */
(simplify
 (minus (bit_and:cs @0 @1) (bit_and:cs @0 (bit_not @1)))
  (minus @1 (bit_xor @0 @1)))

/* Simplify (X & ~Y) | (~X & Y) -> X ^ Y.  */
(simplify
 (bit_ior (bit_and:c @0 (bit_not @1)) (bit_and:c (bit_not @0) @1))
  (bit_xor @0 @1))
(simplify
 (bit_ior:c (bit_and @0 INTEGER_CST@2) (bit_and (bit_not @0) INTEGER_CST@1))
 (if (wi::bit_not (@2) == @1)
  (bit_xor @0 @1)))

/* PR53979: Transform ((a ^ b) | a) -> (a | b) */
(simplify
  (bit_ior:c (bit_xor:c @0 @1) @0)
  (bit_ior @0 @1))

/* Simplify (~X & Y) to X ^ Y if we know that (X & ~Y) is 0.  */
#if GIMPLE
(simplify
 (bit_and (bit_not SSA_NAME@0) INTEGER_CST@1)
 (if (INTEGRAL_TYPE_P (TREE_TYPE (@0))
      && (get_nonzero_bits (@0) & wi::bit_not (@1)) == 0)
  (bit_xor @0 @1)))
#endif

/* 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 -> x  */
(simplify
 (bit_ior @0 integer_zerop)
 @0)

/* 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 & C -> x if we know that x & ~C == 0.  */
#if GIMPLE
(simplify
 (bit_and SSA_NAME@0 INTEGER_CST@1)
 (if (INTEGRAL_TYPE_P (TREE_TYPE (@0))
      && (get_nonzero_bits (@0) & wi::bit_not (@1)) == 0)
  @0))
#endif

/* 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 (element_precision (type) <= element_precision (TREE_TYPE (@0))
       && element_precision (type) <= element_precision (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 (convert1? (bit_ior:c @@0 @1)) (convert2? @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 (element_precision (type) <= element_precision (TREE_TYPE (@0))
      && element_precision (type) <= element_precision (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 and (X ^ Y) & Y as ~X & Y.  */
(for opo (bit_and bit_xor)
     opi (bit_xor bit_and)
 (simplify
  (opo:c (opi: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 bit_xor)
     rop (bit_ior bit_and bit_and)
 (simplify
  (op (convert? (rop:c @@0 @1)) (convert? (rop:c @0 @2)))
  (if (tree_nop_conversion_p (type, TREE_TYPE (@1))
       && tree_nop_conversion_p (type, TREE_TYPE (@2)))
   (rop (convert @0) (op (convert @1) (convert @2))))))

/* Some simple reassociation for bit operations, also handled in reassoc.  */
/* (X & Y) & Y -> X & Y
   (X | Y) | Y -> X | Y  */
(for op (bit_and bit_ior)
 (simplify
  (op:c (convert1?@2 (op:c @0 @@1)) (convert2? @1))
  @2))
/* (X ^ Y) ^ Y -> X  */
(simplify
 (bit_xor:c (convert1? (bit_xor:c @0 @@1)) (convert2? @1))
 (convert @0))
/* (X & Y) & (X & Z) -> (X & Y) & Z
   (X | Y) | (X | Z) -> (X | Y) | Z  */
(for op (bit_and bit_ior)
 (simplify
  (op:c (convert1?@3 (op:c@4 @0 @1)) (convert2?@5 (op:c@6 @0 @2)))
  (if (tree_nop_conversion_p (type, TREE_TYPE (@1))
       && tree_nop_conversion_p (type, TREE_TYPE (@2)))
   (if (single_use (@5) && single_use (@6))
    (op @3 (convert @2))
    (if (single_use (@3) && single_use (@4))
     (op (convert @1) @5))))))
/* (X ^ Y) ^ (X ^ Z) -> Y ^ Z  */
(simplify
 (bit_xor (convert1? (bit_xor:c @0 @1)) (convert2? (bit_xor:c @0 @2)))
 (if (tree_nop_conversion_p (type, TREE_TYPE (@1))
      && tree_nop_conversion_p (type, TREE_TYPE (@2)))
  (bit_xor (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) -> A * B  */
(simplify
 (mult:c (convert1? (negate @0)) (convert2? negate_expr_p@1))
  (if (tree_nop_conversion_p (type, TREE_TYPE (@0))
       && tree_nop_conversion_p (type, TREE_TYPE (@1)))
   (mult (convert @0) (convert (negate @1)))))
 
/* -(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)))

/* (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)
 (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); }))

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

/* Convert ~ (-A) to A - 1.  */
(simplify
 (bit_not (convert? (negate @0)))
 (if (element_precision (type) <= element_precision (TREE_TYPE (@0))
      || !TYPE_UNSIGNED (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 (element_precision (type) <= element_precision (TREE_TYPE (@0))
      || !TYPE_UNSIGNED (TREE_TYPE (@0)))
  (convert (negate @0))))
(simplify
 (bit_not (convert? (plus @0 integer_all_onesp)))
 (if (element_precision (type) <= element_precision (TREE_TYPE (@0))
      || !TYPE_UNSIGNED (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 (convert1? @0) (convert2?: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))))

/* For integral types with undefined overflow and C != 0 fold
   x * C EQ/NE y * C into x EQ/NE y.  */
(for cmp (eq ne)
 (simplify
  (cmp (mult:c @0 @1) (mult:c @2 @1))
  (if (INTEGRAL_TYPE_P (TREE_TYPE (@1))
       && TYPE_OVERFLOW_UNDEFINED (TREE_TYPE (@0))
       && tree_expr_nonzero_p (@1))
   (cmp @0 @2))))

/* For integral types with undefined overflow and C != 0 fold
   x * C RELOP y * C into:

   x RELOP y for nonnegative C
   y RELOP x for negative C  */
(for cmp (lt gt le ge)
 (simplify
  (cmp (mult:c @0 @1) (mult:c @2 @1))
  (if (INTEGRAL_TYPE_P (TREE_TYPE (@1))
       && TYPE_OVERFLOW_UNDEFINED (TREE_TYPE (@0)))
   (if (tree_expr_nonnegative_p (@1) && tree_expr_nonzero_p (@1))
    (cmp @0 @2)
   (if (TREE_CODE (@1) == INTEGER_CST
        && wi::neg_p (@1, TYPE_SIGN (TREE_TYPE (@1))))
    (cmp @2 @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 +- CST1) +- CST2 -> A + CST3  */
  (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 = const_binop (outer_op == inner_op
                                     ? PLUS_EXPR : MINUS_EXPR, type, @1, @2); }
      (if (cst && !TREE_OVERFLOW (cst))
       (inner_op @0 { cst; } ))))))

  /* (CST1 - A) +- CST2 -> CST3 - A  */
  (for outer_op (plus minus)
   (simplify
    (outer_op (minus CONSTANT_CLASS_P@1 @0) CONSTANT_CLASS_P@2)
    (with { tree cst = const_binop (outer_op, type, @1, @2); }
     (if (cst && !TREE_OVERFLOW (cst))
      (minus { cst; } @0)))))

  /* CST1 - (CST2 - A) -> CST3 + A  */
  (simplify
   (minus CONSTANT_CLASS_P@1 (minus CONSTANT_CLASS_P@2 @0))
   (with { tree cst = const_binop (MINUS_EXPR, type, @1, @2); }
    (if (cst && !TREE_OVERFLOW (cst))
     (plus { 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))))

  /* (T)P - (T)(P + A) -> -(T) A */
  (for add (plus pointer_plus)
   (simplify
    (minus (convert @0)
     (convert (add @@0 @1)))
    (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))
     (negate (convert @1)))))

  /* (T)(P + A) - (T)(P + B) -> (T)A - (T)B */
  (for add (plus pointer_plus)
   (simplify
    (minus (convert (add @@0 @1))
     (convert (add @0 @2)))
    (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
             && TREE_CODE (@2) == INTEGER_CST
             && tree_int_cst_sign_bit (@2) == 0))
     (minus (convert @1) (convert @2)))))))


/* Simplifications of MIN_EXPR, MAX_EXPR, fmin() and fmax().  */

(for minmax (min max FMIN FMAX)
 (simplify
  (minmax @0 @0)
  @0))
/* min(max(x,y),y) -> y.  */
(simplify
 (min:c (max:c @0 @1) @1)
 @1)
/* max(min(x,y),y) -> y.  */
(simplify
 (max:c (min:c @0 @1) @1)
 @1)
/* max(a,-a) -> abs(a).  */
(simplify
 (max:c @0 (negate @0))
 (if (TREE_CODE (type) != COMPLEX_TYPE
      && (! ANY_INTEGRAL_TYPE_P (type)
          || TYPE_OVERFLOW_UNDEFINED (type)))
  (abs @0)))
/* min(a,-a) -> -abs(a).  */
(simplify
 (min:c @0 (negate @0))
 (if (TREE_CODE (type) != COMPLEX_TYPE
      && (! ANY_INTEGRAL_TYPE_P (type)
          || TYPE_OVERFLOW_UNDEFINED (type)))
  (negate (abs @0))))
(simplify
 (min @0 @1)
 (switch
  (if (INTEGRAL_TYPE_P (type)
       && TYPE_MIN_VALUE (type)
       && operand_equal_p (@1, TYPE_MIN_VALUE (type), OEP_ONLY_CONST))
   @1)
  (if (INTEGRAL_TYPE_P (type)
       && TYPE_MAX_VALUE (type)
       && operand_equal_p (@1, TYPE_MAX_VALUE (type), OEP_ONLY_CONST))
   @0)))
(simplify
 (max @0 @1)
 (switch
  (if (INTEGRAL_TYPE_P (type)
       && TYPE_MAX_VALUE (type)
       && operand_equal_p (@1, TYPE_MAX_VALUE (type), OEP_ONLY_CONST))
   @1)
  (if (INTEGRAL_TYPE_P (type)
       && TYPE_MIN_VALUE (type)
       && operand_equal_p (@1, TYPE_MIN_VALUE (type), OEP_ONLY_CONST))
   @0)))

/* max (a, a + CST) -> a + CST where CST is positive.  */
/* max (a, a + CST) -> a where CST is negative.  */
(simplify
 (max:c @0 (plus@2 @0 INTEGER_CST@1))
  (if (TYPE_OVERFLOW_UNDEFINED (TREE_TYPE (@0)))
   (if (tree_int_cst_sgn (@1) > 0)
    @2
    @0)))

/* min (a, a + CST) -> a where CST is positive.  */
/* min (a, a + CST) -> a + CST where CST is negative. */
(simplify
 (min:c @0 (plus@2 @0 INTEGER_CST@1))
  (if (TYPE_OVERFLOW_UNDEFINED (TREE_TYPE (@0)))
   (if (tree_int_cst_sgn (@1) > 0)
    @0
    @2)))

/* (convert (minmax ((convert (x) c)))) -> minmax (x c) if x is promoted
   and the outer convert demotes the expression back to x's type.  */
(for minmax (min max)
 (simplify
  (convert (minmax@0 (convert @1) INTEGER_CST@2))
  (if (INTEGRAL_TYPE_P (type)
       && types_match (@1, type) && int_fits_type_p (@2, type)
       && TYPE_SIGN (TREE_TYPE (@0)) == TYPE_SIGN (type)
       && TYPE_PRECISION (TREE_TYPE (@0)) > TYPE_PRECISION (type))
   (minmax @1 (convert @2)))))

(for minmax (FMIN FMAX)
 /* If either argument is NaN, return the other one.  Avoid the
    transformation if we get (and honor) a signalling NaN.  */
 (simplify
  (minmax:c @0 REAL_CST@1)
  (if (real_isnan (TREE_REAL_CST_PTR (@1))
       && (!HONOR_SNANS (@1) || !TREE_REAL_CST (@1).signalling))
   @0)))
/* Convert fmin/fmax to MIN_EXPR/MAX_EXPR.  C99 requires these
   functions to return the numeric arg if the other one is NaN.
   MIN and MAX don't honor that, so only transform if -ffinite-math-only
   is set.  C99 doesn't require -0.0 to be handled, so we don't have to
   worry about it either.  */
(if (flag_finite_math_only)
 (simplify
  (FMIN @0 @1)
  (min @0 @1))
 (simplify
  (FMAX @0 @1)
  (max @0 @1)))
/* min (-A, -B) -> -max (A, B)  */
(for minmax (min max FMIN FMAX)
     maxmin (max min FMAX FMIN)
 (simplify
  (minmax (negate:s@2 @0) (negate:s@3 @1))
  (if (FLOAT_TYPE_P (TREE_TYPE (@0))
       || (ANY_INTEGRAL_TYPE_P (TREE_TYPE (@0))
           && TYPE_OVERFLOW_UNDEFINED (TREE_TYPE (@0))))
   (negate (maxmin @0 @1)))))
/* MIN (~X, ~Y) -> ~MAX (X, Y)
   MAX (~X, ~Y) -> ~MIN (X, Y)  */
(for minmax (min max)
 maxmin (max min)
 (simplify
  (minmax (bit_not:s@2 @0) (bit_not:s@3 @1))
  (bit_not (maxmin @0 @1))))

/* MIN (X, Y) == X -> X <= Y  */
(for minmax (min min max max)
     cmp    (eq  ne  eq  ne )
     out    (le  gt  ge  lt )
 (simplify
  (cmp:c (minmax:c @0 @1) @0)
  (if (ANY_INTEGRAL_TYPE_P (TREE_TYPE (@0)))
   (out @0 @1))))
/* MIN (X, 5) == 0 -> X == 0
   MIN (X, 5) == 7 -> false  */
(for cmp (eq ne)
 (simplify
  (cmp (min @0 INTEGER_CST@1) INTEGER_CST@2)
  (if (wi::lt_p (@1, @2, TYPE_SIGN (TREE_TYPE (@0))))
   { constant_boolean_node (cmp == NE_EXPR, type); }
   (if (wi::gt_p (@1, @2, TYPE_SIGN (TREE_TYPE (@0))))
    (cmp @0 @2)))))
(for cmp (eq ne)
 (simplify
  (cmp (max @0 INTEGER_CST@1) INTEGER_CST@2)
  (if (wi::gt_p (@1, @2, TYPE_SIGN (TREE_TYPE (@0))))
   { constant_boolean_node (cmp == NE_EXPR, type); }
   (if (wi::lt_p (@1, @2, TYPE_SIGN (TREE_TYPE (@0))))
    (cmp @0 @2)))))
/* MIN (X, C1) < C2 -> X < C2 || C1 < C2  */
(for minmax (min     min     max     max     min     min     max     max    )
     cmp    (lt      le      gt      ge      gt      ge      lt      le     )
     comb   (bit_ior bit_ior bit_ior bit_ior bit_and bit_and bit_and bit_and)
 (simplify
  (cmp (minmax @0 INTEGER_CST@1) INTEGER_CST@2)
  (comb (cmp @0 @2) (cmp @1 @2))))

/* 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; }))))))

/* Simplify X << Y where Y's low width bits are 0 to X, as only valid
   Y is 0.  Similarly for X >> Y.  */
#if GIMPLE
(for shift (lshift rshift)
 (simplify
  (shift @0 SSA_NAME@1)
   (if (INTEGRAL_TYPE_P (TREE_TYPE (@1)))
    (with {
      int width = ceil_log2 (element_precision (TREE_TYPE (@0)));
      int prec = TYPE_PRECISION (TREE_TYPE (@1));
     }
     (if ((get_nonzero_bits (@1) & wi::mask (width, false, prec)) == 0)
      @0)))))
#endif

/* Rewrite an LROTATE_EXPR by a constant into an
   RROTATE_EXPR by a new constant.  */
(simplify
 (lrotate @0 INTEGER_CST@1)
 (rrotate @0 { const_binop (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 = ((HOST_WIDE_INT_1U << 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 = HOST_WIDE_INT_M1U;
           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 == (HOST_WIDE_INT_1U << prec) - 1)
               break;
         }
         (if (prec < HOST_BITS_PER_WIDE_INT
              || newmask == HOST_WIDE_INT_M1U)
          (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; }))))))

/* ~(~X >> Y) -> X >> Y (for arithmetic shift).  */
(simplify
 (bit_not (convert1?:s (rshift:s (convert2?@0 (bit_not @1)) @2)))
  (if (!TYPE_UNSIGNED (TREE_TYPE (@0))
       && (element_precision (TREE_TYPE (@0))
           <= element_precision (TREE_TYPE (@1))
           || !TYPE_UNSIGNED (TREE_TYPE (@1))))
   (with
    { tree shift_type = TREE_TYPE (@0); }
     (convert (rshift (convert:shift_type @1) @2)))))

/* ~(~X >>r Y) -> X >>r Y
   ~(~X <<r Y) -> X <<r Y */
(for rotate (lrotate rrotate)
 (simplify
  (bit_not (convert1?:s (rotate:s (convert2?@0 (bit_not @1)) @2)))
   (if ((element_precision (TREE_TYPE (@0))
         <= element_precision (TREE_TYPE (@1))
         || !TYPE_UNSIGNED (TREE_TYPE (@1)))
        && (element_precision (type) <= element_precision (TREE_TYPE (@0))
            || !TYPE_UNSIGNED (TREE_TYPE (@0))))
    (with
     { tree rotate_type = TREE_TYPE (@0); }
      (convert (rotate (convert:rotate_type @1) @2))))))

/* 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.  */
    (if (((inter_int && inside_int) || (inter_float && inside_float))
         && (final_int || final_float)
         && inter_prec >= inside_prec
         && (inter_float || inter_unsignedp == inside_unsignedp))
     (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))
     (ocvt @0))

    /* A truncation to an unsigned type (a zero-extension) should be
       canonicalized as bitwise and of a mask.  */
    (if (GIMPLE /* PR70366: doing this in GENERIC breaks -Wconversion.  */
         && 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 (convert1? (exact_div @0 @@1)) (convert2? @1))
  (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 = const_unop (NEGATE_EXPR, type, @1); }
   (if (!TREE_OVERFLOW (tem) || !flag_trapping_math)
    (minus @0 { tem; })))))

/* Convert x+x into x*2.  */
(simplify
 (plus @0 @0)
 (if (SCALAR_FLOAT_TYPE_P (type))
  (mult @0 { build_real (type, dconst2); })
  (if (INTEGRAL_TYPE_P (type))
   (mult @0 { build_int_cst (type, 2); }))))

(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))

/* True if we can easily extract the real and imaginary parts of a complex
   number.  */
(match compositional_complex
 (convert? (complex @0 @1)))

/* 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)))

/* Simplification moved from fold_cond_expr_with_comparison.  It may also
   be extended.  */
/* This pattern implements two kinds simplification:

   Case 1)
   (cond (cmp (convert1? x) c1) (convert2? x) c2) -> (minmax (x c)) if:
     1) Conversions are type widening from smaller type.
     2) Const c1 equals to c2 after canonicalizing comparison.
     3) Comparison has tree code LT, LE, GT or GE.
   This specific pattern is needed when (cmp (convert x) c) may not
   be simplified by comparison patterns because of multiple uses of
   x.  It also makes sense here because simplifying across multiple
   referred var is always benefitial for complicated cases.

   Case 2)
   (cond (eq (convert1? x) c1) (convert2? x) c2) -> (cond (eq x c1) c1 c2).  */
(for cmp (lt le gt ge eq)
 (simplify
  (cond (cmp (convert1? @1) INTEGER_CST@3) (convert2? @1) INTEGER_CST@2)
  (with
   {
     tree from_type = TREE_TYPE (@1);
     tree c1_type = TREE_TYPE (@3), c2_type = TREE_TYPE (@2);
     enum tree_code code = ERROR_MARK;

     if (INTEGRAL_TYPE_P (from_type)
         && int_fits_type_p (@2, from_type)
         && (types_match (c1_type, from_type)
             || (TYPE_PRECISION (c1_type) > TYPE_PRECISION (from_type)
                 && (TYPE_UNSIGNED (from_type)
                     || TYPE_SIGN (c1_type) == TYPE_SIGN (from_type))))
         && (types_match (c2_type, from_type)
             || (TYPE_PRECISION (c2_type) > TYPE_PRECISION (from_type)
                 && (TYPE_UNSIGNED (from_type)
                     || TYPE_SIGN (c2_type) == TYPE_SIGN (from_type)))))
       {
         if (cmp != EQ_EXPR)
           {
             if (wi::to_widest (@3) == (wi::to_widest (@2) - 1))
               {
                 /* X <= Y - 1 equals to X < Y.  */
                 if (cmp == LE_EXPR)
                   code = LT_EXPR;
                 /* X > Y - 1 equals to X >= Y.  */
                 if (cmp == GT_EXPR)
                   code = GE_EXPR;
               }
             if (wi::to_widest (@3) == (wi::to_widest (@2) + 1))
               {
                 /* X < Y + 1 equals to X <= Y.  */
                 if (cmp == LT_EXPR)
                   code = LE_EXPR;
                 /* X >= Y + 1 equals to X > Y.  */
                 if (cmp == GE_EXPR)
                   code = GT_EXPR;
               }
             if (code != ERROR_MARK
                 || wi::to_widest (@2) == wi::to_widest (@3))
               {
                 if (cmp == LT_EXPR || cmp == LE_EXPR)
                   code = MIN_EXPR;
                 if (cmp == GT_EXPR || cmp == GE_EXPR)
                   code = MAX_EXPR;
               }
           }
         /* Can do A == C1 ? A : C2  ->  A == C1 ? C1 : C2?  */
         else if (int_fits_type_p (@3, from_type))
           code = EQ_EXPR;
       }
   }
   (if (code == MAX_EXPR)
    (convert (max @1 (convert @2)))
    (if (code == MIN_EXPR)
     (convert (min @1 (convert @2)))
     (if (code == EQ_EXPR)
      (convert (cond (eq @1 (convert @3))
                     (convert:from_type @3) (convert:from_type @2)))))))))

/* (cond (cmp (convert? x) c1) (op x c2) c3) -> (op (minmax x c1) c2) if:

     1) OP is PLUS or MINUS.
     2) CMP is LT, LE, GT or GE.
     3) C3 == (C1 op C2), and computation doesn't have undefined behavior.

   This pattern also handles special cases like:

     A) Operand x is a unsigned to signed type conversion and c1 is
        integer zero.  In this case,
          (signed type)x  < 0  <=>  x  > MAX_VAL(signed type)
          (signed type)x >= 0  <=>  x <= MAX_VAL(signed type)
     B) Const c1 may not equal to (C3 op' C2).  In this case we also
        check equality for (c1+1) and (c1-1) by adjusting comparison
        code.

   TODO: Though signed type is handled by this pattern, it cannot be
   simplified at the moment because C standard requires additional
   type promotion.  In order to match&simplify it here, the IR needs
   to be cleaned up by other optimizers, i.e, VRP.  */
(for op (plus minus)
 (for cmp (lt le gt ge)
  (simplify
   (cond (cmp (convert? @X) INTEGER_CST@1) (op @X INTEGER_CST@2) INTEGER_CST@3)
   (with { tree from_type = TREE_TYPE (@X), to_type = TREE_TYPE (@1); }
    (if (types_match (from_type, to_type)
         /* Check if it is special case A).  */
         || (TYPE_UNSIGNED (from_type)
             && !TYPE_UNSIGNED (to_type)
             && TYPE_PRECISION (from_type) == TYPE_PRECISION (to_type)
             && integer_zerop (@1)
             && (cmp == LT_EXPR || cmp == GE_EXPR)))
     (with
      {
        bool overflow = false;
        enum tree_code code, cmp_code = cmp;
        wide_int real_c1, c1 = @1, c2 = @2, c3 = @3;
        signop sgn = TYPE_SIGN (from_type);

        /* Handle special case A), given x of unsigned type:
            ((signed type)x  < 0) <=> (x  > MAX_VAL(signed type))
            ((signed type)x >= 0) <=> (x <= MAX_VAL(signed type))  */
        if (!types_match (from_type, to_type))
          {
            if (cmp_code == LT_EXPR)
              cmp_code = GT_EXPR;
            if (cmp_code == GE_EXPR)
              cmp_code = LE_EXPR;
            c1 = wi::max_value (to_type);
          }
        /* To simplify this pattern, we require c3 = (c1 op c2).  Here we
           compute (c3 op' c2) and check if it equals to c1 with op' being
           the inverted operator of op.  Make sure overflow doesn't happen
           if it is undefined.  */
        if (op == PLUS_EXPR)
          real_c1 = wi::sub (c3, c2, sgn, &overflow);
        else
          real_c1 = wi::add (c3, c2, sgn, &overflow);

        code = cmp_code;
        if (!overflow || !TYPE_OVERFLOW_UNDEFINED (from_type))
          {
            /* Check if c1 equals to real_c1.  Boundary condition is handled
               by adjusting comparison operation if necessary.  */
            if (!wi::cmp (wi::sub (real_c1, 1, sgn, &overflow), c1, sgn)
                && !overflow)
              {
                /* X <= Y - 1 equals to X < Y.  */
                if (cmp_code == LE_EXPR)
                  code = LT_EXPR;
                /* X > Y - 1 equals to X >= Y.  */
                if (cmp_code == GT_EXPR)
                  code = GE_EXPR;
              }
            if (!wi::cmp (wi::add (real_c1, 1, sgn, &overflow), c1, sgn)
                && !overflow)
              {
                /* X < Y + 1 equals to X <= Y.  */
                if (cmp_code == LT_EXPR)
                  code = LE_EXPR;
                /* X >= Y + 1 equals to X > Y.  */
                if (cmp_code == GE_EXPR)
                  code = GT_EXPR;
              }
            if (code != cmp_code || !wi::cmp (real_c1, c1, sgn))
              {
                if (cmp_code == LT_EXPR || cmp_code == LE_EXPR)
                  code = MIN_EXPR;
                if (cmp_code == GT_EXPR || cmp_code == GE_EXPR)
                  code = MAX_EXPR;
              }
          }
      }
      (if (code == MAX_EXPR)
       (op (max @X { wide_int_to_tree (from_type, real_c1); })
           { wide_int_to_tree (from_type, c2); })
       (if (code == MIN_EXPR)
        (op (min @X { wide_int_to_tree (from_type, real_c1); })
            { wide_int_to_tree (from_type, c2); })))))))))

(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 : (!A ? C : X) -> A ? B : C.  */
 /* ???  This matches embedded conditions open-coded because genmatch
    would generate matching code for conditions in separate stmts only.
    The following is still important to merge then and else arm cases
    from if-conversion.  */
 (simplify
  (cnd @0 @1 (cnd @2 @3 @4))
  (if (COMPARISON_CLASS_P (@0)
       && COMPARISON_CLASS_P (@2)
       && invert_tree_comparison
           (TREE_CODE (@0), HONOR_NANS (TREE_OPERAND (@0, 0))) == TREE_CODE (@2)
       && operand_equal_p (TREE_OPERAND (@0, 0), TREE_OPERAND (@2, 0), 0)
       && operand_equal_p (TREE_OPERAND (@0, 1), TREE_OPERAND (@2, 1), 0))
   (cnd @0 @1 @3)))
 (simplify
  (cnd @0 (cnd @1 @2 @3) @4)
  (if (COMPARISON_CLASS_P (@0)
       && COMPARISON_CLASS_P (@1)
       && invert_tree_comparison
           (TREE_CODE (@0), HONOR_NANS (TREE_OPERAND (@0, 0))) == TREE_CODE (@1)
       && operand_equal_p (TREE_OPERAND (@0, 0), TREE_OPERAND (@1, 0), 0)
       && operand_equal_p (TREE_OPERAND (@0, 1), TREE_OPERAND (@1, 1), 0))
   (cnd @0 @3 @4)))

 /* 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 ? -1 : 0), 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:s @0 integer_each_onep@1 integer_zerop@2)))
 (if (VECTOR_TYPE_P (type)
      && TYPE_VECTOR_SUBPARTS (type) == TYPE_VECTOR_SUBPARTS (TREE_TYPE (@1))
      && (TYPE_MODE (TREE_TYPE (type))
          == TYPE_MODE (TREE_TYPE (TREE_TYPE (@1)))))
  (minus @3 (view_convert (vec_cond @0 (negate @1) @2)))))

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


/* 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@3 @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))
        && single_use (@3))
    /* 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.  */
(for cmp (eq ge le)
 (simplify
  (cmp @0 @0)
  (if (! FLOAT_TYPE_P (TREE_TYPE (@0))
       || ! HONOR_NANS (@0))
   { constant_boolean_node (true, type); }
   (if (cmp != EQ_EXPR)
    (eq @0 @0)))))
(for cmp (ne gt lt)
 (simplify
  (cmp @0 @0)
  (if (cmp != NE_EXPR
       || ! FLOAT_TYPE_P (TREE_TYPE (@0))
       || ! HONOR_NANS (@0))
   { constant_boolean_node (false, type); })))
(for cmp (unle unge uneq)
 (simplify
  (cmp @0 @0)
  { constant_boolean_node (true, type); }))
(for cmp (unlt ungt)
 (simplify
  (cmp @0 @0)
  (unordered @0 @0)))
(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@2 @0) (bit_not@3 @1))
  (if (single_use (@2) && single_use (@3))
   (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@2 @0) CONSTANT_CLASS_P@1)
  (if (single_use (@2)
       && (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 (real_equal (TREE_REAL_CST_PTR (@1), &dconst0))
      (switch
       /* sqrt(x) < 0 is always false.  */
       (if (cmp == LT_EXPR)
        { constant_boolean_node (false, type); })
       /* sqrt(x) >= 0 is always true if we don't care about NaNs.  */
       (if (cmp == GE_EXPR && !HONOR_NANS (@0))
        { constant_boolean_node (true, type); })
       /* sqrt(x) <= 0 -> x == 0.  */
       (if (cmp == LE_EXPR)
        (eq @0 @1))
       /* Otherwise sqrt(x) cmp 0 -> x cmp 0.  Here cmp can be >=, >,
          == or !=.  In the last case:

            (sqrt(x) != 0) == (NaN != 0) == true == (x != 0)

          if x is negative or NaN.  Due to -funsafe-math-optimizations,
          the results for other x follow from natural arithmetic.  */
       (cmp @0 @1)))
     (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); }))))))))))))

/* Fold A /[ex] B CMP C to A CMP B * C.  */
(for cmp (eq ne)
 (simplify
  (cmp (exact_div @0 @1) INTEGER_CST@2)
  (if (!integer_zerop (@1))
   (if (wi::eq_p (@2, 0))
    (cmp @0 @2)
    (if (TREE_CODE (@1) == INTEGER_CST)
     (with
      {
        bool ovf;
        wide_int prod = wi::mul (@2, @1, TYPE_SIGN (TREE_TYPE (@1)), &ovf);
      }
      (if (ovf)
       { constant_boolean_node (cmp == NE_EXPR, type); }
       (cmp @0 { wide_int_to_tree (TREE_TYPE (@0), prod); }))))))))
(for cmp (lt le gt ge)
 (simplify
  (cmp (exact_div @0 INTEGER_CST@1) INTEGER_CST@2)
  (if (wi::gt_p (@1, 0, TYPE_SIGN (TREE_TYPE (@1))))
   (with
    {
      bool ovf;
      wide_int prod = wi::mul (@2, @1, TYPE_SIGN (TREE_TYPE (@1)), &ovf);
    }
    (if (ovf)
     { constant_boolean_node (wi::lt_p (@2, 0, TYPE_SIGN (TREE_TYPE (@2)))
                              != (cmp == LT_EXPR || cmp == LE_EXPR), type); }
     (cmp @0 { wide_int_to_tree (TREE_TYPE (@0), prod); }))))))

/* 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)

/* Simple range test simplifications.  */
/* A < B || A >= B -> true.  */
(for test1 (lt le le le ne ge)
     test2 (ge gt ge ne eq ne)
 (simplify
  (bit_ior:c (test1 @0 @1) (test2 @0 @1))
  (if (INTEGRAL_TYPE_P (TREE_TYPE (@0))
       || VECTOR_INTEGER_TYPE_P (TREE_TYPE (@0)))
   { constant_boolean_node (true, type); })))
/* A < B && A >= B -> false.  */
(for test1 (lt lt lt le ne eq)
     test2 (ge gt eq gt eq gt)
 (simplify
  (bit_and:c (test1 @0 @1) (test2 @0 @1))
  (if (INTEGRAL_TYPE_P (TREE_TYPE (@0))
       || VECTOR_INTEGER_TYPE_P (TREE_TYPE (@0)))
   { constant_boolean_node (false, type); })))

/* -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 = const_unop (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 (INTEGRAL_TYPE_P (TREE_TYPE (@0))
       /* 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))
           || (!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
                  && INTEGRAL_TYPE_P (TREE_TYPE (@00))
                  && int_fits_type_p (@10, TREE_TYPE (@00)))))
      (cmp @00 (convert @10))
      (if (TREE_CODE (@10) == INTEGER_CST
           && INTEGRAL_TYPE_P (TREE_TYPE (@00))
           && !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 ? D : 0 where C and D are powers of 2,
   convert this into a shift followed by ANDing with D.  */
(simplify
 (cond
  (ne (bit_and @0 integer_pow2p@1) integer_zerop)
  integer_pow2p@2 integer_zerop)
 (with {
    int shift = wi::exact_log2 (@2) - wi::exact_log2 (@1);
  }
  (if (shift > 0)
   (bit_and
    (lshift (convert @0) { build_int_cst (integer_type_node, shift); }) @2)
   (bit_and
    (convert (rshift @0 { build_int_cst (integer_type_node, -shift); })) @2))))

/* 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); })))))

/* If we have A < 0 ? C : 0 where C is a power of 2, convert
   this into a right shift or sign extension followed by ANDing with C.  */
(simplify
 (cond
  (lt @0 integer_zerop)
  integer_pow2p@1 integer_zerop)
 (if (!TYPE_UNSIGNED (TREE_TYPE (@0)))
  (with {
    int shift = element_precision (@0) - wi::exact_log2 (@1) - 1;
   }
   (if (shift >= 0)
    (bit_and
     (convert (rshift @0 { build_int_cst (integer_type_node, shift); }))
     @1)
    /* Otherwise ctype must be wider than TREE_TYPE (@0) and pure
       sign extension followed by AND with C will achieve the effect.  */
    (bit_and (convert @0) @1)))))

/* 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;
       /* Punt in GENERIC on variables with value expressions;
          the value expressions might point to fields/elements
          of other vars etc.  */
       if (GENERIC
           && ((VAR_P (base0) && DECL_HAS_VALUE_EXPR_P (base0))
               || (VAR_P (base1) && DECL_HAS_VALUE_EXPR_P (base1))))
         ;
       else 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); })))))))))

/* Simplify pointer equality compares using PTA.  */
(for neeq (ne eq)
 (simplify
  (neeq @0 @1)
  (if (POINTER_TYPE_P (TREE_TYPE (@0))
       && ptrs_compare_unequal (@0, @1))
   { neeq == EQ_EXPR ? boolean_false_node : boolean_true_node; })))

/* PR70920: Transform (intptr_t)x eq/ne CST to x eq/ne (typeof x) CST.
   and (typeof ptr_cst) x eq/ne ptr_cst to x eq/ne (typeof x) CST.
   Disable the transform if either operand is pointer to function.
   This broke pr22051-2.c for arm where function pointer
   canonicalizaion is not wanted.  */

(for cmp (ne eq)
 (simplify
  (cmp (convert @0) INTEGER_CST@1)
  (if ((POINTER_TYPE_P (TREE_TYPE (@0)) && !FUNC_OR_METHOD_TYPE_P (TREE_TYPE (TREE_TYPE (@0)))
        && INTEGRAL_TYPE_P (TREE_TYPE (@1)))
      || (INTEGRAL_TYPE_P (TREE_TYPE (@0)) && POINTER_TYPE_P (TREE_TYPE (@1))
          && !FUNC_OR_METHOD_TYPE_P (TREE_TYPE (TREE_TYPE (@1)))))
   (cmp @0 (convert @1)))))

/* 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.  */

/* When one argument is a constant, overflow detection can be simplified.
   Currently restricted to single use so as not to interfere too much with
   ADD_OVERFLOW detection in tree-ssa-math-opts.c.
   A + CST CMP A  ->  A CMP' CST' */
(for cmp (lt le ge gt)
     out (gt gt le le)
 (simplify
  (cmp:c (plus@2 @0 INTEGER_CST@1) @0)
  (if (TYPE_UNSIGNED (TREE_TYPE (@0))
       && TYPE_OVERFLOW_WRAPS (TREE_TYPE (@0))
       && wi::ne_p (@1, 0)
       && single_use (@2))
   (out @0 { wide_int_to_tree (TREE_TYPE (@0), wi::max_value
               (TYPE_PRECISION (TREE_TYPE (@0)), UNSIGNED) - @1); }))))

/* To detect overflow in unsigned A - B, A < B is simpler than A - B > A.
   However, the detection logic for SUB_OVERFLOW in tree-ssa-math-opts.c
   expects the long form, so we restrict the transformation for now.  */
(for cmp (gt le)
 (simplify
  (cmp:c (minus@2 @0 @1) @0)
  (if (single_use (@2)
       && ANY_INTEGRAL_TYPE_P (TREE_TYPE (@0))
       && TYPE_UNSIGNED (TREE_TYPE (@0))
       && TYPE_OVERFLOW_WRAPS (TREE_TYPE (@0)))
   (cmp @1 @0))))

/* Testing for overflow is unnecessary if we already know the result.  */
/* A - B > A  */
(for cmp (gt le)
     out (ne eq)
 (simplify
  (cmp:c (realpart (IFN_SUB_OVERFLOW@2 @0 @1)) @0)
  (if (TYPE_UNSIGNED (TREE_TYPE (@0))
       && types_match (TREE_TYPE (@0), TREE_TYPE (@1)))
   (out (imagpart @2) { build_zero_cst (TREE_TYPE (@0)); }))))
/* A + B < A  */
(for cmp (lt ge)
     out (ne eq)
 (simplify
  (cmp:c (realpart (IFN_ADD_OVERFLOW:c@2 @0 @1)) @0)
  (if (TYPE_UNSIGNED (TREE_TYPE (@0))
       && types_match (TREE_TYPE (@0), TREE_TYPE (@1)))
   (out (imagpart @2) { build_zero_cst (TREE_TYPE (@0)); }))))

/* For unsigned operands, -1 / B < A checks whether A * B would overflow.
   Simplify it to __builtin_mul_overflow (A, B, <unused>).  */
(for cmp (lt ge)
     out (ne eq)
 (simplify
  (cmp:c (trunc_div:s integer_all_onesp @1) @0)
  (if (TYPE_UNSIGNED (TREE_TYPE (@0)) && !VECTOR_TYPE_P (TREE_TYPE (@0)))
   (with { tree t = TREE_TYPE (@0), cpx = build_complex_type (t); }
    (out (imagpart (IFN_MUL_OVERFLOW:cpx @0 @1)) { build_zero_cst (t); })))))

/* 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)))))

 (for logs (LOG LOG2 LOG10 LOG10)
      exps (EXP EXP2 EXP10 POW10)
  /* logN(expN(x)) -> x.  */
  (simplify
   (logs (exps @0))
   @0)
  /* expN(logN(x)) -> x.  */
  (simplify
   (exps (logs @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))
   (if (SCALAR_FLOAT_TYPE_P (type))
    (with {
      tree x;
      switch (exps)
        {
        CASE_CFN_EXP:
          /* Prepare to do logN(exp(exponent)) -> exponent*logN(e).  */
          x = build_real_truncate (type, dconst_e ());
          break;
        CASE_CFN_EXP2:
          /* Prepare to do logN(exp2(exponent)) -> exponent*logN(2).  */
          x = build_real (type, dconst2);
          break;
        CASE_CFN_EXP10:
        CASE_CFN_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))
   (if (SCALAR_FLOAT_TYPE_P (type))
    (with {
      tree x;
      switch (exps)
        {
        CASE_CFN_SQRT:
          /* Prepare to do logN(sqrt(x)) -> 0.5*logN(x).  */
          x = build_real (type, dconsthalf);
          break;
        CASE_CFN_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)
      pows (POW)
      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 ()); })))
  /* pow(expN(x), y) -> expN(x*y).  */
  (simplify
   (pows (exps @0) @1)
   (exps (mult @0 @1))))

 /* tan(atan(x)) -> x.  */
 (for tans (TAN)
      atans (ATAN)
  (simplify
   (tans (atans @0))
   @0)))

/* cabs(x+0i) or cabs(0+xi) -> abs(x).  */
(simplify
 (CABS (complex:C @0 real_zerop@1))
 (abs @0))

/* trunc(trunc(x)) -> trunc(x), etc.  */
(for fns (TRUNC FLOOR CEIL ROUND NEARBYINT RINT)
 (simplify
  (fns (fns @0))
  (fns @0)))
/* f(x) -> x if x is integer valued and f does nothing for such values.  */
(for fns (TRUNC FLOOR CEIL ROUND NEARBYINT RINT)
 (simplify
  (fns integer_valued_real_p@0)
  @0))

/* hypot(x,0) and hypot(0,x) -> abs(x).  */
(simplify
 (HYPOT:c @0 real_zerop@1)
 (abs @0))

/* pow(1,x) -> 1.  */
(simplify
 (POW real_onep@0 @1)
 @0)

(simplify
 /* copysign(x,x) -> x.  */
 (COPYSIGN @0 @0)
 @0)

(simplify
 /* copysign(x,y) -> fabs(x) if y is nonnegative.  */
 (COPYSIGN @0 tree_expr_nonnegative_p@1)
 (abs @0))

(for scale (LDEXP SCALBN SCALBLN)
 /* ldexp(0, x) -> 0.  */
 (simplify
  (scale real_zerop@0 @1)
  @0)
 /* ldexp(x, 0) -> x.  */
 (simplify
  (scale @0 integer_zerop@1)
  @0)
 /* ldexp(x, y) -> x if x is +-Inf or NaN.  */
 (simplify
  (scale REAL_CST@0 @1)
  (if (!real_isfinite (TREE_REAL_CST_PTR (@0)))
   @0)))

/* 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:c @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 powi(x,y) * powi(z,y) -> powi(x*z,y). */
 (simplify
  (mult (POWI:s @0 @1) (POWI:s @2 @1))
   (POWI (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 ()); })))
  /* pow(sqrt(x),y) -> pow(x,y*0.5).  */
  (simplify
   (pows (sqrts @0) @1)
   (pows @0 (mult @1 { build_real (type, dconsthalf); })))
  /* pow(cbrt(x),y) -> pow(x,y/3) iff x is nonnegative.  */
  (simplify
   (pows (cbrts tree_expr_nonnegative_p@0) @1)
   (pows @0 (mult @1 { build_real_truncate (type, dconst_third ()); })))
  /* pow(pow(x,y),z) -> pow(x,y*z) iff x is nonnegative.  */
  (simplify
   (pows (pows tree_expr_nonnegative_p@0 @1) @2)
   (pows @0 (mult @1 @2))))

 /* cabs(x+xi) -> fabs(x)*sqrt(2).  */
 (simplify
  (CABS (complex @0 @0))
  (mult (abs @0) { build_real_truncate (type, dconst_sqrt2 ()); }))

 /* hypot(x,x) -> fabs(x)*sqrt(2).  */
 (simplify
  (HYPOT @0 @0)
  (mult (abs @0) { build_real_truncate (type, dconst_sqrt2 ()); }))

 /* cexp(x+yi) -> exp(x)*cexpi(y).  */
 (for cexps (CEXP)
      exps (EXP)
      cexpis (CEXPI)
  (simplify
   (cexps compositional_complex@0)
   (if (targetm.libc_has_function (function_c99_math_complex))
    (complex
     (mult (exps@1 (realpart @0)) (realpart (cexpis:type@2 (imagpart @0))))
     (mult @1 (imagpart @2)))))))

(if (canonicalize_math_p ())
 /* floor(x) -> trunc(x) if x is nonnegative.  */
 (for floors (FLOOR)
      truncs (TRUNC)
  (simplify
   (floors tree_expr_nonnegative_p@0)
   (truncs @0))))

(match double_value_p
 @0
 (if (TYPE_MAIN_VARIANT (TREE_TYPE (@0)) == double_type_node)))
(for froms (BUILT_IN_TRUNCL
            BUILT_IN_FLOORL
            BUILT_IN_CEILL
            BUILT_IN_ROUNDL
            BUILT_IN_NEARBYINTL
            BUILT_IN_RINTL)
     tos (BUILT_IN_TRUNC
          BUILT_IN_FLOOR
          BUILT_IN_CEIL
          BUILT_IN_ROUND
          BUILT_IN_NEARBYINT
          BUILT_IN_RINT)
 /* truncl(extend(x)) -> extend(trunc(x)), etc., if x is a double.  */
 (if (optimize && canonicalize_math_p ())
  (simplify
   (froms (convert double_value_p@0))
   (convert (tos @0)))))

(match float_value_p
 @0
 (if (TYPE_MAIN_VARIANT (TREE_TYPE (@0)) == float_type_node)))
(for froms (BUILT_IN_TRUNCL BUILT_IN_TRUNC
            BUILT_IN_FLOORL BUILT_IN_FLOOR
            BUILT_IN_CEILL BUILT_IN_CEIL
            BUILT_IN_ROUNDL BUILT_IN_ROUND
            BUILT_IN_NEARBYINTL BUILT_IN_NEARBYINT
            BUILT_IN_RINTL BUILT_IN_RINT)
     tos (BUILT_IN_TRUNCF BUILT_IN_TRUNCF
          BUILT_IN_FLOORF BUILT_IN_FLOORF
          BUILT_IN_CEILF BUILT_IN_CEILF
          BUILT_IN_ROUNDF BUILT_IN_ROUNDF
          BUILT_IN_NEARBYINTF BUILT_IN_NEARBYINTF
          BUILT_IN_RINTF BUILT_IN_RINTF)
 /* truncl(extend(x)) and trunc(extend(x)) -> extend(truncf(x)), etc.,
    if x is a float.  */
 (if (optimize && canonicalize_math_p ()
      && targetm.libc_has_function (function_c99_misc))
  (simplify
   (froms (convert float_value_p@0))
   (convert (tos @0)))))

(for froms (XFLOORL XCEILL XROUNDL XRINTL)
     tos (XFLOOR XCEIL XROUND XRINT)
 /* llfloorl(extend(x)) -> llfloor(x), etc., if x is a double.  */
 (if (optimize && canonicalize_math_p ())
  (simplify
   (froms (convert double_value_p@0))
   (tos @0))))

(for froms (XFLOORL XCEILL XROUNDL XRINTL
            XFLOOR XCEIL XROUND XRINT)
     tos (XFLOORF XCEILF XROUNDF XRINTF)
 /* llfloorl(extend(x)) and llfloor(extend(x)) -> llfloorf(x), etc.,
    if x is a float.  */
 (if (optimize && canonicalize_math_p ())
  (simplify
   (froms (convert float_value_p@0))
   (tos @0))))

(if (canonicalize_math_p ())
 /* xfloor(x) -> fix_trunc(x) if x is nonnegative.  */
 (for floors (IFLOOR LFLOOR LLFLOOR)
  (simplify
   (floors tree_expr_nonnegative_p@0)
   (fix_trunc @0))))

(if (canonicalize_math_p ())
 /* xfloor(x) -> fix_trunc(x), etc., if x is integer valued.  */
 (for fns (IFLOOR LFLOOR LLFLOOR
           ICEIL LCEIL LLCEIL
           IROUND LROUND LLROUND)
  (simplify
   (fns integer_valued_real_p@0)
   (fix_trunc @0)))
 (if (!flag_errno_math)
  /* xrint(x) -> fix_trunc(x), etc., if x is integer valued.  */
  (for rints (IRINT LRINT LLRINT)
   (simplify
    (rints integer_valued_real_p@0)
    (fix_trunc @0)))))

(if (canonicalize_math_p ())
 (for ifn (IFLOOR ICEIL IROUND IRINT)
      lfn (LFLOOR LCEIL LROUND LRINT)
      llfn (LLFLOOR LLCEIL LLROUND LLRINT)
  /* Canonicalize iround (x) to lround (x) on ILP32 targets where
     sizeof (int) == sizeof (long).  */
  (if (TYPE_PRECISION (integer_type_node)
       == TYPE_PRECISION (long_integer_type_node))
   (simplify
    (ifn @0)
    (lfn:long_integer_type_node @0)))
  /* Canonicalize llround (x) to lround (x) on LP64 targets where
     sizeof (long long) == sizeof (long).  */
  (if (TYPE_PRECISION (long_long_integer_type_node)
       == TYPE_PRECISION (long_integer_type_node))
   (simplify
    (llfn @0)
    (lfn:long_integer_type_node @0)))))

/* cproj(x) -> x if we're ignoring infinities.  */
(simplify
 (CPROJ @0)
 (if (!HONOR_INFINITIES (type))
   @0))

/* If the real part is inf and the imag part is known to be
   nonnegative, return (inf + 0i).  */
(simplify
 (CPROJ (complex REAL_CST@0 tree_expr_nonnegative_p@1))
 (if (real_isinf (TREE_REAL_CST_PTR (@0)))
  { build_complex_inf (type, false); }))

/* If the imag part is inf, return (inf+I*copysign(0,imag)).  */
(simplify
 (CPROJ (complex @0 REAL_CST@1))
 (if (real_isinf (TREE_REAL_CST_PTR (@1)))
  { build_complex_inf (type, TREE_REAL_CST_PTR (@1)->sign); }))

(for pows (POW)
     sqrts (SQRT)
     cbrts (CBRT)
 (simplify
  (pows @0 REAL_CST@1)
  (with {
    const REAL_VALUE_TYPE *value = TREE_REAL_CST_PTR (@1);
    REAL_VALUE_TYPE tmp;
   }
   (switch
    /* pow(x,0) -> 1.  */
    (if (real_equal (value, &dconst0))
     { build_real (type, dconst1); })
    /* pow(x,1) -> x.  */
    (if (real_equal (value, &dconst1))
     @0)
    /* pow(x,-1) -> 1/x.  */
    (if (real_equal (value, &dconstm1))
     (rdiv { build_real (type, dconst1); } @0))
    /* pow(x,0.5) -> sqrt(x).  */
    (if (flag_unsafe_math_optimizations
         && canonicalize_math_p ()
         && real_equal (value, &dconsthalf))
     (sqrts @0))
    /* pow(x,1/3) -> cbrt(x).  */
    (if (flag_unsafe_math_optimizations
         && canonicalize_math_p ()
         && (tmp = real_value_truncate (TYPE_MODE (type), dconst_third ()),
             real_equal (value, &tmp)))
     (cbrts @0))))))

/* powi(1,x) -> 1.  */
(simplify
 (POWI real_onep@0 @1)
 @0)

(simplify
 (POWI @0 INTEGER_CST@1)
 (switch
  /* powi(x,0) -> 1.  */
  (if (wi::eq_p (@1, 0))
   { build_real (type, dconst1); })
  /* powi(x,1) -> x.  */
  (if (wi::eq_p (@1, 1))
   @0)
  /* powi(x,-1) -> 1/x.  */
  (if (wi::eq_p (@1, -1))
   (rdiv { build_real (type, dconst1); } @0))))

/* 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 behavior), 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, type)
         && (types_match (@0, @1)
             /* Or the second operand is const integer or converted const
                integer from valueize.  */
             || TREE_CODE (@1) == INTEGER_CST))
      (if (TYPE_OVERFLOW_WRAPS (TREE_TYPE (@0)))
        (op @0 (convert @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 behavior 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)))
       && (wi::bit_and (@4, wi::mask (TYPE_PRECISION (TREE_TYPE (@0)),
                        true, TYPE_PRECISION (type))) == 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))))))))

/* Transform (@0 < @1 and @0 < @2) to use min, 
   (@0 > @1 and @0 > @2) to use max */
(for op (lt le gt ge)
     ext (min min max max)
 (simplify
  (bit_and (op:cs @0 @1) (op:cs @0 @2))
  (if (INTEGRAL_TYPE_P (TREE_TYPE (@0))
       && TREE_CODE (@0) != INTEGER_CST)
   (op @0 (ext @1 @2)))))

(simplify
 /* signbit(x) -> 0 if x is nonnegative.  */
 (SIGNBIT tree_expr_nonnegative_p@0)
 { integer_zero_node; })

(simplify
 /* signbit(x) -> x<0 if x doesn't have signed zeros.  */
 (SIGNBIT @0)
 (if (!HONOR_SIGNED_ZEROS (@0))
  (convert (lt @0 { build_real (TREE_TYPE (@0), dconst0); }))))

/* Transform comparisons of the form X +- C1 CMP C2 to X CMP C2 -+ C1.  */
(for cmp (eq ne)
 (for op (plus minus)
      rop (minus plus)
  (simplify
   (cmp (op@3 @0 INTEGER_CST@1) INTEGER_CST@2)
   (if (!TREE_OVERFLOW (@1) && !TREE_OVERFLOW (@2)
        && !TYPE_OVERFLOW_SANITIZED (TREE_TYPE (@0))
        && !TYPE_OVERFLOW_TRAPS (TREE_TYPE (@0))
        && !TYPE_SATURATING (TREE_TYPE (@0)))
    (with { tree res = int_const_binop (rop, @2, @1); }
     (if (TREE_OVERFLOW (res)
          && TYPE_OVERFLOW_UNDEFINED (TREE_TYPE (@0)))
      { constant_boolean_node (cmp == NE_EXPR, type); }
      (if (single_use (@3))
       (cmp @0 { res; }))))))))
(for cmp (lt le gt ge)
 (for op (plus minus)
      rop (minus plus)
  (simplify
   (cmp (op@3 @0 INTEGER_CST@1) INTEGER_CST@2)
   (if (!TREE_OVERFLOW (@1) && !TREE_OVERFLOW (@2)
        && TYPE_OVERFLOW_UNDEFINED (TREE_TYPE (@0)))
    (with { tree res = int_const_binop (rop, @2, @1); }
     (if (TREE_OVERFLOW (res))
      {
        fold_overflow_warning (("assuming signed overflow does not occur "
                                "when simplifying conditional to constant"),
                               WARN_STRICT_OVERFLOW_CONDITIONAL);
        bool less = cmp == LE_EXPR || cmp == LT_EXPR;
        /* wi::ges_p (@2, 0) should be sufficient for a signed type.  */
        bool ovf_high = wi::lt_p (@1, 0, TYPE_SIGN (TREE_TYPE (@1)))
                        != (op == MINUS_EXPR);
        constant_boolean_node (less == ovf_high, type);
      }
      (if (single_use (@3))
       (with
        {
          fold_overflow_warning (("assuming signed overflow does not occur "
                                  "when changing X +- C1 cmp C2 to "
                                  "X cmp C2 -+ C1"),
                                 WARN_STRICT_OVERFLOW_COMPARISON);
        }
        (cmp @0 { res; })))))))))

/* Canonicalizations of BIT_FIELD_REFs.  */

(simplify
 (BIT_FIELD_REF @0 @1 @2)
 (switch
  (if (TREE_CODE (TREE_TYPE (@0)) == COMPLEX_TYPE
       && tree_int_cst_equal (@1, TYPE_SIZE (TREE_TYPE (TREE_TYPE (@0)))))
   (switch
    (if (integer_zerop (@2))
     (view_convert (realpart @0)))
    (if (tree_int_cst_equal (@2, TYPE_SIZE (TREE_TYPE (TREE_TYPE (@0)))))
     (view_convert (imagpart @0)))))
  (if (INTEGRAL_TYPE_P (TREE_TYPE (@0))
       && INTEGRAL_TYPE_P (type)
       /* On GIMPLE this should only apply to register arguments.  */
       && (! GIMPLE || is_gimple_reg (@0))
       /* A bit-field-ref that referenced the full argument can be stripped.  */
       && ((compare_tree_int (@1, TYPE_PRECISION (TREE_TYPE (@0))) == 0
            && integer_zerop (@2))
           /* Low-parts can be reduced to integral conversions.
              ???  The following doesn't work for PDP endian.  */
           || (BYTES_BIG_ENDIAN == WORDS_BIG_ENDIAN
               /* Don't even think about BITS_BIG_ENDIAN.  */
               && TYPE_PRECISION (TREE_TYPE (@0)) % BITS_PER_UNIT == 0
               && TYPE_PRECISION (type) % BITS_PER_UNIT == 0
               && compare_tree_int (@2, (BYTES_BIG_ENDIAN
                                         ? (TYPE_PRECISION (TREE_TYPE (@0))
                                            - TYPE_PRECISION (type))
                                         : 0)) == 0)))
   (convert @0))))

/* Simplify vector extracts.  */

(simplify
 (BIT_FIELD_REF CONSTRUCTOR@0 @1 @2)
 (if (VECTOR_TYPE_P (TREE_TYPE (@0))
      && (types_match (type, TREE_TYPE (TREE_TYPE (@0)))
          || (VECTOR_TYPE_P (type)
              && types_match (TREE_TYPE (type), TREE_TYPE (TREE_TYPE (@0))))))
  (with
   {
     tree ctor = (TREE_CODE (@0) == SSA_NAME
                  ? gimple_assign_rhs1 (SSA_NAME_DEF_STMT (@0)) : @0);
     tree eltype = TREE_TYPE (TREE_TYPE (ctor));
     unsigned HOST_WIDE_INT width = tree_to_uhwi (TYPE_SIZE (eltype));
     unsigned HOST_WIDE_INT n = tree_to_uhwi (@1);
     unsigned HOST_WIDE_INT idx = tree_to_uhwi (@2);
   }
   (if (n != 0
        && (idx % width) == 0
        && (n % width) == 0
        && ((idx + n) / width) <= TYPE_VECTOR_SUBPARTS (TREE_TYPE (ctor)))
    (with
     {
       idx = idx / width;
       n = n / width;
       /* Constructor elements can be subvectors.  */
       unsigned HOST_WIDE_INT k = 1;
       if (CONSTRUCTOR_NELTS (ctor) != 0)
         {
           tree cons_elem = TREE_TYPE (CONSTRUCTOR_ELT (ctor, 0)->value);
           if (TREE_CODE (cons_elem) == VECTOR_TYPE)
             k = TYPE_VECTOR_SUBPARTS (cons_elem);
         }
     }
     (switch
      /* We keep an exact subset of the constructor elements.  */
      (if ((idx % k) == 0 && (n % k) == 0)
       (if (CONSTRUCTOR_NELTS (ctor) == 0)
        { build_constructor (type, NULL); }
        (with
         {
           idx /= k;
           n /= k;
         }
         (if (n == 1)
          (if (idx < CONSTRUCTOR_NELTS (ctor))
           { CONSTRUCTOR_ELT (ctor, idx)->value; }
           { build_zero_cst (type); })
          {
            vec<constructor_elt, va_gc> *vals;
            vec_alloc (vals, n);
            for (unsigned i = 0;
                 i < n && idx + i < CONSTRUCTOR_NELTS (ctor); ++i)
              CONSTRUCTOR_APPEND_ELT (vals, NULL_TREE,
                                      CONSTRUCTOR_ELT (ctor, idx + i)->value);
            build_constructor (type, vals);
          }))))
      /* The bitfield references a single constructor element.  */
      (if (idx + n <= (idx / k + 1) * k)
       (switch
        (if (CONSTRUCTOR_NELTS (ctor) <= idx / k)
         { build_zero_cst (type); })
        (if (n == k)
         { CONSTRUCTOR_ELT (ctor, idx / k)->value; })
        (BIT_FIELD_REF { CONSTRUCTOR_ELT (ctor, idx / k)->value; }
                       @1 { bitsize_int ((idx % k) * width); })))))))))