/* Straight-line strength reduction.
   Copyright (C) 2012-2013 Free Software Foundation, Inc.
   Contributed by Bill Schmidt, IBM <wschmidt@linux.ibm.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/>.  */

/* There are many algorithms for performing strength reduction on
   loops.  This is not one of them.  IVOPTS handles strength reduction
   of induction variables just fine.  This pass is intended to pick
   up the crumbs it leaves behind, by considering opportunities for
   strength reduction along dominator paths.

   Strength reduction will be implemented in four stages, gradually
   adding more complex candidates:

   1) Explicit multiplies, known constant multipliers, no
      conditional increments. (complete)
   2) Explicit multiplies, unknown constant multipliers,
      no conditional increments. (complete)
   3) Implicit multiplies in addressing expressions. (complete)
   4) Explicit multiplies, conditional increments. (pending)

   It would also be possible to apply strength reduction to divisions
   and modulos, but such opportunities are relatively uncommon.

   Strength reduction is also currently restricted to integer operations.
   If desired, it could be extended to floating-point operations under
   control of something like -funsafe-math-optimizations.  */

#include "config.h"
#include "system.h"
#include "coretypes.h"
#include "tree.h"
#include "gimple.h"
#include "basic-block.h"
#include "tree-pass.h"
#include "cfgloop.h"
#include "gimple-pretty-print.h"
#include "tree-flow.h"
#include "domwalk.h"
#include "pointer-set.h"
#include "expmed.h"
#include "params.h"

/* Information about a strength reduction candidate.  Each statement
   in the candidate table represents an expression of one of the
   following forms (the special case of CAND_REF will be described
   later):

   (CAND_MULT)  S1:  X = (B + i) * S
   (CAND_ADD)   S1:  X = B + (i * S)

   Here X and B are SSA names, i is an integer constant, and S is
   either an SSA name or a constant.  We call B the "base," i the
   "index", and S the "stride."

   Any statement S0 that dominates S1 and is of the form:

   (CAND_MULT)  S0:  Y = (B + i') * S
   (CAND_ADD)   S0:  Y = B + (i' * S)

   is called a "basis" for S1.  In both cases, S1 may be replaced by
   
                S1':  X = Y + (i - i') * S,

   where (i - i') * S is folded to the extent possible.

   All gimple statements are visited in dominator order, and each
   statement that may contribute to one of the forms of S1 above is
   given at least one entry in the candidate table.  Such statements
   include addition, pointer addition, subtraction, multiplication,
   negation, copies, and nontrivial type casts.  If a statement may
   represent more than one expression of the forms of S1 above, 
   multiple "interpretations" are stored in the table and chained
   together.  Examples:

   * An add of two SSA names may treat either operand as the base.
   * A multiply of two SSA names, likewise.
   * A copy or cast may be thought of as either a CAND_MULT with
     i = 0 and S = 1, or as a CAND_ADD with i = 0 or S = 0.

   Candidate records are allocated from an obstack.  They are addressed
   both from a hash table keyed on S1, and from a vector of candidate
   pointers arranged in predominator order.

   Opportunity note
   ----------------
   Currently we don't recognize:

     S0: Y = (S * i') - B
     S1: X = (S * i) - B

   as a strength reduction opportunity, even though this S1 would
   also be replaceable by the S1' above.  This can be added if it
   comes up in practice.

   Strength reduction in addressing
   --------------------------------
   There is another kind of candidate known as CAND_REF.  A CAND_REF
   describes a statement containing a memory reference having 
   complex addressing that might benefit from strength reduction.
   Specifically, we are interested in references for which 
   get_inner_reference returns a base address, offset, and bitpos as
   follows:

     base:    MEM_REF (T1, C1)
     offset:  MULT_EXPR (PLUS_EXPR (T2, C2), C3)
     bitpos:  C4 * BITS_PER_UNIT

   Here T1 and T2 are arbitrary trees, and C1, C2, C3, C4 are 
   arbitrary integer constants.  Note that C2 may be zero, in which
   case the offset will be MULT_EXPR (T2, C3).

   When this pattern is recognized, the original memory reference
   can be replaced with:

     MEM_REF (POINTER_PLUS_EXPR (T1, MULT_EXPR (T2, C3)),
              C1 + (C2 * C3) + C4)

   which distributes the multiply to allow constant folding.  When
   two or more addressing expressions can be represented by MEM_REFs
   of this form, differing only in the constants C1, C2, and C4,
   making this substitution produces more efficient addressing during
   the RTL phases.  When there are not at least two expressions with
   the same values of T1, T2, and C3, there is nothing to be gained
   by the replacement.

   Strength reduction of CAND_REFs uses the same infrastructure as
   that used by CAND_MULTs and CAND_ADDs.  We record T1 in the base (B)
   field, MULT_EXPR (T2, C3) in the stride (S) field, and 
   C1 + (C2 * C3) + C4 in the index (i) field.  A basis for a CAND_REF
   is thus another CAND_REF with the same B and S values.  When at 
   least two CAND_REFs are chained together using the basis relation,
   each of them is replaced as above, resulting in improved code
   generation for addressing.  */


/* Index into the candidate vector, offset by 1.  VECs are zero-based,
   while cand_idx's are one-based, with zero indicating null.  */
typedef unsigned cand_idx;

/* The kind of candidate.  */
enum cand_kind
{
  CAND_MULT,
  CAND_ADD,
  CAND_REF
};

struct slsr_cand_d
{
  /* The candidate statement S1.  */
  gimple cand_stmt;

  /* The base expression B:  often an SSA name, but not always.  */
  tree base_expr;

  /* The stride S.  */
  tree stride;

  /* The index constant i.  */
  double_int index;

  /* The type of the candidate.  This is normally the type of base_expr,
     but casts may have occurred when combining feeding instructions.
     A candidate can only be a basis for candidates of the same final type.
     (For CAND_REFs, this is the type to be used for operand 1 of the
     replacement MEM_REF.)  */
  tree cand_type;

  /* The kind of candidate (CAND_MULT, etc.).  */
  enum cand_kind kind;

  /* Index of this candidate in the candidate vector.  */
  cand_idx cand_num;

  /* Index of the next candidate record for the same statement.
     A statement may be useful in more than one way (e.g., due to
     commutativity).  So we can have multiple "interpretations"
     of a statement.  */
  cand_idx next_interp;

  /* Index of the basis statement S0, if any, in the candidate vector.  */
  cand_idx basis;

  /* First candidate for which this candidate is a basis, if one exists.  */
  cand_idx dependent;

  /* Next candidate having the same basis as this one.  */
  cand_idx sibling;

  /* If this is a conditional candidate, the defining PHI statement
     for the base SSA name B.  For future use; always NULL for now.  */
  gimple def_phi;

  /* Savings that can be expected from eliminating dead code if this
     candidate is replaced.  */
  int dead_savings;
};

typedef struct slsr_cand_d slsr_cand, *slsr_cand_t;
typedef const struct slsr_cand_d *const_slsr_cand_t;

/* Pointers to candidates are chained together as part of a mapping
   from base expressions to the candidates that use them.  */

struct cand_chain_d
{
  /* Base expression for the chain of candidates:  often, but not
     always, an SSA name.  */
  tree base_expr;

  /* Pointer to a candidate.  */
  slsr_cand_t cand;

  /* Chain pointer.  */
  struct cand_chain_d *next;

};

typedef struct cand_chain_d cand_chain, *cand_chain_t;
typedef const struct cand_chain_d *const_cand_chain_t;

/* Information about a unique "increment" associated with candidates
   having an SSA name for a stride.  An increment is the difference
   between the index of the candidate and the index of its basis,
   i.e., (i - i') as discussed in the module commentary.

   When we are not going to generate address arithmetic we treat
   increments that differ only in sign as the same, allowing sharing
   of the cost of initializers.  The absolute value of the increment
   is stored in the incr_info.  */

struct incr_info_d
{
  /* The increment that relates a candidate to its basis.  */
  double_int incr;

  /* How many times the increment occurs in the candidate tree.  */
  unsigned count;

  /* Cost of replacing candidates using this increment.  Negative and
     zero costs indicate replacement should be performed.  */
  int cost;

  /* If this increment is profitable but is not -1, 0, or 1, it requires
     an initializer T_0 = stride * incr to be found or introduced in the
     nearest common dominator of all candidates.  This field holds T_0
     for subsequent use.  */
  tree initializer;

  /* If the initializer was found to already exist, this is the block
     where it was found.  */
  basic_block init_bb;
};

typedef struct incr_info_d incr_info, *incr_info_t;

/* Candidates are maintained in a vector.  If candidate X dominates
   candidate Y, then X appears before Y in the vector; but the
   converse does not necessarily hold.  */
static vec<slsr_cand_t> cand_vec;

enum cost_consts
{
  COST_NEUTRAL = 0,
  COST_INFINITE = 1000
};

/* Pointer map embodying a mapping from statements to candidates.  */
static struct pointer_map_t *stmt_cand_map;

/* Obstack for candidates.  */
static struct obstack cand_obstack;

/* Hash table embodying a mapping from base exprs to chains of candidates.  */
static htab_t base_cand_map;

/* Obstack for candidate chains.  */
static struct obstack chain_obstack;

/* An array INCR_VEC of incr_infos is used during analysis of related
   candidates having an SSA name for a stride.  INCR_VEC_LEN describes
   its current length.  */
static incr_info_t incr_vec;
static unsigned incr_vec_len;

/* For a chain of candidates with unknown stride, indicates whether or not
   we must generate pointer arithmetic when replacing statements.  */
static bool address_arithmetic_p;

/* Produce a pointer to the IDX'th candidate in the candidate vector.  */

static slsr_cand_t
lookup_cand (cand_idx idx)
{
  return cand_vec[idx - 1];
}

/* Callback to produce a hash value for a candidate chain header.  */

static hashval_t
base_cand_hash (const void *p)
{
  tree base_expr = ((const_cand_chain_t) p)->base_expr;
  return iterative_hash_expr (base_expr, 0);
}

/* Callback when an element is removed from the hash table.
   We never remove entries until the entire table is released.  */

static void
base_cand_free (void *p ATTRIBUTE_UNUSED)
{
}

/* Callback to return true if two candidate chain headers are equal.  */

static int
base_cand_eq (const void *p1, const void *p2)
{
  const_cand_chain_t const chain1 = (const_cand_chain_t) p1;
  const_cand_chain_t const chain2 = (const_cand_chain_t) p2;
  return operand_equal_p (chain1->base_expr, chain2->base_expr, 0);
}

/* Use the base expr from candidate C to look for possible candidates
   that can serve as a basis for C.  Each potential basis must also
   appear in a block that dominates the candidate statement and have
   the same stride and type.  If more than one possible basis exists,
   the one with highest index in the vector is chosen; this will be
   the most immediately dominating basis.  */

static int
find_basis_for_candidate (slsr_cand_t c)
{
  cand_chain mapping_key;
  cand_chain_t chain;
  slsr_cand_t basis = NULL;

  // Limit potential of N^2 behavior for long candidate chains.
  int iters = 0;
  int max_iters = PARAM_VALUE (PARAM_MAX_SLSR_CANDIDATE_SCAN);

  mapping_key.base_expr = c->base_expr;
  chain = (cand_chain_t) htab_find (base_cand_map, &mapping_key);

  for (; chain && iters < max_iters; chain = chain->next, ++iters)
    {
      slsr_cand_t one_basis = chain->cand;

      if (one_basis->kind != c->kind
	  || one_basis->cand_stmt == c->cand_stmt
	  || !operand_equal_p (one_basis->stride, c->stride, 0)
	  || !types_compatible_p (one_basis->cand_type, c->cand_type)
	  || !dominated_by_p (CDI_DOMINATORS,
			      gimple_bb (c->cand_stmt),
			      gimple_bb (one_basis->cand_stmt)))
	continue;

      if (!basis || basis->cand_num < one_basis->cand_num)
	basis = one_basis;
    }

  if (basis)
    {
      c->sibling = basis->dependent;
      basis->dependent = c->cand_num;
      return basis->cand_num;
    }

  return 0;
}

/* Record a mapping from the base expression of C to C itself, indicating that
   C may potentially serve as a basis using that base expression.  */

static void
record_potential_basis (slsr_cand_t c)
{
  cand_chain_t node;
  void **slot;

  node = (cand_chain_t) obstack_alloc (&chain_obstack, sizeof (cand_chain));
  node->base_expr = c->base_expr;
  node->cand = c;
  node->next = NULL;
  slot = htab_find_slot (base_cand_map, node, INSERT);

  if (*slot)
    {
      cand_chain_t head = (cand_chain_t) (*slot);
      node->next = head->next;
      head->next = node;
    }
  else
    *slot = node;
}

/* Allocate storage for a new candidate and initialize its fields.
   Attempt to find a basis for the candidate.  */

static slsr_cand_t
alloc_cand_and_find_basis (enum cand_kind kind, gimple gs, tree base, 
			   double_int index, tree stride, tree ctype,
			   unsigned savings)
{
  slsr_cand_t c = (slsr_cand_t) obstack_alloc (&cand_obstack,
					       sizeof (slsr_cand));
  c->cand_stmt = gs;
  c->base_expr = base;
  c->stride = stride;
  c->index = index;
  c->cand_type = ctype;
  c->kind = kind;
  c->cand_num = cand_vec.length () + 1;
  c->next_interp = 0;
  c->dependent = 0;
  c->sibling = 0;
  c->def_phi = NULL;
  c->dead_savings = savings;

  cand_vec.safe_push (c);
  c->basis = find_basis_for_candidate (c);
  record_potential_basis (c);

  return c;
}

/* Determine the target cost of statement GS when compiling according
   to SPEED.  */

static int
stmt_cost (gimple gs, bool speed)
{
  tree lhs, rhs1, rhs2;
  enum machine_mode lhs_mode;

  gcc_assert (is_gimple_assign (gs));
  lhs = gimple_assign_lhs (gs);
  rhs1 = gimple_assign_rhs1 (gs);
  lhs_mode = TYPE_MODE (TREE_TYPE (lhs));
  
  switch (gimple_assign_rhs_code (gs))
    {
    case MULT_EXPR:
      rhs2 = gimple_assign_rhs2 (gs);

      if (host_integerp (rhs2, 0))
	return mult_by_coeff_cost (TREE_INT_CST_LOW (rhs2), lhs_mode, speed);

      gcc_assert (TREE_CODE (rhs1) != INTEGER_CST);
      return mul_cost (speed, lhs_mode);

    case PLUS_EXPR:
    case POINTER_PLUS_EXPR:
    case MINUS_EXPR:
      return add_cost (speed, lhs_mode);

    case NEGATE_EXPR:
      return neg_cost (speed, lhs_mode);

    case NOP_EXPR:
      return convert_cost (lhs_mode, TYPE_MODE (TREE_TYPE (rhs1)), speed);

    /* Note that we don't assign costs to copies that in most cases
       will go away.  */
    default:
      ;
    }
  
  gcc_unreachable ();
  return 0;
}

/* Look up the defining statement for BASE_IN and return a pointer
   to its candidate in the candidate table, if any; otherwise NULL.
   Only CAND_ADD and CAND_MULT candidates are returned.  */

static slsr_cand_t
base_cand_from_table (tree base_in)
{
  slsr_cand_t *result;

  gimple def = SSA_NAME_DEF_STMT (base_in);
  if (!def)
    return (slsr_cand_t) NULL;

  result = (slsr_cand_t *) pointer_map_contains (stmt_cand_map, def);
  
  if (result && (*result)->kind != CAND_REF)
    return *result;

  return (slsr_cand_t) NULL;
}

/* Add an entry to the statement-to-candidate mapping.  */

static void
add_cand_for_stmt (gimple gs, slsr_cand_t c)
{
  void **slot = pointer_map_insert (stmt_cand_map, gs);
  gcc_assert (!*slot);
  *slot = c;
}

/* Look for the following pattern:

    *PBASE:    MEM_REF (T1, C1)

    *POFFSET:  MULT_EXPR (T2, C3)        [C2 is zero]
                     or
               MULT_EXPR (PLUS_EXPR (T2, C2), C3)
                     or
               MULT_EXPR (MINUS_EXPR (T2, -C2), C3)

    *PINDEX:   C4 * BITS_PER_UNIT

   If not present, leave the input values unchanged and return FALSE.
   Otherwise, modify the input values as follows and return TRUE:

    *PBASE:    T1
    *POFFSET:  MULT_EXPR (T2, C3)
    *PINDEX:   C1 + (C2 * C3) + C4  */

static bool
restructure_reference (tree *pbase, tree *poffset, double_int *pindex,
		       tree *ptype)
{
  tree base = *pbase, offset = *poffset;
  double_int index = *pindex;
  double_int bpu = double_int::from_uhwi (BITS_PER_UNIT);
  tree mult_op0, mult_op1, t1, t2, type;
  double_int c1, c2, c3, c4;

  if (!base
      || !offset
      || TREE_CODE (base) != MEM_REF
      || TREE_CODE (offset) != MULT_EXPR
      || TREE_CODE (TREE_OPERAND (offset, 1)) != INTEGER_CST
      || !index.umod (bpu, FLOOR_MOD_EXPR).is_zero ())
    return false;

  t1 = TREE_OPERAND (base, 0);
  c1 = mem_ref_offset (base);
  type = TREE_TYPE (TREE_OPERAND (base, 1));

  mult_op0 = TREE_OPERAND (offset, 0);
  mult_op1 = TREE_OPERAND (offset, 1);

  c3 = tree_to_double_int (mult_op1);

  if (TREE_CODE (mult_op0) == PLUS_EXPR)

    if (TREE_CODE (TREE_OPERAND (mult_op0, 1)) == INTEGER_CST)
      {
	t2 = TREE_OPERAND (mult_op0, 0);
	c2 = tree_to_double_int (TREE_OPERAND (mult_op0, 1));
      }
    else
      return false;

  else if (TREE_CODE (mult_op0) == MINUS_EXPR)

    if (TREE_CODE (TREE_OPERAND (mult_op0, 1)) == INTEGER_CST)
      {
	t2 = TREE_OPERAND (mult_op0, 0);
	c2 = -tree_to_double_int (TREE_OPERAND (mult_op0, 1));
      }
    else
      return false;

  else
    {
      t2 = mult_op0;
      c2 = double_int_zero;
    }

  c4 = index.udiv (bpu, FLOOR_DIV_EXPR);

  *pbase = t1;
  *poffset = fold_build2 (MULT_EXPR, sizetype, t2,
			  double_int_to_tree (sizetype, c3));
  *pindex = c1 + c2 * c3 + c4;
  *ptype = type;

  return true;
}

/* Given GS which contains a data reference, create a CAND_REF entry in
   the candidate table and attempt to find a basis.  */

static void
slsr_process_ref (gimple gs)
{
  tree ref_expr, base, offset, type;
  HOST_WIDE_INT bitsize, bitpos;
  enum machine_mode mode;
  int unsignedp, volatilep;
  double_int index;
  slsr_cand_t c;

  if (gimple_vdef (gs))
    ref_expr = gimple_assign_lhs (gs);
  else
    ref_expr = gimple_assign_rhs1 (gs);

  if (!handled_component_p (ref_expr)
      || TREE_CODE (ref_expr) == BIT_FIELD_REF
      || (TREE_CODE (ref_expr) == COMPONENT_REF
	  && DECL_BIT_FIELD (TREE_OPERAND (ref_expr, 1))))
    return;

  base = get_inner_reference (ref_expr, &bitsize, &bitpos, &offset, &mode,
			      &unsignedp, &volatilep, false);
  index = double_int::from_uhwi (bitpos);

  if (!restructure_reference (&base, &offset, &index, &type))
    return;

  c = alloc_cand_and_find_basis (CAND_REF, gs, base, index, offset,
				 type, 0);

  /* Add the candidate to the statement-candidate mapping.  */
  add_cand_for_stmt (gs, c);
}

/* Create a candidate entry for a statement GS, where GS multiplies
   two SSA names BASE_IN and STRIDE_IN.  Propagate any known information
   about the two SSA names into the new candidate.  Return the new
   candidate.  */

static slsr_cand_t
create_mul_ssa_cand (gimple gs, tree base_in, tree stride_in, bool speed)
{
  tree base = NULL_TREE, stride = NULL_TREE, ctype = NULL_TREE;
  double_int index;
  unsigned savings = 0;
  slsr_cand_t c;
  slsr_cand_t base_cand = base_cand_from_table (base_in);

  /* Look at all interpretations of the base candidate, if necessary,
     to find information to propagate into this candidate.  */
  while (base_cand && !base)
    {

      if (base_cand->kind == CAND_MULT
	  && operand_equal_p (base_cand->stride, integer_one_node, 0))
	{
	  /* Y = (B + i') * 1
	     X = Y * Z
	     ================
	     X = (B + i') * Z  */
	  base = base_cand->base_expr;
	  index = base_cand->index;
	  stride = stride_in;
	  ctype = base_cand->cand_type;
	  if (has_single_use (base_in))
	    savings = (base_cand->dead_savings 
		       + stmt_cost (base_cand->cand_stmt, speed));
	}
      else if (base_cand->kind == CAND_ADD
	       && TREE_CODE (base_cand->stride) == INTEGER_CST)
	{
	  /* Y = B + (i' * S), S constant
	     X = Y * Z
	     ============================
	     X = B + ((i' * S) * Z)  */
	  base = base_cand->base_expr;
	  index = base_cand->index * tree_to_double_int (base_cand->stride);
	  stride = stride_in;
	  ctype = base_cand->cand_type;
	  if (has_single_use (base_in))
	    savings = (base_cand->dead_savings
		       + stmt_cost (base_cand->cand_stmt, speed));
	}

      if (base_cand->next_interp)
	base_cand = lookup_cand (base_cand->next_interp);
      else
	base_cand = NULL;
    }

  if (!base)
    {
      /* No interpretations had anything useful to propagate, so
	 produce X = (Y + 0) * Z.  */
      base = base_in;
      index = double_int_zero;
      stride = stride_in;
      ctype = TREE_TYPE (base_in);
    }

  c = alloc_cand_and_find_basis (CAND_MULT, gs, base, index, stride,
				 ctype, savings);
  return c;
}

/* Create a candidate entry for a statement GS, where GS multiplies
   SSA name BASE_IN by constant STRIDE_IN.  Propagate any known
   information about BASE_IN into the new candidate.  Return the new
   candidate.  */

static slsr_cand_t
create_mul_imm_cand (gimple gs, tree base_in, tree stride_in, bool speed)
{
  tree base = NULL_TREE, stride = NULL_TREE, ctype = NULL_TREE;
  double_int index, temp;
  unsigned savings = 0;
  slsr_cand_t c;
  slsr_cand_t base_cand = base_cand_from_table (base_in);

  /* Look at all interpretations of the base candidate, if necessary,
     to find information to propagate into this candidate.  */
  while (base_cand && !base)
    {
      if (base_cand->kind == CAND_MULT
	  && TREE_CODE (base_cand->stride) == INTEGER_CST)
	{
	  /* Y = (B + i') * S, S constant
	     X = Y * c
	     ============================
	     X = (B + i') * (S * c)  */
	  temp = tree_to_double_int (base_cand->stride)
		 * tree_to_double_int (stride_in);
	  if (double_int_fits_to_tree_p (TREE_TYPE (stride_in), temp))
	    {
	      base = base_cand->base_expr;
	      index = base_cand->index;
	      stride = double_int_to_tree (TREE_TYPE (stride_in), temp);
	      ctype = base_cand->cand_type;
	      if (has_single_use (base_in))
		savings = (base_cand->dead_savings 
			   + stmt_cost (base_cand->cand_stmt, speed));
	    }
	}
      else if (base_cand->kind == CAND_ADD
	       && operand_equal_p (base_cand->stride, integer_one_node, 0))
	{
	  /* Y = B + (i' * 1)
	     X = Y * c
	     ===========================
	     X = (B + i') * c  */
	  base = base_cand->base_expr;
	  index = base_cand->index;
	  stride = stride_in;
	  ctype = base_cand->cand_type;
	  if (has_single_use (base_in))
	    savings = (base_cand->dead_savings
		       + stmt_cost (base_cand->cand_stmt, speed));
	}
      else if (base_cand->kind == CAND_ADD
	       && base_cand->index.is_one ()
	       && TREE_CODE (base_cand->stride) == INTEGER_CST)
	{
	  /* Y = B + (1 * S), S constant
	     X = Y * c
	     ===========================
	     X = (B + S) * c  */
	  base = base_cand->base_expr;
	  index = tree_to_double_int (base_cand->stride);
	  stride = stride_in;
	  ctype = base_cand->cand_type;
	  if (has_single_use (base_in))
	    savings = (base_cand->dead_savings
		       + stmt_cost (base_cand->cand_stmt, speed));
	}

      if (base_cand->next_interp)
	base_cand = lookup_cand (base_cand->next_interp);
      else
	base_cand = NULL;
    }

  if (!base)
    {
      /* No interpretations had anything useful to propagate, so
	 produce X = (Y + 0) * c.  */
      base = base_in;
      index = double_int_zero;
      stride = stride_in;
      ctype = TREE_TYPE (base_in);
    }

  c = alloc_cand_and_find_basis (CAND_MULT, gs, base, index, stride,
				 ctype, savings);
  return c;
}

/* Given GS which is a multiply of scalar integers, make an appropriate
   entry in the candidate table.  If this is a multiply of two SSA names,
   create two CAND_MULT interpretations and attempt to find a basis for
   each of them.  Otherwise, create a single CAND_MULT and attempt to
   find a basis.  */

static void
slsr_process_mul (gimple gs, tree rhs1, tree rhs2, bool speed)
{
  slsr_cand_t c, c2;

  /* If this is a multiply of an SSA name with itself, it is highly
     unlikely that we will get a strength reduction opportunity, so
     don't record it as a candidate.  This simplifies the logic for
     finding a basis, so if this is removed that must be considered.  */
  if (rhs1 == rhs2)
    return;

  if (TREE_CODE (rhs2) == SSA_NAME)
    {
      /* Record an interpretation of this statement in the candidate table
	 assuming RHS1 is the base expression and RHS2 is the stride.  */
      c = create_mul_ssa_cand (gs, rhs1, rhs2, speed);

      /* Add the first interpretation to the statement-candidate mapping.  */
      add_cand_for_stmt (gs, c);

      /* Record another interpretation of this statement assuming RHS1
	 is the stride and RHS2 is the base expression.  */
      c2 = create_mul_ssa_cand (gs, rhs2, rhs1, speed);
      c->next_interp = c2->cand_num;
    }
  else
    {
      /* Record an interpretation for the multiply-immediate.  */
      c = create_mul_imm_cand (gs, rhs1, rhs2, speed);

      /* Add the interpretation to the statement-candidate mapping.  */
      add_cand_for_stmt (gs, c);
    }
}

/* Create a candidate entry for a statement GS, where GS adds two
   SSA names BASE_IN and ADDEND_IN if SUBTRACT_P is false, and
   subtracts ADDEND_IN from BASE_IN otherwise.  Propagate any known
   information about the two SSA names into the new candidate.
   Return the new candidate.  */

static slsr_cand_t
create_add_ssa_cand (gimple gs, tree base_in, tree addend_in,
		     bool subtract_p, bool speed)
{
  tree base = NULL_TREE, stride = NULL_TREE, ctype = NULL;
  double_int index;
  unsigned savings = 0;
  slsr_cand_t c;
  slsr_cand_t base_cand = base_cand_from_table (base_in);
  slsr_cand_t addend_cand = base_cand_from_table (addend_in);

  /* The most useful transformation is a multiply-immediate feeding
     an add or subtract.  Look for that first.  */
  while (addend_cand && !base)
    {
      if (addend_cand->kind == CAND_MULT
	  && addend_cand->index.is_zero ()
	  && TREE_CODE (addend_cand->stride) == INTEGER_CST)
	{
	  /* Z = (B + 0) * S, S constant
	     X = Y +/- Z
	     ===========================
	     X = Y + ((+/-1 * S) * B)  */
	  base = base_in;
	  index = tree_to_double_int (addend_cand->stride);
	  if (subtract_p)
	    index = -index;
	  stride = addend_cand->base_expr;
	  ctype = TREE_TYPE (base_in);
	  if (has_single_use (addend_in))
	    savings = (addend_cand->dead_savings
		       + stmt_cost (addend_cand->cand_stmt, speed));
	}

      if (addend_cand->next_interp)
	addend_cand = lookup_cand (addend_cand->next_interp);
      else
	addend_cand = NULL;
    }

  while (base_cand && !base)
    {
      if (base_cand->kind == CAND_ADD
	  && (base_cand->index.is_zero ()
	      || operand_equal_p (base_cand->stride,
				  integer_zero_node, 0)))
	{
	  /* Y = B + (i' * S), i' * S = 0
	     X = Y +/- Z
	     ============================
	     X = B + (+/-1 * Z)  */
	  base = base_cand->base_expr;
	  index = subtract_p ? double_int_minus_one : double_int_one;
	  stride = addend_in;
	  ctype = base_cand->cand_type;
	  if (has_single_use (base_in))
	    savings = (base_cand->dead_savings
		       + stmt_cost (base_cand->cand_stmt, speed));
	}
      else if (subtract_p)
	{
	  slsr_cand_t subtrahend_cand = base_cand_from_table (addend_in);

	  while (subtrahend_cand && !base)
	    {
	      if (subtrahend_cand->kind == CAND_MULT
		  && subtrahend_cand->index.is_zero ()
		  && TREE_CODE (subtrahend_cand->stride) == INTEGER_CST)
		{
		  /* Z = (B + 0) * S, S constant
		     X = Y - Z
		     ===========================
		     Value:  X = Y + ((-1 * S) * B)  */
		  base = base_in;
		  index = tree_to_double_int (subtrahend_cand->stride);
		  index = -index;
		  stride = subtrahend_cand->base_expr;
		  ctype = TREE_TYPE (base_in);
		  if (has_single_use (addend_in))
		    savings = (subtrahend_cand->dead_savings 
			       + stmt_cost (subtrahend_cand->cand_stmt, speed));
		}
	      
	      if (subtrahend_cand->next_interp)
		subtrahend_cand = lookup_cand (subtrahend_cand->next_interp);
	      else
		subtrahend_cand = NULL;
	    }
	}
      
      if (base_cand->next_interp)
	base_cand = lookup_cand (base_cand->next_interp);
      else
	base_cand = NULL;
    }

  if (!base)
    {
      /* No interpretations had anything useful to propagate, so
	 produce X = Y + (1 * Z).  */
      base = base_in;
      index = subtract_p ? double_int_minus_one : double_int_one;
      stride = addend_in;
      ctype = TREE_TYPE (base_in);
    }

  c = alloc_cand_and_find_basis (CAND_ADD, gs, base, index, stride,
				 ctype, savings);
  return c;
}

/* Create a candidate entry for a statement GS, where GS adds SSA
   name BASE_IN to constant INDEX_IN.  Propagate any known information
   about BASE_IN into the new candidate.  Return the new candidate.  */

static slsr_cand_t
create_add_imm_cand (gimple gs, tree base_in, double_int index_in, bool speed)
{
  enum cand_kind kind = CAND_ADD;
  tree base = NULL_TREE, stride = NULL_TREE, ctype = NULL_TREE;
  double_int index, multiple;
  unsigned savings = 0;
  slsr_cand_t c;
  slsr_cand_t base_cand = base_cand_from_table (base_in);

  while (base_cand && !base)
    {
      bool unsigned_p = TYPE_UNSIGNED (TREE_TYPE (base_cand->stride));

      if (TREE_CODE (base_cand->stride) == INTEGER_CST
	  && index_in.multiple_of (tree_to_double_int (base_cand->stride),
				   unsigned_p, &multiple))
	{
	  /* Y = (B + i') * S, S constant, c = kS for some integer k
	     X = Y + c
	     ============================
	     X = (B + (i'+ k)) * S  
	  OR
	     Y = B + (i' * S), S constant, c = kS for some integer k
	     X = Y + c
	     ============================
	     X = (B + (i'+ k)) * S  */
	  kind = base_cand->kind;
	  base = base_cand->base_expr;
	  index = base_cand->index + multiple;
	  stride = base_cand->stride;
	  ctype = base_cand->cand_type;
	  if (has_single_use (base_in))
	    savings = (base_cand->dead_savings 
		       + stmt_cost (base_cand->cand_stmt, speed));
	}

      if (base_cand->next_interp)
	base_cand = lookup_cand (base_cand->next_interp);
      else
	base_cand = NULL;
    }

  if (!base)
    {
      /* No interpretations had anything useful to propagate, so
	 produce X = Y + (c * 1).  */
      kind = CAND_ADD;
      base = base_in;
      index = index_in;
      stride = integer_one_node;
      ctype = TREE_TYPE (base_in);
    }

  c = alloc_cand_and_find_basis (kind, gs, base, index, stride,
				 ctype, savings);
  return c;
}

/* Given GS which is an add or subtract of scalar integers or pointers,
   make at least one appropriate entry in the candidate table.  */

static void
slsr_process_add (gimple gs, tree rhs1, tree rhs2, bool speed)
{
  bool subtract_p = gimple_assign_rhs_code (gs) == MINUS_EXPR;
  slsr_cand_t c = NULL, c2;

  if (TREE_CODE (rhs2) == SSA_NAME)
    {
      /* First record an interpretation assuming RHS1 is the base expression
	 and RHS2 is the stride.  But it doesn't make sense for the
	 stride to be a pointer, so don't record a candidate in that case.  */
      if (!POINTER_TYPE_P (TREE_TYPE (rhs2)))
	{
	  c = create_add_ssa_cand (gs, rhs1, rhs2, subtract_p, speed);

	  /* Add the first interpretation to the statement-candidate
	     mapping.  */
	  add_cand_for_stmt (gs, c);
	}

      /* If the two RHS operands are identical, or this is a subtract,
	 we're done.  */
      if (operand_equal_p (rhs1, rhs2, 0) || subtract_p)
	return;

      /* Otherwise, record another interpretation assuming RHS2 is the
	 base expression and RHS1 is the stride, again provided that the
	 stride is not a pointer.  */
      if (!POINTER_TYPE_P (TREE_TYPE (rhs1)))
	{
	  c2 = create_add_ssa_cand (gs, rhs2, rhs1, false, speed);
	  if (c)
	    c->next_interp = c2->cand_num;
	  else
	    add_cand_for_stmt (gs, c2);
	}
    }
  else
    {
      double_int index;

      /* Record an interpretation for the add-immediate.  */
      index = tree_to_double_int (rhs2);
      if (subtract_p)
	index = -index;

      c = create_add_imm_cand (gs, rhs1, index, speed);

      /* Add the interpretation to the statement-candidate mapping.  */
      add_cand_for_stmt (gs, c);
    }
}

/* Given GS which is a negate of a scalar integer, make an appropriate
   entry in the candidate table.  A negate is equivalent to a multiply
   by -1.  */

static void
slsr_process_neg (gimple gs, tree rhs1, bool speed)
{
  /* Record a CAND_MULT interpretation for the multiply by -1.  */
  slsr_cand_t c = create_mul_imm_cand (gs, rhs1, integer_minus_one_node, speed);

  /* Add the interpretation to the statement-candidate mapping.  */
  add_cand_for_stmt (gs, c);
}

/* Help function for legal_cast_p, operating on two trees.  Checks
   whether it's allowable to cast from RHS to LHS.  See legal_cast_p
   for more details.  */

static bool
legal_cast_p_1 (tree lhs, tree rhs)
{
  tree lhs_type, rhs_type;
  unsigned lhs_size, rhs_size;
  bool lhs_wraps, rhs_wraps;

  lhs_type = TREE_TYPE (lhs);
  rhs_type = TREE_TYPE (rhs);
  lhs_size = TYPE_PRECISION (lhs_type);
  rhs_size = TYPE_PRECISION (rhs_type);
  lhs_wraps = TYPE_OVERFLOW_WRAPS (lhs_type);
  rhs_wraps = TYPE_OVERFLOW_WRAPS (rhs_type);

  if (lhs_size < rhs_size
      || (rhs_wraps && !lhs_wraps)
      || (rhs_wraps && lhs_wraps && rhs_size != lhs_size))
    return false;

  return true;
}

/* Return TRUE if GS is a statement that defines an SSA name from
   a conversion and is legal for us to combine with an add and multiply
   in the candidate table.  For example, suppose we have:

     A = B + i;
     C = (type) A;
     D = C * S;

   Without the type-cast, we would create a CAND_MULT for D with base B,
   index i, and stride S.  We want to record this candidate only if it
   is equivalent to apply the type cast following the multiply:

     A = B + i;
     E = A * S;
     D = (type) E;

   We will record the type with the candidate for D.  This allows us
   to use a similar previous candidate as a basis.  If we have earlier seen

     A' = B + i';
     C' = (type) A';
     D' = C' * S;

   we can replace D with

     D = D' + (i - i') * S;

   But if moving the type-cast would change semantics, we mustn't do this.

   This is legitimate for casts from a non-wrapping integral type to
   any integral type of the same or larger size.  It is not legitimate
   to convert a wrapping type to a non-wrapping type, or to a wrapping
   type of a different size.  I.e., with a wrapping type, we must
   assume that the addition B + i could wrap, in which case performing
   the multiply before or after one of the "illegal" type casts will
   have different semantics.  */

static bool
legal_cast_p (gimple gs, tree rhs)
{
  if (!is_gimple_assign (gs)
      || !CONVERT_EXPR_CODE_P (gimple_assign_rhs_code (gs)))
    return false;

  return legal_cast_p_1 (gimple_assign_lhs (gs), rhs);
}

/* Given GS which is a cast to a scalar integer type, determine whether
   the cast is legal for strength reduction.  If so, make at least one
   appropriate entry in the candidate table.  */

static void
slsr_process_cast (gimple gs, tree rhs1, bool speed)
{
  tree lhs, ctype;
  slsr_cand_t base_cand, c, c2;
  unsigned savings = 0;

  if (!legal_cast_p (gs, rhs1))
    return;

  lhs = gimple_assign_lhs (gs);
  base_cand = base_cand_from_table (rhs1);
  ctype = TREE_TYPE (lhs);

  if (base_cand)
    {
      while (base_cand)
	{
	  /* Propagate all data from the base candidate except the type,
	     which comes from the cast, and the base candidate's cast,
	     which is no longer applicable.  */
	  if (has_single_use (rhs1))
	    savings = (base_cand->dead_savings 
		       + stmt_cost (base_cand->cand_stmt, speed));

	  c = alloc_cand_and_find_basis (base_cand->kind, gs,
					 base_cand->base_expr,
					 base_cand->index, base_cand->stride,
					 ctype, savings);
	  if (base_cand->next_interp)
	    base_cand = lookup_cand (base_cand->next_interp);
	  else
	    base_cand = NULL;
	}
    }
  else 
    {
      /* If nothing is known about the RHS, create fresh CAND_ADD and
	 CAND_MULT interpretations:

	 X = Y + (0 * 1)
	 X = (Y + 0) * 1

	 The first of these is somewhat arbitrary, but the choice of
	 1 for the stride simplifies the logic for propagating casts
	 into their uses.  */
      c = alloc_cand_and_find_basis (CAND_ADD, gs, rhs1, double_int_zero,
				     integer_one_node, ctype, 0);
      c2 = alloc_cand_and_find_basis (CAND_MULT, gs, rhs1, double_int_zero,
				      integer_one_node, ctype, 0);
      c->next_interp = c2->cand_num;
    }

  /* Add the first (or only) interpretation to the statement-candidate
     mapping.  */
  add_cand_for_stmt (gs, c);
}

/* Given GS which is a copy of a scalar integer type, make at least one
   appropriate entry in the candidate table.

   This interface is included for completeness, but is unnecessary
   if this pass immediately follows a pass that performs copy 
   propagation, such as DOM.  */

static void
slsr_process_copy (gimple gs, tree rhs1, bool speed)
{
  slsr_cand_t base_cand, c, c2;
  unsigned savings = 0;

  base_cand = base_cand_from_table (rhs1);

  if (base_cand)
    {
      while (base_cand)
	{
	  /* Propagate all data from the base candidate.  */
	  if (has_single_use (rhs1))
	    savings = (base_cand->dead_savings 
		       + stmt_cost (base_cand->cand_stmt, speed));

	  c = alloc_cand_and_find_basis (base_cand->kind, gs,
					 base_cand->base_expr,
					 base_cand->index, base_cand->stride,
					 base_cand->cand_type, savings);
	  if (base_cand->next_interp)
	    base_cand = lookup_cand (base_cand->next_interp);
	  else
	    base_cand = NULL;
	}
    }
  else 
    {
      /* If nothing is known about the RHS, create fresh CAND_ADD and
	 CAND_MULT interpretations:

	 X = Y + (0 * 1)
	 X = (Y + 0) * 1

	 The first of these is somewhat arbitrary, but the choice of
	 1 for the stride simplifies the logic for propagating casts
	 into their uses.  */
      c = alloc_cand_and_find_basis (CAND_ADD, gs, rhs1, double_int_zero,
				     integer_one_node, TREE_TYPE (rhs1), 0);
      c2 = alloc_cand_and_find_basis (CAND_MULT, gs, rhs1, double_int_zero,
				      integer_one_node, TREE_TYPE (rhs1), 0);
      c->next_interp = c2->cand_num;
    }

  /* Add the first (or only) interpretation to the statement-candidate
     mapping.  */
  add_cand_for_stmt (gs, c);
}

/* Find strength-reduction candidates in block BB.  */

static void
find_candidates_in_block (struct dom_walk_data *walk_data ATTRIBUTE_UNUSED,
			  basic_block bb)
{
  bool speed = optimize_bb_for_speed_p (bb);
  gimple_stmt_iterator gsi;

  for (gsi = gsi_start_bb (bb); !gsi_end_p (gsi); gsi_next (&gsi))
    {
      gimple gs = gsi_stmt (gsi);

      if (gimple_vuse (gs) && gimple_assign_single_p (gs))
	slsr_process_ref (gs);

      else if (is_gimple_assign (gs)
	       && SCALAR_INT_MODE_P
	            (TYPE_MODE (TREE_TYPE (gimple_assign_lhs (gs)))))
	{
	  tree rhs1 = NULL_TREE, rhs2 = NULL_TREE;

	  switch (gimple_assign_rhs_code (gs))
	    {
	    case MULT_EXPR:
	    case PLUS_EXPR:
	      rhs1 = gimple_assign_rhs1 (gs);
	      rhs2 = gimple_assign_rhs2 (gs);
	      /* Should never happen, but currently some buggy situations
		 in earlier phases put constants in rhs1.  */
	      if (TREE_CODE (rhs1) != SSA_NAME)
		continue;
	      break;

	    /* Possible future opportunity: rhs1 of a ptr+ can be
	       an ADDR_EXPR.  */
	    case POINTER_PLUS_EXPR:
	    case MINUS_EXPR:
	      rhs2 = gimple_assign_rhs2 (gs);
	      /* Fall-through.  */

	    case NOP_EXPR:
	    case MODIFY_EXPR:
	    case NEGATE_EXPR:
	      rhs1 = gimple_assign_rhs1 (gs);
	      if (TREE_CODE (rhs1) != SSA_NAME)
		continue;
	      break;

	    default:
	      ;
	    }

	  switch (gimple_assign_rhs_code (gs))
	    {
	    case MULT_EXPR:
	      slsr_process_mul (gs, rhs1, rhs2, speed);
	      break;

	    case PLUS_EXPR:
	    case POINTER_PLUS_EXPR:
	    case MINUS_EXPR:
	      slsr_process_add (gs, rhs1, rhs2, speed);
	      break;

	    case NEGATE_EXPR:
	      slsr_process_neg (gs, rhs1, speed);
	      break;

	    case NOP_EXPR:
	      slsr_process_cast (gs, rhs1, speed);
	      break;

	    case MODIFY_EXPR:
	      slsr_process_copy (gs, rhs1, speed);
	      break;

	    default:
	      ;
	    }
	}
    }
}

/* Dump a candidate for debug.  */

static void
dump_candidate (slsr_cand_t c)
{
  fprintf (dump_file, "%3d  [%d] ", c->cand_num,
	   gimple_bb (c->cand_stmt)->index);
  print_gimple_stmt (dump_file, c->cand_stmt, 0, 0);
  switch (c->kind)
    {
    case CAND_MULT:
      fputs ("     MULT : (", dump_file);
      print_generic_expr (dump_file, c->base_expr, 0);
      fputs (" + ", dump_file);
      dump_double_int (dump_file, c->index, false);
      fputs (") * ", dump_file);
      print_generic_expr (dump_file, c->stride, 0);
      fputs (" : ", dump_file);
      break;
    case CAND_ADD:
      fputs ("     ADD  : ", dump_file);
      print_generic_expr (dump_file, c->base_expr, 0);
      fputs (" + (", dump_file);
      dump_double_int (dump_file, c->index, false);
      fputs (" * ", dump_file);
      print_generic_expr (dump_file, c->stride, 0);
      fputs (") : ", dump_file);
      break;
    case CAND_REF:
      fputs ("     REF  : ", dump_file);
      print_generic_expr (dump_file, c->base_expr, 0);
      fputs (" + (", dump_file);
      print_generic_expr (dump_file, c->stride, 0);
      fputs (") + ", dump_file);
      dump_double_int (dump_file, c->index, false);
      fputs (" : ", dump_file);
      break;
    default:
      gcc_unreachable ();
    }
  print_generic_expr (dump_file, c->cand_type, 0);
  fprintf (dump_file, "\n     basis: %d  dependent: %d  sibling: %d\n",
	   c->basis, c->dependent, c->sibling);
  fprintf (dump_file, "     next-interp: %d  dead-savings: %d\n",
	   c->next_interp, c->dead_savings);
  if (c->def_phi)
    {
      fputs ("     phi:  ", dump_file);
      print_gimple_stmt (dump_file, c->def_phi, 0, 0);
    }
  fputs ("\n", dump_file);
}

/* Dump the candidate vector for debug.  */

static void
dump_cand_vec (void)
{
  unsigned i;
  slsr_cand_t c;

  fprintf (dump_file, "\nStrength reduction candidate vector:\n\n");
  
  FOR_EACH_VEC_ELT (cand_vec, i, c)
    dump_candidate (c);
}

/* Callback used to dump the candidate chains hash table.  */

static int
base_cand_dump_callback (void **slot, void *ignored ATTRIBUTE_UNUSED)
{
  const_cand_chain_t chain = *((const_cand_chain_t *) slot);
  cand_chain_t p;

  print_generic_expr (dump_file, chain->base_expr, 0);
  fprintf (dump_file, " -> %d", chain->cand->cand_num);

  for (p = chain->next; p; p = p->next)
    fprintf (dump_file, " -> %d", p->cand->cand_num);

  fputs ("\n", dump_file);
  return 1;
}

/* Dump the candidate chains.  */

static void
dump_cand_chains (void)
{
  fprintf (dump_file, "\nStrength reduction candidate chains:\n\n");
  htab_traverse_noresize (base_cand_map, base_cand_dump_callback, NULL);
  fputs ("\n", dump_file);
}

/* Dump the increment vector for debug.  */

static void
dump_incr_vec (void)
{
  if (dump_file && (dump_flags & TDF_DETAILS))
    {
      unsigned i;

      fprintf (dump_file, "\nIncrement vector:\n\n");
  
      for (i = 0; i < incr_vec_len; i++)
	{
	  fprintf (dump_file, "%3d  increment:   ", i);
	  dump_double_int (dump_file, incr_vec[i].incr, false);
	  fprintf (dump_file, "\n     count:       %d", incr_vec[i].count);
	  fprintf (dump_file, "\n     cost:        %d", incr_vec[i].cost);
	  fputs ("\n     initializer: ", dump_file);
	  print_generic_expr (dump_file, incr_vec[i].initializer, 0);
	  fputs ("\n\n", dump_file);
	}
    }
}

/* Recursive helper for unconditional_cands_with_known_stride_p.
   Returns TRUE iff C, its siblings, and its dependents are all
   unconditional candidates.  */

static bool
unconditional_cands (slsr_cand_t c)
{
  if (c->def_phi)
    return false;

  if (c->sibling && !unconditional_cands (lookup_cand (c->sibling)))
    return false;

  if (c->dependent && !unconditional_cands (lookup_cand (c->dependent)))
    return false;

  return true;
}

/* Determine whether or not the tree of candidates rooted at
   ROOT consists entirely of unconditional increments with
   an INTEGER_CST stride.  */

static bool
unconditional_cands_with_known_stride_p (slsr_cand_t root)
{
  /* The stride is identical for all related candidates, so
     check it once.  */
  if (TREE_CODE (root->stride) != INTEGER_CST)
    return false;

  return unconditional_cands (lookup_cand (root->dependent));
}

/* Replace *EXPR in candidate C with an equivalent strength-reduced
   data reference.  */

static void
replace_ref (tree *expr, slsr_cand_t c)
{
  tree add_expr, mem_ref, acc_type = TREE_TYPE (*expr);
  unsigned HOST_WIDE_INT misalign;
  unsigned align;

  /* Ensure the memory reference carries the minimum alignment
     requirement for the data type.  See PR58041.  */
  get_object_alignment_1 (*expr, &align, &misalign);
  if (misalign != 0)
    align = (misalign & -misalign);
  if (align < TYPE_ALIGN (acc_type))
    acc_type = build_aligned_type (acc_type, align);

  add_expr = fold_build2 (POINTER_PLUS_EXPR, TREE_TYPE (c->base_expr),
			  c->base_expr, c->stride);
  mem_ref = fold_build2 (MEM_REF, acc_type, add_expr,
			 double_int_to_tree (c->cand_type, c->index));

  /* Gimplify the base addressing expression for the new MEM_REF tree.  */
  gimple_stmt_iterator gsi = gsi_for_stmt (c->cand_stmt);
  TREE_OPERAND (mem_ref, 0)
    = force_gimple_operand_gsi (&gsi, TREE_OPERAND (mem_ref, 0),
				/*simple_p=*/true, NULL,
				/*before=*/true, GSI_SAME_STMT);
  copy_ref_info (mem_ref, *expr);
  *expr = mem_ref;
  update_stmt (c->cand_stmt);
}

/* Replace CAND_REF candidate C, each sibling of candidate C, and each
   dependent of candidate C with an equivalent strength-reduced data
   reference.  */

static void
replace_refs (slsr_cand_t c)
{
  if (gimple_vdef (c->cand_stmt))
    {
      tree *lhs = gimple_assign_lhs_ptr (c->cand_stmt);
      replace_ref (lhs, c);
    }
  else
    {
      tree *rhs = gimple_assign_rhs1_ptr (c->cand_stmt);
      replace_ref (rhs, c);
    }

  if (c->sibling)
    replace_refs (lookup_cand (c->sibling));

  if (c->dependent)
    replace_refs (lookup_cand (c->dependent));
}

/* Calculate the increment required for candidate C relative to 
   its basis.  */

static double_int
cand_increment (slsr_cand_t c)
{
  slsr_cand_t basis;

  /* If the candidate doesn't have a basis, just return its own
     index.  This is useful in record_increments to help us find
     an existing initializer.  */
  if (!c->basis)
    return c->index;

  basis = lookup_cand (c->basis);
  gcc_assert (operand_equal_p (c->base_expr, basis->base_expr, 0));
  return c->index - basis->index;
}

/* Calculate the increment required for candidate C relative to
   its basis.  If we aren't going to generate pointer arithmetic
   for this candidate, return the absolute value of that increment
   instead.  */

static inline double_int
cand_abs_increment (slsr_cand_t c)
{
  double_int increment = cand_increment (c);

  if (!address_arithmetic_p && increment.is_negative ())
    increment = -increment;

  return increment;
}

/* If *VAR is NULL or is not of a compatible type with TYPE, create a
   new temporary reg of type TYPE and store it in *VAR.  */

static inline void
lazy_create_slsr_reg (tree *var, tree type)
{
  if (!*var || !types_compatible_p (TREE_TYPE (*var), type))
    *var = create_tmp_reg (type, "slsr");
}

/* Return TRUE iff candidate C has already been replaced under
   another interpretation.  */

static inline bool
cand_already_replaced (slsr_cand_t c)
{
  return (gimple_bb (c->cand_stmt) == 0);
}

/* Helper routine for replace_dependents, doing the work for a 
   single candidate C.  */

static void
replace_dependent (slsr_cand_t c, enum tree_code cand_code)
{
  double_int stride = tree_to_double_int (c->stride);
  double_int bump = cand_increment (c) * stride;
  gimple stmt_to_print = NULL;
  slsr_cand_t basis;
  tree basis_name, incr_type, bump_tree;
  enum tree_code code;
  
  /* It is highly unlikely, but possible, that the resulting
     bump doesn't fit in a HWI.  Abandon the replacement
     in this case.  Restriction to signed HWI is conservative
     for unsigned types but allows for safe negation without
     twisted logic.  */
  if (!bump.fits_shwi ())
    return;

  basis = lookup_cand (c->basis);
  basis_name = gimple_assign_lhs (basis->cand_stmt);
  if (cand_code == POINTER_PLUS_EXPR)
    {
      incr_type = sizetype;
      code = cand_code;
    }
  else
    {
      incr_type = TREE_TYPE (gimple_assign_rhs1 (c->cand_stmt));
      code = PLUS_EXPR;
    }

  if (bump.is_negative ()
      && cand_code != POINTER_PLUS_EXPR)
    {
      code = MINUS_EXPR;
      bump = -bump;
    }

  bump_tree = double_int_to_tree (incr_type, bump);

  if (dump_file && (dump_flags & TDF_DETAILS))
    {
      fputs ("Replacing: ", dump_file);
      print_gimple_stmt (dump_file, c->cand_stmt, 0, 0);
    }

  if (bump.is_zero ())
    {
      tree lhs = gimple_assign_lhs (c->cand_stmt);
      gimple copy_stmt = gimple_build_assign (lhs, basis_name);
      gimple_stmt_iterator gsi = gsi_for_stmt (c->cand_stmt);
      gimple_set_location (copy_stmt, gimple_location (c->cand_stmt));
      gsi_replace (&gsi, copy_stmt, false);
      if (dump_file && (dump_flags & TDF_DETAILS))
	stmt_to_print = copy_stmt;
    }
  else
    {
      tree rhs1 = gimple_assign_rhs1 (c->cand_stmt);
      tree rhs2 = gimple_assign_rhs2 (c->cand_stmt);
      if (cand_code != NEGATE_EXPR
	  && ((operand_equal_p (rhs1, basis_name, 0)
	       && operand_equal_p (rhs2, bump_tree, 0))
	      || (operand_equal_p (rhs1, bump_tree, 0)
		  && operand_equal_p (rhs2, basis_name, 0))))
	{
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    {
	      fputs ("(duplicate, not actually replacing)", dump_file);
	      stmt_to_print = c->cand_stmt;
	    }
	}
      else
	{
	  gimple_stmt_iterator gsi = gsi_for_stmt (c->cand_stmt);
	  gimple_assign_set_rhs_with_ops (&gsi, code, basis_name, bump_tree);
	  update_stmt (gsi_stmt (gsi));
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    stmt_to_print = gsi_stmt (gsi);
	}
    }
  
  if (dump_file && (dump_flags & TDF_DETAILS))
    {
      fputs ("With: ", dump_file);
      print_gimple_stmt (dump_file, stmt_to_print, 0, 0);
      fputs ("\n", dump_file);
    }
}

/* Replace candidate C, each sibling of candidate C, and each
   dependent of candidate C with an add or subtract.  Note that we
   only operate on CAND_MULTs with known strides, so we will never
   generate a POINTER_PLUS_EXPR.  Each candidate X = (B + i) * S is
   replaced by X = Y + ((i - i') * S), as described in the module
   commentary.  The folded value ((i - i') * S) is referred to here
   as the "bump."  */

static void
replace_dependents (slsr_cand_t c)
{
  enum tree_code cand_code = gimple_assign_rhs_code (c->cand_stmt);

  /* It is not useful to replace casts, copies, or adds of an SSA name
     and a constant.  Also skip candidates that have already been
     replaced under another interpretation.  */
  if (cand_code != MODIFY_EXPR
      && cand_code != NOP_EXPR
      && c->kind == CAND_MULT
      && !cand_already_replaced (c))
    replace_dependent (c, cand_code);

  if (c->sibling)
    replace_dependents (lookup_cand (c->sibling));

  if (c->dependent)
    replace_dependents (lookup_cand (c->dependent));
}

/* Return the index in the increment vector of the given INCREMENT.  */

static inline unsigned
incr_vec_index (double_int increment)
{
  unsigned i;
  
  for (i = 0; i < incr_vec_len && increment != incr_vec[i].incr; i++)
    ;

  gcc_assert (i < incr_vec_len);
  return i;
}

/* Count the number of candidates in the tree rooted at C that have
   not already been replaced under other interpretations.  */

static unsigned
count_candidates (slsr_cand_t c)
{
  unsigned count = cand_already_replaced (c) ? 0 : 1;

  if (c->sibling)
    count += count_candidates (lookup_cand (c->sibling));

  if (c->dependent)
    count += count_candidates (lookup_cand (c->dependent));

  return count;
}

/* Increase the count of INCREMENT by one in the increment vector.
   INCREMENT is associated with candidate C.  If an initializer
   T_0 = stride * I is provided by a candidate that dominates all
   candidates with the same increment, also record T_0 for subsequent use.  */

static void
record_increment (slsr_cand_t c, double_int increment)
{
  bool found = false;
  unsigned i;

  /* Treat increments that differ only in sign as identical so as to
     share initializers, unless we are generating pointer arithmetic.  */
  if (!address_arithmetic_p && increment.is_negative ())
    increment = -increment;

  for (i = 0; i < incr_vec_len; i++)
    {
      if (incr_vec[i].incr == increment)
	{
	  incr_vec[i].count++;
	  found = true;

	  /* If we previously recorded an initializer that doesn't
	     dominate this candidate, it's not going to be useful to
	     us after all.  */
	  if (incr_vec[i].initializer
	      && !dominated_by_p (CDI_DOMINATORS,
				  gimple_bb (c->cand_stmt),
				  incr_vec[i].init_bb))
	    {
	      incr_vec[i].initializer = NULL_TREE;
	      incr_vec[i].init_bb = NULL;
	    }
	  
	  break;
	}
    }

  if (!found)
    {
      /* The first time we see an increment, create the entry for it.
	 If this is the root candidate which doesn't have a basis, set
	 the count to zero.  We're only processing it so it can possibly
	 provide an initializer for other candidates.  */
      incr_vec[incr_vec_len].incr = increment;
      incr_vec[incr_vec_len].count = c->basis ? 1 : 0;
      incr_vec[incr_vec_len].cost = COST_INFINITE;
      
      /* Optimistically record the first occurrence of this increment
	 as providing an initializer (if it does); we will revise this
	 opinion later if it doesn't dominate all other occurrences.
         Exception:  increments of -1, 0, 1 never need initializers.  */
      if (c->kind == CAND_ADD
	  && c->index == increment
	  && (increment.sgt (double_int_one)
	      || increment.slt (double_int_minus_one))
	  && (gimple_assign_rhs_code (c->cand_stmt) == PLUS_EXPR
	      || gimple_assign_rhs_code (c->cand_stmt) == POINTER_PLUS_EXPR))
	{
	  tree t0 = NULL_TREE;
	  tree rhs1 = gimple_assign_rhs1 (c->cand_stmt);
	  tree rhs2 = gimple_assign_rhs2 (c->cand_stmt);
	  if (operand_equal_p (rhs1, c->base_expr, 0))
	    t0 = rhs2;
	  else if (operand_equal_p (rhs2, c->base_expr, 0))
	    t0 = rhs1;
	  if (t0
	      && SSA_NAME_DEF_STMT (t0)
	      && gimple_bb (SSA_NAME_DEF_STMT (t0)))
	    {
	      incr_vec[incr_vec_len].initializer = t0;
	      incr_vec[incr_vec_len++].init_bb
		= gimple_bb (SSA_NAME_DEF_STMT (t0));
	    }
	  else
	    {
	      incr_vec[incr_vec_len].initializer = NULL_TREE;
	      incr_vec[incr_vec_len++].init_bb = NULL;
	    }
	}
      else
	{
	  incr_vec[incr_vec_len].initializer = NULL_TREE;
	  incr_vec[incr_vec_len++].init_bb = NULL;
	}
    }
}

/* Determine how many times each unique increment occurs in the set
   of candidates rooted at C's parent, recording the data in the
   increment vector.  For each unique increment I, if an initializer
   T_0 = stride * I is provided by a candidate that dominates all
   candidates with the same increment, also record T_0 for subsequent
   use.  */

static void
record_increments (slsr_cand_t c)
{
  if (!cand_already_replaced (c))
    record_increment (c, cand_increment (c));

  if (c->sibling)
    record_increments (lookup_cand (c->sibling));

  if (c->dependent)
    record_increments (lookup_cand (c->dependent));
}

/* Return the first candidate in the tree rooted at C that has not
   already been replaced, favoring siblings over dependents.  */

static slsr_cand_t
unreplaced_cand_in_tree (slsr_cand_t c)
{
  if (!cand_already_replaced (c))
    return c;

  if (c->sibling)
    {
      slsr_cand_t sib = unreplaced_cand_in_tree (lookup_cand (c->sibling));
      if (sib)
	return sib;
    }

  if (c->dependent)
    {
      slsr_cand_t dep = unreplaced_cand_in_tree (lookup_cand (c->dependent));
      if (dep)
	return dep;
    }

  return NULL;
}

/* Return TRUE if the candidates in the tree rooted at C should be
   optimized for speed, else FALSE.  We estimate this based on the block
   containing the most dominant candidate in the tree that has not yet
   been replaced.  */

static bool
optimize_cands_for_speed_p (slsr_cand_t c)
{
  slsr_cand_t c2 = unreplaced_cand_in_tree (c);
  gcc_assert (c2);
  return optimize_bb_for_speed_p (gimple_bb (c2->cand_stmt));
}

/* Add COST_IN to the lowest cost of any dependent path starting at
   candidate C or any of its siblings, counting only candidates along
   such paths with increment INCR.  Assume that replacing a candidate
   reduces cost by REPL_SAVINGS.  Also account for savings from any
   statements that would go dead.  */

static int
lowest_cost_path (int cost_in, int repl_savings, slsr_cand_t c, double_int incr)
{
  int local_cost, sib_cost;
  double_int cand_incr = cand_abs_increment (c);

  if (cand_already_replaced (c))
    local_cost = cost_in;
  else if (incr == cand_incr)
    local_cost = cost_in - repl_savings - c->dead_savings;
  else
    local_cost = cost_in - c->dead_savings;

  if (c->dependent)
    local_cost = lowest_cost_path (local_cost, repl_savings, 
				   lookup_cand (c->dependent), incr);

  if (c->sibling)
    {
      sib_cost = lowest_cost_path (cost_in, repl_savings,
				   lookup_cand (c->sibling), incr);
      local_cost = MIN (local_cost, sib_cost);
    }

  return local_cost;
}

/* Compute the total savings that would accrue from all replacements
   in the candidate tree rooted at C, counting only candidates with
   increment INCR.  Assume that replacing a candidate reduces cost
   by REPL_SAVINGS.  Also account for savings from statements that
   would go dead.  */

static int
total_savings (int repl_savings, slsr_cand_t c, double_int incr)
{
  int savings = 0;
  double_int cand_incr = cand_abs_increment (c);

  if (incr == cand_incr && !cand_already_replaced (c))
    savings += repl_savings + c->dead_savings;

  if (c->dependent)
    savings += total_savings (repl_savings, lookup_cand (c->dependent), incr);

  if (c->sibling)
    savings += total_savings (repl_savings, lookup_cand (c->sibling), incr);

  return savings;
}

/* Use target-specific costs to determine and record which increments
   in the current candidate tree are profitable to replace, assuming
   MODE and SPEED.  FIRST_DEP is the first dependent of the root of
   the candidate tree.

   One slight limitation here is that we don't account for the possible
   introduction of casts in some cases.  See replace_one_candidate for
   the cases where these are introduced.  This should probably be cleaned
   up sometime.  */

static void
analyze_increments (slsr_cand_t first_dep, enum machine_mode mode, bool speed)
{
  unsigned i;

  for (i = 0; i < incr_vec_len; i++)
    {
      HOST_WIDE_INT incr = incr_vec[i].incr.to_shwi ();

      /* If somehow this increment is bigger than a HWI, we won't
	 be optimizing candidates that use it.  And if the increment
	 has a count of zero, nothing will be done with it.  */
      if (!incr_vec[i].incr.fits_shwi () || !incr_vec[i].count)
	incr_vec[i].cost = COST_INFINITE;

      /* Increments of 0, 1, and -1 are always profitable to replace,
	 because they always replace a multiply or add with an add or
	 copy, and may cause one or more existing instructions to go
	 dead.  Exception:  -1 can't be assumed to be profitable for
	 pointer addition.  */
      else if (incr == 0
	       || incr == 1
	       || (incr == -1
		   && (gimple_assign_rhs_code (first_dep->cand_stmt)
		       != POINTER_PLUS_EXPR)))
	incr_vec[i].cost = COST_NEUTRAL;
      
      /* FORNOW: If we need to add an initializer, give up if a cast from
	 the candidate's type to its stride's type can lose precision.
	 This could eventually be handled better by expressly retaining the
	 result of a cast to a wider type in the stride.  Example:

           short int _1;
	   _2 = (int) _1;
	   _3 = _2 * 10;
	   _4 = x + _3;    ADD: x + (10 * _1) : int
	   _5 = _2 * 15;
	   _6 = x + _3;    ADD: x + (15 * _1) : int

         Right now replacing _6 would cause insertion of an initializer
	 of the form "short int T = _1 * 5;" followed by a cast to 
	 int, which could overflow incorrectly.  Had we recorded _2 or
	 (int)_1 as the stride, this wouldn't happen.  However, doing
         this breaks other opportunities, so this will require some
	 care.  */
      else if (!incr_vec[i].initializer
	       && TREE_CODE (first_dep->stride) != INTEGER_CST
	       && !legal_cast_p_1 (first_dep->stride,
				   gimple_assign_lhs (first_dep->cand_stmt)))

	incr_vec[i].cost = COST_INFINITE;

      /* If we need to add an initializer, make sure we don't introduce
	 a multiply by a pointer type, which can happen in certain cast
	 scenarios.  FIXME: When cleaning up these cast issues, we can
         afford to introduce the multiply provided we cast out to an
         unsigned int of appropriate size.  */
      else if (!incr_vec[i].initializer
	       && TREE_CODE (first_dep->stride) != INTEGER_CST
	       && POINTER_TYPE_P (TREE_TYPE (first_dep->stride)))

	incr_vec[i].cost = COST_INFINITE;

      /* For any other increment, if this is a multiply candidate, we
	 must introduce a temporary T and initialize it with
	 T_0 = stride * increment.  When optimizing for speed, walk the
	 candidate tree to calculate the best cost reduction along any
	 path; if it offsets the fixed cost of inserting the initializer,
	 replacing the increment is profitable.  When optimizing for
         size, instead calculate the total cost reduction from replacing
	 all candidates with this increment.  */
      else if (first_dep->kind == CAND_MULT)
	{
	  int cost = mult_by_coeff_cost (incr, mode, speed);
	  int repl_savings = mul_cost (speed, mode) - add_cost (speed, mode);
	  if (speed)
	    cost = lowest_cost_path (cost, repl_savings, first_dep,
				     incr_vec[i].incr);
	  else
	    cost -= total_savings (repl_savings, first_dep, incr_vec[i].incr);

	  incr_vec[i].cost = cost;
	}

      /* If this is an add candidate, the initializer may already
	 exist, so only calculate the cost of the initializer if it
	 doesn't.  We are replacing one add with another here, so the
	 known replacement savings is zero.  We will account for removal
	 of dead instructions in lowest_cost_path or total_savings.  */
      else
	{
	  int cost = 0;
	  if (!incr_vec[i].initializer)
	    cost = mult_by_coeff_cost (incr, mode, speed);

	  if (speed)
	    cost = lowest_cost_path (cost, 0, first_dep, incr_vec[i].incr);
	  else
	    cost -= total_savings (0, first_dep, incr_vec[i].incr);

	  incr_vec[i].cost = cost;
	}
    }
}

/* Return the nearest common dominator of BB1 and BB2.  If the blocks
   are identical, return the earlier of C1 and C2 in *WHERE.  Otherwise,
   if the NCD matches BB1, return C1 in *WHERE; if the NCD matches BB2,
   return C2 in *WHERE; and if the NCD matches neither, return NULL in
   *WHERE.  Note: It is possible for one of C1 and C2 to be NULL.  */

static basic_block
ncd_for_two_cands (basic_block bb1, basic_block bb2,
		   slsr_cand_t c1, slsr_cand_t c2, slsr_cand_t *where)
{
  basic_block ncd;

  if (!bb1)
    {
      *where = c2;
      return bb2;
    }

  if (!bb2)
    {
      *where = c1;
      return bb1;
    }

  ncd = nearest_common_dominator (CDI_DOMINATORS, bb1, bb2);
      
  /* If both candidates are in the same block, the earlier
     candidate wins.  */
  if (bb1 == ncd && bb2 == ncd)
    {
      if (!c1 || (c2 && c2->cand_num < c1->cand_num))
	*where = c2;
      else
	*where = c1;
    }

  /* Otherwise, if one of them produced a candidate in the
     dominator, that one wins.  */
  else if (bb1 == ncd)
    *where = c1;

  else if (bb2 == ncd)
    *where = c2;

  /* If neither matches the dominator, neither wins.  */
  else
    *where = NULL;

  return ncd;
}

/* Consider all candidates in the tree rooted at C for which INCR
   represents the required increment of C relative to its basis.
   Find and return the basic block that most nearly dominates all
   such candidates.  If the returned block contains one or more of
   the candidates, return the earliest candidate in the block in
   *WHERE.  */

static basic_block
nearest_common_dominator_for_cands (slsr_cand_t c, double_int incr,
				    slsr_cand_t *where)
{
  basic_block sib_ncd = NULL, dep_ncd = NULL, this_ncd = NULL, ncd;
  slsr_cand_t sib_where = NULL, dep_where = NULL, this_where = NULL, new_where;
  double_int cand_incr;

  /* First find the NCD of all siblings and dependents.  */
  if (c->sibling)
    sib_ncd = nearest_common_dominator_for_cands (lookup_cand (c->sibling),
						  incr, &sib_where);
  if (c->dependent)
    dep_ncd = nearest_common_dominator_for_cands (lookup_cand (c->dependent),
						  incr, &dep_where);
  if (!sib_ncd && !dep_ncd)
    {
      new_where = NULL;
      ncd = NULL;
    }
  else if (sib_ncd && !dep_ncd)
    {
      new_where = sib_where;
      ncd = sib_ncd;
    }
  else if (dep_ncd && !sib_ncd)
    {
      new_where = dep_where;
      ncd = dep_ncd;
    }
  else
    ncd = ncd_for_two_cands (sib_ncd, dep_ncd, sib_where,
			     dep_where, &new_where);

  /* If the candidate's increment doesn't match the one we're interested
     in, then the result depends only on siblings and dependents.  */
  cand_incr = cand_abs_increment (c);

  if (cand_incr != incr || cand_already_replaced (c))
    {
      *where = new_where;
      return ncd;
    }

  /* Otherwise, compare this candidate with the result from all siblings
     and dependents.  */
  this_where = c;
  this_ncd = gimple_bb (c->cand_stmt);
  ncd = ncd_for_two_cands (ncd, this_ncd, new_where, this_where, where);

  return ncd;
}

/* Return TRUE if the increment indexed by INDEX is profitable to replace.  */

static inline bool
profitable_increment_p (unsigned index)
{
  return (incr_vec[index].cost <= COST_NEUTRAL);
}

/* For each profitable increment in the increment vector not equal to
   0 or 1 (or -1, for non-pointer arithmetic), find the nearest common
   dominator of all statements in the candidate chain rooted at C
   that require that increment, and insert an initializer
   T_0 = stride * increment at that location.  Record T_0 with the
   increment record.  */

static void
insert_initializers (slsr_cand_t c)
{
  unsigned i;
  tree new_var = NULL_TREE;

  for (i = 0; i < incr_vec_len; i++)
    {
      basic_block bb;
      slsr_cand_t where = NULL;
      gimple init_stmt;
      tree stride_type, new_name, incr_tree;
      double_int incr = incr_vec[i].incr;

      if (!profitable_increment_p (i)
	  || incr.is_one ()
	  || (incr.is_minus_one ()
	      && gimple_assign_rhs_code (c->cand_stmt) != POINTER_PLUS_EXPR)
	  || incr.is_zero ())
	continue;

      /* We may have already identified an existing initializer that
	 will suffice.  */
      if (incr_vec[i].initializer)
	{
	  if (dump_file && (dump_flags & TDF_DETAILS))
	    {
	      fputs ("Using existing initializer: ", dump_file);
	      print_gimple_stmt (dump_file,
				 SSA_NAME_DEF_STMT (incr_vec[i].initializer),
				 0, 0);
	    }
	  continue;
	}

      /* Find the block that most closely dominates all candidates
	 with this increment.  If there is at least one candidate in
	 that block, the earliest one will be returned in WHERE.  */
      bb = nearest_common_dominator_for_cands (c, incr, &where);

      /* Create a new SSA name to hold the initializer's value.  */
      stride_type = TREE_TYPE (c->stride);
      lazy_create_slsr_reg (&new_var, stride_type);
      new_name = make_ssa_name (new_var, NULL);
      incr_vec[i].initializer = new_name;

      /* Create the initializer and insert it in the latest possible
	 dominating position.  */
      incr_tree = double_int_to_tree (stride_type, incr);
      init_stmt = gimple_build_assign_with_ops (MULT_EXPR, new_name,
						c->stride, incr_tree);
      if (where)
	{
	  gimple_stmt_iterator gsi = gsi_for_stmt (where->cand_stmt);
	  gsi_insert_before (&gsi, init_stmt, GSI_SAME_STMT);
	  gimple_set_location (init_stmt, gimple_location (where->cand_stmt));
	}
      else
	{
	  gimple_stmt_iterator gsi = gsi_last_bb (bb);
	  gimple basis_stmt = lookup_cand (c->basis)->cand_stmt;

	  if (!gsi_end_p (gsi) && is_ctrl_stmt (gsi_stmt (gsi)))
	    gsi_insert_before (&gsi, init_stmt, GSI_SAME_STMT);
	  else
	    gsi_insert_after (&gsi, init_stmt, GSI_SAME_STMT);

	  gimple_set_location (init_stmt, gimple_location (basis_stmt));
	}

      if (dump_file && (dump_flags & TDF_DETAILS))
	{
	  fputs ("Inserting initializer: ", dump_file);
	  print_gimple_stmt (dump_file, init_stmt, 0, 0);
	}
    }
}

/* Create a NOP_EXPR that copies FROM_EXPR into a new SSA name of
   type TO_TYPE, and insert it in front of the statement represented
   by candidate C.  Use *NEW_VAR to create the new SSA name.  Return
   the new SSA name.  */

static tree
introduce_cast_before_cand (slsr_cand_t c, tree to_type,
			    tree from_expr, tree *new_var)
{
  tree cast_lhs;
  gimple cast_stmt;
  gimple_stmt_iterator gsi = gsi_for_stmt (c->cand_stmt);

  lazy_create_slsr_reg (new_var, to_type);
  cast_lhs = make_ssa_name (*new_var, NULL);
  cast_stmt = gimple_build_assign_with_ops (NOP_EXPR, cast_lhs,
					    from_expr, NULL_TREE);
  gimple_set_location (cast_stmt, gimple_location (c->cand_stmt));
  gsi_insert_before (&gsi, cast_stmt, GSI_SAME_STMT);

  if (dump_file && (dump_flags & TDF_DETAILS))
    {
      fputs ("  Inserting: ", dump_file);
      print_gimple_stmt (dump_file, cast_stmt, 0, 0);
    }

  return cast_lhs;
}

/* Replace the RHS of the statement represented by candidate C with 
   NEW_CODE, NEW_RHS1, and NEW_RHS2, provided that to do so doesn't
   leave C unchanged or just interchange its operands.  The original
   operation and operands are in OLD_CODE, OLD_RHS1, and OLD_RHS2.
   If the replacement was made and we are doing a details dump,
   return the revised statement, else NULL.  */

static gimple
replace_rhs_if_not_dup (enum tree_code new_code, tree new_rhs1, tree new_rhs2,
			enum tree_code old_code, tree old_rhs1, tree old_rhs2,
			slsr_cand_t c)
{
  if (new_code != old_code
      || ((!operand_equal_p (new_rhs1, old_rhs1, 0)
	   || !operand_equal_p (new_rhs2, old_rhs2, 0))
	  && (!operand_equal_p (new_rhs1, old_rhs2, 0)
	      || !operand_equal_p (new_rhs2, old_rhs1, 0))))
    {
      gimple_stmt_iterator gsi = gsi_for_stmt (c->cand_stmt);
      gimple_assign_set_rhs_with_ops (&gsi, new_code, new_rhs1, new_rhs2);
      update_stmt (gsi_stmt (gsi));

      if (dump_file && (dump_flags & TDF_DETAILS))
	return gsi_stmt (gsi);
    }

  else if (dump_file && (dump_flags & TDF_DETAILS))
    fputs ("  (duplicate, not actually replacing)\n", dump_file);

  return NULL;
}

/* Strength-reduce the statement represented by candidate C by replacing
   it with an equivalent addition or subtraction.  I is the index into
   the increment vector identifying C's increment.  NEW_VAR is used to
   create a new SSA name if a cast needs to be introduced.  BASIS_NAME
   is the rhs1 to use in creating the add/subtract.  */

static void
replace_one_candidate (slsr_cand_t c, unsigned i, tree *new_var,
		       tree basis_name)
{
  gimple stmt_to_print = NULL;
  tree orig_rhs1, orig_rhs2;
  tree rhs2;
  enum tree_code orig_code, repl_code;
  double_int cand_incr;

  orig_code = gimple_assign_rhs_code (c->cand_stmt);
  orig_rhs1 = gimple_assign_rhs1 (c->cand_stmt);
  orig_rhs2 = gimple_assign_rhs2 (c->cand_stmt);
  cand_incr = cand_increment (c);

  if (dump_file && (dump_flags & TDF_DETAILS))
    {
      fputs ("Replacing: ", dump_file);
      print_gimple_stmt (dump_file, c->cand_stmt, 0, 0);
      stmt_to_print = c->cand_stmt;
    }

  if (address_arithmetic_p)
    repl_code = POINTER_PLUS_EXPR;
  else
    repl_code = PLUS_EXPR;

  /* If the increment has an initializer T_0, replace the candidate
     statement with an add of the basis name and the initializer.  */
  if (incr_vec[i].initializer)
    {
      tree init_type = TREE_TYPE (incr_vec[i].initializer);
      tree orig_type = TREE_TYPE (orig_rhs2);

      if (types_compatible_p (orig_type, init_type))
	rhs2 = incr_vec[i].initializer;
      else
	rhs2 = introduce_cast_before_cand (c, orig_type,
					   incr_vec[i].initializer,
					   new_var);

      if (incr_vec[i].incr != cand_incr)
	{
	  gcc_assert (repl_code == PLUS_EXPR);
	  repl_code = MINUS_EXPR;
	}

      stmt_to_print = replace_rhs_if_not_dup (repl_code, basis_name, rhs2,
					      orig_code, orig_rhs1, orig_rhs2,
					      c);
    }

  /* Otherwise, the increment is one of -1, 0, and 1.  Replace
     with a subtract of the stride from the basis name, a copy
     from the basis name, or an add of the stride to the basis
     name, respectively.  It may be necessary to introduce a
     cast (or reuse an existing cast).  */
  else if (cand_incr.is_one ())
    {
      tree stride_type = TREE_TYPE (c->stride);
      tree orig_type = TREE_TYPE (orig_rhs2);
      
      if (types_compatible_p (orig_type, stride_type))
	rhs2 = c->stride;
      else
	rhs2 = introduce_cast_before_cand (c, orig_type, c->stride, new_var);
      
      stmt_to_print = replace_rhs_if_not_dup (repl_code, basis_name, rhs2,
					      orig_code, orig_rhs1, orig_rhs2,
					      c);
    }

  else if (cand_incr.is_minus_one ())
    {
      tree stride_type = TREE_TYPE (c->stride);
      tree orig_type = TREE_TYPE (orig_rhs2);
      gcc_assert (repl_code != POINTER_PLUS_EXPR);
      
      if (types_compatible_p (orig_type, stride_type))
	rhs2 = c->stride;
      else
	rhs2 = introduce_cast_before_cand (c, orig_type, c->stride, new_var);
      
      if (orig_code != MINUS_EXPR
	  || !operand_equal_p (basis_name, orig_rhs1, 0)
	  || !operand_equal_p (rhs2, orig_rhs2, 0))
	{
	  gimple_stmt_iterator gsi = gsi_for_stmt (c->cand_stmt);
	  gimple_assign_set_rhs_with_ops (&gsi, MINUS_EXPR, basis_name, rhs2);
	  update_stmt (gsi_stmt (gsi));

	  if (dump_file && (dump_flags & TDF_DETAILS))
	    stmt_to_print = gsi_stmt (gsi);
	}
      else if (dump_file && (dump_flags & TDF_DETAILS))
	fputs ("  (duplicate, not actually replacing)\n", dump_file);
    }

  else if (cand_incr.is_zero ())
    {
      tree lhs = gimple_assign_lhs (c->cand_stmt);
      tree lhs_type = TREE_TYPE (lhs);
      tree basis_type = TREE_TYPE (basis_name);
      
      if (types_compatible_p (lhs_type, basis_type))
	{
	  gimple copy_stmt = gimple_build_assign (lhs, basis_name);
	  gimple_stmt_iterator gsi = gsi_for_stmt (c->cand_stmt);
	  gimple_set_location (copy_stmt, gimple_location (c->cand_stmt));
	  gsi_replace (&gsi, copy_stmt, false);

	  if (dump_file && (dump_flags & TDF_DETAILS))
	    stmt_to_print = copy_stmt;
	}
      else
	{
	  gimple_stmt_iterator gsi = gsi_for_stmt (c->cand_stmt);
	  gimple cast_stmt = gimple_build_assign_with_ops (NOP_EXPR, lhs,
							   basis_name,
							   NULL_TREE);
	  gimple_set_location (cast_stmt, gimple_location (c->cand_stmt));
	  gsi_replace (&gsi, cast_stmt, false);

	  if (dump_file && (dump_flags & TDF_DETAILS))
	    stmt_to_print = cast_stmt;
	}
    }
  else
    gcc_unreachable ();
  
  if (dump_file && (dump_flags & TDF_DETAILS) && stmt_to_print)
    {
      fputs ("With: ", dump_file);
      print_gimple_stmt (dump_file, stmt_to_print, 0, 0);
      fputs ("\n", dump_file);
    }
}

/* For each candidate in the tree rooted at C, replace it with
   an increment if such has been shown to be profitable.  */

static void
replace_profitable_candidates (slsr_cand_t c)
{
  if (!cand_already_replaced (c))
    {
      double_int increment = cand_abs_increment (c);
      tree new_var = NULL;
      enum tree_code orig_code = gimple_assign_rhs_code (c->cand_stmt);
      unsigned i;

      i = incr_vec_index (increment);

      /* Only process profitable increments.  Nothing useful can be done
	 to a cast or copy.  */
      if (profitable_increment_p (i) 
	  && orig_code != MODIFY_EXPR
	  && orig_code != NOP_EXPR)
	{
	  slsr_cand_t basis = lookup_cand (c->basis);
	  tree basis_name = gimple_assign_lhs (basis->cand_stmt);
	  replace_one_candidate (c, i, &new_var, basis_name);
	}
    }

  if (c->sibling)
    replace_profitable_candidates (lookup_cand (c->sibling));

  if (c->dependent)
    replace_profitable_candidates (lookup_cand (c->dependent));
}

/* Analyze costs of related candidates in the candidate vector,
   and make beneficial replacements.  */

static void
analyze_candidates_and_replace (void)
{
  unsigned i;
  slsr_cand_t c;

  /* Each candidate that has a null basis and a non-null
     dependent is the root of a tree of related statements.
     Analyze each tree to determine a subset of those
     statements that can be replaced with maximum benefit.  */
  FOR_EACH_VEC_ELT (cand_vec, i, c)
    {
      slsr_cand_t first_dep;

      if (c->basis != 0 || c->dependent == 0)
	continue;

      if (dump_file && (dump_flags & TDF_DETAILS))
	fprintf (dump_file, "\nProcessing dependency tree rooted at %d.\n",
		 c->cand_num);

      first_dep = lookup_cand (c->dependent);

      /* If this is a chain of CAND_REFs, unconditionally replace
	 each of them with a strength-reduced data reference.  */
      if (c->kind == CAND_REF)
	replace_refs (c);

      /* If the common stride of all related candidates is a
	 known constant, and none of these has a phi-dependence,
	 then all replacements are considered profitable.
	 Each replaces a multiply by a single add, with the
	 possibility that a feeding add also goes dead as a
	 result.  */
      else if (unconditional_cands_with_known_stride_p (c))
	replace_dependents (first_dep);

      /* When the stride is an SSA name, it may still be profitable
	 to replace some or all of the dependent candidates, depending
	 on whether the introduced increments can be reused, or are
	 less expensive to calculate than the replaced statements.  */
      else
	{
	  unsigned length;
	  enum machine_mode mode;
	  bool speed;

	  /* Determine whether we'll be generating pointer arithmetic
	     when replacing candidates.  */
	  address_arithmetic_p = (c->kind == CAND_ADD
				  && POINTER_TYPE_P (c->cand_type));

	  /* If all candidates have already been replaced under other
	     interpretations, nothing remains to be done.  */
	  length = count_candidates (c);
	  if (!length)
	    continue;

	  /* Construct an array of increments for this candidate chain.  */
	  incr_vec = XNEWVEC (incr_info, length);
	  incr_vec_len = 0;
	  record_increments (c);

	  /* Determine which increments are profitable to replace.  */
	  mode = TYPE_MODE (TREE_TYPE (gimple_assign_lhs (c->cand_stmt)));
	  speed = optimize_cands_for_speed_p (c);
	  analyze_increments (first_dep, mode, speed);

	  /* Insert initializers of the form T_0 = stride * increment
	     for use in profitable replacements.  */
	  insert_initializers (first_dep);
	  dump_incr_vec ();

	  /* Perform the replacements.  */
	  replace_profitable_candidates (first_dep);
	  free (incr_vec);
	}

      /* TODO:  When conditional increments occur so that a 
	 candidate is dependent upon a phi-basis, the cost of
	 introducing a temporary must be accounted for.  */
    }
}

static unsigned
execute_strength_reduction (void)
{
  struct dom_walk_data walk_data;

  /* Create the obstack where candidates will reside.  */
  gcc_obstack_init (&cand_obstack);

  /* Allocate the candidate vector.  */
  cand_vec.create (128);

  /* Allocate the mapping from statements to candidate indices.  */
  stmt_cand_map = pointer_map_create ();

  /* Create the obstack where candidate chains will reside.  */
  gcc_obstack_init (&chain_obstack);

  /* Allocate the mapping from base expressions to candidate chains.  */
  base_cand_map = htab_create (500, base_cand_hash,
			       base_cand_eq, base_cand_free);

  /* Initialize the loop optimizer.  We need to detect flow across
     back edges, and this gives us dominator information as well.  */
  loop_optimizer_init (AVOID_CFG_MODIFICATIONS);

  /* Set up callbacks for the generic dominator tree walker.  */
  walk_data.dom_direction = CDI_DOMINATORS;
  walk_data.initialize_block_local_data = NULL;
  walk_data.before_dom_children = find_candidates_in_block;
  walk_data.after_dom_children = NULL;
  walk_data.global_data = NULL;
  walk_data.block_local_data_size = 0;
  init_walk_dominator_tree (&walk_data);

  /* Walk the CFG in predominator order looking for strength reduction
     candidates.  */
  walk_dominator_tree (&walk_data, ENTRY_BLOCK_PTR);

  if (dump_file && (dump_flags & TDF_DETAILS))
    {
      dump_cand_vec ();
      dump_cand_chains ();
    }

  /* Analyze costs and make appropriate replacements.  */
  analyze_candidates_and_replace ();

  /* Free resources.  */
  fini_walk_dominator_tree (&walk_data);
  loop_optimizer_finalize ();
  htab_delete (base_cand_map);
  obstack_free (&chain_obstack, NULL);
  pointer_map_destroy (stmt_cand_map);
  cand_vec.release ();
  obstack_free (&cand_obstack, NULL);

  return 0;
}

static bool
gate_strength_reduction (void)
{
  return flag_tree_slsr;
}

struct gimple_opt_pass pass_strength_reduction =
{
 {
  GIMPLE_PASS,
  "slsr",				/* name */
  OPTGROUP_NONE,                        /* optinfo_flags */
  gate_strength_reduction,		/* gate */
  execute_strength_reduction,		/* execute */
  NULL,					/* sub */
  NULL,					/* next */
  0,					/* static_pass_number */
  TV_GIMPLE_SLSR,			/* tv_id */
  PROP_cfg | PROP_ssa,			/* properties_required */
  0,					/* properties_provided */
  0,					/* properties_destroyed */
  0,					/* todo_flags_start */
  TODO_verify_ssa			/* todo_flags_finish */
 }
};